MECHANICAL AND MICROSTRUCTURAL STUDY OF
SILICON CARBIDE AND PYROLYTIC CARBON
COATINGS IN TRISO FUEL PARTICLES
A thesis submitted to The University of Manchester for the degree of
Doctor of Philosophy
In the Faculty of Engineering and Physical Science
2012
Huixing Zhang
Material Science Centre School of Materials
List of Contents
2
List of Contents
List of Contents 2
Abstract 6
Declaration 7
Copyright Statement 8
Acknowledgement 9
List of Figures 10
List of Tables 17
CHAPTER 1 Introduction 19
11 TRI-Isotropic (TRISO) fuel particles 19
12 Failure mechanism 21
121 Traditional pressure vessel failure mode 21
122 Stress concentration mode 22
13 Goals of dissertation 24
14 References 26
CHAPTER 2 Literature Review 28
21 Introduction 28
22 Microstructure of silicon carbide 29
221 Atomic structure 29
222 Defects in SiC 31
2221 Stacking faults and dislocations 31
2222 Non-stoichiometric and point defects 36
23 Properties of silicon carbide 41
231 Youngrsquos modulus 41
232 Hardness 45
233 Fracture toughness 52
234 Fracture strength 55
235 Effect of thermal treatment on SiC 59
24 Microstructure and properties of pyrolytic carbon 60
241 Microstructure of pyrolytic carbon 61
242 Mechanical properties of pyrolytic carbon 65
List of Contents
3
2421 Youngrsquos modulus and hardness 65
2422 Deformation mechanism 67
2423 Effect of thermal treatment on properties of PyC 70
25 Summary 70
26 References 72
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Coatings Measured by
Indentation 83
31 Introduction 83
32 Experimental details 85
33 Results 88
331 Hardness and Youngrsquos modulus 88
332 Microstructure of low temperature FBCVD SiC 91
333 Deformation behaviour under the indentation 97
34 Discussion 100
341 Influence of porosity on Youngrsquos modulus 101
342 Mechanism for High hardness 102
343 Deformation mechanism under nano-indentation 104
35 Conclusions 105
36 References 107
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC Coatings 112
41 Introduction 112
42 Experimental details 113
43 Results and discussion 117
431 VIF fracture toughness study 117
432 Influence of non-stoichiometries on the VIF fracture toughness 121
433 Microstructural analysis of fracture behaviour under the indenter 122
44 Conclusions 126
45 References 127
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings 131
51 Introduction 131
52 Experimental details 132
List of Contents
4
521 Materials 132
522 Test method and analysis 133
523 Characterisation methods 135
53 Results and discussions 136
531 Fracture strength and dimensional effect 136
532 Observe and qualify the effect of interfacial roughness on fracture strength
140
533 Characterise and quantify the interfacial roughness 143
5331 Self-affine theory introduction and experimental setup 143
5332 Results of self-affine theory 144
534 Quantify the influence of interface roughness on fracture strength 146
54 Conclusions 149
55 References 150
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings 154
61 Introduction 154
62 Experimental details 155
63 Results 156
631 Fracture strength of SiC coatings 156
632 Change in morphologies 160
633 Evolution in microstructure 163
64 Discussion 167
641 Influence of interfacial roughness and pores on fracture strength 167
642 Mechanism of microstructural change 169
65 Conclusions 171
66 References 172
CHAPTER 7 Microstructure and Mechanical Properties of Pyrolytic Carbon
Coatings 175
71 Introduction 175
72 Experimental details 176
73 Results 178
731 Microstructure of PyC coatings 178
7311 Raman spectroscopy 178
7312 Domain sizes 181
List of Contents
5
7313 Evolution of crystallinity 182
732 Mechanical properties of PyC coatings 185
7321 Force-displacement curve 185
7322 Youngrsquos modulus and the mean pressure 187
74 Discussions 188
741 Disorders and their changes after thermal treatment 189
742 Hysteresis after indentation 191
743 Mechanical property of low density PyC coatings 192
744 Mechanical Property of high density PyC coatings 193
74 Conclusions 195
75 References 197
CHAPTER 8 Conclusions and Future Works 201
81 Conclusions 201
82 Suggestions for future work 203
Abstract
6
Abstract
Mechanical and Microstructural Study of Silicon carbide and Pyrolytic Carbon
Coatings in TRISO Fuel Particles
The University of Manchester
Huixing Zhang
Doctor of Philosophy in Materials Science
TRISO fuel particles have been developed as nuclear fuels used for a generation IV
nuclear reactor high temperature reactor Such particle consists of a fuel kernel
pyrolytic carbon (PyC) and silicon carbide (SiC) coatings This study has been carried
out to establish a relationship between mechanical properties and microstructures of
SiC coating and PyC coatings produced by fluidized bed chemical vapour deposition
Indentations were used to measure hardness Youngrsquos modulus and fracture behaviour
of SiC and PyC coatings Fracture strength of SiC coatings was measured by crush
test Microstructure of SiC and PyC was mainly characterised by transmission
scanning electron microscopy and Raman spectroscopy
For SiC coatings produced at 1300 ordmC Youngrsquos modulus is an exponential function of
relative density Hardness of SiC coatings is higher than the bulk SiC produced by
CVD and it is attributed to the high density of dislocations and their interactions The
deformation mechanism of SiC coatings under indentation is explained by presence of
defects such as grain boundaries and nano-pores The fracture of these coatings
beneath the Vickers indentation is the Palmqvist cracks and indentation fracture
toughness was in the range of 35-49 MPa m12
The stress-induced micro-cracks are
assumed to be the mechanism for the high indentation fracture toughness Different
hardness and fracture toughness in these SiC coatings are attributed to influences of
defects and grain morphology
Measurement of fracture strength was carried out on SiC coatings deposited at
1300-1500 ordmC Weibull modulus and fracture strength of the full shell are dominated
by the ratio of radius to thickness of coatings and decrease linearly with the increase
of this ratio The influence of SiCPyC interfacial roughness on fracture strength of
the SiC was quantified by self-affine theory The fracture strength decreases linearly
with the increase of the roughness ratio which is the long-wavelength roughness
characteristic After thermal treatment at 2000 ordmC fracture strength decreased in SiC
coatings due to the formation of pores which are results of diffusion of native defects
in as-deposited SiC coatings and the change of Weibull modulus is related to the size
and distribution of pores
For low density PyC coatings Youngrsquos modulus and the mean pressure increase with
the increase of the density however for high density PyC coatings they are
determined by interstitial defects The hysteresis deformation behaviour under
nano-indenation has been found be affected by density variation and thermal
treatment which is proposed to be due to the disorder structure in PyC coatings
Declaration
7
Declaration
No Portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Copyright Statment
8
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this thesis)
owns any copyright in it (the lsquolsquoCopyrightrsquorsquo) and she has given the University of
Manchester certain rights to use such Copyright including for administrative
purposes
ii Copies of this thesis either in full or in extracts and whether in hard or electronic
copy may be made only in accordance with the Copyright Desings and Patents Act
1988 (as amended) and regulations issued under it or where appropriate in
accordance with licensing agreements which the University has from time to time
This page must form part of any such copies made
iii The ownership of certain Copyright patens designs trade marks and other
intellectual property (the lsquolsquoIntellectual Property Rightsrsquorsquo) and any reproductions of
copyright works in the thesis for example graphs and tables (lsquolsquoReproductionsrsquorsquo)
which may be described in this thesis may not be owned by the author and may be
owned by third parties Such intellectual Properties Rights and Reproductions cannot
and must not be made available for use without the prior written permission of the
owner(s) of the relevant Intellectual Property Rights andor Reproductions
iv Further information on the conditions under which disclosure publication and
commercialization of this thesis the Copyright and any Intellectual Property andor
Reproductions described in it may take place is available in the University IP policy
(see httpwwwcampusmanchesteracukmedialibrarypoliciesintellectual-property
Pdf) in any relevant Thesis restriction declarations deposited in the University
Library The University Libraryrsquos regulations (see
httpwwwmanchesteracuklibraryaboutusregulations) and in the Universityrsquos
policy on presentation of Thesis
Acknowledgement
9
Acknowledgement
I will always be appreciative to Professor Ping Xiao for his support and guidance
during this project period and his enthusiasm for work and positive attitude towards
life inspired me I am thankful for what he shared about his own experience doing
research which impressed me and motivated me to make improvement
I would like to thank in particular Dr Eddie Loacutepez-Honorato for his patient guidance
on my experiments and valuable advices on my project His caution on preparing
delicate specimen infected me and helped me through my project He was always
there listening my ideas and discussing with me and he has set an example for being
a good researcher
I give my thanks to all the members in ceramic coating group old and new and I
treasure and appreciate this chance working with you
I would like to give my great gratitude to Dr Alan Harvey for his kind help on
transmission electron microscopy Mr Andrew Forest and Mr Kenneth Gyves on
nano- and micro-indentation Mr Andrew Zadoroshnyj on Raman spectroscopy Dr
Ali Gholinia and Dr Ferridon Azough on TEM sample preparation Dr Judith
Shackleton and Mr Gary Harrison on X-ray diffraction Mr Christopher Wilkins and
Mr Michael Faulkner on scanning electron microscopy and Mr Stuart Mouse on
tensile tests
I am grateful to my dear friends Yola David and Dean and you make my life more
colourful and interesting I would like to thank my beloved parents and brother for
your love care and support and you are great examples of hard work and kindness
My thanks also go to the ORS scheme the CSC grant and the F-BRIDGE for their
financial support during my PhD studies
List of Figures
10
List of Figures
CHAPTER 1 Introduction
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Fig 12 Behaviour of coated layers in fuel a particle [10]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
CHAPTER 2 Literature Review
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
List of Figures
11
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation[62]
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
List of Figures
12
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC coatings Measured by
Indentation
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
List of Figures
13
BF-TEM and (b) DF-TEM
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for extra-Si SiC coatings
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
Fig 45 Cross-sectional SEM image of stoichiometric SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
List of Figures
14
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a)
extra-C SiC (b) extra-Si SiC
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
Fig 58 Log-log representation of the height-height correlation function ∆h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
List of Figures
15
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC coatings
Fig 61 Weibull plots of local fracture strength (L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
Fig 62 Weibull modulus plots of fracture strength of the whole shell (F
f ) before
(black triangle) and after (red circle) thermal treatment
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after thermal treatment (c) and (d) SiC2
before and after thermal treatment (e) and (f) SiC3 before and after thermal treatment
(g) and (h) SiC4 before and after thermal treatment Dashed and solid arrows indicate
growth direction and pores respectively
Fig 64 The IPyCSiC interfacial morphology of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermal treated at 2000 degC (right in
each figure) The white arrow points towards to the interface irregularities (except for
thermal treated SiC4 coating (d)) black circle represents the pores in SiC coatings
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermal treated
at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and SiC2 inset
shows the peak shift of as-deposited (dash line) and after thermal treatment (solid
line) (b) is SiC4 and inset is the high angle diffraction peak after thermal treatment
showing splitting while it is a single peak in as-deposited coating
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
List of Figures
16
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
List of Tables
17
List of Tables
CHAPTER 2 Literature Review
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Table 23 Elastic tensors of 3C-SiC at room-temperature
Table 24 Vickers and nano-indentation hardness of polycrystalline CVD SiC
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Table 26 Summary of the hardness and Youngrsquos modulus for pyrolytic carbon
measured by different methods
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Measured by Indentation
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχv
along the radial and tangential directions
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Table 52 Summary of measured and calculated parameters for all the coatings
List of Tables
18
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Table 54 Results and variations influences on fracture strength for SiC coating
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings
Table 61 Deposition conditions of SiC coatings
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the whole shell before and after thermal
treatment
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
Table 71 PyC coatings deposition conditions and physical properties
Table 72 Domain size (XRD) of as-deposited and thermal treated PyC coatings
Table 73 Changes of mechanical properties after thermal treatment of PyC coatings
Table 74 The parameters used to explain different mechanical properties of high
density PyC
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
CHAPTER 1 Introduction
19
CHAPTER 1 Introduction
11 TRI-Isotropic (TRISO) fuel particles
A fission reaction is about that a large atomic nucleus (such as Uranium-235) is hit by
a neutron and absorbs the neutron forming a larger unstable nucleus The unstable
larger atomic nuclear breaks into two small nuclei and releases a high amount of
energy more neutrons beta and alpha particles and gamma The energy release is
much greater than for traditional fuels eg 1 g Uranium nuclear fuel releases the
same amount of energy as approximately 3 tonne of coal [1] The energy can be
transferred through the cooling system and used to boil the water to make steam to
drive a turbine and electrical generator in a nuclear power station
The high-temperature gas cooled reactor is one of the most promising candidates for
the production of nuclear energy according to its unique features For example it has
high coolant outlet temperature (850-1000 degC) which provides more efficient
electricity production due to the increased difference of the hot and cold coolant
temperatures [2] Furthermore it has the safety advantages due to the enclosure of the
fuel kernel (such as UO2 UC) within few layers of ceramic coatings Currently the
most common technique to fabricate fuels for operating the next generation
high-temperature gas cooled reactors is the TRISO fuel particles coating system [3]
The TRISO system was designed not only to retain all fission products during neutron
irradiation but also to withstand the thermo-mechanical stresses generated during
service [4]
CHAPTER 1 Introduction
20
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Figure 11 is the schematic of TRISO fuel particles embedded in a graphite matrix A
TRISO fuel particle consists of a fuel kernel and coating layers of porous pyrolytic
carbon (PyC) called buffer layer inner dense PyC (IPyC) silicon carbide (SiC) and an
outer dense PyC (OPyC) [5] and these layers were designed to have different
purposes The buffer layer absorbs metallic fission products recoils from kernel and
provides a space for fission product gases It also takes the volume change caused by
the kernel swelling without transmitting forces to outer layers The dense and
isotropic IPyC layer stops the chlorine from reacting with the kernel during deposition
of SiC and provides a firm substrate for the SiC layer Furthermore it protects the
SiC layer from most of the fission products and carbon monoxide during operation
The OPyC layer protects SiC layer during the remainder of the fabrication process
and provides structural stability to the particle during irradiation [3] The high
mechanical properties of SiC are needed to contain the high pressure generated in the
kernel and withstand the stress developed by the dimensional change of IPyC [3]
CHAPTER 1 Introduction
21
12 Failure mechanism
The radiation effects on the performance of the fuel particles such as fundamental
performance characteristics and fission product relsease mechanisms have been well
understood Different testing conditions (eg temperature up to 1300 degC and the does
of neutron) reflected the senariors encountered real applications [6-8]
During irradiation a number of potential failure mechanisms were revealed according
to several tests of coated fuel particles conducted in material test reactors and in
real-time operating HTR reactors [6-8] Chemically the corrosion of SiC by the
fission product palladium has been observed in almost all kinds of fuel compositions
and is considered as one of the key factors influencing the fuel performance However
this could be avoided by limiting the fuel temperature irradiation time or increase the
thickness of SiC layer [9] Mechanically the built up of the internal gas pressure (eg
CO) of irradiated particle and the neutron induced embrittlement of PyC coatings
could promote the failutre of the TRISO fuel particle The primary mechanisms which
may result in mechanical failure of TRISO fuel particles and lead ultimately to fission
product release depends significantly on the magnitude of the de-bonding strength
between IPyC and SiC layers [3 9]
121 Traditional pressure vessel failure mode
In this mode the failure was assumed to occur due to simple overload of the SiC layer
due to internal pressure build-up from fission gas [10] Both IPyC and OPyC layers
shrink during operation because of the irradiation exposure [11] This causes
compression stress in the SiC layer and tensile stress in the PyC layers Failure of the
SiC layer can only occur if the internal gas pressure is high enough to overcome the
compressive stress and critical stress of the SiC layer itself
CHAPTER 1 Introduction
22
Fig 12 Behaviour of coated layers in fuel a particle [10]
Figure 12 shows the basic behaviour modelled in a three layers standard model [10]
It shows that both IPyC and OPyC layers shrink and creep during irradiation but the
SiC layer exhibits only elastic deformation A portion of gas pressure is transmitted
through the IPyC layer to the SiC The pressure continually increases as irradiation of
the particle goes However if the PyC layer could remain in tension the failure by
fracture of SiC layer would be less likely to happen in this mode When the failure of
the PyC layer occurs a tensile hoop stress in the SiC layer is generated This leads to
the development of the stress concentration mode provided by the fracture of the inner
PyC layer
122 Stress concentration mode
In this mode it is been proposed that there is a point at which the fracture strength of
the IPyC would be exceeded during exposure When this occurs a radial crack will
form in the IPyC layer The crack could either penetrate through the SiC layer or
partially de-bonding the IPyCSiC interface This would lead to severe stress
concentration near the crack tip and it could reach the maximum of 440 MPa
according to previous simulation work [10] Once de-bonding goes through the whole
interface the source of stress in the SiC layer would be fission product gas build-up
CHAPTER 1 Introduction
23
and this case has similar failure mechanism of traditional pressure vessel failure mode
Although this process could decrease the probability of failure compared with the
stress concentration case the probability of failure may be higher than the traditional
failure mode Because the stress generated in the SiC layer after de-bonding would
increase [3]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
All these behaviours make it easier for the SiC layer to reach its fracture strength and
lead to the radial crack and failure of the SiC results in an instantaneous release of
elastic energy that should be sufficient to cause simultaneous failure of the
pyrocarbon layer Shown in Fig 13 is a photomicrograph illustrating the failure of a
TRISO coating According to the above discussion all the carbon layers are partially
designed to support or protect the SiC layer The SiC layer serves as the main
containment barrier for gas and metallic fission products [3] and high mechanical
properties of the SiC layer are needed However without appropriate microstructure
and mechanical properties of the PyC layer the stresses or structural changes
introduced in this layer during the irradiation process could result in the failure of the
whole particle [9 12] Furthermore mechanical properties such as the hardness (It is
CHAPTER 1 Introduction
24
the resistance to plasticpermanent deformation of materials under constant load from
a sharp object) Youngrsquos modulus (It reflects the resistance to reversible deformation
of a material) fracture toughness (It describes the ability of a material containing a
crack to resist fracture) and fracture strength (It is the maximum stress at which a
specimen fails via fracture) of SiC and PyC coatings are also important factors for the
safety design and evaluation of the TRISO coating system [10]
13 Goals of dissertation
Due to the importance of mechanical properties of SiC and PyC layers in keeping the
integrity of TRISO fuel particles and providing adequate information for modelling
the probability of failure of particles a good understanding of the elastic plastic and
fracture properties and their relation with microstructure is necessary Therefore all
the work carried out in this project is aimed at studying the relationship between
microstructure and mechanical properties of these two layers aiming to provide a
fundamental understanding about the deformation mechanism and solve the practical
issues
Due to small scale of SiC and PyC coatings two main techniques used to measure
mechanical properties are micronano-indenation and crush test Furthermore to study
the effect of microstructures on mechanical properties characterization techniques
such as transmissionscanning electron microscope and Raman spectroscopy are
widely used in the current work
In this thesis Chapter 2 reviews the recent progress in microstructural characterisation
and mechanical properties of SiC and PyC related materials which provides basic
information with regard to future study about hardness Youngrsquos modulus
deformation mechanism and fracture behaviour in these
Chapter 3 studies the influences of microstructure on hardness and Youngrsquos modulus
CHAPTER 1 Introduction
25
of SiC coatings and focuses on understanding the deformation mechanism of SiC
under nano-indentation The fracture toughness of these SiC coatings is measured by
Vickers-indentation and the importance of crack modes is discussed in Chapter 4
In Chapter 5 the fracture strength of SiC coatings in TRISO fuel particles is measured
and influence of the IPyCSiC interface on fracture strength is discussed Effect of
thermal treatment on fracture strength and microstructure of SiC coatings deposited at
different conditions are introduced in Chapter 6
Chapter 7 investigates the microstructure and mechanical properties of PyC coatings
with focus on deformation mechanism under indentation and the effect of density and
disorders on mechanical properties before and after thermal treatment
At last the main results and conclusions together with suggestions on future work are
given in Chapter 8
CHAPTER 1 Introduction
26
14 References
[1] httpnuclearinfonetNuclearpowerTheScienceOfNuclearPower
[2] J J Powers Fuel performance modelling of high burnup transuranic TRISO fuels
Disertation of Master University of California Berkeley 2009
[3] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[4] D L Hanson J J Saurwein D W McEachern A S Shoeny Development plan
for advanced high temperature coated-particle fuels Report Nopc000513
[5] httpwwwmpafrprocessphp
[6] W Burck H Nabielek A Christ H Ragos AW Mehner HTR coated particle
fuel irradiation behaviour and performance prediction Specialists meeting on
gas-cooled reactor fuel development and spent fuel treatment IWGGCR-8 1983
174-88
[7] H Nickel H Nabielek G Pott A W Mehner Long-time experience with the
development of HTR fuel elements in Germany Nucl Eng Des 217 (2002)
141-51
[8] H Nabielek W Kuhnlein W Schenk W Heit A Christ and H Ragoss
Development of advanced HTR fuel elements Nucl Eng Des 121 (1990)
199-210
[9] K G Miller D A Petti J Varacalle T Maki Consideration of the effects on
fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[10] A C Kadak R G Ballinger M JDriscoll et al Modular pebble bed reactor
project university research consortium Annual report INEELEXT-2000-01034
MIT-ANP-PR-075
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
CHAPTER 1 Introduction
27
treatment J Nucl Mater 374 (2008) 445-52
[12] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
CHAPTER 2 Literature Review
28
CHAPTER 2 Literature Review
21 Introduction
To model the probability of failure of fuel particles a number of key mechanical
properties of silicon carbide (SiC) are needed such as Youngrsquos modulus hardness
fracture toughness and fracture strength [1 2] These properties could be affected by
the microstructure of SiC coatings such as orientation porosities grain size and
defects [1-5] The small dimensions of the SiC coating limits the techniques available
to measure its mechanical properties However the development of the
nano-indentation has provided an important tool for probing the mechanical properties
of small volumes of material From the load ndash displacement data many mechanical
properties such as hardness Youngrsquos modulus and even fracture behaviour can be
determined [6] When an indentation system is used in conjunction with a focused ion
beam system and a transmission electron microscope images of deformation under
the nano-indentation can be obtained and the 3-D crack morphology can even be
reconstructed [7] Since there is a need to explain the high mechanical properties of
SiC deposited at temperature of 1300 ordmC by fluidized-bed chemical vapour deposition
[8] this combination of techniques could provide fundamental understanding of the
deformation mechanisms during indentation Another important parameter is fracture
strength and there have always been efforts to establish one method to characterise
fracture strength of SiC for example by brittle-ring test [9] whole particle crush test
[10] and modified crush test [5] Furthermore the high temperature application of SiC
and the compact of fuel pellet could affect the microstructure of SiC [2] which would
lead to the changes of mechanical properties
CHAPTER 2 Literature Review
29
The pyrolytic carbon (PyC) has been introduced by previous studies [11-14] and is
important in helping the SiC act as the main loading bearing layer The high
mechanical properties such as Youngrsquos modulus and anelasticity of PyC are necessary
to protect from damage caused by internal stresses and by external mechanical
interactions [12] However cracking and debonding between the SiC and inner PyC
layers could increase the probability of failure of TRISO fuel particles [13 14] It was
shown that without appropriate microstructure and mechanical properties of PyC the
structural or stress changes introduced in the coating during irradiation process could
result in total failure of the particle [11 13] The microstructure of PyC varied under
different deposition conditions [15] and it dominates the mechanical properties of
PyC coatings Therefore in this Chapter we review both the microstructure of SiC
and PyC including atomic structure morphology and defects and their mechanical
properties eg hardness Youngrsquos modulus deformation behaviour etc
22 Microstructure of silicon carbide
221 Atomic structure
The basic structural unit in SiC is a covalently bonded tetrahedron a carbon atom is at
the centre of four silicon atoms (C-Si4) and vice versa (Si-C4) The length of each
bond and the local atomic environment are nearly identical while the stacking
sequence of the tetrahedral bonded Si-C bilayers could be different The different
stacking sequences give SiC more than 250 polytypes [16] of which the 3C 4H 6H
and 15R are the most common The leading number of polytypes shows the repetition
of the SindashC pair and the letter C H and R represents the cubic hexagonal and
rhombohedral crystals respectively The 3C is the only cubic polytype in which the
stacking sequence of the planar unit of Si and C in tetrahedral coordination is depicted
as ABCABC in the lt111gt direction The cubic SiC crystal is called β-SiC and all
the other polytypes are α-SiC The crystal structures of 3C- 4H- 6H- and 15R-SiC
are schematically illustrated in Fig 21(a) [17] and corresponding XRD images were
CHAPTER 2 Literature Review
30
shown in Fig 21(b) [18]
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Although the transformation of SiC polytypes is primarily dependent on temperature
it could be affected by purity of the pre-existing phase pressure andor stacking faults
[19-22] The cubic form of SiC (β -SiC) is believed to be more stable than the
hexagonal structure (α-SiC eg 6H-SiC) below 2100 ordmC [19] However the polytype
of 2H-SiC which has the simplest stacking sequence is rarely observed at higher
temperature Krishna et al [20] reported that single crystals of 2H-SiC can be easily
transformed to 3C-SiC on annealing in argon at temperatures above 1400 ordmC It was
CHAPTER 2 Literature Review
31
found that the pre-existence of α-SiC (except 2H-SiC) could promote β-SiC
transformation to α-SiC while the transformation from α-SiC (6H-SiC) back to β-SiC
(3C-SiC) needs high temperature and pressure [21]
It has also been shown that the phase transformation could be closely related to
pre-existing defects such as stacking faults and their distribution [18] of which the
concentration is high even in single crystal SiC [22] Furthermore due to their low
formation energy the other intrinsic defects such as vacancies interstitials and
antisites were found to be common in SiC [23] These defects could affect mechanical
properties of SiC [8] so it is important to review their structure and properties
222 Defects in SiC
2221 Stacking faults and dislocations
A stacking fault is a disordered part of the ordered sequence in fcc crystal and the
most common stacking faults in cubic SiC are intrinsic and extrinsic stacking faults
(ISF and ESF) [24] For ISF the resulting stacking sequence is ABCACABC
if a double layer B is removed (condensation of vacancies) as for instance shown in
Fig 22[24] The ESF could be thought of as adding a double layer to the stacking
sequence (condensation of interstitials) resulting stacking sequence of
ABCACBCABChellip
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
CHAPTER 2 Literature Review
32
Another interpretation of the stacking faults is related to a twist of the three equivalent
bonds between two bilayers by 180deg [24] There may be an intrinsic shear stress
which could promote the glide of partial dislocations and thereby result in a faulted
crystal containing an error in stacking sequence so itrsquos reasonable to interpret
stacking faults in this way [25] Compared with dislocations and vacancies no bonds
are broken by stacking faults leading to a small energy difference between faulty and
perfect structures [26]
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
[27] [28] [24] [29] [30] [31] [32]
ESF (mJ m-1
) -15 -- -28 -6 -61 -154 -323
ISF (mJ m-1
) 12 34 -34 14 138 111 -71
Table 21 lists the formation energy of stacking faults in SiC and it shows that
extrinsic stacking faults have much lower formation energy than intrinsic stacking
faults in fact the values become negative The negative formation energy of stacking
faults in 3C-SiC means they can be formed very easily even more easily than perfect
3C-SiC As a result the stacking faults in 3C-SiC are spontaneously formed and most
likely in the form of extrinsic faults in the lt111gt direction Furthermore due to the
low energy of formation the length of a stacking fault can only be limited by the size
of the crystal or the presence of other defects that act as obstacles [33]
CHAPTER 2 Literature Review
33
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
The morphology of stacking faults in SiC observed by TEM is given in Fig 23 It
shows that the stacking faults could form a small domain (around 1 nm thick in Fig
23(a)) with different distances between small domains When a large concentration of
stacking faults exists in SiC it has been claimed that a conversion of cubic SiC to
hexagonal SiC on the nano-scale could happen by twinning [35] Furthermore the
stacking sequence of the faulted 3C-SiC was previously treated as random mixing of
α-type unit structures such as 6H and 4H in the 3C structure [36] Therefore it is
important to identify the properties and the microstructure of stacking faults of SiC
layers in TRISO fuel particles because the presence of α-SiC could result in reduction
of strength under irradiation which was due to enhanced possibility of anisotropic
swelling of α-SiC under irradiation compared to β-SiC [37]
(a) (b)
(c)
CHAPTER 2 Literature Review
34
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Figure 24 gives the XRD images of SiC in TRISO fuel particle deposited by fluidized
bed chemical vapour deposition showing the extra peak at 2θ~335ordm a high
background intensity at the peak at 2θ~353ordm and the broadening of the 3C peaks [8]
This is different from the perfect atomic structure of 3C-SiC as shown in Fig 21(b)
According to a previous simulation study [18] this kind of XRD diffraction pattern
could be caused by the existence of a high density of stacking faults and twins in the
regular cubic sequences It was demonstrated that it was unlikely to be due to the
presence of 2H-SiC or other polytypes [18] and two possible explanations were given
First two types of crystalline 3C-SiC with different populations of faults and twins
and second one type of crystal having clusters of faulted regions In SiC single
crystals although the concentration of stacking faults and twins is high the density of
dislocations is low (102-10
5cm
2) compared with metallic materials [22]
Figure 25 shows schematic images of the dislocations in face centred cubic (fcc)
crystals (β-SiC) The perfect dislocation is the (111) lt110gt system with burgers
vector of b=a2[110] (0308 nm) in SiC as shown in Fig 25(a) The perfect
dislocation could be easily dissociated into two partial dislocations of a6[121] and a6
CHAPTER 2 Literature Review
35
[21-1] as shown in Fig5 (a) and (b) because this reduces the total energy As a result
of this split a stacking fault must also be produced between the two partial
dislocations [38] Figure 25 (c) and (d) are lt110gt projections showing the Shockley
and Frank partial dislocations and their formation all related to the formation of
stacking faults
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
(a)
(b)
(c) (d)
CHAPTER 2 Literature Review
36
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
By comparing with previous studies [39-41] it is found that the relationship between
dislocation and stacking faults is complex The stacking faults have influences on the
mechanical properties for example enhancing the mobility of dislocations [39]
Different roles of stacking faults in II-VI heterostructures and devices have been
observed and results indicate that the stacking faults serve as the sources of misfit
dislocations [40] It is necessary to study the propagation of stacking faults or the
formation of stacking faults under stress and their influence on the properties of SiC
For example generation of stacking faults is shown to have occurred during the
fracture process together with the corresponding partial dislocation Furthermore
Agarwal et al [41] observed the growth of stacking faults from certain basal plane
dislocation within the base layer of the SiC
2222 Non-stoichiometric and point defects
Another common class of defects in SiC are non-stoichiometric (excess silicon or
carbon) and point defects [23 41 42] The purity of SiC may have effect on the
crystal structure strength corrosion resistance thermal conductivity diffusion
coefficient and other coating properties depending on its amount [43] The purity
could also affect defects in SiC eg if the stoichiometry deviates (even less than 1)
the concentrations of point defects in cubic SiC were found to be elevated [23]
Although the effect of point defects on general behaviour of nuclear fuel during
application process is not clear but their effect on microstructure evolution during
thermal treatment could be significant [44]
Silicon in SiC Stoichiometric 3C-SiC has generally been obtained at temperatures
between 1500 and 1600 [45] with carbon and silicon codeposited above and below
this temperature range By adding propylene as another carbon source the deposition
temperature of stoichiometric SiC could be reduced to about 1300 [8] The extra-Si
CHAPTER 2 Literature Review
37
SiC is less commonly investigated compared with the extra-C SiC because it has
been found that during the irradiation process the extra-Si plays a negative role in
material properties due to its low melting point [1] It has been found that the effect of
excess-Si on the Youngrsquos modulus and hardness it is more likely depending on its
amount and location [8 46]
Raman spectroscopy is an effective way to identify free Si both in amorphous and
crystalline phases eg it detected excess-Si when the XRD result showed the SiC was
stoichiometric [8] If the extra-Si is high (could be detected by XRD) TEM could be
used to detect its location and characterise the Si lattice contrast For example TEM
was carried out using both high resolution [35 47] and dark field imaging modes [48]
The HRTEM images in Fig 26 show the 3C-SiC crystallite with Si inclusions in
which nano-crystalline 3C-SiC and Si are separated by a weakly crystallized
interphase
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
(a)
(b) (c)
β-SiC
β-SiC
β-SiC
β-SiC
Si
Si
025 nm
025 nm
025 nm
0 312 nm
0312 nm
CHAPTER 2 Literature Review
38
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
Figure 27 shows bright-field and dark-field images of extra-Si SiC It shows the
crystalline Si as bright points in the dark background located at the grain boundaries
[48] The above observations were carried out in SiC with more than 1 at excess Si
(by comparing the intensity of Si Raman peak) as such observations are difficult
when the amount of excess Si is low Since the Youngrsquos modulus in SiC with low
amount of excess Si was comparable to that of stoichiometric SiC[8 46] it may have
unique properties that are worth further exploitation
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Carbon in SiC Excess C can also be identified by Raman spectroscopy but it is more
difficult to quantify its content and observe where this extra carbon exists due to its
small atomic number A comparative method was used to measure the content of
excess carbon by combining Raman spectroscopy auger electron spectroscopy
electron probe microanalysisand X-ray photoelectron spectroscopy [49] Once the
carbon concentration was measured (by above methods) the ratio of free excess to
SiC peak intensity (I796I1600) of Raman spectroscopy could be obtained as shown in
Fig 28 and the excess carbon concentration in the nearly stoichiometric SiC could
(a) (b)
CHAPTER 2 Literature Review
39
be estimated [49]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
There are few reports regarding the location of excess C in SiC The research carried
out by KKaneko et al [50] in carbon-doped hot pressed szlig-SiC showed that grain
boundaries were found to be free of any second phase by HRTEM although excess C
is found to form the second graphite phase Mykhaylyk and Gadzira revealed that
extra-C atoms are located as planar defects [51] The C atoms in the β-SiC structure
were supposed to arrange either as diamond-like carbon interlayers or as
non-correlated point defects after sintering of the as-synthesized powder at high
pressures and high temperature Since it showed that the presence of excess C atoms
in SiC crystal structure changes the local atomic environment [52] they may exist
within the SiC crystal and be correlated with other defects
The above discussion about the excess Si and C indicates that their influences on
properties of SiC depend on their content and that they could be discussed together
with the other point defects when their amount is low (less than 1 at ) [23]
Point defects in SiC SiC has eight kinds of point defects which keep the tetrahedral
symmetry of the perfect SiC crystal [23] They are carbon vacancies (Vc) silicon
vacancies (VSi ) carbon antisites (CSi) silicon antisite (Sic) a tetrahedral interstitial
silicon atom surrounded by four Si atoms (SiTSi) a tetrahedral interstitial silicon atom
CHAPTER 2 Literature Review
40
surrounded by four C atoms (SiTC) a tetrahedral interstitial carbon atom surrounded
by four Si atoms (CTSi) and a tetrahedral interstitial carbon atom surrounded by four
C atoms (CTC) [23] The formation energies for these defects are listed in Table 22
Due to their low formation energies the individual antisites and vacancies
particularly CSi were expected to appear even in as-deposited coatings [53 54]
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Vc VSi Sic CSi SiTSi SiTC CTSi CTC
Ef (eV) 59 68 73 11 150 147 86 110
The importance of point defects for different applications of SiC was studied and
these properties were studied in the relation to the properties of the point defects
including their formation annealing and interaction with each other [53] According
to Raulsrsquos study [54] the actual results of diffusion of CSi are more likely to be the
formation of CSi clusters which could be promoted by the diffusion of vacancies For
the coexistence of self-interstitials and vacancies (eg in irradiated material) it has
been found that the annealing temperature for VSi and Vc by recombination in β-SiC
were about 500 ordmC and 750 ordmC respectively [55] For as-deposited β-SiC without
interstitials the annealing process was only dominated by the out-diffusion of
vacancies the disappearances of VSi and Vc were found at temperature of 1400 ordmC and
1600 ordmC respectively [54] It is also been found that the migration of silicon vacancies
is easier than carbon vacancies due to its lower migration energy barrier Furthermore
in the case of excess carbon inside SiC the carbon clusters may form in SiC after
annealing and the size of the cluster depends on the content of interstitial carbon [56]
The general atomic-scale microstructure of SiC was reviewed above which showed
high degree of defects such as stacking faults dislocations vacancies and antisites
CHAPTER 2 Literature Review
41
The kind and concentration of these defects could affect the mechanical properties
such as hardness Youngrsquos modulus and fracture behaviour of SiC Since variation of
mechanical properties could also be due to other microstructural factors such as grain
size and density the relationship between microstructure and mechanical properties
are further reviewed in the following session
23 Properties of silicon carbide
231 Youngrsquos modulus
Youngrsquos modulus is physically related to the atomic spacing atomic bond strength
and bond density It is accepted that high-purity SiC material eg CVD SiC exhibits
the highest elastic modulus and that a porous microstructure with a high
concentration of impurities could decrease the elastic modulus [1 57] In contrast
neither grain size nor polytype was recognized as having a significant effect on the
elastic modulus of SiC in coated fuel [1 58]
Table 23 Elastic tensors of 3C-SiC at room-temperature
C11 (GPa) C12 (GPa) C44 (GPa) Z Ref
3C-SiC a 3523 1404 2329 18196 [59]
3C-SiC b 511 128 191 10026 [1]
3C-SiC c 390 142 256 -- [60]
3C-SiC a 420 126 287 19503 [61]
a Theoretical calculations
b Sonic resonance measurement
c Raman Spectroscopy
According to the definition of Youngrsquos modulus an important factor which could
affect its value for SiC material is the texture which is the degree of anisotropy (lack
of randomness with regard to the orientation) of SiC crystals The Youngrsquos modulus is
different by a combining of elastic tensors for deformation of the crystal in different
CHAPTER 2 Literature Review
42
orientation The elastic tensors or the stiffness tensors reflect the linear stress-strain
relation of a material There are 81 elastic tensors because the stresses and strains
have 9 components each However due to the symmetries of the SiC the tensors were
reduced to 3 unknown values They could be measured by sonic resonant method [1]
and Raman spectroscopy [60] based on vibrational theory of the crystal lattice They
are defined for SiC in Table 23 and will cause the variation of Youngrsquos modulus for
anisotropic materials The elastic tensors for 3C-SiC identified by previous theoretical
and experimental results [59-61] are substantially different from the current updates
of sonic resonance data The difference could be caused by the difference of the size
of SiC mateirals which could introduce the influences of defects such as grain
boundaries and stacking faults It was proposed to be more reasonable estimation for
SiC in TRISO fuel particle [1]
A measurement of the anisotropy in β-SiC (faced centre cubic crystals) is the ratio of
the two shear moduli [3] 100 shear modulus and 110 shear modulus μ0 and μ1
respectively which is
0 44
1 11 12
2CZ
C C
(1)
the parameter Z is known as the Zener ratio or elastic anisotropy factor (given for
different elastic tensor Table 23) When Zgt1 the Youngrsquos modulus is minimum
along lt100gt and a maximum along lt111gt and the representational surfaces for
Youngrsquos modulus in cubic crystals is shown in Fig 29 For the case when Z=1 the
cubic crystal would also be isotropic and the representation surface would be
spherical
CHAPTER 2 Literature Review
43
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
If the samples were random polycrystals which means samples are isotropic the
theoretical Youngrsquos modulus can be unambiguously given by [3]
3
[1 ( 3 )]E
B
(2)
While bulk modulus and shear modulus are
11 122
3
C CB
(3)
1
0 1
1 0
52( 6 )
(4)
where 0 44C 1 11 12( ) 2C C and
01
0 0
3( 2 )
5 (3 4 )
B
B
(5)
The theoretical value can be gained when the elastic constants are known Using the
Eqs (2-5) the theoretical Youngrsquos modulus E was calculated to be 496 GPa for
isotropic SiC materials when the elastic tensor obtained by Lambrecht et al was used
The calculated value is close to the Youngrsquos modulus measured by nano-indentation
(about 527 GPa) of isotropic bulk CVD SiC [62] But this value is higher than the
Youngrsquos modulus measured by nano-indentation of SiC in TRISO fuel particle which
is about 450 GPa [8 46]
By using the elastic tensors measured by sonic resonance in Snead et alrsquos study [1]
CHAPTER 2 Literature Review
44
the calculated Z (10026) is very close to 1 and it means the Youngrsquos modulus in
TRISO coated fuel particle may show no orientation effect According to Eqs (2-5)
the calculated Youngrsquos modulus is about 459 GPa under the elastic tensors given in
Ref [1] This value is close to the Youngrsquos modulus measured by nano-indentation in
TRISO fuel particle regardless of the orientation effect [1 8 46] Therefore for
TRISO fuel particle the recommended elastic tensors measured by sonic resonances
were supposed to be appreciable due to the scale and the microstructure similarities of
SiC materials [1]
Another significant factor which affects the Youngrsquos modulus is the density The
elastic modulus E at room temperature can be empirically expressed in an exponential
function of porosity pV as [63]
0 exp( )pE E CV (6)
where 0E is the elastic modulus and C is a constant of 357 for a pore-free bulk CVD
SiC pV is the ratio of the relative density difference to the theoretical density of SiC
(322 gcm3)
The relationship between density and Youngrsquos modulus of different kinds of SiC
materials measured by different methods were summarised in a previous study [1] as
shown in Fig 210 It has been found that the standard deviation of elastic modulus of
SiC is about plusmn 10 when the density is higher than 99 and increased to plusmn 15 for
porosity higher than 1
CHAPTER 2 Literature Review
45
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
232 Hardness
In a brittle material indentation hardness is defined as the mean pressure the material
will support under load and it is a complex property which could involve crack
initiation and propagation and the development of new surfaces during the
indentation process [1] Furthermore the value of hardness measured by indentation
also depends on external factors Due to the difference in dimensions of materials
such as the bulk small scale and thin film materials indentation on the nano- micro-
and even macro-scale have been used to measure the hardness [64] The hardness of
β-SiC related material has mainly been investigated by Vickers and nano-indentation
techniques (introduced in the later part of this session according to Ref [65]) as
summarized in Table 24 Reviews have found that the nano-hardness is generally
higher than Vickers hardness [1] which was attributed to the indentation size effect
Although few hardness values of β-SiC are available to be compared (given in Table
24) it shows the difference of hardness within a given sample Regardless of external
influences on the measurement of hardness generally it can be affected by grain size
or grain morphology [46] density composition and defects [1 8 66] To identify the
CHAPTER 2 Literature Review
46
controlling factor for hardness it is necessary to understand the deformation
mechanism of SiC under indentation
Table 24 Vickers and nano-indentation hardness of β-SiC related materials
Deformation mechanism Research into the deformation mechanism of SiC have
shown the availability of dislocation related plasticity [70] phase transformation
(cubic phase to amorphous) [71 72] fracture mechanisms [73] and also the
combination of any two or three [62 73]
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
First the dislocation related plastic deformation was found in single crystal 6H-SiC
[70] and the propagation morphology of dislocations was observed after indentation
as shown in Fig 211 This observation confirmes that the dislocation slip is a
Materials Vickers hardness (GPa) Nano-hardness (GPa) Ref
Single β-SiC (001) 28 -- [67]
CVD β-SiC 207-32 325-406 [466668]
FBCVD β-SiC -- 36-42 [8]
Sintered β-SiC 211-239 -- [69]
500 nm
CHAPTER 2 Literature Review
47
mechanism of plastic deformation from nucleation of a few dislocation loops (at or
near the theoretical strength) to extensive dislocation plasticity
Furthermore the dislocation related plastic deformation in polycrystalline CVD β-SiC
(with micro meters grain size) was first observed by Zhao et al [62] It was found that
the initiation of the plastic deformation was reflected by the burst (pop-in) of the
force-displacement curve which is similar as the initiation of plastic deformation in
metallic materials as shown in Fig 212(a)
According to the Hertzian contact theory [74] the burst was attributed to initiation of
the dislocation glide by comparing the shear stress generated under the indentation at
that load with the theoretical shear stress in β-SiC [62] During the whole indentation
process it was shown that shear slip is the predominant deformation mechanism and
that cracks were associated with the shear faults Figure 212(b) is one of the TEM
images showing the microstructure under indentation and it shows the dislocation
induced shear bands at one side of indent [62] which depend on the orientation of
grains
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation [62]
Second following the observations of phase transformation under indentation in
silicon [75] and the formation of SiC amorphous phase during high speed machining
(a) (b)
CHAPTER 2 Literature Review
48
process [71] the investigation of phase transformation under indentation was carried
out in SiC [7274] It has been demonstrated thermodynamically that the direct
amorphization is less likely to happen under nano-indentation [76] The
amorphization observed in single crystal SiC was attributed to the formation
propagation and accumulation of dislocations which formed the disordered phase at
the maximum stress region under a punch indentation [71] In SiC with nanometers
grain size the molecular dynamic study indicated thedominated deformation under
nano-indenation is a crossover of the indentation-induced crystallization to
disordering leading to amorphization [72] as shown in Fig 213
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Further studies demonstrated that the phase transformation from β-SiC to α-SiC is not
possible under nano-indentation because a pressure of nearly 100 GPa is needed [76]
even when assisted by high dislocation density shear stress and temperature This
simulation work concluded that the primary response of β-SiC to nano-indentation is
dislocation nucleation and propagation which has been confirmed by experimental
observations [62]
Third the plastic deformation of β-SiC under indentation was divided into two parts
CHAPTER 2 Literature Review
49
which are primary dislocation initiation and propagation and the formation of micro
cracks [73] The former contributes to 13 of plastic deformation under indentation
while the later provides 23 of total deformation The hardness related plastic
deformation could be explained well by this mechanism which included above two
process as discussed in previous studies [1 46 62] Moreover considering the effect
of micro cracks the deformation mechanism under indentation could be related to
other factors which could contribute to the formation of micro cracks such as
porosity grain boundaries and stacking faults in SiC [3]
Youngrsquos modulus and hardness of coatings in TRISO fuel particle can be measured by
nanoindentation due to the limitation of small dimension A typical
load-displacement curve and the deformation pattern under nanoindentation of an
elastic-plastic sample during and after indentation are shown in Fig 214 in which the
hc is contact indentation depth and hs is the displacement of the surface at the perimeter
of the contact [65] The peak load and displacement are Pmax and hmax respectively
and the diameter of the contact circle is 2a During unloading process the elastic
displacements are recovered and when the indenter is fully withdrawn the final depth
of the residual hardness impression is hf [65]
Nanoindentation hardness is the ratio of the load to the projected contact area of the
indentation The mean pressure that the material can support under indentation is
defined as the hardness From the loadndashdisplacement curve as in Fig 214(a) hardness
can be gain when the load is at the maximum value
A
PH max (7)
where A is the projected contact area
CHAPTER 2 Literature Review
50
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
The elastic modulus of the indented sample can be inferred from the initial unloading
contact stiffness S=dPdh ie the slope of the initial portion of the unloading curve A
geometry-independent relation involving contact stiffness contact area and elastic
modulus can be derived as follows
2A
S E
(8)
where szlig is a constant that depends on the geometry of the indenter (szlig=1034 for a
Berkovich indenter) [65] and Er is the reduced elastic modulus which accounts for the
fact that elastic deformation occurs in both the sample and the indenter Er is given by
CHAPTER 2 Literature Review
51
22 11 1 i
r i
vv
E E E
(9)
where E and υ are the elastic modulus and Poissonrsquos ratio for the sample respectively
and Ei and υi are the same quantities for the indenter For diamond Ei=1141 GPa and
υi=007[65]
For an indenter with a known geometry the projected contact area is a function of the
contact depth The area function for a perfect Berkovich indenter is given
by 2245 cA h Indenters used in practical nanoindentation testing are not ideally sharp
Therefore tip geometry calibration or area function calibration is needed A series of
indentations is made on fused quartz at depths of interest A plot of A versus hc can be
curve fit according to the following functional form
11 12 1 1282 4
1 2 3 8245 c c c c cA h C h C h C h C h (10)
where C1 through C8 are constants In some cases only the first three constants were
considered
The contact depth can be estimated from the load-displacement data using
maxmaxc
Ph h
S (11)
Where ε is a constant that depends on the indenter geometry (ε=075 for a Berkovich
indenter)
It is worth noting that high Youngrsquos modulus and hardness does not gurantee the
suitability of ceramic material to an engineering application because of the
importance of other mechanical properties such as fracture toughness and fracture
strength
CHAPTER 2 Literature Review
52
233 Fracture toughness
The definition of fracture toughness from Munz and Fett is [77] if a component or a
test specimen with a crack is loaded the stress intensity K1 increases with increasing
load until unstable crack propagation occurs at a critical value of K1 This critical
value is the fracture toughness (KIC) Therefore the measurement of fracture
toughness should be made on sample with a pre-crack however due to the small size
of SiC coating methods could be used are limited Although the most recently
developed micro-beam bending test could measure the fracture toughness of SiC in
TRISO fuel particles [78] this process is costly and time consuming because it
involves the preparation of micro-beams and notched cantilevers by focused ion beam
milling which limites the application of this technique
Indentation is now one of the most commonly used techniques to evaluate the fracture
toughness of ceramics and coating systems because it is easy to perform does not
need special samples and causes only negligible surface damage However some
researchers have declared that the indentation method is not suitable for the
measurement of fracture toughness [79 80] They concluded that the indentation
method does appear to represent some form of a complex crack arrest phenomenon
but that this occurrs in the presence of a multiple-crack path and a highly complex
residual stress field
Despite of these considerations the indentation method is an effective way to
compare the fracture behaviour of materials [80] particularly for small size specimens
and it provides information about the crack initiation and propagation Figure 215 is
the most typical characterization of the crack system generated by Vickers indentation
[81] This crack system is termed as median-radial cracking and consists of
approximately semi-circular cracks
CHAPTER 2 Literature Review
53
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
The mode of crack initiation and propagation under an indenter proposed by Chiang
et al explains many of the features observed in indentation crack patterns and is the
most recent advance [82] It was found that radial cracks are the first to initiate
trigged by a combination of the highly tensile surface stress field and the availability
of surface flaws [74 82] These cracks grow on unloading and can either propagate
into the plastic zone (half penny cracks) or terminate in the elastic zone (Palmqvist
cracks) [83] depending on the microstructure of the material
For different types of crack modes such as half-penny and Palmqvist cracks different
equations were developed based on theoretical analysis of stress field and empirically
calibrations to calculate the fracture toughness under indentation For example in the
half penny crack model the Vickers indentation fracture toughness was most
frequently determined using the relationship proposed by Anstis et al [84] This
equation was first inferred based on isotropic materials and it is suitable for general
application to well-developed cracks [84]
1 2
3 2( )IC
E PK
H c (12)
Where P is the indentation load c is the radial crack length from indentation centre to
crack tip E and H are the Youngrsquos Modulus and hardness of the materialand χ
denoted as the geometrical constant which is independent of the materials The Eq
CHAPTER 2 Literature Review
54
(12) was developed on the basis of half penny cracking in homogeneous brittle
materials under high load for example in glasses [84]
The above information shows that it is possible to compare fracture toughness under
indentation in SiC coatings with different microstructures The fracture toughness of
SiC could depend on a large number of factors such as grain size porosity micro
cracks and inclusions which could dissipate the fracture energy from the main crack
[3] According to a previous review [1] fracture toughness of SiC peaks at the grain
size range of 1-5 microm So fracture toughness of SiC in TRISO fuel particle is likely to
be influenced by the grain size due to the similar range of grain size Although micro
cracks and pores could improve fracture toughness they would decrease the strength
[3] which is detrimental for the safe design of fuel particles Over several decades
studies have worked to improve the fracture toughness by introducing a
heterogeneous microstructure such as weak grain boundary phases [85] In the
heterogeneous phase toughening mechanism the cracks could initiate in or be
reflected into weak defects and thereby dissipate the fracture energy for the main
crack propagation Furthermore the distribution of grain boundary character (the
crystallagraphic type and frequency of grain boundaries) and morphology could
influence the fracture toughness [85 86] Different grain boundary orientations and
their frequency were found to affect the fracture toughness by controlling the
intergranular fracture of materials [86] Different grain morphologies such as
elongated grains could increase the fracture toughness by crack bridging or by
generating micro cracks along grain boundaries or triple junctions [85] No
heterogeneous phase is supposed to exist in SiC in TRISO fuel particles so the
fracture toughness is most likely to be affected by grain morphologies or as-deposited
defects
According to the Griffth fracture theory once the size of the critical flaw is the same
the fracture toughness is propotional to the fracture strength which is another
CHAPTER 2 Literature Review
55
parameter used in modelling of the probability of the failure of fuel particle
234 Fracture strength
For brittle materials the fracture strength is best considered as a distribution rather
than a fixed value as the flaws (such as surface cracks pores and inclusions) from
which fracture initiates vary in size and type (result in different frature strength value)
between nominally identical samples [3] The Weibull approach is a commonly used
empirical method to characterise the strength of a brittle material It assumes a simple
power-law stress function (eg in Eqs (18-20)) for the survival of the elements
which is integrated over the body volumesurface area (as shown in Eqs (19) and
(21)) In many cases this function gives results in the form of Weibull modulus (m in
Eq (19)) and characterstic strength which describe the width and magnitude of the
strength distribution [3] The Weibull modulus is the slope of Log-Log distribution
function of the survival of elements and strength (Eq (19)) For engineering
application the high Weibull modulus represents the small variation of the fracture
strengthes for a given material
Higher Weibull modulus reflects lower variability of the strength and it is typically in
the range of 5-20 [3] The commonly used strength test methods for bulk ceramics are
uniaxial tension three- and four-point bending However the small dimensions of
TRISO fuel particles make it difficult to measure the strength by those conventional
methods As a consequence some specific methods were developed in the last few
decades such as O-ring test [87 88] C-ring test [88] hemisphere bending [10]
internal pressurization [89] and crush test [5 89 90] The schematic of easily
repetitive fracture strength test geometries are given in Fig 216 and the obtained
fracture strength by different methods was shown in Table 25
CHAPTER 2 Literature Review
56
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Methods L
f (MPa) Weibull Modulus F
f (MPa) Ref
O-ring compression 596-1412 41-66 -- 87
O-ring compression 1050-1890 48-94 -- 88
C-ring Compression 980-2200 40-90 -- 88
Semi-spherical bend 720-1350 70-80 340-620 10
Inner pressurization -- 43-62 222-448 89
Crush test -- 58-75 356-427 89
Crush test 770-1324 40-73 330-647 5
Crush test 1484-1721 135-183 1045-1091 90
L
f Local fracture strength F
f Fracture strength of the full particle
The local fracture strength is in the range of 596-2200 MPa and the fracture strength
of the whole particle varies from 222 MPa to 1091 MPa Such significant variation is
tought to be caused by the differences in specimen size and loading mode which were
related to the nature of the Weibull distribution [1 3] It has been demonstrated that
specimens with larger volumesurface area (under the same loading mode) have lower
strength because there is an increased probability that a larger flaw exists in a larger
body Similarly when there is no volume difference the loading mode which stresses
larger area has lower local fracture strength [3] These discussions show the
importance of regulating the fracture strength test method and producing specimens
with regular shape and size
CHAPTER 2 Literature Review
57
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
The modified crush test developed by Byun et al [5] is recommended for the fracture
strength measurement of SiC in TRISO fuel particles because it considered the effect
of contacting area between SiC shell and plunger which reduced the variation and
uncertainty of the stress distribution under tensile stress
Modified crush test When a partial spherical shell is diametrically loaded by an
external load F concentrated on a small circular contact area of radius 0 the
maximum membrane stress and bending stress are given by [91]
2
1 2
1membrane
FC
t
(13)
CHAPTER 2 Literature Review
58
2 2
1bending
FC
t
(14)
where ν is the Poisson ratio t is the thickness of shell and C1 and C2 were defined as
2
1 0115004022050 C (15)
)27031exp(204412 C (16)
2 2 2 1 4
0[12(1 ) ( )]r R t (17)
max membrane bending (18)
where max (L
f ) is the fracture strength for locally loaded specimens R is the outer
diameter of shell t is the thickness of the SiC shell The distribution of local fracture
strength is analysed by the Weibull distribution function which presents the
cumulative probability of failure P as [5]
mL
f
E
m
s
F
fSdAP
00
exp1exp1
(19)
where L
f m 0 and ES are the local fracture strength the Weibull modulus the
characteristic sterngth and the size effect factor respectively The size effect factor is
dAS
m
s L
f
F
f
E
Byun et al [5] used the probability estimator as follows
1
N
iPi (20)
where iP is the probability of failure for the i th-ranked strength and N is the
CHAPTER 2 Literature Review
59
sample size The increased probability that the full SiC shell has more critical flaws
compared with the stress-weighted surface is corrected by the size effect and the
fracture strength of the full shell (F
f ) is given
L
f
m
L
f
m
F
E
L
EF
ftR
r
S
S
1
2
2
0
1
)(4
(21)
After adjusting the size effect the fracture strength of the full particl of different SiC
coatings could be compared In a previou study [87] the difference of the fracture
strength was attributed to the microstructural variations which were determined by
deposition conditions [87] More detailed analysis [510] showed that the variation of
fracture strength was due to factors such as porosity roughness of the IPyCSiC
interface and grain size For example Evans et al [10] observed that the surface
roughness influenced the failure of the particle withstrength improved by reducing
the inner surface roughness According to above discussion the variation of Weibull
modulus could be attributed to the different test methods flaw distribution and sample
size [3 5]
Micostructure and mechanical properties of as-deposited SiC are reviewed above
which may change after high temperature treatment and the degree of evolution could
be different due to variational deposition conditions of SiC coatings As summarized
in a previous study [92] one of the critical properties for SiC layers in TRISO fuel
particle is that the microstructure remains unchanged after thermal treatment at 2000
ordmC for 1 hour in an inert atmosphere as determined by electron microscopy and X-ray
diffraction
235 Effect of thermal treatment on SiC
The SiC with perfect crystal structure tends to have good high temperature thermal
stability however due to the concentration and type of imperfections generated
CHAPTER 2 Literature Review
60
during deposoition process its thermal stability could be affected Defects such as
stacking faults vacancies and interstitials in as-deposited SiC coatings affect the
microstructural change after thermal treatment [93-96] For example the phase
transformation from β- to α-SiC generally happened at temperatures above 2100 ordmC
[19] but it could take place at lower temperature (gt 1700 ordmC) in special cases (eg
CVD β-SiC deposited on Si substrate with high amount of stacking faults) [93]
During high temperature thermal treatment (about 2000 ordmC) of CVD β-SiC one
significant microstructural change would be the annihilation of stacking faults [94
95] A thermodynamics study [94] has shown that the mechanism of reduction of the
stacking faults was due to the diffusion of Si or C atoms and it also demonstrated that
the migration energy of Si atoms was smaller than C atoms Considering the
abundance of intrinsic defects (section 222) there has been little investigation of
their effects on microstructure change of β-SiC after thermal treatment Furthermore
the effects of high temperature thermal treatment on mechanical properties such as
the hardness Youngrsquos modulus [97] and strength [98] have been carried out Their
results showed that mechanical properties showed little change when the treatment
temperature was lower than 2000 ordmC while there was decrease in the strength after
thermal treatment at 2100 ordmC
24 Microstructure and properties of pyrolytic carbon
In this part the microstructure of carbon related material is reviewed first which is
followed by the measurement of Youngrsquos modulus and hardness Furthermore to
know the controlling factor on mechanical properties of PyC coatings different
deformation mechanisms under indentation are introduced A brief review about effect
of thermal treatment on properties of PyC coatings is given
CHAPTER 2 Literature Review
61
241 Microstructure of pyrolytic carbon
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
The graphite structure consists of graphene sheets having localized in-plane σ (sp2)
hybrids bonds and delocalized out of plane π (pz) orbital bonds connecting graphene
sheets The out-of-plane bond is a van der Waals interaction which is much weaker
than sp2 and sp
3 hybrids Pyrolytic carbon is a material with some covalent bonding
between its graphene layers as a result of imperfections (defects) in its structure [99]
Figure 217 gives schematics and TEM images showing different microstructures of
PyC with different densities The growth features are polyhedral or conical shape in
high density pyrolytic carbon (Fig 217 (ab)) but are globular in low density
pyrolytic carbon (Fig 217(cd)) [15] It shows that the microstructure of pyrolytic
carbon consists of growth features between 200 nm- 1000 nm in size (Fig 217 (b)
and (d)) [15] Pores were formed at the boundaries or triple junctions between growth
(a) (b)
(c) (d)
CHAPTER 2 Literature Review
62
features
According to previous studies [15101] individual growth features contain crystallites
(domains) as shown schematically in Fig 218(a) They are composed of a series of
curved graphene layers randomly rotated with respect to each other along the c-axis
[101] The dimensions of the crystal were described by La (diameter of crystal along
the χ direction) and Lc (height of the crystal perpendicular to χy plane) as shown in
Fig 218(a) Regarding the definition of the PyC there are defects within the growth
features together with crystallites A local atomic structure of less ordered graphene
layers is shown in Fig 218(b) which could reflect the plane defects in graphene
layers [102]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
A high density of defects such as dislocation loops and kink bands were observed in
ball milled graphite by HRTEM as shown in Fig 219(a) The distorted
microstructure of graphite was also inferred from the striped diffraction points in
selected area electron diffraction image (Fig 219(b)) [103] since the diffraction
pattern gives information on orientation of crystal planes Compared with ball milled
graphite the HRTEM image of pyrolytic carbon has higher amount of defects as
shown in Fig 19(c) which is reflected from the highly distorted lattice planes and low
texture The selected area electron diffraction image of pyrolytic carbon (Fig 219(d)
with eperture diameter of 200 nm) showed arc shaped diffraction patterns [15 104]
The arc represents the overlap of diffraction patterns from different graphite domains
CHAPTER 2 Literature Review
63
with different orientations and this indicats that the microstructure is more distorted
eg smaller domain size and increased random orientation of domains In heavily
disordered PyC it is not possible to observe the individual dislocations or other
defects which is thought to be due to the numerous defects such as tilt boundaries
which obscure individual defects as described in Ref [105]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
Raman spectroscopy is one of the most effective techniques to characterise the defects
in carbon materials and has previously been used to characterise the microstructure of
PyC [15 106] These spectra can identify even quantify the microstructure such as
crystallite boundaries and size disorders (5-memebered rings) and chemical bonding
type Figure 220 shows the evolution of the Raman spectra with the change of the
CHAPTER 2 Literature Review
64
in-plane defect types The carbon spectra of Fig 220(a-c) showed increased and
broadened D signal and the main in-plane defects observed in these structures were
supposed to be domain boundaries [15] In Fig 220(d-e) the D signal became shaper
which was attributed to the formation of five-member rings [15]
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
The high density of disorders such as in-plane domain boundaries makes the Raman
bands become broder and overlapped with each other as shown in Fig 220(c) which
inferred the structure of turbostratic or high density PyC [10 15] According to
previous studies [106 107] the broadened Raman bonds could be deconvoluted into a
number of peaks which correspond to different types of disordered structure in
carbon materials Figure 221 is an example of a first order Raman spectra fitted with
Lorentzian and Gaussian functions and it includs I (~1170 cm-1
) D (~1330 cm-1
) Drdquo
(~1500 cm-1
) G (~1580 cm-1
) and Drsquo(~1618 cm-1
) bands [106] The Drdquo peak was
CHAPTER 2 Literature Review
65
attributed to amorphous carbon with a certain amount of sp3 carbon [106108] which
could reflect the interstitial defects coupling to the graphene layers or adjacent
domains [109]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
242 Mechanical properties of pyrolytic carbon
The different deformation mechanism of carbon materials compared to ceramic
materials results in distinct force-displacement curves which show the complete
recovery of the unloading curve [110 111] Therefore we describe the mechanical
properties of PyC coatings and deformation mechanism of carbon materials
2421 Youngrsquos modulus and hardness
Due to the importance of PyC in the nuclear industry mechanical properties were
measured by three-point bending [102 112] and nano-indentation [113-115] Table
26 gives the Youngrsquos modulus and hardness of PyC measured by different methods
In three-point bending tests the mechanical properties were functions of density
orientation angle and domain size No individual factor could clearly explain the
variation in Youngrsquos modulus strength or fracture toughness [112116] In previous
nano-indentation tests the low density PyC was found to have low hardness and
Youngrsquos modulus [114] whereas the influence on mechanical properties was
CHAPTER 2 Literature Review
66
uncertain which could be due to lack of investigation about the deformation
mechanisms
Table 26 Summary of the hardness and Youngrsquos modulus for PyC measured by
different methods
Methods Density range
(gcm3)
Youngrsquos modulus
(GPa)
Hardness
(GPa)
Ref
3-point-bending 150-212 310-427 -- 112
137-206 165-281 -- 116
Nano-indentation 185-190 255 + 2 -- 114
165-203 235-270 30-44 115
155-187 70-150 05-18 115
135-212 125-346 15-48 113
Youngrsquos modulus was changed from PSI to GPa
Figure 222 is a schematic of the typical force-displacement curve of different kinds
of materials under indentation [65110111] The curve of carbon materials shows a
completely recovery and no net displacement after unloading as shown in Fig
222(a) In carbon materials the force-displacement curve formed a closed loop and
this phenomenon was called anelastic deformation behaviour [14 117] This was
related to the internal friction of materials but there is controversy regarding the
sources of the internal friction [14105111] Since the force-displacement curve gives
information about the energy change during indentation the deformation behaviour of
carbon material can be analysed by the energy method
The energy distribution under indentation is shown in Fig 222 which includs the
hysteresis energy (Uh) and unloading energy (Uunloading) and the total energy (loading
energy Uloading) is the sum of the above two energies [110] As shown in Fig 222 the
ratio of the hysteresis energy to total loading energy could be different for different
microstructure of carbon materials [118] The ratio could be used to estimate the
CHAPTER 2 Literature Review
67
flexibility of elasticityductility [110119] For example a low ratio corresponds to
higher elasticity whist a high ratio meants higher ductility
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
The different force-displacement curve of carbon materials was compared with the
irreversible deformation behaviour of materials with linear elasticity such as SiC as
shown in Fig 214(a) [65] In linear elastic deformation the final displacement of hf
was left after complete unloading and the unloading curve nearly followed the linear
relationship Furthermore the area between the loading and unloading curves
represents the energy consumed by the plastic deformation which could be due to the
movement of dislocations and formation of micro cracks [1 62]
2422 Deformation mechanism
Reversible slip and sliding friction theory In this theory the complete recovery of
strain was due to the reversible slip of graphene planes and the energy loss was
attributed to the friction during the slip which was caused by a compressive stress on
the graphene layers [110111] The theory was obtained by considering an arbitrary
grain located at some position in a radially declining hydrostatic stress field below a
spherical indenter as shown in Fig 223 [110111] The force was resolved into
CHAPTER 2 Literature Review
68
compressive stress perpendicular to and shear stress parallel to the slip plane By
using the equation proposed by Kelly [120] the shear component (τ τ0 shear stress
with and without friction respectively) may be expressed as τ= τ0 +μσ where μ is a
friction coefficient and σ is normal stress component To initiate slip between
graphene layers the shear stress needs to exceed some critical value Therefore the
inter-layer slip with friction was supposed to be the mechanism of anelastic
deformation The authors [110111] also concluded that the hysteresis during
unloading appeared to be a natural result of friction between the graphene layers but
additional mechanisms were supposed to be operating in the different forms of
graphitic materials Furthermore the study did not give a clear explanation about how
the reversibility of the basal plane slip was realized
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Dislocation pileup theory This idea was derived from isotropic carbon after thermal
treatment at the temperature range of 880-2600 ordmC by using micro indentation [121]
The authors attributed the unique unloadingreloading behaviour of the
well-graphitized carbons to the slip of dislocation networks on graphitic basal planes
which is partially or fully reversible It is supposed that the dislocations could pile up
at grain boundaries as in metals The stress at grain boundaries due to dislocation pile
ups could reverse the dislocation movement during indentation unloading but it did
CHAPTER 2 Literature Review
69
not explain why deformation behaviour of PyC is unlike that of metals This is also
the reason that other researches [105] doubt this theory because it fails to explain the
nature of the reversible behaviour [121]
Kink band theory It was suggested that the origin of the loops obtained in single
polycrystalline and porous carbons is the formation of incipient kink band and kink
bands [105] The kink band model was proposed by Frank and Stroh [122] as
shown in Fig 224 which showed pairs of dislocations of opposite sign nucleate and
grow at the tip of a thin elliptical kink (not clear about the nature) The stability of
kink bands depended on a shear stress [122]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
In this theory since the dislocations were confined to the basal plane the hysteresis
process was attributed to the reversible movement of the dislocation along a long
distance The same mechanism was used to explain the deformation behaviour of the
bulk polycrystalline graphite The microstructural change under indentation should
first be related to the kink band initiation and then further microstructure change
could be reflected in the accumulation of other chemical bonds which could resist
dislocation glide
CHAPTER 2 Literature Review
70
2423 Effect of thermal treatment on properties of PyC
The effect of thermal treatment on the microstructure of carbon materials has been
widely studied [112 123 124] The change of the microstructure of carbon materials
during thermal treatment mainly involves the growth of the domain size (in-plane
crystal size along a axis) La and (along c axis crystal size) Lc with the increase of
temperature For different kinds of carbon materials these evolutions started at
different temperatures For example the crystal growth in-plane happened at 400-600
ordmC for graphitisable carbon and could continue up to high temperature the
coalescence of crystallites along the c-axis started above 1000-1200 ordmC the
coalescence of crystallites along ab direction occurred at temperature above 1400 ordmC
[124] For carbons with strong cross-linking (non-graphitisable) the coalescence of
domains usually happened at temperatures higher than 2400 ordmC [124] Although the
increase in anisotropy and density during processing of coated particle fuel was
reported by Hunn et al [11] no change in texture was identified on PyC due to the
post deposition of SiC shown in Lopeacutez-Honorato et alrsquos study [125] Furthermore no
significant change of mechanical properties was obtained after thermal treatment at
temperatures in the range 1000-1980 ordmC in PyC coatings with density of about 19
gcm3 [97] however a decrease of Youngrsquos modulus was observed in high density
(above 2 gcm3) PyC coatings [125] It was assumed that certain microstructures of
PyC would be less affected by thermal treatment
25 Summary
The microstructure and mechanical properties of SiC and PyC were reviewed in this
Chapter and the information obtained is summarized below
(1) It is common for SiC to have defects such as stacking fautls and dislocations
non-stoichiometry and point defects due to their low formation energy
particularly in SiC deposited by chemical vapour deposition
CHAPTER 2 Literature Review
71
(2) Defects interact with each other Stacking faults could be the result of gliding
of partial dislocations Vacancies promoted diffusion of antisites forming
antisite clusters
(3) The Youngrsquos modulus of SiC coatings in TRISO fuel particle is affected
mainly by texture and porosity
(4) Hardness related plastic deformation in single and polycrystalline (nano-meter
or micro-meter grain size) SiC is related to dislocation propagation fracture
of crystallites or phase transformation
(5) A combination of indentation together with electron microscopy is an
effective way to study the fracture behaviour of SiC coatings in TRISO fuel
particle
(6) Fracture strength of SiC coating in TRISO fuel particle varies significantly in
different measurements and the modified crush test is recommended The
interface roughness and porosity are found to be main factors controlling
fracture strength of SiC coatings
(7) The typical change of microstructure after thermal treatment in SiC is the
annihilation of stacking faults through the diffusion of vacancies
(8) The disorder in PyC coatings could be significant such as domain boundaries
and 5-membered rings Raman spectroscopy together with transmission
electron microscopy are important techniques to characterize these disorders
(9) Carbon related materials show hysteretic deformation behaviour under
indentation Different deformation mechanisms are proposed which all relate
to the slip of graphene layers
CHAPTER 2 Literature Review
72
26 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modeling J Nucl Mater 371 (2007)
329-77
[2] DT Goodin Accident condition performance of fuels for high-temperature gas
-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[3] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
[4] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
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[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
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Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[6] X Li B Bhushan A review of nanoindentation continuous stiffness
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[7] A Grabulov U Ziese HW Zandbergen TEMSEM investigation of
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fatigue and 3-D crack reconstruction by focused ion beam Scripta Matterialia 57
(2007) 635-38
[8] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
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[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
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[10] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
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56 (1973) 36-41
CHAPTER 2 Literature Review
73
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
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Nucl Mater 374 (2008) 445-52
[12] D G Martin Considerations pertaining to the achievement of high burn-ups in
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[13] G K Miller D A Petti D J Varacalle J T Maki Consideration of the effects
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Nucl Mater 295 (2001) 205-12
[14] G K Miller D A Petti J T Maki Consideration of the effects of partial
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J Nucl Mater 334 (2004) 79-89
[15] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
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microstructure Carbon 47 (2009) 396-410
[16] R Cheung Silicon carbide microelectromechnical systems for harsh
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[17] M Iwami Silicon carbide fundamentals Nuclear instruments and methods in
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equipment 466 (2001) 406-11
[18] V V Pujar J D Cawley Effect of stacking faults on the X-ray diffraction
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[19] W F Knippenberg Growth phenomena in silicon carbide Philips Res Report
18 (1963) 161-274
[20] P Krishna RC Marshall CE Ryan The discovery of a 2H-3C solid state
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[21] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
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[22] R Stevens Defects in silicon carbide J Mater Sci 7 (1972) 517-21
CHAPTER 2 Literature Review
74
[23] C Wang J Bernholc Formation energies abundances and the electronic
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[24] P Kaumlckell JFurthmuumlller FBechstedt Stacking faults in group-IV crystals an ab
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[25] U Lindefelt H Iwata S Oumlberg P R Briddon Stacking faults in 3C- 4H and
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[26] P T B Shaffer A review of the structure of silicon carbide Acta Crystal Sec B
25 (1969) 477-88
[27] P J H Denteneer W v Haeringen Stacking-fault energies in semiconductors
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[28] X G Ning H Q Ye Experimental determination of the intrinsic stackingfault
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[29] P J H Denteneer W v Haeringen Ground-state properties of wurtzite silicon
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[30] P J H Denteneer Stacking-fault energies in silicon diamond and silicon
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[31] K Karch G Wellenhofer P Pavone U Roumlssler D Strauch Proceedings of the
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[32] C Cheng V Heine and R J Needs Atomic relaxation in silicon carbide
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[33] M Marinova A Mantzari E K Polychroniadis Some recent results on the
3C-SiC structural defects Solid State Phenom 159 (2010) 39-48
[34] VV Pujar JD Cawley Computer simulations of diffraction effects due to
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[35] B Reznik DGerthsen W Zhang K J Huumlttinger Microstructure of SiC
deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499ndash508
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75
[36] T Mitani S Nakashima H Okumura et al Raman Scattering Analyses of
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[37] G Newsome LL Snead T Hinoki et al Evaluation of neutron irradiated
silicon carbide and silicon carbide composites J Nucl Mater 371 (2007) 76-89
[38] httpwwwtfuni-kieldematwisamatdef_enkap_5backboner5_4_2html
[39] P Pirouz J W Yang Polytypic transformations in SiC the role of TEM
Ultramicroscopy 51 (1993)189-214
[40] S Guha J M DePuydt J Qiu Role of stacking faults as misfit dislocation
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devices Appl Phys Lett 63 (1993) 3023-25
[41] AK Agarwal SKrishnaswami JRichmond et al Influence of basal plane
dislocation induced stacking faults on the current gain in SiC BJTs Mater Sci
Forum 527-29 (2006) 1409-12
[42] N W Mueggenburg H M Jaeger S R Nagel Stress transmission through
three-dimensional ordered granular arrays Phys Rev E 66 (2002) 031304
[43] S Somiya Y Inomata Silicon carbide ceramics-2 ceramic research and
development in Japan p1-18
[44] A Gali N T Son E Janzeacuten Electrical characterization of metastable carbon
clusters in SiC A theoretical study Phys Rev B 73 (2006) 033204-08
[45] C Chu Y Luand M Hon Growth characteristics of β-SiC by chemical vapour
deposition J Mater Sci 27 (1992) 3883-88
[46] J Tan Mechanical properties of SiC in TRISO fuel particle PhD Thesis
University of Manchester 2010
[47] Z R Huang B Liang DL Jiang S H Tan Preparation of nanocrystal SiC
powder by chemical vapour deposition J Mater Sci 31 (1996) 4327-32
[48] R A Shatwell K L Dyos C P Rentice Y Ward R J Young
Microstructural analysis of silicon carbide monofilaments J Microscopy 201
(2001) 179-88
CHAPTER 2 Literature Review
76
[49] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[50] K Kaneko M Kawasaki T Nagano et al Determination of the chemical width
of grain boundaries of boron- and carbon-doped hot-pressed β-SiC by HAADF
imaging and ELNES line-profile Acta Materialia 48 (2000) 903-10
[51] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[52] O O Mykhaylyk YZ Khimyak JP Attfield Phase Segregation in Silicon
Carbide-Carbon Solid Solutions from XRD and NMR Studies Chem Mater 14
(2002) 1348-35
[53] E Janzeacuten N T Son N Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[54] E Rauls Th Frauenheim A Gali PDeaacutek Theoretical study of vacancy
diffusion and vacancy-assisted clustering of antisites in SiC Phys Rev B 68
(2003) 155208-09
[55] N T Son P N Hai E Janzeacuten Carbon vacancy-related defect in 4H and 6H SiC
Phys Rev B 63 (2001) 201201-04
[56] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-10
[57] J M Grow R A Levy Micromechanical characterization of chemically vapor
deposited ceramic films J Mater Res 9 (1994) 2072-78
[58] T D Guldn H Nickel Coated particle fuels Nucl Technol 35 (1977) 206-35
[59] KB Tolpygo Optical elastic and piezoelectric properties of ionic and valence
crystals with ZnS type lattice Sov Phys Solid State 2 (1961) 2367
[60] D W Feldman J H Parker Jr J W Choyke L Patrick Phonon dispersion
curves by Raman scattering in SiC polytypes 3C 4H 6H 15R and 21R Phys
Rev 173 (1968) 787-93
CHAPTER 2 Literature Review
77
[61] W R L Lambrecht B Segall M Methfessel M van Schilfgaarde Calculated
elastic constants and deformation potentials of cubic SiC Phys Rev B 44
(1991) 3685-94
[62] X Zhao R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of silicon carbide under contact load at room temperature J
Am Ceram Soc 94 (2011) 3509-14
[63] R W Rice Mechanical properties of ceramics and composites 1st ed New
York Marcel Dekker 2000 p 457-534
[64] O Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
mechanism of plastic deformation in macro-micro- and nanoindentation
processes J PhyD Appl Phys 41 (2008) 074016-24
[65]W C Oliver GMPharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7(1992)1564-83
[66] MC Osborne JC Hay LL Snead Mechanical- and physical-property changes
of neutron-irradiated chemical-vapour-deposited silicon carbide J Am Ceram
Soc 82 (1999) 2490-96
[67] D M Teter Computational alchemy the search for new superhard materials
MRS Bull 23 (1995) 22-27
[68] S Nagappa M Zupan CA Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
Materialia 59 (2008) 995 -98
[69] M J Slavin G D Quinn Mechanical property evaluation at elevated
temperature of sintered β-silicon carbide Inter J High Tech Ceram 2 (1986)
47-63
[70] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
related isostructural materials to nanoindentation Slip vs densification Mater
Res Soc Symp P 522 (1998) 113-18
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78
[71] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[72] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[73] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
materials with a density functional theory J Appl Phys 104 (2008) 053508-16
[74] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000
[75] I Zarudi J Zou L C Zhang Microstructures of phases in indented silicon A
high resolution characterization Appl Phys Lett 82 (2003) 874
[76] M Mishra I Szlufarska Possibility of high-pressure transformation during
nanoindentation of SiC Acta Mater 57 (2009) 6256-6165
[77] D Munz T Fett Ceramics Mechcanical properties failure properties failure
behavior and materials selection Springer Verlag NewYork 1999 p 20
[78] X Zhao RM Langford J Tan P Xiao Mechanical properties of SiC coatings
on spherical particles measured using the micro-beam method Scripta Mater 59
(2008) 39ndash42
[79] G D Quinn RC Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[80] R Morrell Fracture toughness testing for advanced technical ceramics
internationally agreed good practice Adv Appl Ceram 105 (2006)1-11
[81] R E Cook G M Pharr Direct observation and analysis of indentation cracking
in glasses and ceramics J Am Ceram Soc 73 (1990) 787 - 817
[82] S S Chiang D B Marshall AG Evans The response of solids to elasticplastic
indentation I stresses and residual stresses J Appl Phys 53 (1982) 298-311
[83] M T Laugier Palmqvist toughness in Wc-Co composites viewed as a ductile
brittle transition J Mater Sci Lett 6 (1987) 768-70
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[84] G R Anstis P Chantikul B R Lawn D B Marshall A critical-evaluation of
indentation techniques for measuring fracture-toughness 1 Direct Crack
Measurements J Am CeramSoc 64 (1981) 533-38
[85] X F Zhang Q Yang L C D Jonghe Microstructure development in
hot-pressed silicon carbide effects of aluminium boron and carbon additives
Acta Mater 51 (2003) 3849-60
[86] T Watanabe The impact of grain boundary character distribution on fracture in
polycrystals Mater Sci Eng A 176 (1994) 39-49
[87] S J Xu J G Zhou B Yang B Z Zhang Effect of deposition temperature on
the properties of pyrolytic SiC 224 (1995) 12-16
[88] K Bongartz E Gyarmati H Schuster K Tauber Brittle ring test ndash method for
measuring strength and Youngs modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[89] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the Tri-Isotropic-Coated fuel particle
J Am Ceram Soc 90 (2007) 184-91
[90] J W Kim TSByun YKatoh Optimization of fracture strength tests for the SiC
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[91] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[92] SDKurbakov TAMireev Deposition of high-density silicon carbide coatings
by fluidized-bed pyrolysis of chlorinated silane derivatives Solid Fuel Chem 43
(2009) 113-23
[93] M Hundhausen R Puumlsche J Roumlhrl L Ley Characterization of defects in
silicon carbide by Raman spectroscopy Phys Stat Sol 245 (2008) 1356-68
[94] N Shirahata K Kijima A Nakahira and K Tanaka Thermal stability of
stacking faults in beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
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[95] W S Seo C H Pai K Koumoto H Yanagida Microstructure development and
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443-47
[96] Z G Cambaz G N Yushin Y Gogotsi K L Vyshnyakova L N
Pereselentseva Formation of carbide-derived carbon on beta-silicon carbide
whiskers J Am Ceram Soc 89 (2006) 509-14
[97] I J V Rooyen J H Neethling J Mahlangu Influence of temperature on the
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comparative study Proceedings of the 4th international topical meeting on high
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Washington DC USA HTR 2008-58189
[98] I J v Rooyen J H Neethling P M v Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[99] httpenwikipediaorgwikiPyrolytic_carbon
[100]J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
[101]Z Q Li C J Lu Z P Xia Y Zhou Z Luo X-ray diffraction patterns of
graphite and turbostratic carbon Carbon 45 (2007) 1686-95
[102]W P Hoffman W C Hurley P M Liu T W Owens The surface topography
of non-shear treated pitch and PAN carbon fibers as viewed by the STM J
Mater Res 6 (1991) 1685-94
[103]J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[104]P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
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81
[105]M W Barsoum A Murugaiah S R Kalidindi T Zhen YGogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[106]J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy
electron diffraction and few other techniques Carbon 44 (2006) 1833-44
[107]A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
[108]A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-phonon coupling doping and nonadiabatic defects Solid State
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[109]J N Rouzaud A Oberlin Carbon films Structure and microtexture (optical and
electron microscopy Raman spectroscopy) Thin Solid Films 105 (1983) 75-96
[110]N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[111]N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philosophical Magazine A 82 (2002) 1873-81
[112]J C Bokros R J Price Deformation and fracture of pyrolytic carbons
deposited in a fluidized bed Carbon 3 (1966) 503-19
[113]E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure
and mechanical properties of pyrolytic carbon produced by fluidized bed
chemical vapour deposition Nucl Eng Des 238 (2008) 3121-28
[114]C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by
different techniques Thin solid films 469-70 (2004) 214-20
[115]G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
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[116]J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[117]L M Brown In H Libelt R Talreja Fatigue and creep of composites
materials Riskilde Denmark Riso National Laboratory 1982 p 1-18
[118]M Skai The Meyer hardness A measure for plasticity J Mater Res 14 (1999)
3630-39
[119]M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics ndash adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[120]B T Kelly The physics of graphite Applied Science Publications London
1981
[121]M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated
carbons J Am Ceram Soc 85 (2002) 1522-28
[122]F C Frank A N Stroh On the theory of kinking Proc Phys Soc 65 (1952)
811-21
[123]R F Franklin Royal Society London A London 1951 209 196
[124]F G Emmerich Evolution with heat treatment of crystallinity in carbons
Carbon 33 (1995) 1709-15
[125]E Loacutepez-Honorato P J Meadows R A Shatwell P Xiao Characterization
of the anisotropy of pyrolytic carbon by Raman spectroscopy Carbon 48 (2010)
881-90
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
83
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC
Coatings Measured by Indentation
31 Introduction
The silicon carbide (SiC) coating is the most important component for structural
integrity of Tri-isotropic (TRISO) fuel particles as it sustains most of the internal
pressure produced by the fission gases produced in the kernel [1-3] Youngrsquos modulus
and hardness are mechanical properties used in modeling to estimate the failure
probability of TRISO fuel particles [4] The values at room temperature are used due
to the fact that the Youngrsquos modulus slightly decreased at elevated temperature in SiC
material and the higher value could be kept until the temperature reached 2000 degC [1]
It was also found that SiC material with higher hardness at room temperature
maintains higher hardness values at temperatures up to 1600 degC [1] To achieve a
reliable fuel design a better understanding of the mechanical properties of the SiC
layer at room temperature needs to be established
It is difficult to use traditional methods to measure hardness and Youngrsquos modulus
due to the small dimension of the TRISO fuel particles (~1 mm) Nano-indentation
has made it possible to measure the hardness and Youngrsquos modulus accurately [5 6]
for a coating of such a small dimension Furthermore this method also offers the
ability to study the deformation behaviour under the indentation [7-12] as the
indentation stress field is of a localized character
Loacutepez-Honorato et alrsquos [5] study of SiC deposited at 1300 degC by fluidized bed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
84
chemical vapour deposition (FBCVD) showed that the SiC coatings produced under
those conditions had high hardness (gt 42 GPa) and Youngrsquos modulus (~455 GPa)
They found that even samples with the composition of SiC+C or SiC+Si showed high
mechanical properties It was shown that the coatings had sub-micrometer (lt1 μm
diameter) grain size but due to the complex microstructure the mechanism controlling
the hardness and Youngrsquos modulus was unknown Researchers [10 11 13-16] have
made efforts to study the deformation mechanism under indentation in SiC single
crystals and polycrystals (with a grain size lt 100 nm or grain size gt 1μm) Szlufarska
et al [15] suggested a crossover mechanism from indentation-induced crystallization
to deformation-dominated amorphization in nano-crystalline SiC
From the work reported [11 16 17] it is clear that dislocation initiation and
propagation is the primary response for the plastic deformation under an indentation
in single crystal and polycrystalline (gt 1μm) SiC Further it has also been found
while studying the microstructure [11 16 17] that defects such as stacking faults and
dislocations were present in these polycrystalline (gt 1 μm) SiC materials
(nano-indentation hardness less than 36 GPa) However the amount of defects were
lower compared to the low temperature (ie 1300 o
C vs 1500 o
C) FBCVD SiC [5]
The discrepancies in the microstructure and mechanical properties still demand
further explanation on the deformation mechanism of low temperature FBCVD SiC
This chapter focus on the fundamental study on the mechanical properties of SiC we
have investigated the Youngrsquos modulus and hardness of three sub-micrometer FBCVD
SiC coatings using the indentation method The microstructure and mechanical
properties are explained on the basis of defects observed with a transmission electron
microscope (TEM) The deformation behaviour underneath a nano-indentation is
discussed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
85
32 Experimental details
Silicon carbide (SiC) coatings were produced on top of highly-dense pyrolytic carbon
coatings using fluidized-bed chemical vapour deposition (FBCVD) method The SiC
coatings with varied stoichiometry and deposited at low temperature of 1300 oC by
Loacutepez-Honorato et alrsquos [5] were chosen and studied in this Chapter Table 1 gives the
deposition conditions of these coatings which were found and demonstrated to give
superberb mechanical properties in prevous studies [5] Figure 31(a) and (b) show the
polished cross-section (x-y plane) and (b) polished external surface section (x-z plane)
of TRISO fuel particles (defining the directions used in the later part of this Chapter)
Densities were measured by the Archimedes method in ethanol (density is the mean
value of three tests the weight of SiC shells is 01-03 g) Composition was measured
by Raman spectroscopy (Renishaw 1000 Raman system with a 514 nm argon laser
source) with a single spot measurements of around 1 microm diameter through an times50
objective lens as shown in Fig 31 (c) Two peaks at around 794 and 970 cm-1
are for
SiC and the asymmetric peaks around 200-500 cm-1
and 1500 cm-1
are acoustic SiC
and second order SiC respectively (S1 coating) [5] Carbon peaks are around 1360
and 1600 cm-1
(S2 coating) and the peak at 520 cm-1
represents silicon (S3 coating)
[5] It was estimated that the excess C amount is less than 1 at in S2 by measuring
the intensity ratios of I1600I794 and compared to previous study [18] where Raman
spectroscopy and elemental analysis (EPMA AES and XPS) were used
The phase and composition were also analysed using X-ray diffraction (XRD PW
1830 Philips Eindhoven The Netherlands) with Cu Kα1 radiation Figure 31(d)
shows the XRD spectra of the three types of SiC coatings All three coatings exhibit
the β-SiC phase A very small shoulder peak around 2θ=345deg was also obtained from
the coatings which indicated the presence of stacking faults No evidence of a Si or C
peak was found in the XRD result This was probably due to the fact that the
additional levels of Si and C were very small (le 1at ) and it would be difficult to
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
86
identify these traces using XRD [5 19]
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
Codes H2MTCS (volvol) Additives Temperature Density (gcm3)
S1 (SiC) 10 01vol Propylene 1300 o
C 3173 + 0029
S2 (SiC+C) 10 10 vol Propylene 1300 o
C 3135 + 0034
S3 (SiC+Si) 10 -- 1300 o
C 3188 + 0002
SiC+C or SiC+Si means that nearly stoichiometric SiC with low excess C or Si less than 1 at
Productions of samples are contributed by Dr Eddie Loacutepez-Honorato
SiC coated fuel particles were hot mounted in copper-loaded conductive resin To
reduce the influence of the surface roughness the FBCVD SiC coatings were first
ground down to obtain a flat surface where the nano-indentation could be carried out
The flat surface was further polished using increasingly finer diamond suspensions
until frac14 μm and finally polished using a 003 μm colloidal silica suspension The
thickness of the coating after final polishing was estimated to be around 60 μm A
final surface roughness of lt 5 nm was detected by atomic force microscopy (AFM)
Youngrsquos modulus and hardness were measured using a nano-indenterTM
XP (MTS
System Corp USA) and a micro-indenter (CSM Instruments Switzerland)
Nano-indentation was made using a Berkovich indenter calibrated with a standard
silica specimen Before the measurement the initial contact of the indenter with the
specimen surface was checked and the compliance of the loading column was
corrected Arrays of indentations were performed on each specimen with an interval
of 20 times the indentation depth between each indentation The penetration depth for
the measurement of Youngrsquos modulus and hardness was 500 nm All data were
analysed using the Oliver and Pharr method [7] Micro-indentation was made using a
Vickers indenter at a maximum load of 3 N and the interval between each indentation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
87
was also kept to 20 times the indentation depth of ~26 μm
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
(c)
(d)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
88
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Moreover a high purity (gt999995) and fully dense polycrystalline 3C-SiC bulk
(diameter 3 cm thickness 15 cm) sample fabricated by static CVD (Rohm amp Haas
Ltd UK) was used as a reference sample in order to confirm the accurate mechanical
property measurements for FBCVD SiC coatings The Raman spectroscopy of bulk
CVD SiC was the inset in Fig 31(b) and no excess C or Si was found in it
To observe the grain morphology more clearly the finely polished (no scratch could
be seen under optical microscopes times50) cross-section (Fig 1(a)) of the coatings were
chemically etched using Murakamirsquos solution (10 g sodium hydroxide and 10 g
potassium ferricyanide in 100 ml of boiling water) The surface morphology of
coatings was characterized using scanning electron microscopy (Field emission gun
Philips XL30 FEG-SEM) A transmission electron microscope TEM (FEG-TEM
Tecnai TM
G2 F30 U-TWIN 300KV) was used to study the microstructure of the
coating layer before and after indentation For cross-sectional analysis of indentations
TEM samples were made from thin plates which are parallel to one edge and through
the center of Berkovich indentation using a focused ion beam (FIB FEI Nova 600
Dual Beam system) milling For high resolution TEM (HRTEM) the samples were
prepared using an ion beam milling method
33 Results
331 Hardness and Youngrsquos modulus
Figure 32 shows the typicl load-displacement curve of SiC coatings and the hardness
(H) and Youngrsquos modulus (E) as a function of composition of the three types of
coatings The load-displacment curve (Fig 32(a)) shows a smooth character of the
deformation process during nanoindentation There is multiple mini lsquopop-inrsquo events
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
89
reflected on the hardness curve which started at the beginning from the low
indentation load These mini lsquopop-inrsquo can not provide enough consumption of the
internal stresses induced by indenter as it was needed for the initiation and
propagation of dislocations so no well-pronounced lsquopop-inrsquo effect was observed from
the load-displacement curve
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Measurements were made on the x-z plane of SiC coatings (Fig 31(b)) and static
bulk CVD SiC for both micro- and nano-indentation to give reliable comparison with
previous studies [20-23] In the reference material the nano-hardness (36 GPa) and
Youngrsquos modulus (496 GPa) of bulk CVD SiC are nearly the same as in a previous
(c) (b)
(a)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
90
study [20] namely 36 GPa and 503 GPa respectively From Fig 32(b) it can be seen
that S1 has a higher hardness compared with S2 and S3 Further the values of
hardness obtained by nano-indentation (Fig 32(b)) are higher than by
micro-indentation for all samples
For low temperature FBCVD coatings the nano-hardness varies in the range 39 GPa
to 44 GPa whereas the micro-hardness varies between 36 GPa - 42 GPa These values
are at least 8 higher than the bulk static CVD SiC which has a nano-hardness ~36
GPa and a micro-hardness ~32 GPa (see Fig 32(b)) Moreover the low temperature
FBCVD SiC coatings have higher hardness as compared to a previous study of CVD
SiC for which the hardness values varied in the range of 25-39 GPa as measured by
nano-indentation under the similar experimental conditions [20-23]
In FBCVD SiC coatings Youngrsquos modulus of all three coatings is lower than the bulk
CVD SiC (see Fig 32(c)) which is an average Youngrsquos modulus (438 GPa) of
polycrystalline CVD SiC reported by Roy et al[24] The difference in hardness and
Youngrsquos modulus data could not be simply explained by the existence of C or Si due
to their low concentration (lt 1 at ) and location in the coatings which has been
addressed in detail in previous study [25] Therefore the difference of hardness and
modulus could be related to other microstructure such as pores which could vary
from atomic scale to micrometres which is discussed in the following session
Both nano- and micro-hardness results (Fig 32(b)) are higher than the available data
for polycrystalline CVD SiC [20-23] as discussed above and the correct measurement
of SiC coatings with small dimensions was ensured by comparing with the bulk CVD
SiC As mentioned the hardness and Youngrsquos modulus measured by
micro-indentation are slightly lower than the values measured by nano-indentation
because cracks were formed under micro-indentation due to the higher indentation
load
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
91
332 Microstructure of low temperature FBCVD SiC
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Figure 33 shows SEM images of the three etched FBCVD SiC coatings In all three
coatings the width and length of columnar grains were found to be approximately 200
nm and 1-2 μm respectively These are found to be much smaller than the SiC coating
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
92
produced at a temperature of 1500 degC which had width ~1μm and length ~4-5 μm
[17] They are also smaller than the SiC showing dislocation movement under the
indentation deformation zone which was produced at temperature of 1500-1600 degC
by FBCVD and 1500 degC by static CVD with grain size of 1-5 μm and 5-10 μm
respectively [11 16]
Although the grain size is in a similar range for three coatings (as mentioned above)
due to different deposition conditions the grain morphologies of three coatings vary
First a less laminar structure was observed in the S1 coating (see Fig 33 (a)) as
compared to the coatings with excess C or Si (Fig 33 (c) and (e)) Fig 33 (b) shows
the existence of triple junctions (dashed circle) that could resist the movement of
grain boundaries and dislocation slip [12] Pores were also observed along the laminar
structure after etching In the S2 coating it has a large amount of a laminar structure
running through a single grain (laminar structure parallel to growh direction) as
illustrated in Fig3 (d) The information of grain morphology in S2 was mostly a
laminar structure perpendicular to the growth direction after etching (Fig 33(d))
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
To get more information about the grains morphology in S2 coating a TEM image
05 μm
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
93
was taken and shown in Fig 34 Figure 34 shows that grains in S2 coating interact
(branch-like grain growth pattern on the lower-left part of Fig 34) with each other
which is similar as in sample S1 (Fig 33(b)) and grains form branch like structures
In the S3 coating (as can be seen in Fig 33 (f)) a parallel growth of grains with less
interaction among grains was observed
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
According to a previous study [25] about definition of grain boundary the grain
boundary in the S3 coating is smooth while in the S1 and S2 coating the grain
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
94
boundaries are rough which could result in branch-like grain growth pattern It could
be attributed to the different CSi ratio in reaction gas which produce SiC with
different morphologies on the (111) crystal plane which may have three different
morphologies rough smooth and pyramidal defect [26] Grains with differently
finished surfaces could lead to different grain growth morphologies because of
different surface energy For example in rough grain boundaries of S1 and S2
coatings branch like crystals were found as in Fig 33(b) and Fig 34
Figure 35 shows bright field TEM images of the S1 coating S2 and S3 coatings The
columnar grains were observed to grow perpendicular to the coating surface which
was consistent with the SEM results Further nano porous layers normal to the
coating growth direction are observed in the S2 coating (see Fig5 (b)) The formation
of porosity in thin films could be due to differences in diffusion of growth species the
incident molecule direction and deposition of secondary phases such as excess Si or C
[27]
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
BF-TEM and (b) DF-TEM
At low deposition temperatures the probability of a precursor reaching the edge of the
nucleus is considerably lower compared with that of arriving on the top due to a low
surface diffusion As these nuclei grow the areas immediately around them will suffer
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
95
from a shadowing effect blocking the arrival of new molecules and the formation of
new nuclei Since the diffusivity of atoms is low and no new nuclei are formed in
those regions gaps will be formed among grains A wrinkled like defect layer was
seen in the S3 coating (Fig 35 (c)) which could be attributed to the interruption of
the SiC crystallization growth during the deposition process such as crystal lattice
misorientation as seen in Fig 36
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
No obvious laminar defect was observed in the S1 coating by TEM this could be due
5 nm
(a) (b)
5 nm
5 nm
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
96
to less interruption during deposition process According to above observation it was
proposed that the laminar structure observed in SEM images indicates some
instability during the fabrication process resulting in the deposition of the nano- and
micro-pores and misorientation This was attributed the variations in circulation and
deposition occurring close to the nozzle or at the hot zone [5]
Stacking faults were observed for all three types of samples as shown in Fig 35 with
a higher density than for the SiC deposited at a temperature of 1500 C [11 16 17]
These stacking faults could cause an intrinsic residual stress due to the coexistence of
the partial dislocations This was supported by the high resolution TEM images
(shown in Fig 37) exhibiting wave pattern fringes and they could only be observed
in one direction which is determined by the intrinsic stress
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Since the dislocation mobility under nano-indentation deformation has not been fully
understood in hard ceramic materials therefore it is significant to study this
behaviour in FBCVD SiC coatings with a sub-micrometer grain size However it is
difficult to observe the dislocations under the two-beam or weak beam dark field
2 nm
(a)
(111)
[110]
(111)
Sessile
dislocations
(b)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
97
conditions due to the high density of defects In the present study the reversed fast
Fourier transform (FFT) images of the corresponding high resolution TEM images
was used to obtain information about the dislocations This method has been used in
many cases for dislocation observations [28]
Figure 38(a) shows a high resolution TEM image of a S1 coating which was taken as
a representative image to compare the atomic structure of all three coatings Figure
38(b) is the reverse FFT image using the marked inset diffraction pattern of Fig
37(a) in which sessile and glide dislocations can be observed The dislocation
density was calculated from the total number of glide dislocations divided by the area
in the image [29 30] From the analysis of images shown in Fig 38 the dislocation
density in S1 coatings was found to be 1013
cm2 The same magnitude of dislocations
density was found in the S2 and S3 coatings as shown in Fig 37 (three HRTEM
images were analysed for each coating)
333 Deformation behaviour under the indentation
The deformation zone under the indentation was investigated through the images of
FIB milled TEM samples in order to study the deformation mechanism of the low
temperature FBCVD SiC coatings Figure 39 shows the bright field TEM images
showing the mechanical behaviour of a S1 coating under nano-indentation on the x-z
plane (Fig 31(b)) at a maximum indentation depth of 500 nm
Figure 39(a) is an overview of the deformation area under an indentation A median
crack has formed just underneath the surface and has a direction aligned with the
indenter tip impression A higher magnification image around the elastic and plastic
interface is shown in Fig 39(b) It can be seen that a large amount of inter-granular
and trans-granular micro cracks were produced around the median crack initiation
zone This is substantially different from the dislocation-related plastic deformation
behaviour [10 11 16 31] which usually has a severe plastically deformed region
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
98
with few or no cracks Moreover the micro cracks were also observed in the C and D
zones under the indentation
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Figure 39(c) shows that micro cracks that are formed along the grain boundaries
which tend to follow the shear band direction with the formation of a few
trans-granular cracks In Fig 39(d) it can be seen that shear band micro cracks were
formed in one single grain (see inset in the left bottom corner of Fig 39(d)) This
single grain has a large amount of defects which are supposed to be the as-deposited
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
99
defects as shown in Fig 35(a) Shear band cracks were also observed just underneath
the indenter tip (right top inset in Fig 39(d)) As a result a shear band dominated
deformation zone can be seen in Fig 39(c d) under the indentation in a S1 coating
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
The S2 and S3 coatings only show a micro crack pattern which is different from S1
coating Figure 310 gives the TEM images of the S2 and S3 coatings showing the
mechanical reaction underneath the indentation It can be seen from Fig 310(a) and
Fig 310(c) that the median cracks are not always produced under the indentation for
S2 and S3 coatings However some irregular cracks in S3 coatings and lateral cracks
in S2 were produced In particular in the S3 coating (Fig 310(b)) more micro cracks
either intragrain or transgrain were found than in the S1 and S2 coatings This is due
to the fact that the most micro cracks propagate along the grain boundaries in S1 and
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
100
S2 coatings (Fig 39(b) and Fig 310(d)) A careful analysis of the TEM images
shows that only micro cracks were found under the indentation and no
dislocation-induced shear band was observed This is different from previous studies
on the deformation behaviour of polycrystalline SiC [11 16 31] For example in bulk
polycrystalline CVD SiC [11] it was found that it has more dislocation slip bands
rather than micro cracks either in grains or along grain boundaries even though the
indentation load is higher than the load used in the FBCVD SiC based materials The
possible reason of this discrepancy is discussed later Moreover no amorphous phase
and α-SiC phase was formed under the indentation observed by diffraction and bright
field TEM images which is consistent with the work of Mishra and Szlufarska [32]
34 Discussion
High hardness and Youngrsquos modulus were obtained in the sub-micrometer grain size
coatings produced at a low temperature by FBCVD In the S1 coatings the
nano-hardness is ~22 higher while the micro-hardness is ~31 higher compared to
a commercial CVD SiC The higher hardness was also obtained in S2 and S3 coatings
All the coatings retained a higher Youngrsquos modulus than those SiC materials having
high hardness in previous study (equal or higher than 40 GPa nano-hardness) [33]
making these coatings unique among polycrystalline phase brittle ceramic material
Under nano-indentation only micro cracks were found in the deformation zone The
results seem to be consistent with the conventional view of the failure mechanism of
brittle ceramics at room temperature [34] The lack of dislocation and the high Peierls
force are reasons for fracture to occur in brittle materials However
dislocation-related plastic deformation routinely occurred in hardness testing because
the indentation stress field offers conditions of stress conductive to plastic
deformation [11 13 16 34] Molecular dynamic simulations even demonstrate that
13 of the hardness-related deformation is from dislocation-related plastic deformation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
101
while 23 comes from fracture in SiC [31] It is rare to see a deformation zone
dominated by micro cracks in polycrystalline SiC such as in FBCVD SiC coatings
(Fig9 and Fig10 and see for example Ref [11 16 31]) With the above questions
we first estimated the factors controlling Youngrsquos modulus in FBCVD SiC coatings
followed by a study of the mechanism of superior hardness and deformation under an
indentation which influence the hardness in the three coatings
341 Influence of porosity on Youngrsquos modulus
Youngrsquos modulus presents a material constant for uniaxial tensile deformation which
is physically related to the atomic spacing inter atomic bond strength and bond
density In a low temperature FBCVD SiC coating it was shown from XRD
measurements that a shoulder peak was observed in addition to the β-SiC (111)
diffraction peak which corresponded to a crystal plane spacing of ~0266 nm (Fig
31(c)) Moreover we found that the XRD peak shifted to a lower diffraction angle
compared with the bulk CVD SiC According to the XRD pattern in Fig 31(c) the
crystal lattice constants of about 04366 04368 and 04368 nm for S1 S2 and S3
coatings were obtained respectively However the crystal lattice constant for bulk
CVD SiC is ~04359 nm (XRD pattern obtained by the same condition was shown in
Ref 25)
Further crystal orientation impurities and porosity may affect the Youngrsquos modulus
As the Youngrsquos modulus on the x-z plane (Fig 31(b)) was similar to the value
obtained along the cross-section (Fig 31(a)) [5 25] which meant that the orientation
has no effect on Youngrsquos modulus Moreover as discussed before the effect of C or Si
in S2 was found to have no effect on the difference of hardness and Youngrsquos modulus
Excluding these two factors (orientation and impurities) the effect of porosity on
variation of the elastic properties in three coatings was investigated The presence of
nano-pores in S2 coating as in Fig 35(b) results in a lower density Although no
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
102
pores were directly observed by TEM in the S1 and S3 coatings their density is lower
than the theoretical density of SiC Thus the elastic modulus E at room temperature
can be expressed in an exponential function of porosity pV [35] as
0 exp( )pE E CV (1)
where 0E = 496 GPa is the elastic modulus and C = 357 is a constant for a pore-free
bulk CVD SiC pV is the ratio of the relative density difference to the theoretical
density of SiC (322 gcm3)
The calculated Youngrsquos modulus for S1 S2 and S3 coatings is 465 plusmn 15 446 plusmn 17 and
473 plusmn 1 GPa respectively which follows a trend similar to the experimental data
presented in Fig 32 It was concluded that the different Youngrsquos modulus in the three
low temperature FBCVD SiC coatings is attributed to porosity although the
experimental Youngrsquos modulus data of FBCVD SiC coatings is slightly lower than the
values calculated using the Eq(1) The difference between calculated and measured
value of FBCVD SiC coatings is due to the fact that the 0E from pore-free bulk
CVD SiC instead of pore-free FBCVD SiC coatings (not available) FBCVD SiC
coatings have larger crystal lattice constant (~0437 nm) than bulk CVD SiC (~04359
nm) as discussed above Since the expanded lattice constant leads to a decrease of the
Youngrsquos modulus according to a previous study [20] the 0E of pore-free FBCVD SiC
coating is expected to be lower than bulk CVD SiC
342 Mechanism for High hardness
From previous studies [10 11 16 31] dislocation nucleation and glide is the primary
response of SiC under nano-indentation Formation of shear bands due to dislocations
has also been reported [11] which were found under the plastic deformation zone
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
103
when indentations were made on a particular grain in polycrystalline SiC and at the
grain boundaries Moreover dislocation nucleation is also correlated with the discrete
pop-ins observed in the force-displacement curve [32] No pop-ins was found due to
the presence of a large amount of dislocations in the present study Dislocation
mobility can be estimated similar to the case of a metallic material having intrinsic
dislocations Mishra and Szlufarska [32] worked on the dislocation mobility in
3C-SiC using large-scale molecular dynamics simulations The results indicated that
dislocation mobility decreased by dislocation interaction as its density reached a
saturation value This is similar to the work hardening effect in a metallic material [34]
We estimated the stress ( ) needed for dislocation to move using Taylorrsquos work
hardening equation [34] given by
1 2
0 Gb (2)
where 0 is the shear stress for a dislocation to move without any obstacle and the
value of 0 taken was 75 GPa [13] is a numerical constant depending on the
locking strength of a nod The value of taken was 8 [36] b is Burgers vector
where b = 0178 nm for a Shockley partial dislocation in SiC initiated and gliding on a
close packed (111) plane and is the density of glide dislocations G is the shear
modulus which can be written as
2(1 )
EG
(3)
where is the Poissonrsquos ratio and E is the Youngrsquos modulus The dislocation density
was ~03times1012
cm2 The calculated shear stress according to Eq (2) was ~52 GPa and
this value is much higher than the theoretical shear stress which is in the range of
295-4312 GPa obtained from previous reports [37-39] The theoretical shear stress is
the maximum stress provided for the dislocation nucleation and propagation in SiC
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
104
crystals Therefore the dislocation-related yield behaviour could not occur under the
plastic deformation zone in sub-micrometer FBCVD SiC coatings
The superior hardness value in FBCVD SiC coatings is attributed to the immobility of
the dislocations In the case of the SiC-C solid solution [40] the occurrence of a high
density of dislocations causes a strain-hardening effect Furthermore given that
dislocations could be motivated by the shear stress a phase transformation from a
crystalline phase to an amorphous could occur [32] However no amorphous phase
was observed under the nano-indentation (Fig 37 and 8) nor was dislocation
movement band observed in this study This suggests that the dislocation-related
phase transformation did not occur under the indentation
343 Deformation mechanism under nano-indentation
The hardness-related plastic deformation which occurs due to the nucleation and
propagation of micro cracks in FBCVD SiC coatings can be explained as follows
(i) The onset of plastic deformation under the indentation occurs as the maximum
shear stress approaches the yield stress [41] According to 15H Y (Y is the yield
stress H is the hardness) the yield stress in FBCVD SiC coatings is around 26 GPa
The yield stress is lower than the stress needed for the movement of dislocations and
the theoretical shear stress [37-39] This indicates that the hardness-related plastic
deformation first occurred by the nucleation of defect-induced cracks which
propagated to the indented surface (see inset (top right) in Fig 39(d)) The
deformation impression was accommodated by the densification of defects such as
the pores dislocation pile ups and grain boundaries as in Fig 33(b)
(ii) The shear stress was used to promote the movement of dislocations under the
indentation and form slip bands in previous studies [10 11 42] The highest amount
of micro cracks were observed in FBCVD SiC coatings contrary to plastic
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
105
deformation under the indentation found in previous studies [10 11 42] The micro
cracks formed in the hardness-related plastic deformation zone is the Mode-II crack)
[43] as shown in Fig 39(c) and (d) Unlike Mode-I which is dominated by the tensile
stress a Mode-II crack is the consequence of a confined shear stress [34] At the
interface of the elasticplastic deformation branch-like micro cracks were observed
as in Fig 39(b) The above discussions distinguish the hardness-related plastic
deformation mechanism in FBCVD from previous studies on ceramics which showed
dislocations are the main deformation mechanism underneath the indentation [31 44]
A unique hardness-related plastic deformation mechanism was used to explain the
difference in hardness of all three types of FBCVD SiC coatings According to Qian
et al [45] the hardness could reach an asymptotic value with the saturation of the
micro cracks growth population In three FBCVD SiC coatings studied here different
amounts of micro cracks were found (Fig 39(b) and Fig 310(b d)) and micro cracks
nucleated at stress concentration zones such as the grain boundaries or defects within
the grains Thus the difference in hardness was attributed to the grain morphologies
as shown in Fig 33 which gives different degree of resistance to the initiation and
propagation of micro cracks In the S1 coating triple junctions hamper grain
boundary shear by forming interlocks [12] which could resist and deflect the initiation
and propagation of micro cracks In the S2 coating elongated grains interact with the
surrounding small grains which could also provide interlocks (Fig 33(d) and Fig
34) The slightly lower hardness of the S2 coating as compared to the S1 coating is
due to the nano pores as seen in Fig 35(b) A lack of triple junctions and grain
interactions could be the reason for the lower hardness in the S3 coating as it has a
parallel crystalline morphology which has less constraint towards the initiation and
propagation of cracks
35 Conclusions
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
106
The microstructure and mechanical properties of three types of FBCVD SiC coatings
(SiC SiC+C and SiC+Si) were studied FBCVD SiC coatings with a sub-micrometer
grain size were deposited on simulated TRISO fuel particles by FBCVD at a low
temperature (1300 oC) The mechanical properties were studied using micro and
nano-indention The microstructures were studied using SEM and TEM It was
found that the Youngrsquos modulus of all three coatings differ which was attributed due
to the presence of nano-pores The high hardness of FBCVD SiC coatings was due to
the large amount of defects particularly the high density of dislocations It is found
that the interactions between dislocations reduced their mobility and make
dislocation-related plastic deformation unavailable We suggest that the work
hardening effect is the reason for the high hardness in the sub-micrometer grain size
FBCVD SiC coatings A hardness related-deformation mechanism was attributed to
the initiation and propagation of micro cracks The nano-indentation indent volume is
most likely be accommodated by the densification of defects such as the pores As a
result the hardness difference in FBCVD SiC coatings is due to the different grain
morphologies producing different amounts of micro cracks
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
107
36 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[2] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[3] D A Petti J Buongiorno J T Maki R R Hobbins G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[4] A C Kadak R Gnallinger M J Driscoll S Yip D G Wilson H C No J
Wang H Maclean T Galen C Wang J Lebenhaft T Zhai D A Petti W K
Terry H D Gougar A M Ougouag C H Oh R L Morre G K Miller J T
Maki G R Smolik D J Varacalle Modular pebble bed reactor Modular pebble
bed reactor project University research consortium annual report Beijing 2000
[5] E Lopez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[6] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram P Xiao Youngs modulus measurements of SiC coatings on spherical
particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[7] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[8] C H Chien S R Jian C T Wang J Y Juang J C Huang Y S Lai
Cross-sectional transmission electron microscopy observations on the Berkovich
indentation-induced deformation microstructures in GaN thin films J Phys D
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Appl Phys 40 (2007) 3985-90
[9] T C Tan C A Merrill J B Orton A K Cheetham Anisotropic mechanical
properties of polymorphic hybrid inorganic-organic framework materials with
different dimensionalities Acta Mater 57 (2009) 3481-96
[10] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
related isostructural materials to nanoindentation Slip vs densification Mater
Res Soc Symp P 522 (1998) 113-18
[11] X Zhao X R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of 3C-SiC upon indentation at room temperature J Am
Ceram Soc 94 (2011) 3509-14
[12] D Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
mechanism of plastic deformation in macro- micro- and nanoindentation
processes J Phys D Appl Phys 41 (2008) 074016-24
[13] H P Chen R K Kalia A Nakano P Vashishta I Szlufarska
Multimillion-atom nanoindentation simulation of crystalline silicon carbide
Orientation dependence and anisotropic pileup J Appl Phys 102 (2007)
063514-22
[14] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[15] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[16] G Chollon J M Vallerot D Helary S Jouannigot Structural and textural
changes of CVD-SiC to indentation high temperature creep and irradiation J Eu
Ceram Soc 27 (2007) 1503-11
[17] D Heacutelary X Bourrat ODugne G Maveyraud M Peacuterez O Guillermier
Microstructures of silicon carbide and pyrocarbon coatings for fuel particles for
high temperature reactors 2nd international topical meeting on high temperature
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reactor technology Beijing China 2004
[18] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[19] T Fukuzaki K Tanaka K Nishimoto Y Mur K Nishio and R Tamura
Magnetic property and microstructure of Nd-Fe-B-M (M=Si C) bulk
pnanocomposite magnets prepared by spark plasma sintering method - art no
012015 J Phys Conf Ser 106 (2008) 12015-124
[20] M C Osborne J C Hay L L Snead D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[21] K H Park S Kondo Y Katoh A Kohyama Mechanical properties of beta-SiC
after Si- and dual Si plus He-ion irradiation at various temperatures Fusion Sci
Technol 44 (2003) 455-59
[22] S Nagappa M Zupan C A Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
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[23] C Bellan J Dhers Evaluation of young modulus of CVD coatings by different
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[24] S Roy C Zorman M Mehregany R Deanna C Deeb The mechanical
properties of polycrystalline 3C-SiC films grown on polysilicon substrates by
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044108-20
[25] J Tan Mechanical properties of SiC in TRISO fuel particle Thesis University of
Manchester 2010
[26] M J Hernandez G Ferro T Chassagne J Dazord Y Monteil Study of surface
defects on 3C-SiC films grown on Si (111) by CVD J Cryst Growth 253 (2003)
95-101
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[27] E S Machlin Materials science in microelectronics I The relationships between
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ed Oxford Elsevier Science 2005
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[28] A Nakamura T Yamamoto Y Ikuhara Direct observation of basal dislocation
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[29] H Y Shin S K Kwon Y I Chang M J Cho K H Park Reducing
dislocation density in GaN films using a cone-shaped patterned sapphire substrate
J Cryst Growth 311 (2009) 4167-70
[30] W D Callister Materials science and engineering An introduction 7th ed
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[31] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
materials with a density functional theory J Appl Phys 104 (2008) 053508-16
[32] M Mishra I Szlufarska Possibility of high-pressure transformation during
nanoindentation of SiC Acta Mater 57 (2009) 6156-65
[33] A R Beaber L J Qi J Hafiz P H Mcmurry J V R Heberlein W W
Gerberich S L Girshick Nanostructured SiC by chemical vapor deposition and
nanoparticle impaction Surf Coat Tech 202 (2007) 871-75
[34] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
p162-91
[35] R W Rice Mechanical properties of ceramics and composites 1st ed New
York Marcel Dekker 2000 p457-534
[36] U Messerschmidt Dislocation dynamics during plastic deformation Part 2
Ceramic Single Crystals Springer Series in Materials Science On line 2010
p264
[37] S Ogata J Li N Hirosaki Y Shibutani S Yip Ideal shear strain of metals and
ceramics Phys Rev B 70 (2004) 104104-10
[38] Y Umeno Y Kinoshita T Kitamura Ab initio DFT study of ideal shear
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111
strength of polytypes of silicon carbide Strength Mater 40 (2008) 2-6
[39] Y Umeno M Cerny Effect of normal stress on the ideal shear strength in
covalent crystals Phys Rev B 77 (2008) 100101-04
[40] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[41] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000 p139-77
[42] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[43] A A Wereszczak K E Johanns O M Jadaan Hertzian Ring Crack Initiation
in Hot-Pressed Silicon Carbides J Am Ceram Soc 92 (2009) 1788-95
[44] S L Lloyd A Castellero F Giuliani Y Long K K Mclaughlin J M
Molina-Aldareguia N A Stelmashenko L J Vandeperre W J Clegg
Observations of nanoindents via cross-sectional transmission electron microscopy
a survey of deformation mechanisms P Roy Soc a-Math Phy 461 (2005)
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[45] J Qian L L Daemen Y Zhao Hardness and fracture toughness of moissanite
Diam Relat Mater 14 (2005) 1669-72
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
112
CHAPTER 4 Vickers Indentation Fracture Toughness of
SiC Coatings
41 Introduction
Silicon carbide (SiC) layer is considered to be the most important component for
structural integrity as during the operation of a nuclear reactor it has the ability to
sustain most of the internal pressure caused by gaseous fission products produced in
the kernel and retain most of the fission products [1-4] Previous work was focused on
the investigation of mechanical properties (Youngrsquos modulus and fracture strength) of
SiC coatings on TRISO particles using different techniques such as a ring test [5 6]
a crush test [7 8] a micro-cantilever test [9] and indentation [10 11] However few
reports exist on the measurement of the fracture toughness of SiC coatings even
though it is a property used in modeling to estimate the failure probability of TRISO
fuel particles [12] For example Kadak et al [12] used a fracture toughness value of
33 plusmn 053 MPa m12
This value was obtained from bulk SiC produced by a static
CVD method The fracture toughness value may well differ for SiC coatings produced
by fluidized bed chemical vapour deposition (FBCVD) on TRISO fuel particles [10]
Because microstructure of SiC produced by static CVD and FBCVD methods could
vary significantly For example the static CVD SiC usually has larger grain size and
high density while FBCVD SiC with large grain size is usually accompanied with
porosity [13] Different grain size range and porosity fraction can lead to variation of
fracture toughness [1 2] Therefore the fracture toughness value of bulk SiC may not
be truly representative of SiC coatings used in nuclear fuel applications To our
knowledge the only available data on the fracture toughness of a SiC layer on TRISO
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
113
fuel particle is reported by Zhao et al[9] where the fracture toughness was measured
by the micro-beam method However this method is time consuming and expensive
restricting its implementation as a standard characterization technique where
repetitive measurements are required to confirm the reproducibility of experimental
data
In this Chapter micro-indentation is used to investigate the fracture behaviour of
different SiC coatings produced (on TRISO fuel particles) by FBCVD due to its
capacity to measure the mechanical properties in a small area and produce visible
cracks [14-16] The fracture behaviour under an indenter is also studied using a
transmission electron microscope (TEM) in order to give better understanding of the
fracture mechanism The characteristics of the SiC microstructures are then correlated
with their fracture behaviour
42 Experimental details
The SiC coatings used are the same as the ones in Chapter 3 and the deposition
conditions were shown in Table 31 Chapter 3
For the micro-indentation study SiC coated fuel particles were hot mounted in
copper-loaded conductive resin (to get better SEM images) and then ground to a
cross-section (as shown in Fig 31(a)) or polished a flat external surface (as shown in
Fig 31(b)) In this Chapter the y direction is called radial direction x is called
tangential direction according to Fig 31(a) and (b) The samples were then polished
using increasingly fine diamond suspensions to 14 μm Indentation fracture
toughness measurements were performed using a Vickers diamond indenter (CSM
Instruments Switzerland) Due to the through-thickness (in the radial direction)
failure behaviour of a SiC coating in a TRISO fuel particle under tensile stresses
generated from gases due to nuclear reactions similar tensile stresses could be
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
114
generated from indentation of polished external surface of TRISO particles which
could generate cracks along the radial direction (y direction in Fig 31(b)) of the
TRISO particles as well The indentations were carried out under a maximum load of
3 N (corresponding to a maximum indentation depth of ~26 μm) To avoid PyC
influence the thickness of SiC coatings (in the section as shown in Fig 31(b)) were
kept to ~60 μm after polishing which is more than 20 times the indentation depth
In this case the elastic zone has not expanded to the substrate according to the
criterion that indentation depth is less than 10 of coating thickness [17] For each
sample six indents were made on the polished external surface of SiC perpendicular
to the radial direction with a separation of 70 μm between each indent
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference [25]
The calculation of the VIF fracture toughness must account for the crack profile under
the indenter whether the cracks are of the Palmqvist mode or half-penny mode which
are illustrated in Fig 41 The halfpenny crack system is formed by the joining of
radial cracks as shown in Fig 41(a) while the Palmqvist crack system is always
shallow as shown in Fig 41(b)
To observe the crack impression under the indenter on the polished external surface
an indentation (as in Fig 42(a)) with a final indentation depth of 26 μm was
sequentially polished with 6 μm diamond suspensions The surface was polished until
the plastic deformation zone was exposed together with the radial cracks (as shown in
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
115
Fig 42(b) Afterwards polishing continued until the removal of the plastic
deformation zone (as shown in Fig 42(c)) The surface showed no cross-over
cracking present as illustrated in Fig 41(a) and this confirms the presence of the
Palmqvist mode cracks on the polished external surface of SiC coatings under the
Vickers indenter The three polished samples showed the same crack propagation
mode and this is consistent with previous reports [18 19] where a Palmqvist crack
system has been observed in SiC at low loads (lt 10 N)
The Palmqvist crack mode allows the VIF fracture toughness to be calculated using
the equation proposed by Laugier [15 16] given as
1 2 23
3 2( ) ( )IC v
a E PK
l H c
(1)
In Eq (1) the geometrical constant v is a calibrated value using the already known
fracture toughness due to the variation in use of the Vickers hardness or the
nano-hardness [14 16 20 21] The 2a and l are the lengthes of diagonal and radial
crack length of Vickers indentation (as shown later in Fig 43) respectively c=a+l
the E and H are Youngrsquos modulus and hardness measured by nano-indentation P is
the load of Vickers indentation Therefore this geometrical constant was calibrated
before it was used to calculate the VIF fracture toughness of SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
116
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
117
The only already known fracture toughness was measured on the cross-section of
extra-Si SiC coatings using a micro-beam bending method [9] so the calibration of
v was carried out on the cross section (as in Fig 31(a)) of the same coating
According to Eq(1) the hardness (H ) and Youngrsquos modulus (E) are nano-hardness
and Youngrsquos modulus as measured in a previous study [22] P is the load a is the
impression half diagonal l is the crack length and c is the half diagonal crack length
(see later in Fig 43) To get the load and dimensional values of indentations a total
of 8 indentations at different loads (3 35 and 4 N) were applied on the cross-section
of the extra-Si SiC coating
The crack lengths were measured using a scanning electron microscope (Philips XL30
FEG-SEM) FEG-TEM (Tecnai TM
G2 F30 U-TWIN 300KV) which was used to
study the fracture behaviour under the indenter For the TEM study the cross
sectional specimens for the indents were prepared using focused ion beam milling
(FIB FEI Nova 600 Dual Beam system) Note that due to the large deformation zone
(gt10 μm diameter) and radial crack length (gt15 μm) observed from micro-indent
impression it was not possible to produce a sufficiently large TEM sample by the FIB
technique This limitation restricted us to study the fracture behaviour under a sharper
indenter (Berkovich) with lower load
43 Results and discussion
431 VIF fracture toughness study
Figure 43 is the crack morphology observed in S3 (SiC + Si) coating cross-section It
shows that the fracture resistance is different in the tangential and radial directions of
the cross-section which is consistent with the previous measurements along these
directions measured by the micro beam method [9] Different crack lengths along the
tangential and radial directions observed from 8 indentations are illustrated in Table
41 Correspondingly fracture toughness values of 347 MPa m12
and 672 MPa m12
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
118
taken from Ref [9] were used as the standard values for the tangential and radial
directions of the SiC coating respectively According to Eq (1) taking into account
observed and measured parameters (KIC a c l H and E) the geometric constant
value v was calculated in each indentation for each direction (Table 41)
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for S3 SiC coatings
Table 41 illustrates the indentation parameters and the calibrated geometrical
constant v for the Palmqvist crack mode According to the results shown in Table
41 the calibrated mean value of v is 002008plusmn000273 and this value is within
the range of the geometrical constant value (0014-0023) from previous theoretical
studies [14 23] By using nano-indentation hardness and Youngrsquos modulus v was
taken as 002 for the calculation of the VIF fracture toughness in SiC layers in this
study which is the upper limit of 0016plusmn0004 used for previous studies of bulk
CVD SiC using the HE from micro-indentation [14 24-27]
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
119
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχ
v along the radial and tangential directions
Load Radial direction
Tangential direction
a (μm) c (μm) l (μm) χv a (μm) c (μm) l (μm) χv
3 N 6650 13125 6475 0020368 6685 18285 11600 0023088
6900 13090 6190 0019473 6995 15470 8475 0015013
6675 11895 5220 0015749 6120 16615 10495 0019880
6695 13130 6435 0020249 6555 15935 9380 0017057
6790 12610 5820 0017997 6425 18275 11850 0023783
35 N 7195 14970 7775 0022404 7235 20790 13555 0024930
6670 14080 7410 0020721 6715 18160 11445 0019412
4 N 7770 15855 8085 0020967 7390 20240 12850 0020187
χv 002008 plusmn 000273
Note The geometrical constantsχv presented in Table 41 were calculated using Eq(1) The fracture
toughness along the radial (672 MPa m12
) and tangential directions (347 MPa m12
) were taken from
Ref 9
Although the Vickers indentation method for fracture toughness measurement has
been discredited as a mean to obtain true fracture toughness [28] and always gives a
lower fracture toughness value than that obtained using the standard methods (such as
single edge V-norched bending)[1] the values obtained can be compared with each
other This is particular important for small samples and thin coatings since Vickers
indentation provides a method to quantify fracture behaviour when it is not feasible to
obtain true fracture toughness However to get reasonable comparison of Vickers
indentation fracture toughness in SiC coatings the following conditions should be
met
(1) SiC materials produced four regular radial cracks along the corners of the
Vickers indenter For indentation at the polished external surface of SiC
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
120
coatings deposited by FBCVD similar fracture resistance along different
orientation at the surface should be obtained
(2) The calibration of the geometrical constant should be made v was obtained
as 002 based on previous experimental results (see above)
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
Sample Grain size range (μm) Vickers toughness (MPa m12
)
S1 (SiC) 02-2 351plusmn042
S2 (SiC + C) 02-2 403plusmn043
S3 (SiC + Si) 02-2 493plusmn016
Table 42 presents the measured VIF fracture toughness on the polished external
surface using equation (1) for the SiC coatings in which the deposition conditions and
grain size were given It can be seen that the SiC coating with excess Si (S3) has
highest indentation fracture toughness followed by SiC with excess carbon (S2) and
stoichiometric SiC coatings (S1)
Vickers indentation fracture toughness values obtained in this study are slightly higher
than that of commercial CVD β-SiC which has been reported to vary from 24 to 33
MPa m12
measured by the same method [24 26 27] The VIF fracture toughness of
49 MPa m12
for extra-Si SiC measured on a polished external surface is between
347 and 672 MPa m12
when measured on a cross section by micro-beam method [9]
This is consistent with the observation of radial crack length differences ndash the crack
length on the polished external surface is between those in the tangential and radial
direction on the cross-section It is suggested that Vickers indentation is an effective
method for the characterization of fracture behaviour of FBCVD SiC coatings
Moreover the high hardness and Youngrsquos modulus of these three coatings [22] do not
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
121
cause a decrease in fracture toughness which is explained in the later part of this
paper
432 Influence of non-stoichiometries on the VIF fracture toughness
The VIF fracture toughness in S2 SiC coating is ~14 higher than the value for S1
SiC coatings and this can not be attributed to heterogeneous toughening due to the
excess carbon being at the grain boundaries Due to the low content of excess C it is
difficult to identify such an excess at the grain boundaries [29] Previous work
reported in Ref[30] showed that there was no presence of carbon at the grain
boundaries for a concentration up to 1 wt excess C In our case a similar situation
was found in S3 SiC coating where excess Si has not been found along the grain
boundaries Previous studies had [31 32] shown that excess Si in SiC was observed in
grains or near the grain boundaries by TEM only when the amount of excess Si is
high enough (such that it could be detected by XRD or a much higher Raman
spectroscopic intensity)Thus it is assumed that the excess Si could not be considered
as giving heterogeneous toughening which caused a ~43 higher VIF fracture
toughness in the S3 SiC than the S1 SiC coatings As a result the small amount of
excess carbon or silicon in SiC coatings does not seem to have influence on the VIF
fracture toughness through serving as the heterogeneous phase along the grain
boundary
The excess Si or C could be related to different grain morphologies according to
previous study [33] where it was observed that different SiC ratios in the reaction
gas produced rough smooth and irregular pyramid-like grain surfaces This further
affects the growth morphology and cohesion stress between grains For example the
smooth grain surface favours the parallel grain growth The weak grain boundary
cohesion could be the micro crack initiation zone while the strong grain boundary
could transfer the stress to stress concentration zone Here the role of grain
morphology is studied later in terms of stress concentration zone under indentation
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
122
433 Microstructural analysis of fracture behaviour under the indenter
SiC coating under nano-indentation on the polished external surface at a maximum
indentation load of 160 mN It can be seen that the median crack propagation root
deflected slightly and changed from intergranular to transgranular fracture as shown
in Fig 44(a) It is worth noticing that the median crack observed under
nano-indentation was not found under indentation because the indentation cracking
mode depends on the condition of the indenter tip [34] Higher magnification images
(Fig 44(b)) show that a large number of micro cracks were produced at the
elasticplastic interface
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
123
Both intergranular and transgranular cracks were observed near the median crack
initiation zone These cracks are under a tensile stress dominated by Mode I cracks as
the elastic-plastic stress field gives the highest tensile stress around this interface
according to a previous report (see Ref [35]) Moreover micro-cracks were observed
surrounding the median crack and also at the median crack tip as shown in Fig 44(c)
and Fig 44(d) respectively Figure 44(c) illustrates that the micro-cracks are along
the grain boundaries while the micro-cracks around the crack tip were found to both
pass through the grains and along grain boundaries (Fig 44(d))
Non-stoichiometric SiC coatings (S2 and S3) show quite different crack morphologies
under the indenter from that in the stoichiometric SiC (S1) coating as shown in Fig
310 in chapter 3 It can be seen that the propagation root of median cracks in S3 SiC
and S2 SiC coatings were affected by the microstructures as in Fig 310(a) and (c) in
chapter 3 Moreover a lateral crack was found in the S2 SiC coating The irregular
median crack propagation route in non-stoichiometric SiC coatings seems to be
related to the laminar structure
Fig 45 Cross-sectional SEM image of the S1 SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
Figure 45 shows the cross section of S1 SiC coating and the laminar structure (as
indicated by the dashed lines) is perpendicular to the grain growth direction It was
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
124
discussed in chapter 3 that the laminar structure is due to either nano-pores or a high
concentration of stacking faults and it is much less evident in the stoichiometric SiC
coating as compared to the coatings with impurities [22] In the S3 SiC coating (Fig
310(b) in chapter 3) a larger amount of micro cracks either intergranular or
transgranular were found under the indenter than in the S1 and S2 SiC coatings
The fracture mechanism of materials is influenced by their microstructure and the
fracture toughness could be enhanced by changing it For example ceramics
containing micro-cracks during fabrication could be associated with good fracture
behaviour but low strength and hardness since the micro-cracks usually serve as the
failure origins A better solution is to fabricate materials with microstructures that can
form stress induced micro-cracks under an external force [36] In FBCVD SiC a
number of micro cracks were observed under the indenter (Fig 44(b) Fig 310(b)
and (d) in chapter 3) from where the main cracks initiated and propagated away from
this zone According to a previous study although the tip of the main crack leaves the
micro-cracked zone under the indenter the wake region can provide stress shielding
against some further crack extension [37]
Thus the micro-cracks under the indentation (Fig 44(b) Fig 310(a) and (c) in
chapter 3) seem to be a mechanism for the toughening behaviour of FBCVD SiC by
dissipating the fracture energy for brittle fracture Micro-cracks were also found near
the main crack tip and surrounding the main crack for example in the stoichiometric
SiC coating (Fig 44(c) and (d)) This further confirms the toughening behaviour
through micro-cracking In CVD SiC which has a slightly lower fracture toughness
(around 33 MPa m12
) only a few micro-cracks were observed under the indentation
[38] which could be caused by indentation-induced slip bands As a result the
micro-cracks formed under the indentation near the main crack seem to be the reason
for the high VIF fracture toughness in SiC coatings when a high hardness is obtained
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
125
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a) S2
SiC (b) S3 SiC
Stress concentration zones are known to facilitate the nucleation of micro-cracks so a
large amount of micro-faults (eg pores) and weak grain boundaries (inducing the
micro-cracks under an external stress) could increase the VIF fracture toughness A
higher VIF fracture toughness in the extra-C SiC than in stoichiometric SiC coatings
may be due to the presence of the nano-pores (as shown in Fig 35(b) in chapter 3)
The S3 SiC has an even higher VIF fracture toughness than the S2 SiC coating and
this may correspond to a larger number of micro-cracks under the indentation We
assume this difference is due to their varied grain boundary morphologies as shown
in Fig 46 For example we observed different length of cracks on the cross section
(Fig 43) with cracks parallel to the grain growth direction shorter than cracks
perpendicular to the grain growth direction This is because along grain growth
direction itrsquos more likely to produce micro-cracks along the grain boundary As we see
in Fig 46 grains interact with each other in extra-C SiC (Fig 46(a)) forming branch
grains while in S3 SiC grains grow parallel (Fig 46(b)) According to a previous
study it is easier for parallel grains to form a transgranular fracture when the grain
boundaries are along the loading axis [39] This can explain the larger number of
transgranular micro-cracks under the indentation in the extra-Si SiC compared to the
extra-C coatings (Fig 310(b) in chapter 3) which caused different VIF fracture
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
126
toughness This different grain morphology could be caused by the
non-stoichiometries and further work needs to be done to study how excess C or Si
affects the microstructure of the SiC
44 Conclusions
In summary micro-indentation on the polished external surface of the SiC coating in
TRISO particles has been successfully applied to measure the VIF fracture toughness
of the silicon carbide (SiC) Three different types of SiC coatings (stoichiometric SiC
SiC with excess silicon and SiC with excess carbon) produced on spherical particles
by FBCVD were analysed The VIF fracture toughness (measured on the polished
external surface) in these three coatings investigated in this study was observed to
vary between 35 and 49 MPa m12
The results have shown that the VIF fracture
toughness is influenced by the microstructure and non-stoichiometry of SiC coatings
For FBCVD SiC coatings a high VIF fracture toughness accompanied with superior
hardness was attributed to the formation of micro-cracks The difference in VIF
fracture toughness was proposed to be dominated by the laminar defects and grain
morphologies in the SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
127
45 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo and D A Petti
Handbook of SiC properties for fuel performance modeling J Nucl Mater 371
(2007) 329-77
[2] N Swaminathan P J Kamenski D Morgan and I Szlufarska Effects of grain
size and grain boundaries on defect production in nanocrystalline 3C-SiC Acta
Mater 58 (2010) 2843-53
[3] G K Miller D A Petti D J Varacalle and J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[4] D A Petti J Buongiorno J T Maki R R Hobbins and G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[5] K Bongartz E Gyarmati H Schuster and K Tauber Brittle Ring Test - Method
for Measuring Strength and Youngs Modulus on Coatings of Htr Fuel Particles J
Nucl Mater 62 (1976) 123-37
[6] K Bongartz E Gyarmati H Nickel H Schuster and W Winter Measurement of
Youngs Modulus and Fracture Stress on Htr Particle Coatings by Brittle Ring Test
J Nucl Mater 45 (1972) 261-64
[7] M W Kim J H Kim H K Lee J Y Park W J Kim and D K Kim Strength
of chemical vapor deposited silicon carbide films using an internal pressurization
test J Ceram Process Res 10 (2009) 373-77
[8] T S Byun J D Hunn J H Miller L L Snead and J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[9] X Zhao R M Langford J Tan and P Xiao Mechanical properties of SiC
coatings on spherical particles measured using the micro-beam method Scripta
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
128
Mater 59 (2008) 39-42
[10] E Lopez-Honorato P J Meadows J Tan and P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[11] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram and P Xiao Youngs modulus measurements of SiC coatings on
spherical particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[12] ACKadak RGNallinger MJDriscoll SYip DGWilson HCNo JWang
HMaclean TGalen and CWang et al Modular Pebble Bed Reactor Project
University Research Consortium Annual Report Beijing 2000
[13] J I Federer Parametric Study of Silicon-Carbide Coatings Deposited in a
Fluidized-Bed Thin Solid Films 40 (1977) 89-96
[14] G R Anstis P Chantikul B R Lawn and D B Marshall A Critical-Evaluation
of Indentation Techniques for Measuring Fracture-Toughness 1 Direct Crack
Measurements J Am CeramSoc 64 (1981) 533-38
[15] M T Laugier Palmqvist Toughness in Wc-Co Composites Viewed as a Ductile
Brittle Transition J Mater Sci Lett 6 (1987) 768-70
[16] M T Laugier Palmqvist Indentation Toughness in Wc-Co Composites J Mater
Sci Lett 6 (1987) 897-900
[17] W D Nix and R Saha Effects of the substrate on the determination of thin film
mechanical properties by nanoindentation Acta Mater 50 (2002) 23-38
[18] J Lankford and D L Davidson Crack-Initiation Threshold in Ceramic Materials
Subject to Elastic-Plastic Indentation J Mater Sci 14 (1979) 1662-68
[19] Z Li A Ghosh A S Kobayashi and R C Bradt Indentation
Fracture-Toughness of Sintered Silicon-Carbide in the Palmqvist Crack Regime J
Am CeramSoc 72 (1989) 904-11
[20] H Hatta M Zoguchi M Koyama Y Furukawa and T Sugibayashi
Micro-indentation method for evaluation of fracture toughness and thermal
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
129
residual stresses of SiC coating on carboncarbon composite Adv Compos Mater
12 (2003) 155
[21] C B Ponton and R D Rawlings Vickers Indentation Fracture-Toughness Test 1
Review of Literature and Formulation of Standardized Indentation Toughness
Equations Mater Sci Tech Ser 5 (1989) 865-72
[22] H Zhang E Lopez-Honorato A Javed X Zhao and P Xiao Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc In Press (2011)
[23] A Leonardi F Furgiuele S Syngellakis and R J K Wood Analytical
Approaches to Stress Intensity Factor Evaluation for Indentation Cracks J Am
Ceram Soc 92 (2009) 1093-97
[24] M C Osborne J C Hay L L Snead and D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[25] R D Dukino and M V Swain Comparative Measurement of Indentation
Fracture-Toughness with Berkovich and Vickers Indenters J Am CeramSoc 75
(1992) 3299-304
[26] K H Park S Kondo Y Katoh and A Kohyama Mechanical properties of
beta-SiC after Si- and dual Si plus He-ion irradiation at various temperatures
Fusion Sci Technol 44 (2003) 455-59
[27] S Nogami S Ohtsuka M B Toloczko A Hasegawa and K Abe Deformation
during surface modification of silicon carbide using rare-gas ion-beam irradiation
Pricm 4 Forth Pacific Rim International Conference on Advanced Materials and
Processing Vols I and Ii 1367-70 3028 (2001)
[28] G D Quinn and R C Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[29] J Tan Mechanical properties of SiC in TRISO fuel particle PhDThesis
University of Manchester Manchester 2010
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
130
[30] K Kaneko M Kawasaki T Nagano N Tamari and S Tsurekawa
Determination of the chemical width of grain boundaries of boron- and
carbon-doped hot-pressed beta-SiC by HAADF imaging and ELNES line-profile
Acta Mater 48 (2000) 903-10
[31] B Reznik D Gerthsen W G Zhang and K J Huttinger Microstructure of SiC
deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499-508
[32] R A Shatwell K L Dyos C Prentice Y Ward and R J Young Microstructural
analysis of silicon carbide monofilaments J Microsc-Oxford 201 (2001) 179-88
[33] M J Hernandez G Ferro T Chassagne J Dazord and Y Monteil Study of
surface defects on 3C-SiC films grown on Si(111) by CVD J Cryst Growth 253
(2003) 95-101
[34] D S Harding W C Oliver and G M Pharr Cracking during nanoindentation
and its use in the measurement of fracture toughness Thin Films Stresses and
Mechanical Properties V 356 (1995) 663-68
[35] ACFischer-Cripps Introduction to contact mechanics Springer New York
2000
[36] DJGreen An introduction to the mechanical properties of ceramics Cambridge
University Press Cambridge 1998
[37] S B Biner A Numerical-analysis of crack-growth in microcracking brittle solids
Acta Metall Mater 42 (1994) 3643-51
[38] K H Park T Hinoki and A Kohyama Influence of irradiation-induced defects
on fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[39] H Horii and S Nematnasser Brittle failure in compression - splitting faulting
and brittle-ductile transition Philos T Roy Soc A 319 (1986) 337-74
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
131
CHAPTER 5 Influence of Interfacial Roughness on Fracture
Strength of SiC Coatings
51 Introduction
During the irradiation process of TRI-Isotropic (TRISO) fuel particles the high
tensile stress could be accumulated at crack tips These tips were due to direct
penetration of the cracks formed in the PyC layer or the high stress concentration as a
result of the debonding of IPyCSiC interface [1 2] When the tensile stress inside of
the particle exceeded the critical fracture stress of the SiC coating it caused the
failure of the whole particle [3] Furthermore the fracture strength is a main
parameter used in modeling the probability of failure of fuel particles so it is
important to measure the fracture strength of SiC to determine their performance
which is determined from the maximum tensile stress
Different methods such as hemi-spherical bending [4] crush test [5 6] and inner
pressure [6] were introduced to measure the fracture strength of SiC coating in
TRISO fuel particle The fracture strength was in a range and could be characterised
by the Weibull distribution function [4-6] The common vague conclusion derived
from previous results is the significant effect of the IPyCSiC interface on the fracture
strength [4-6] The interface was also found to affect the primary failure mechanism
by determining if the load can transmit through the SiC [6] Previous analyses are
consistent with the well-known prescription that the fracture strength of ceramic
materials varies largely and it is dependent on the size and surface condition of the
specimen [7-9] Among these methods the latest modified crush test proposed by
Byun et al[510] showed a well controlled scatter of the fracture strength in a given
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
132
sample
Although the importance of the interface has been noticed the lack of an accurate and
scientific description of the interface has limited the further study about its
relationship with the fracture strength Roughness is a commonly used terminology to
describe the interface and it could be measured by atomic force microscope and
characterised by the standard deviation of the vertical features [11 12] However
roughness is not enough to describe the interface and to relate it to fracture strength
[13] Due to the importance of the statistical analysis for ceramic materials the
self-affine theory was used to characterise the complex interface numerically
according to previous studies [14-17] A self-affine interface is characterised by a
correlation length the saturation roughness and the roughness exponent [18] A
similarly straightforward approach was applied to demonstrate the importance of the
interfacial roughness on the mechanical properties [19] showing that interfaces with
big and sharp irregularity fail first
In this work the modified crush test was used to measure the fracture strength of a
SiC layer deposited at different temperatures The IPyCSiC interface was well
described by self-affine theory Therefore the effect of the IPyCSiC interface and
dimension of particles together with other possible influences such as porosity and
grain size on the fracture strength were discussed The improvement of this work is
being able to do statistical analysis on the interfacial roughness
52 Experimental details
521 Materials
In this Chapter the buffer pyrolytic carbon and dense pyrolytic carbon coatings were
deposited on the top of ZrO2 kernel (~ Φ500 μm) by fluidized bed chemical vapour
deposition Thirteen SiC coatings were deposited at different temperature flow rate
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
133
MTS concentration and added gas as shown in Table 51 The deposition conditions
were chosen according to previous studies to get different microstructures and more
deposition mechanisms of SiC coating can be found in Ref [20] For fracture strength
measurement the SiC particles were mounted with thermoplastic resin and ground to
about 55 portion of the sphere and polished using increasingly fine diamond
suspensions until frac14 μm SiC shells were released from surrounded PyC layers by
oxidizing at 700 ordmC for 8 hours and further washed in an ultrasonic bath with acetone
for 5 minutes
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Sample Temperature
(ordmC)
MTS
(vol )
Added gas concentration Flow rate
(LMin)
Radius
Thickness (~)
S1 1300 91 05vol C3H
6 600 72
S2 1300 91 01vol C3H
6 600 76
S3 1280 91 01vol C3H
6 600 83
S4 1300 91 -- 600 85
S5 1400 19 57vol Ar 778 87
S6 1500 22 82vol Ar 700 90
S7 1500 19 89vol Ar 778 101
S8 1500 22 79vol Ar 700 112
S9 1400 19 57vol Ar 777 117
S10 1300 19 57vol Ar 778 129
S11 1500 19 89vol Ar 777 151
S12 1500 22 76vol Ar 700 158
S13 1500 19 57vol Ar 778 190
The difference between sample S5 and S9 S7 and S11 is the thickness of the PyC layer MTS
methyltrichlorosilane Lmin the flow rate measured in liter per minute To produce SiC coatings with
particular microstructures and compositions different deposition conditions were chosen which were
contributed to Dr Eddie Lopez-Honorator
522 Test method and analysis
The crush test taking the contact area into consideration was used in this study [2 5
21] and the loading profile of the crush system is shown in Fig 51 When a partial
spherical shell (Radius R thickness t) was diametrically loaded by an external load F
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
134
concentrated on a small circular area (radius 0 ) the maximum membrane stress and
bending stress could be calculated by the equations developed by Roark and Young
[21] The combination of the maximum bending and membrane stress (Local fracture
strengthL
f ) in the inner side of the shell was the maximum fracture strength for
partially loaded shell (around 55 of the sphere)
The fracture strength of brittle SiC coating is best considered as a distribution rather
than a fixed number and the most widely used expression for characterisation is the
cumulative distribution functionmdashWeibull distribution function [7 22] In the current
study the distribution of local fracture strength and fracture strength for a full
spherical shell were characterised by the Weibull distribution The Weibull modulus m
is derived from the local fracture strength (Eq 14 in Chapter 2) The calculation of the
fracture strength for the full spherical shell (F
f ) is based on the size effect (scaling
factor mtRr 122
0 ))(4( R radius of the particle t thickness of SiC shell 0
radius of residual impression after loading) which is equal to the partial strength
divided by the scaling factor [5 7] More details about fracture strength calculation
are available in Ref [5]
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
According to a previous study [5] one reason for the difference of local fracture
10 ordm
t
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
135
strength in a given batch of coating is due to different sizes of residual impression
( 0 ) under which the distribution of defects could be different To reduce the
influence of the 0 the radius (R) at the edge of the residual impression was kept at
an angle of around 10ordm (as shown in Fig 51) from the loading axis by inserting
different kind of soft metal It varied slightly (the ratio of standard deviation to mean
value is around 10) in each batch of SiC
The crush test was carried out in a universal tensile machine INSTRON 5569
(INSTRON High Wycombe Bucks) with a 100 N maximum load cell For each batch
of SiC shell (except for S13) at least 30 specimens were tested at room temperature
with a crosshead speed of 0005 mms The failure load recorded by the tensile
machine was used as the fracture load The individual impression left on the soft
metal (Nickel alloy cold worked copper or brass) was marked under corresponding
load and its diameter was measured by optical microscope (times100 ZESIS Company
German)
523 Characterisation methods
A Philips XL30 FEG-SEM (Philips Eindhoven Netherlands) was used to characterise
IPyCSiC interfacial roughness grain size and porosity from the finely polished cross
section of SiC coatings Characterisation of the IPyCSiC interfacial roughness was
realized by editing the SEM images (in the magnification of times1600) with the Image J
software and extracted it as a line from the background SEM image The interfacial
roughness could be described by a series of pairs of x (distance tangential to the
interface) and y (distance normal to the interface) coordinates assuming the interface
is flat at a scale of 70 microm
Porosity was measured by controlling the threshold of SEM images (times1600 TIF) at a
gray level and adjusted to distinguish pores from grains with the Image J software
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
136
Pore fraction was defined as the ratio of the pores and the total area of the SEM image
Grain size of FBCVD SiC coatings varied in a range and in a columnar shape It was
characterised by measuring mean width and length of single crystals from SEM
images (times6400) and the grain size of the coatings is represented by the mean width
timeing the length of grains A FEG-TEM (TecnaiTM G2
F30 U-TWIN) was used to
observe the IPyCSiC interfacial roughness and TEM samples were prepared by
focused ion beam milling The linear regression method was used to analyze and
quantify the influences of parameters on the fracture strength and Weibull modulus
53 Results and discussions
531 Fracture strength and dimensional effect
Table 52 gives the summary of the measured and calculated parameters for all the
coatings It includes the diameter of impression (mean value 2 0 ) force (mean value
F) Weibull modulus (derived from local fracture strength m) local fracture strength
(L
fmean value) and fracture strength for the full spherical shell (
F
fmean value)
Table 52 Summary of measured and calculated parameters for all the coatings
Sample 2 0 μm F N L
f MPa Modulus (m) Scaling Factor
For Size Effect
F
f MPa
S 1 15239 2235 1784 7397 185 963
S 2 15043 1999 1599 7687 183 872
S 3 14898 1540 1446 7459 187 774
S 4 16052 2042 1620 8261 178 908
S 5 17018 2573 1810 7927 178 1018
S 6 16220 1885 1648 6953 193 855
S 7 14662 1691 1974 7755 190 1019
S 8 14905 1336 1717 7102 198 868
S 9 13040 1088 1825 6495 223 820
S10 16410 1215 1472 6801 204 722
S11 16165 1006 1430 6104 219 652
S12 14677 903 1512 6616 205 737
S13 11586 489 1762 4912 300 587
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
137
As given in Table 52 a significant difference (49-257 N) of the load among SiC
coatings was obtained According to a previous study [5] the variation is mainly
caused by different thicknesses (varied from 30 μm to 60 μm) of SiC coatings
because the relatively thin coating tends to reach higher strength concentration at
fracture
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
The Weibull modulus derived from the local fracture strength (as given in Fig 52) is
in the range of 49-86 (as shown in Table 52) and it falls into the category of moduli
for ceramics materials (from 5 to 30) This range of Weibull modulus is similar to the
values obtained from the brittle ring tests which also gave a similar range of the local
fracture strength [23 24] In different batches of SiC coatings it was found that the
Weibull modulus decreases linearly with the increase of the ratio of outer radius (R) to
the thickness of SiC coatings ( tR ) as shown in Fig 53 The ratio of Rt accounts
for up to 778 (2R from linear regression) of differences of the modulus This is
because the tR ratio is a critical dimension value for the strength distribution of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
138
SiC shell and it represents the relative thickness of SiC coating The higher the ratio
is the thinner the SiC coating So it corresponds to the larger inner surface area
resulting in larger scattering sizes of the critical flaws This observation is consistent
with the previous finite element modeling results showing that the Weibull modulus is
related to the sample dimension [10]
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
As given in Table 52 the scaling factor (effective area-parameter based on the local
fracture strength) between the local fracture strength and the fracture strength of the
full shell are in the range of 18-30 The results are consistent with Byun et alrsquos study
(19-31) [5] and it indicated the importance of the size effect on the fracture strength
of the full shell
The fracture strength for the full spherical shell of thirteen SiC coatings were given in
the form of Weibull plots as shown in Fig 54 The mean fracture strength for the full
spherical shell was in the range of 587-1019 MPa (as given in Table 52) which is
higher than the range of 330-650 MPa obtained by Byun et al [5] This is because the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
139
Rt ratio (above 11) in Ref [5] falls into the higher value categary in current work as
shown in Fig 53
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Because the Weibull modulus is dominated by the tR ratio (Fig 53) its influence on
fracture strength for a full spherical shell could also be from this ratio as shown in
Fig 55 It shows that the fracture strength for the full shell decreases nearly linearly
with the increase of the tR ratio which produces a difference of 6528 (2R derived
from linear curve fit which represents fair agreement) of differences In this work the
similar range of Rt ratio (above 11) corresponds to the fracture strength lower than
850 MPa (as shown in Fig 55) which reduced the difference from previous results
[5] Furthermore the fracture strength of about 1000 MPa was obtained when the Rt
was about 8 [25] and it is similar as the result given in Fig 55 This again
demonstrated the importance of the geometry on the fracture strength of SiC coating
Therefore it is important to eliminate the external influence and study the influences
of microstructures such as interfacial roughness porosity and grain size on fracture
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
140
strength which are discussed in the following parts
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
532 Observe and qualify the effect of interfacial roughness on fracture strength
According to Griffith fracture theory the fracture strength (L
f ) is a function of the
critical flaw size (C) and the fracture toughness ( ICK ) as shown in the following
equation [26]
12( )
L ICf
K Z
Yc (1)
Y is a loading geometrical parameter Z is the flaw size parameter The magnitude of
the critical flaw size could be related to the IPyCSiC interfacial irregularities
The interfacial flaw shape of SiC coatings is modeled from the surface morphology of
PyC coating during deposition process as shown in Fig 56(a) The crack was taken
as a semi-circular surface crack as given in Fig 56(b) where Y is 2 and Z is 16 (Y
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
141
Z are geometrical constants introduced in Eq (1) [26] The fracture toughness of SiC
coatings in TRISO fuel particle was taken to be 33 MPamiddotm12
according to previous
report [27] Taking the result of the local fracture strength from individual SiC coating
into Eq (1) the magnitude of the critical flaw size C could be obtained
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Figure 46 shows the redraws of the IPyCSiC interfacial roughness from SEM images
and the calculated critical flaw sizes according to Eq (1) (range and mean values) for
all specimens are given in the right columns If the fracture initiated at the IPyCSiC
interface as proposed in previous studies [4-6] the calculated critical flaw size range
of each type of SiC coating was expected to match the size range of the interfacial
irregularities
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
142
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
In Fig 57 most of the calculated critical flaw sizes according to Eq (1) are in the
same magnitude as the flaw size observed directly from the interfacial profile images
and this indicates that the dominant effect of the surface roughness on the local
fracture strength For example the direct observation of the biggest flaw size from the
profile is about 43 μm and 26 μm in sample S9 and S13 respectively and they are in
the range of the calculated defect sizes of 09-65 μm and 17-47 μm for S9 and S13
respectively However exceptions were found such as specimens S1 and S2 which
show slightly higher calculated surface flaw size than the observation from SEM
images Furthermore it is difficult to accurately characterise the difference of the
interfacial roughness by observing the converted images and give specific
information (such as shape) of single profile (shown in Fig 57) The estimation of
the shape of surface irregularities to be half-circular could also result in the error on
the critical flaw size calculation [7] To give a direct estimation about the influence of
interfacial roughness on local fracture strength the scaling behavior of IPyCSiC
interface need to be characterised by a statisticalnumerical method
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
143
533 Characterise and quantify the interfacial roughness
Self-affine theory has become a standard tool in the study of various rough interfaces
[18 28 29] Here it was the first time being proposed to describe the IPyCSiC
interfacial roughness accurately and scientifically and then was used to quantify the
relationship between interfacial roughness and local (intrinsic) fracture strength and
fracture strength of the full shell
5331 Self-affine theory introduction and experimental setup
In order to describe the IPyCSiC interfacial roughness with specific parameters an
easy way is using a height-height function [29 30]
2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)
where the x axis is along the IPyCSiC interface and ( )h x is the surface height profile
The amplitude of the roughness ( )h x is correlated with the length scale x and
lt gt denotes the spatial average over ( )h x in a planar reference surface If the
interfacial roughness of IPyCSiC were self-affine the correlation of x and
h should follow the power law relationship (Eq (2)) and it could be obtained by the
log-log plot of x and h The (for self-affine surface 0lt lt1) is the roughness
exponent and it describes the degree of surface roughness at short length scales [31]
This short length scale is shorter than correlation length ξ which is another parameter
used to describe the self-affine surface (besides the surface roughness h and
roughness exponent ) It is the average distance between the features in the surface
profiles within which the surface variations are correlated [28] Therefore the small
(close to 0) characterises extremely jagged or irregular interfaces while large
value characterise interface with smooth hills and valleys [32]
For all the samples the scaling properties of IPyCSiC interface (as shown in Fig 57)
are characterised by their one-dimensional height-height correlation function Eq (2)
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
144
The characteristic parameters of the digitalized IPyCSiC interfacial roughness are as
follows The resolution between two points along x axis is 020833 μm and x
changes by timing the resolution with integer (1 2 3hellip15) According to previous
self-affine theory study [16] the number of recorded points along the x axis was
taken in the range of 250-400 in this work corresponding to the length of 50-70 μm
for different IPyCSiC interfaces
5332 Results of self-affine theory
Figure 58 is a log-log plot showing the variation of h as a function of the distance
x for three SiC coatings The h varied as a power law of x (solid line ) when
x ltξ while remained nearly constant ˗ saturation roughness (σ0 dashed parallel
lines) for x gtξThese results indicated that these three IPyCSiC interfacial
roughness were self-affine with the roughness exponent of around 063-067 For the
rest of the samples the same scaling characterisation method was used Theξ σ0 and
are given in Table 53
Fig 58 Log-log representation of the height-height correlation function h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
ξ3 ξ12 ξ6
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
145
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Sample σ0 (μm) ζ ξ(μm) σ0ξ
S 1 02378 05903 06250 03804
S 2 04142 06950 08333 04971
S 3 06701 06673 16666 04021
S 4 06825 05244 14583 04680
S 5 05271 06308 14581 03615
S 6 08500 06343 20833 04080
S 7 04293 05162 14583 02944
S 8 07452 05107 14583 05110
S 9 05453 06099 12500 04362
S10 06953 05490 13044 05330
S11 05806 04949 10417 05574
S12 07584 06899 16666 04550
S13 05522 02971 18750 02945
The roughness exponent values for the 93 of IPyCSiC interface were in the range
of 05-07 (as shown in Table 53) This indicated the self-affine measurement is
reliable according to Schmittbuhl and Vilottersquos review [14] which showed that this
range of roughness exponents could have the minimum characterisation errors
Furthermore these roughness exponents are comparable except specimen S13 and it
was consistent with the observation of the interfacial roughness (Fig 57) in which
only specimen S13 showed the high degree of high frequency and short wavelength
irregularities (the dark pits in S13 profile) According to previous study [31] the
concentration of the roughness exponent values could be attributed to the same
original mechanism of the IPyCSiC interface which was produced by the FBCVD
under different conditions As a result the different roughness exponent value could
not describe the difference of the IPyCSiC interface
As shown in Table 53 the saturation roughness (σ0) and correlation length (ξ) are in
the range of 024-085 μm 063-208 μm respectively (Table 53) According to
previous studies [16 17 30] the σ0 and ξ couldnrsquot represent the interfacial
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
146
irregularities correlated with the critical flaw size Because the σ0 value range was
nearly one magnitude lower than the calculated critical flow size (mean value range of
2-4 μm) and the dimension of ξ was perpendicular to the calculated critical flaw size
direction Furthermore it was found that σ0 and ξ values were correlated to the sample
size (recorded points) [16] With the increase of the sample size for the same profile
both the ξ and the σ0 values increased and indicated these two parameters may not be
intrinsic properties of the samples However the roughness ratio σ0ξ is constant
which was found in both the current work and previous study [16]
As a result of above discussions the roughness ratio of σ0ξ was proposed to
characterise the interfacial roughness which could represent the sharpness of the
interfacial irregularities according to Ref [30] For example the low ξ value
corresponded to narrow surface irregularity when the σ0 and values were the same
With the increase of the σ0 value the surface irregularity became deep and narrow
which was hazard to the mechanical properties according to previous simulation work
on the fracture strength of SiC coatings [22] The above observations and analysis
results are supported by previous study [31] when length scale x gt ξ (shown in
Fig 58) the roughness ratio σ0ξ describes mainly the long-wavelength roughness
characteristics which could be statistically equal to the effect of the critical flaw size
on fracture strength
534 Quantify the influence of interface roughness on fracture strength
Figure 59 gives the influence of roughness ratio on the local fracture strength and it
contributes to nearly 50 (R2 from linear regression) of variation of the local fracture
strength It shows that the local fracture strength decrease linearly with the increase of
the roughness ratio This result approves previous findings about the importance of
the interfacial roughness [4-6] and is correlated with the Griffth fracture theory (Eq
(1)) about the importance of the shape and dimension of critical flaws Furthermore
the relation between interfacial roughness has been characterised quantitatively and a
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
147
linear relationship between roughness ratio and local fracture strength is proposed
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Except for the interfacial roughness the local fracture strength could also be affected
by the fracture toughness as shown in Eq (1) Although Vickers-indentation fracture
behavior of SiC coatings was different due to the laminar defects and grain
morphology [33] the fracture toughness of SiC was found to be insensitive to the
microstructure of materials [34] This could be attributed to the fact that
Vickers-indentation provided a static propagation of the crack while the real fracture
toughness was measured dynamically In this work the fast fracture process could
overtake the effect of microstructure on the different static fracture behaviour [5 25]
Since porosity and grain size were main microstructural variations in SiC coatings [1]
their effects on fracture strength were estimated
The characterisation and quantification of grain size and porosity were shown in Table
54 The grain size was found to have no effect on fracture strength according to
previous studies [5] which was also indicated from the regress analysis (R2 is close to
0) No influence was found by regressing the local fracture strength on pores
Therefore the dominant influence on the local fracture strength is from the roughness
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
148
ratio
Table 54 Results and variations influences on fracture strength for SiC coating
Specimen S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S10 S11 S12 S13
Grain size
(μm2)
04 06 06 08 20 20 20 28 20 08 20 28 25
Porosity
(Area )
0 0 0 0 05 04 12 09 03 0 08 21 20
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
Because the fracture strength for a full spherical shell is a function of the Weibull
modulus and local fracture strength [5] it was affected by factors such as the
dimension ratio of thickness to radius of the coating (as shown in Fig 55) the
roughness ratio (as shown in Fig 510) Figure 510 shows the influence of roughness
ratio on fracture strength of the full shell The linear relationship was found in 12
samples as indicated by the dashed line in Fig 510 and it could explain about 68
(2R from linear regression) of difference in fracture strength of the full particle The
high roughness ratio would decrease the fracture strength of the full shell linearly The
deviated point of sample S13 could be due to its largest Rt ratio (as shown in Fig
55) which may have over taken the effect of the roughness ratio (Work about the size
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
149
effect on the fracture strength has being carried out)
54 Conclusions
The fracture strength of SiC coatings deposited under different conditions were
measured by the modified crush test and analyzed by the statistical analysis (Weibull
function and Self-affine theory) The influences on fracture strength were studied
such as the IPyCSiC interfacial roughness specimen size and porosities Following
results were obtained
(1) Weibull modulus and fracture strength of the full shell were significantly affected
by the ratio of radius to thickness of SiC coating and both of them decrease
linearly with the increase of the ratio
(2) The dominant effect of the IPyCSiC interfacial roughness on intrinsic fracture
strength was found by matching the SEM images with the calculated critical flaw
size based on the Griffith fracture theory
(3) The interfacial roughness were successfully characterised by a
numericalstatistical method and the roughness ratio representing the shape of the
irregularities was proposed to be a unique parameter among different coatings
(4) The difference of the local fracture strength was dominated by the roughness ratio
and it decreased linearly with the increase of the roughness ratio It is been the
first time that the interfacial roughness was numerically related to the fracture
strength
(5) Microstructures such as grain boundaries and porosity were found to have
neglectable influence on fracture strength
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
150
55 References
[1] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[2] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the tri-isotropic-coated fuel particle J
Am Ceram Soc 90 (2007) 184-91
[3] T Nozawa L L Snead Y Katoh J H Miller E Lara-Curzio Determining the
shear properties of the PyCSiC interface for a model TRISO fuel J Nucl Mater
350 (2006) 182-94
[4] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
Fuel Particles for High-Temperature Gas-Cooled Reactors J Am Ceram Soc 56
(1973) 36-41
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[6] S G Hong T S Byun RA Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the TRI-Isotropic-coated fuel particle
J Am Ceram Soc 90 (2007) 184-91
[7] D J Green An introduction to the mechanical properties of ceramics Cambridge
solid state science series Cambridge Cambridge University press 1998
[8] R Danzer Some notes on the correlation between fracture and defect statistics
Are Weibull statistics valid for very small specimens J Eur Ceram Soc 26
(2006) 3043-49
[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
Transgranular Cleavage J Mech Phys Solids 34 (1986) 477-97
[10] J W Kim T S Byun Y Katoh Optimization of fracture strength tests for the
TRISO layers of coated fuel particles by finite element analysis 33rd international
conference on advanced ceramics and composites Daytona Beach FL2009
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
151
[11] W N W Chen X Nie A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
Ceram Soc 92 (2009) 1287-95
[12] R T Wu X Wang A Atkinson On the interfacial degradation mechanisms of
thermal barrier coating systems Effects of bond coat composition Acta Mater 58
(2010) 5578-85
[13] X Nie W N W Chen A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
Ceram Soc 92 (2009) 1287-95
[14] J Schmittbuhl J P Vilotte S Roux Reliability of Self-Affine Measurements
Phys Rev E 51 (1995) 131-47
[15] J T M De Hosson G Palasantzas Roughness effect on the measurement of
interface stress Acta Mater 48 (2000) 3641-45
[16] L Ponson H Auradou M Pessel V Lazarus J P Hulin Failure mechanisms
and surface roughness statistics of fractured Fontainebleau sandstone Phys Rev
E 76 (2007) 036108-14
[17] L Ponson H Auradou P Vie J P Hulin Low self-affine exponents of
fractured glass ceramics surfaces Phys Rev Lett 97 (2006) 125501-4
[18] F Spaepen Interfaces and stresses in thin films Acta Mater 48 (2000) 31-42
[19] W G Sloof T S Hille T J Nijdam A S J Suiker S Turteltaub Damage
growth triggered by interface irregularities in thermal barrier coatings Acta Mater
57 (2009) 2624-30
[20] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[21] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[22] G K Miller D A Petti J T Maki D L Knudson An evaluation of the effects
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
152
of SiC layer thinning on failure of TRISO-coated fuel particles J Nucl Mater
355 (2006) 150-62
[23] K Bongartz E Gyarmati H Schuster KTauber The brittle ring test A method
for measuring strength and Youngrsquos modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[24] K Minato K Fukuda K Ikawa Strength of silicon-carbide coating layers of
fuel Pparticles for high-temperature gas-cooled reactors J Nucl Sci Tech 19
(1982) 69-77
[25] J W Kim T S Byun Y T Katoh Optimization of fracture tests for the SiC
layer of coated fuel particles by finite element analysis Ceram Nucl Appl DOI
1010029780470584002 ch13 2010
[26] S Gonzalez B Ferrari R Moreno C Baudin Strength analysis of
self-supported films produced by aqueous electrophoretic deposition J Am
Ceram Soc 88 (2005) 2645-48
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] B N Dev A Roy K Bhattacharjee H P Lenka D P Mahapatra Ge growth
on self-affine fractal Si surfaces influence of surface roughness J Phys D Appl
Phys 42 (2009) 145303-10
[29] J Feder Fractals Plenum New York 1988
[30] J T M De Hosson R Van Tijum Effects of self-affine surface roughness on the
adhesion of metal-polymer interfaces J Mater Sci 40 (2005) 3503-08
[31] G Palasantzas Roughness spectrum and surface width of self-affine fractal
surfaces via the K-correlation model Phys Rev B 48 (1993) 14472-78
[32] P Meakin Fractals scaling and growth far from equilibrium Cambridge
Cambridge University Press 1998
[33] H Zhang E Loacutepez-Honorato A Javed I Shapiro and P Xiao A study of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
153
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc 95 (2012) 1086-92
[34] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany and A H
Heuer Fracture toughness of polycrystalline silicon carbide thin films Apply
Phys Lett 86 (2005) 071920-22
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
154
CHAPTER 6 Effect of Thermal Treatment on
Microstructure and Fracture Strength of SiC Coatings
61 Introduction
The mechanical properties of the as-deposited SiC coatings have been widely studied
eg Youngrsquos modulus and hardness [1-3] fracture toughness [4] and fracture strength
[5] etc However after it experiences the high temperature the composition and the
microstructure of the SiC coating may change which consequently influences the
mechanical properties It has been found that mechanical properties of SiC such as
Youngrsquos modulus and hardness are less affected when experiencing the current fuel
operation temperature (less than 1600 ordmC) [1 6] even after thermal treatment
temperatures of 1980 ordmC [7] To enhance the operational temperature of the high
temperature reactor in the future design it would be necessary to understand the
evolution of microstructure and mechanical properties of SiC coatings at even higher
temperature Some research [8-10] has been carried out to study the effect of high
temperature (more than 2000 ordmC) thermal treatment on the density and microstructure
of the fuel particle Itrsquos concluded that fuel failure and fission product release
dependent on SiC thermal stability at high temperature [9] Rooyen et al[11]
measured the annealing temperature effect on the fracture strength of SiC coatings It
is found that the fracture strength increases after thermal treatment at temperature up
to 2000 ordmC decreases in strength after thermal treatment at 2100 ordmC However no
clear explanation was given on this result
Due to the importance of the SiC on the safety of this fuel it is necessary to study the
thermal stability of SiC and characterise any change in microstructure and mechanical
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
155
properties It has been previously found that SiC deposited at 1300 ordmC with the
addition of propylene and methyltrichlorosilane as gas precursors not only have good
mechanical properties such as hardness and Youngrsquos modulus [3] fracture toughness
[4] but also have high silver and palladium diffusion resistance [12 13] Therefore in
this Chapter we thermally treated SiC coatings deposited at a range of temperature
(1300-1500 ordmC) at 2000 ordmC for 1 hour in argon atmosphere The change of fracture
strength and thermal stability of SiC coating were studied in terms of composition and
microstructural change of the coatings after thermal treatment
62 Experimental details
Four batches of SiC coatings (with nearly stoichiometry) deposited by Fluidized bed
chemical vapour deposition at different tempearure were chosen to study the thermal
treatment effect on the evolution of the microstructure and fracture strength Table 61
gives the deposition conditions of coatings studied and symbols used to describe each
sample The stoichiometry was measured by the Raman spectroscopy (Renishaw 1000
Raman microprobe system with 514 nm Argon laser) The laser beam was focused on
the surface of the cross section through a times50 objective lens
Table 61 Deposition conditions of SiC coatings
Sample Temperature
(oC)
MTS concentration
(vol)
Added gas
concentration
Stoichiometry
SiC1 1280 91 01vol C3H6 SiC
SiC2 1300 91 01vol C3H6 SiC+C
SiC3 1400 19 57vol Ar SiC
SiC4 1500 22 79vol Ar SiC+C
The inner side of the coating is stoichiometric (23 of the thickness) while outside of the coating is
SiC with excess C The microstructure characterization was done in the inner side coating while the
fracture strength measurement is related to the full coating SiC+C means that the C peak around
1300-1500 cm-1
was observed in SiC coating Chosen of deposition conditions was contributed to Dr
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
156
Eddie Lopez-Honorato
The sample preparation for fracture strengths measurement is the same as described in
Chapter 5 As introduced before thermal treatment was carried out at 2000 ordmC for 1
hour in argon protected atmosphere on SiC half shells The same fracture strength test
and equipment settings as described in Chapter 5 were used in this Chapter
In addition to Raman spectroscopy the microstructure of SiC coatings before and
after thermal treatment was also characterised using X-ray diffraction (PW 1830
Philips) with a Cu Kα1 radiation source The XRD samples were the SiC segments
(fractured SiC shells without external residual stress) Scanning electron microscopy
(Philips XL30 FEG-SEM) was used to characterise the change in morphologies of
SiC coatings Porosity was measured by setting a threshold of the SEM images
(times1600 TIF) at a gray level and adjusted to distinguish pores from grains with Image
J software Three SEM images were measured for each SiC coating Average pore size
(diameter nm) and the pore fraction (area ratio of pores to the total area as observed
by SEM) were obtained For transmission electron microscopy (TEM) the specimens
were prepared by crushing the SiC shell and dispersing the fragments on a carbon
holy film copper grid and crystal structures were characterised using an FEG-TEM
(TecnaiTM G2
F30 U-TWIN)
63 Results
631 Fracture strength of SiC coatings
Figure 61 shows the Weibull distribution of the local fracture strength ( L
f ) in SiC
coatings before and after thermal treatment at 2000 ordmC It gives a direct observation on
the decrease of the local fracture strength in coating SiC2 SiC3 and SiC4 after
thermal treatment while the local fracture strength of coating SiC1 is nearly
overlapped with the as-deposited coating The magnitude of the mean local fracture
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
157
strength (as summarised in Table 62) could represent the decrease trend of the full
batch of the coating in current study
Fig 61 Weibull plots of local fracture strength ( L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
The Weibull modulus (m) was obtained by linearly fitting the curves shown in Fig 61
It shows that the Weibull modulus decreased by 14 07 and 21 in coating SiC1 SiC3
and SiC4 respectively however it increased slightly (by 12) in SiC2 after heat
treatment As shown in Fig 61 the Weibull modulus derived from linear fitting is
affected by the deviation of few points from the linear distribution of the local fracture
strength (as shown in Fig 61) For example in sample SiC3 the slightly decrease
could be attributed to the deviation of the lowest points According to previous study
[14] the slight decrease (07) of Weibull modulus in SiC3 could be neglected since
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
158
the deviated points could be caused by different failure mechanisms involved in the
fracture process [14]
Fig 62 Weibull modulus plots of fracture strength of the full shell ( F
f ) before
(black triangle) and after (red circle) thermal treatment
Figure 62 shows the Weibull plots of fracture strength of the full shell ( F
f ) before
and after thermal treatment at 2000 degC In the same batch of coatings (the same size
effect) the fracture strength of the full shell increase with the increase of the Weibull
modulus and local fracture strength according to previous study [5] Therefore the
decrease of local fracture strength and increase of the modulus in SiC2 could explain
the slight change (decreased 25 MPa obtained from Table 62) of the fracture strength
of the full shell after thermal treatment In the other three samples the fracture
strength of the full shell decreased significantly (more than 110 MPa obtained from
Table 62) after thermal treatment due to the decrease of local fracture strength and
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
159
unchanged modulus)
Table 62 summarized the results of the fracture strength measured before and after
thermal treatment at 2000 degC including the Weibull modulus (m) derived from the
distribution of the local fracture strength ( L
f ) the mean local fracture strength and
fracture strength of the full shell ( F
f ) After thermal treatment the mean local
fracture strength of coatings decreased significantly except SiC1 coating which
retained the same level as in as-deposited coating The mean fracture strength of the
full shell was reduced after thermal treatment in a different degree but the change of
Weibull modulus is more complex which shows both decreased and increased values
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the full shell before and after thermal
treatment
Sample m (from
L
f )
as deposited 2000degC
L
f MPa
as deposited 2000degC
F
f MPa
as deposited 2000degC
SiC1 75 61 1445 1421 774 660
SiC2 77 89 1599 1395 872 847
SiC3 65 58 1824 1333 820 548
SiC4 74 53 1717 1443 858 587
As concluded from Fig 61 Fig 62 and Table 62 the fracture strength decreases
less in coatings deposited at lower temperature (about 1300 degC) than those deposited
at higher temperature (1400-1500 degC) This is consistent with previous study about
high properties of SiC coatings deposited at low temperature such as the hardness
Youngrsquos modulus and resistance to the fission products [12 13 15]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
160
632 Change in morphologies
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after (c) and (d) SiC2 before and after
(e) and (f) SiC3 before and after (g) and (h) SiC4 before and after thermal treatment
Dashed and solid arrows indicate growth direction and pores respectively
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
161
Figure 63 gives the SEM images showing the microstructure of SiC coatings before
and after thermal treatment at 2000 ordmC Before thermal treatment no pores were found
in SiC1 and SiC2 coatings (Fig 63(a) and (c)) while nano-pores were found in SiC3
coating (Fig 63(e)) and even bigger (micrometres) pores were occasionally found in
SiC4 coating (Fig 63(g)) Among four as-deposited coatings SiC4 has highest area
fraction of pores (~09) followed by SiC3 (~03) coating (Fig 63 (a) (c) (e) and
(g) summarized in Table 63)
After thermal treatment at 2000 ordmC pores with different size and area fraction were
observed in all the coatings even though as-deposited SiC1 and SiC2 were free of
pores as shown in Fig 63(b) (d) (f) and (h) The amount of pores formed in treated
SiC1 coating (area fraction of ~05 ) is lower than the other three coatings which
have similar area fraction of pores (~14 ~13 and ~15 for SiC2 SiC3 and
SiC4 respectively given in Table 63) Similar to the content of the pores the pore
size (mean size of ~50 nm) in SiC1 is smaller than in the other coatings (gt 100 nm)
Among coatings SiC2 SiC3 and SiC4 much larger pores (micro-meter sized as in
Fig 63(f) and (h)) were produced in SiC3 and SiC4 coatings after thermal treatment
compared with nano-sized pores in SiC2 Furthermore it is found that most of pores
in coatings SiC2 SiC3 and SiC4 were formed along the grain boundaries and triple
junctions as we can see from Fig 63(d) (f) and (h)
The pores are uniformly distributed through the coatings and no area free of pores or
area with highly concentrated pores is observed However there are connections of
pores (2 or 3 pores formed closely) in SiC2 SiC3 and SiC4 as indicated by solid
arrows in Fig 63(d) (f) and (h) and the diameter of the porous connection zone
(black circle in Fig 63(d) (f) and (h)) could be in the magnitude of few micrometres
The connection of pores could easily become larger pores of few micrometres
diameter under external tensile strength due to the high strength concentration [14]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
162
Fig 64 The IPyCSiC interfacial roughness of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermally treated at 2000 degC (right
in each figure) The white arrow points towards to the interface irregularities (except
for thermally treated SiC4 coating (d)) black circle represents the pores in SiC
coatings
Figure 64 gives the evolution of interfacial roughness in different coatings after
thermal treatment at 2000 ordmC to study their influence on the change of fracture
strength Compared with the as-deposited coating the changes of the interfacial
roughness in SiC1 are similar to SiC3 which show the smoother interface with
interval of irregularities were observed Fig 64(a) and (c) However different from
as-deposited coatings with defects mainly at the interface defects (pores) are also
observed through the coating after thermal treatment (as seen in Fig 61(b) (f) and
Fig 64(a) (c)) Furthermore the size of pores is in the same magnitude as their
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
163
interfacial roughness (shown in Fig 64(a) and (c))
The change of the interfacial roughness in SiC2 is more significant than SiC1 and
SiC3 since pores formed as part of the interface (indicated by arrows in Fig 64(b))
and they are larger than the pores formed in the coating (circle in Fig 64(b))
Different from others three coatings the IPyCSiC interface of SiC4 becomes
smoother (Fig 64(e)) after thermal treatment compared with as-deposited coating so
the defects (pores) within the coating are bigger than surface irregularities
633 Evolution in microstructure
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermally
treated at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and
SiC2 inset shows the peak shift of as-deposited (dash line) and after thermal
treatment (solid line) (b) is SiC4 and inset is the high angle diffraction peak after
thermal treatment showing splitting while it is a single peak in as-deposited coating
Figure 65 gives XRD results of the as-deposited and thermally treated samples
which show the presence of the β-SiC in coatings The peak presents at 2θ~335ordm is
from the crystallographic errors which could either be due to the stacking faults or
the disordered α-SiC according to previous descriptions [16 17] It is found that the
intensity ratio of the 2θ~335ordm peak to the (111) plane peak (2θ~356ordm) decreased after
thermal treatment in all the coatings The coating SiC4 also shows the split of high
angle diffraction peaks (inset of the Fig 65(b) 2θ~613ordm and 713ordm) which is
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
164
attributed to the X-ray double diffraction and this implies the high crystallites after
thermal treatment
Figure 66 is the HRTEM image of sample SiC4 after thermal treatment in which the
stacking faults and micro twins could still be seen The stacking sequence of
ABCACBACBACB was observed as shown in the dashed square zone in Fig 66
According to study about crystal structure [18] this stacking sequence is supposed to
be the micro twins compared with the rest 3C stacking sequence rather than the
6H-SiC domain Furthermore the (111) peak shifted to the high angle after thermal
treatment in all the coatings as shown in the inset of Fig 65(a) which corresponded
to the decrease of the crystal constant
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Figure 67 gives the Raman spectroscopic results of SiC coatings before and after
thermal treatment The carbon peak at 1300-1600 cm-1
was found in the as-deposited
SiC2 and SiC4 coatings According to previous studies [4 19] the intensity ratio of
I1600I796 indicated that the estimated amount of excess C was less than 05 at in
this study The peak between TO and LO peaks (around 882 cm-1
) was attributed to
the stacking faults or highly disordered stacking faults cluster [3 15 20-22]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
165
After thermal treatment the weak carbon related peaks appeared at around 1395 cm-1
and 1600 cm-1
(G band) in sample SiC1 SiC2 and SiC4 The peak around 1395 cm-1
could represent the methyl group and amorphous carbon structures and G band is due
to the stretching mode of all pairs of sp2 atoms in chains and rings [23] The arising of
the 2D peak (also called G peak 2715 cm-1
) after thermal treatment was observed in
sample SiC2 SiC3 and SiC4 which is the second order of zone-boundary phonons
[24]Considering the amount of excess carbon in SiC coatings the symmetry of the
2D peak indicates that the carbon after treatment is more likely to be graphene rather
than graphite [24] which means the concentration of excess C is low in SiC coatings
It is also found that the intensity ratio of the disordered stacking faults (around 882
cm-1
) to the TO peak decreases in all samples after thermal treatment (shown in Fig
67)
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings The lower line is before thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
166
treatment and the upper line is after thermal treatment at 2000 degC in individual
sample
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
Sample Porosity ()
As 2000degC
Stoichiometry
As 2000degC
Critical Defects
As 2000degC
SiC1 0 05 0 C clusters Inter Inter+ Pore
SiC2 0 14 C clusters Ordered C Inter Inter
SiC3 03 13 0 Ordered C Inter Inter+ Pore
SiC4 09 15 C cluster Ordered C Inter Pore
First order Raman spectroscopy (1200-1600 cm-1
) Represents the carbon structure related to the
methyl group or amorphous carbon structures (contains SP2 and SP
3) [23] Second order (2700 cm
-1)
single layer grapheme related carbon materials [24]
Represents the interface irregularities
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
Furthermore the narrowing of the TO peak was found (the inset in Fig 67 (b)) in the
Raman spectroscopy Although it could be an overlap of two peaks at around 796 cm-1
and 789 cm-1
in coatings before and after thermal treatment the peak at 789 cm-1
corresponding to the stacking sequence of ABCACBhellip [25] is more likely to be
micro-twins in current study(as shown in Fig 66) Table 63 summarized the main
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
167
morphological and microstructural change of SiC coatings before and after thermal
treatment
Particularly for sample SiC3 except for the appearance of weak 2D peak after thermal
treatment without visible first order carbon peaks in the sample SiC3 the precipitates
were also observed from both inner and outside of the shell These precipitates were
demonstrated to be the single 3C-SiC crystal by Raman spectroscopy as shown in Fig
68 Raman spectra of precipitates represents the incident direction of the laser is
perpendicular to the SiC single crystal (111) plane which the LO mode at around 970
cm-1
is forbidden when Raman spectra were obtained in a backscattering geometry
[22] (The appearance of the forbidden LO band might be due to to finite collecting
angle of the spectrometer)
64 Discussion
641 Influence of interfacial roughness and pores on fracture strength
To evaluate the critical flaw size we used the equation 1
2( )
L ICf
K Z
Yc for tensile
strength (local fracture strength) and the case for the semi-circular surface crack
(Y=125 [26]) of radius c and inside holes (Y= π12
[14]) of diameter 2a When the
fracture toughness ( ICK ) of the SiC coating was taken as 33 MPa m-12
[27] the
critical surface defect radius and the diameter of the inside pores were calculated to be
in the range of 15 ndash 78 microm obtained from all the coatings The mean critical flaw
size is in the range of 30 ndash 40 microm after thermal treatment The calculated critical
flaw sizes are in the same magnitude as the defects observed at the IPyCSiC interface
and the pores in the SiC coatings after thermal treatment (see in Fig 63 and Fig 64)
Therefore the decrease of the local fracture strength after thermal treatment could be
related to the formation of these defects in SiC coatings Accordingly the sources of
critical defects were summarized in Table 63 for coatings before and after thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
168
treatment The interfacial roughness and pores within the coating compete to be the
critical flaws Once the size of interfacial irregularities is lower than critical flaw size
and rarely distributed their effect on fracture strength could be decreased or even
excluded according to previous study [14] Therefore the pores inside the coating
with the diameter of 2a would be considered as the main failure origins [14] These
could explain the decrease of local fracture strength in coatings SiC2 SiC3 and SiC4
which have micrometer pores formed within the coatings andor at the interface while
the local fracture strength is less affected in coating SiC1 due to formation of
nanometer pores
The Weibull modulus is related to the specimen size loading method and defects
distribution [5 14] In this study the specimen size and the loading morphology could
be excluded for one kind of SiC coating so the change of the modulus is due to the
degree of the scattering of the critical flaw size under the tensile strength The
interfacial irregularities in SiC2 became narrower and deeper (about 4 microm of depth as
shown in Fig 64(c)) after thermal treatment and they are also bigger than the pores
generated within the coating So the critical flaw in SiC2 after thermal treatments is
due to the interfacial irregularities (Table 62) with less scattered size under the
loading area than as-deposited coating which increased the Weibull modulus
However the critical defects in the other coatings include pores within the coatings
(shown in Fig 64 and Table 62) For example in SiC4 the critical flaw is only from
pores within the coating after thermal treatment due to the lack of interstitial
irregularities (Fig 64(h)) This enlarged the distribution of critical flaws after thermal
treatment which leads to the decrease of the Weibull modulus in different degree The
change of the fracture strength of the full shell depends on both Weibull modulus and
local fracture strength as discussed before [5] Our result showed that the SiC coating
deposited at low temperature of 1300 ordmC produced less critical flaws and smaller
decrease of the fracture strength of the full shell (see Table 63)
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
169
642 Mechanism of microstructural change
Changes in SiC coatings after thermal treatment include the formation of pores the
decreased intensity of the 2θ~335 ordm peak (crystallographic errors) in XRD the arising
of Raman peaks around 1395 cm-1
and 2715 cm-1
According to previous studies [8
10 21 25 28 29] we propose that these changes after thermal treatment could be
attributed to phase transformation or the diffusion of defects such as vacancies and
interstitials
If the 2θ~335ordm peak is from amorphous α-SiC its intensity ratio to (111) diffraction
peak would increase after heat treatment Because the presence of α-SiC phase in
β-SiC could promote the transformation of β-SiC into α-SiC [29] Conversely the
intensity of 2θ~335ordm peak decreased after thermal treatment in this work as observed
in Fig 65 and no α-SiC phase segregation (Fig 66) was found by HRTEM after
thermal treatment Furthermore the transformation from disordered α-SiC into β-SiC
after thermal treatment is also excluded because high pressure and high temperature
are needed for this process to happen [29] Therefore it is concluded that the 2θ~335ordm
peak derived from stacking faults and they could be annihilated at current
environment according to previous studies [8 28 30]
Stacking faults were surrounded by defects such as dislocations vacancies and
interstitials [10 15 31] so the high density of stacking faults in this work
corresponded to the high amount of native defects The annihilation of stacking faults
after thermal treatment indicated the reduction of these defects and it could reduce
the lattice constant In this work the decrease of the lattice constant was found after
thermal treatment as indicated by the peak shift of (111) plane in XRD results (Fig
65) and the crystallisation (ordering) was also reflected from the decreased intensity
of the 2θ~335ordm peak (Fig 65) and Raman defect peak (around 882 cm-1
) (Fig 67)
Therefore the formation of pores is due to the annealing of defects through the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
170
diffusion of vacancies or interstitials which are common even in high-purity CVD
SiC [32] However diffusion of native defects depended on their concentration which
was constrained by different composition of SiC (deviation from stoichiometry) [31]
For example for the C-rich cubic SiC the dominant defect is the CSi antisite (Si atom
site was occupied by C atom in tetrahedral structure) [31]
According to above analysis the formation mechanism of pores could be governed by
different kinds of defects In SiC1 coating the smallest and least content of pores
formed after thermal treatment is most likely caused by the annealing of stacking
faults surrounded by the dislocations and vacancies which is consistent with previous
study about the thermal treatment effect on stoichiometric SiC [28] In SiC coating
with excess carbon the microstructure evolution could be more complex as
demonstrated by the presence of the graphene layer (Raman peak at 2700 cm-1
)
According to previous studies [31 33] this is attributed to the existence of the CSi
antisite and vacancies which form the vacancy cluster and antisite clusters after
thermal treatment at 2000 degC
The microstructure change in SiC3 coating is different from SiC1 The diffusion
mechanism in SiC3 was supposed to be involved with the interstitials since the single
SiC crystal precipitate was found out of the coating(Fig 68) This also resulted in
higher amount of the pores in SiC3 than in SiC1 after thermal treatment It is
proposed that the different diffusion mechanism found in stoichiometric SiC1 (Si and
C vacancies) and SiC3 (tetragonal interstitials) could be due to different deposition
conditions which produced different kinds of dominant native defects The larger
pores formed in SiC3 and SiC4 could be due to larger grain size than SiC1 and SiC2
(different deposition temperature) because most of pores were near to the grain
boundaries and triple junctions (as shown in Fig 63(d) (f) and (h)) The diffusion of
native defects also affects the interfacial irregularities and the diffusion mechanism in
SiC coatings is being studied in our research group
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
171
65 Conclusions
The SiC coatings deposited at temperature range of 1300-1500 degC with composition
near-to the stoichiometry were thermally treated at 2000 degC in Ar atmosphere for 1
hour to study the effect of thermal treatment on microstructure and fracture strength
The following conclusions were obtained
(1) The local (intrinsic) fracture strength decreased in a varied degree after
thermal treatment and it was due to the formation of pores along the IPyCSiC
interface and in the coatings
(2) The Weibull modulus decreased once the pores have similarbigger size
asthan interfacial irregularities and distribute uniformly within coatings while
it increased with the size of pores much smaller than interfacial irregularities
after thermal treatment
(3) After thermal treatment no phase transformation was found in SiC coatings
and the crystallographic error (2θ~335 ordm) detected by XRD was demonstrated
to be stacking faults which were annihilated during this process
(4) The formation of pores after thermal treatment was attributed to the diffusion
of intrinsic defects such as vacancies interstitials and antisites Different
content and size of pores were observed in different coatings which are
presumed to have different kinds of native defects in as-deposited coatings
produced at different conditions
(5) The vacancies are supposed to be the dominant defects in stoichiometric SiC
deposited at 1280 ordmC however in other coatings the dominant defects could
be a combination of vacancies antisites and interstitials based on Raman
results before and after thermal treatment Furthermore the diffusion of native
defects also affects interfacial roughness after thermal treatment which needs
further study
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
172
66 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook of
SiC properties for fuel performance modeling J Nucl Mater 371 (2007) 329-77
[2] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[3] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidised
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
[4] H Zhang E Loacutepez-Honorato A Javed I Shapiro P Xiao A study of the
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc (2011) DOI
101111j1551-2916201105044x
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of fracture
stress for the SiC Layer of TRISO-Coated fuel particles using a modified crush
test method Int J Appl Ceram Tech 7 (2010) 327-37
[6] G H Lohnert H Nabielek W Schenk The fuel-element of the Htr-module a
prerequisite of an inherently safe reactor Nucl Eng Des 109 (1988) 257-63
[7] I J Van Rooyen J H Neethling J Mahlangu Influence of temperature on the
micro-and nanostructures of experimental PBMR TRISO coated particles A
comparative study Proceedings of the 4th
international topical meeting on high
temperature reactor technology HTR 2008 September 28-October 1 2008
Washington DC USA HTR 2008-58189
[8] Y Kurata K Ikawa K Iwamoto The effect of heat-treatment on density and
structure of SiC J Nucl Mater 92 (1980) 351-53
[9] D T Goodin Accident condition performance of fuels for high-temperature
gas-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[10] N Shirahata K Kijima A Nakahira K Tanaka Thermal stability of stacking
faults in Beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
173
[11] J van Rooyen J H Neethling P M van Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[12] E Loacutepez-Honorato K Fu P J Meadows J Tan and P Xiao Silicon carbide
coatings resistant to attack by palladium J Am Ceram Soc 93 (2010) 4135-41
[13] E Loacutepez-Honorato H Zhang D X Yang P Xiao Silver diffusion in silicon
carbide J Am Ceram Soc 94 (2011) 3064-71
[14] D J Green An Introduction to the Mechanical Properties of Ceramics
Cambridge University Press Cambridge 1998
[15] H Zhang E Loacutepez-Honorato A Javed X Zhao J Tan P Xiao A Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc (2012) DOI101016jjeurceramsoc201112014
[16] H Tateyama H Noma Y Adachi M Komatsu Prediction of stacking faults in
βndashSilicon carbide X-Ray and NMR studies Chem Mater 9 (1997) 766- 72
[17] K R Carduner S S Shinozaki M J Okosz C R Peters T J Whalen
Characterization of β-Silicon carbide by silicon-29 solid-state NMR transmission
electron microscopy and powder X-ray diffraction J Am Ceram Soc 73 (1990)
2281-86
[18] httptfuni-kieldematwisamatdef_enkap_6advancedt6_3_2html
[19] S M Dong G Chollon C Larbrugere M Lahaye A Guette J L Brunee M
Couzi R Naslain and D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[20] M Havel D BaronL Mazerolles P Colomban Phonon confinement in SiC
nanocrystals comparison of the size determination using transmission electron
microscopy and Raman spectroscopy Appl Spet 61 (2007) 855-59
[21] V V Pujar J D Cawley Effect of stacking faults on the X-Ray diffraction
profiles of 3C-SiC powder J Am Ceram Soc 78 (1995) 774-82
[22] Y L Ward R J Young R A Shatwell Effect of excitation wavelength on the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
174
Raman scattering from optical phonons in silicon carbide monofilaments J Appl
Phys 102 (2007) 023512 -17
[23] X J Li J Hayashi C Z Li FT-Raman spectroscopic study of the evolution of
char structure during the prolysis of a victorian brown coal Fuel 85 (2006)
1700-07
[24] A C Ferrari J C Meyer V Scardaci C Casiraghi M Lazzeri F Mauri S
Piscanec D Jiang K S Novoselov S Roth A K Geim Raman spectrum of
graphene and graphene layers Phys Rev Lett 97 (2006) 187401-04
[25] S Nakashima H Harima Raman investigation of SiC polytypes Phys Stat Sol
A-Appl Res 162 (1997) 39-64
[26] GKBasal Effect of flaw shape on strength of seramics J Am Ceram Soc 59
(1976) 87-8
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] K Koumoto S Takeda CH Pai High-resolution electron microscopy
observation of stacking faults in βndashSiC J Am Ceram Soc 72 (1989) 1985-87
[29] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J Am Ceram Soc 84 (2001) 3013-16
[30] K Koumoto S Takeda C H Pai T Sato H Yanagida High-resolution electron
microscopy observations of stacking faults in β-SiC J Am Ceram Soc 72 (1989)
1985-87
[31] C Wang J Bernholc Formation energies abundances and the electronic
structure of native defects in cubic SiC Phys Rev B 38 (1998) 12752-55
[32] E Janzen N T Son B Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[33] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-09
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
175
CHAPTER 7 Microstructure and Mechanical Properties of
Pyrolytic Carbon Coatings
71 Introduction
Pyrolytic carbon (PyC) coatings forming part of the TRI-Isotropic (TRISO) fuel
particle are important for the stability of this type of nuclear fuel Without appropriate
microstructure and mechanical properties of PyC coatings the stress generated inside
the particle due to internal gas pressure andor the dimensional change (anisotropic
shrinkage or creep) introduced in this layer during irradiation process could result in
the failure of the full particle [1-5] Fundamental understanding about relationship
between mechanical properties and microstructure of PyC coatings could help to
analyse the failure mechanism and model the probability of failure of TRISO fuel
particles [1 5] However their relations in PyC are complex [3 6-8] Kaae [7] found
that mechanical properties were related to the density crystal size and anisotropy but
they are not controlled by a single variable For example Youngrsquos modulus increased
with density for isotropic carbons with constant crystallite size but decreased with
increasing anisotropy for carbon with constant density and crystalline size In a
separate work [3] density had a dominant effect on the hardness and Youngrsquos
modulus in relative low density PyC coatings whereas no controlling factor was
given for high density PyC coatings
Nano-indentation is an effective way to study microstructural effects on mechanical
properties of PyC coatings because it could help with the understanding of the
deformation mechanism and measure Youngrsquos modulus and hardness spontaneously
Among studies on mechanical properties in carbon related materials under
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
176
depth-sensing indentation [3 9-15] few explanations about the nature of their
deformation mechanism have been discussed [9 10 13 15] First the hysteresis was
assumed to due to the slip of graphene layers in nano-meter grains and the energy
loss was attributed to the friction between graphene layers under compression stress
[9 10] Second the dislocation pileups were assumed to be responsible for energy
loss [13] but this idea failed to account for the reversible deformation [15] The most
recent theory suggested that the origin of the hysteresis was due to the formation of
(incipient) kink bands [15] This theory was found to be a universal explanation for
most laminar structured materials but the nature of initial kink band was not clear
[15]
During pressing process of TRISO fuel particles into fuel elements they experience a
final thermal treatment of 1 h above 1800 ordmC to drive off any residual impurities and
improve thermal conductivity of the fuel compact [16] The evolution of
microstructure of carbon related materials have been widely studied [17-20] Few
researches measured changes of mechanical properties after thermal treatment [19
20] but there is a lack of understanding about effect of microstructural evolution on
mechanical properties in PyC coatings Therefore in this Chapter together with the
microstructural properties the deformation mechanism under indentation influences
on mechanical properties and their change after thermal treatment in PyC coatings are
studied
72 Experimental details
Pyrolytic carbon (PyC) was coated on alumina particles (Φ 500 μm) by fluidised bed
chemical vapour deposition by Dr Eddie Loacutepez-Honorato and PyC coatings with
different density was chosen to study the mechanical properties Table 61 gives the
density and texture (orientation angle) of PyC coatings and more about deposition
mechanism could be found in Ref [21] The number of sample sequence Ci (i=1
2hellip11) starts from highest density to lowest density with density of 19 gcm3 as
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
177
border line to distinguish highlow density PyC which was measured by the
Archimedes method in ethanol For thermal treatment the coatings were first
grounded into fragments and then removed the alumina kernel The fragments of PyC
were then thermal treated at 1800 degC and 2000 degC for 1 hour in argon atmosphere For
further understanding of microstructural evolution during thermal treatment sample
C5 was thermal treated at 1300 1400 1500 and 1600 degC for 1 hour
Table 71 PyC coatings with different density and orientation angle
PyC
(High density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
PyC
(Low density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
C1 2122plusmn0059 58 C6 1855plusmn0050 63
C2 2087plusmn0183 37 C7 1738plusmn0013 73
C3 2047plusmn0030 60 C8 1635plusmn0008 71
C4 2029plusmn0015 43 C9 1603plusmn0024 71
C5 2000plusmn0061 43 C10 1414plusmn0002 85
C11 1400plusmn0024 81
Orientation angle was obtained from the full width of half maximum of azimuthal intensity scan of
SAED pattern for more information in Ref [22] Productions of PyC coatings measurement of
orientation and density measurement are contributed by Dr Eddie Loacutepez-Honorato et al
The selected area electron diffraction (SAED) patterns were obtained with the use of a
FEG-TEM (see Chapter 3) and orientation angle was measured by the azimuthal
intensity scans of SAED pattern (selected aperture diameter of 200 nm) Further
details about this measurement were shown in a previous study [22] Transmission
electron microscopy (TEM) samples were obtained by focus ion beam milling High
resolution TEM samples were prepared by dispersing the fragments on a carbon holey
film copper grid X-ray diffraction (see Chapter 3) was used to obtain domain sizes of
PyC coatings After correction of intrinsic instrumental effect the out of plane and
in-plane domain sizes (along c-axis and a-axis in graphite crystal structure) Lc and La
were qualitatively estimated from XRD data by applying the Scherrer equation to the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
178
(002) and (110) reflections respectively [23] In as-deposited PyC coatings the (110)
peak was too weak to estimate accurately on the La Raman spectroscopy (633 nm
Helium ion laser source) was performed by single spot measurements (spot size was
carefully controlled to be the same for each test) of around 2 μm diameter using a times50
objective lens The laser power of less than 05 mW (10) was used with the step
size of 60 seconds and twice accumulations For each sample 5 different positions
were measured The band fitting of the first order spectra was carried out with
GRAMS32 software
To reduce the influence of surface roughness on indentation test the PyC coatings
were ground with successive finer grades of SiC paper and polished down to a 1 microm
grid diamond paste The same nano-indentation as in Chapter 3 was used The
measurements were performed at fixed loading rate of 1 mNS reaching the
maximum load of 100 mN For each coating at least 25 indentations were conducted
on the sample surface to increase the reliability of the results The Olive and Pharr
method [24] was used to analyse all the data
73 Results
731 Microstructure of PyC coatings
In order to study the influences of microstructure on mechanical properties it is
necessary to know the nature of structure which makes one sample from another eg
disorders domain size crystallinity etc and their evolution after thermal treatment
7311 Raman spectroscopy
Figure 71 is a Raman spectroscopy for an as-deposited high density PyC coating (C5
200 gcm3) which exhibits two relatively broad Raman bands at around 1335 cm
-1
and 1600 cm-1
The first band corresponds to the D band which is attributed to double
resonant Raman scattering and represents the in-plane defects [21 25 26] The
second band is an overlap of broadened G (1580 cm-1
) and D (1620 cm-1
) bands due
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
179
to high disordered pyrolytic carbon [27] The G band is due to the stretching modes of
pairs of sp2 atoms in graphene planes whereas D represents the similar defects
structure as the D band [18 27] It is convenient to consider 1600 cm-1
band a single
G peak for practical purposes when comparing different samples or the overall
structural evolution of a given PyC coating [27]
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
According to previous studies [25-32] on fitting similar Raman spectra shown in Fig
71 a simple two-symmetric-line fit (D and G bands) could not fit it well Therefore
the Raman spectra of high density PyC coatings (C1-C5 gt 19 gcm3) were
deconvoluted into above peaks at about 1220 cm-1
1335 cm-1
1500 cm-1
and 1600
cm-1
( Fig 71) The band at about 1500 cm-1
(Drsquorsquo) is attributed to interstitial defects
which could act as coupling (covalent band) between two graphene layers or adjacent
overlapped domains [25 28] The I band at around 1220 cm-1
is due to C-C on hydro
aromatic rings [28] The Raman spectra mean the high degree of in-plane andor
out-of-plane disorders in high density PyC coatings represented mainly by the full
width at half maximum (FWHM) of the D band [28] and intensity ratio (the area ratio
of the 1500 cm-1
peak to the sum of four peaks shown in Fig 71) of the Drdquo bands
[25] respectively
D
I
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
180
Figure 72 is the Raman spectra of high density PyC coating C5 after thermal
treatment at temperature of 1300 1400 1600 and 1800 ordmC The FWHM of the D band
decreased significantly from about 150 cm-1
(as-deposited) to about 106 cm-1
(1400
ordmC) and then to about 40 cm-1
(1800 ordmC) Similarly the intensity ratio of the Drdquo was
reduced from about 0135 (as-deposited) to about 0110 (1400 ordmC) and then to about
0078 (1800 ordmC) Another change is the split of G and D bands after thermal treatment
at 1800 ordmC (Fig 72) The above changes indicate that disorders in high density PyC
coatings are low energy structural defects ie degree of disorder is low according to a
previous study [28]
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
181
After thermal treatment the degree of microstructural changes of low density PyC
coatings C6-C8 (164-186 gcm3) is slightly different from even lower density
coatings C9-C11 (140-160 gcm3) so they are described separately Figure 73 shows
Raman spectra of low density PyC coatings (a) C7 and (b) C10 before and after
thermal treatment at 1800 ordmC Similar to high density PyC the as-deposited coatings
C6-C8 contains four Raman bands After thermal treatment the FWHM of the D peak
in C7 decreased from about 120 cm-1
to 57 cm-1
and the intensity ratio of interstitial
defects was also reduced (from 0116 to 0042 Fig 73(b)) In coating C10 only
slightly decrease of FWHM of the D peak (from about 83 cm-1
to 57 cm-1
) was found
after thermal treatment at 1800 ordmC (Fig 73(b)) No split of the G and D bands was
observed in low density PyC coatings
With increase in density of PyC the FWHM of the D band the concentration of the
Drdquo band and the degree of their changes after thermal treatment increase considerably
which suggest that the disorder defects in PyC are different with variation of density
and thermal treatments change the degree of the disorder
7312 Domain sizes
Table 72 summarises the out-of-plane domain size (crystallite size perpendicular to
the graphene plane Lc) and in-plane domain size (crystallite size along the graphene
plane La) measured by XRD in PyC coatings before and after thermal treatment The
Lc is in the range of 1-3 nm in all the as-deposited coatings and it is slightly bigger in
high density (about 2-3 nm) coatings than low density (about 1-2 nm) coatings After
thermal treatment at 1800 ordmC the Lc increased significantly which is about 5 times
and 2-3 times larger than in as-deposited high density and low density PyC coatings
respectively It is 2-4 times larger in high density PyC than low density PyC coatings
The La in high density (about 6 nm) is larger than low density PyC coatings (3-4 nm)
after thermal treatment at 1800 ordmC Both Lc and La remained unchanged after thermal
treatment at 2000 ordmC in all PyC coatings (This is explained in section 741) The
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
182
increase of domain size indicated the ordering process in PyC coatings after thermal
treatment which may involve annealing of different kinds of disorders
Table 72 Domain size of as-deposited and thermal treated PyC coatings
Sample As deposited 1800 2000
Lc (nm) La (nm) Lc (nm) La (nm) Lc (nm) La (nm)
High density (gt19 gcm3)
C1 21 -- 112 -- 116 53
C2 21 -- 132 63 154 69
C3 22 -- 98 66 111 63
C4 24 -- 95 57 118 63
C5 20 -- 120 60 152 73
Low density (lt 19 gcm3)
C6 22 -- 50 42 56 44
C7 18 -- 38 36 50 34
C8 14 -- 31 33 27 39
C9 11 -- 27 32 31 34
C10 17 -- 24 33 27 35
C11 11 -- 27 35 27 33
7313 Evolution of crystallinity
Figure 74 is the TEM images of high density PyC (C5) before and after thermal
treatment The dark field TEM show bright areas (Fig 74(a) and (b)) that represent
graphene layers with similar orientation in the selected direction of the diffraction
pattern A decrease of the orientation angle from 43 ordm to 25 ordm is found after thermal
treatment at 1800 ordmC which is obtained from the full width at half maximum of
azimuthal intensity scan of SAED pattern (insets in Fig4(a) and (b)) A bright field
TEM image of a conical microstructure after thermal treatment (Fig 74(c) dashed
rectangle in Fig 74(b)) which shows the voids at the top of conical structures The
above observations show that thermal treatment increases anisotropy and results in the
volume shrinkage and generation of voids in high density PyC coatings
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
183
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Figure 75 is the typical HRTEM away from the top of conical growth feature (eg
OA=43 ordm
OA=25 ordm
Top
Voids
100 nm
(c)
(a) (b)
5 nm
Moireacute
fringes
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
184
white circle in Fig 74(c)) in high density PyC coatings (C1) before and after thermal
treatment at 1800 ordmC The wrinkled short graphene fringes in as deposited high
density PyC (Fig 75(a)) were replaced by distorted planes in a larger scale with a
bigger radius of curvature (white arrow in Fig 75(b)) The common number of
parallel layers (Fig 75(a) (002) plane white parallel lines) is 2-4 in as-deposited C1
which increased to about 30 (Fig 75(b) between white parallel lines) The moireacute
fringes were observed after thermal treatment (black arrow in Fig 75(b)) which
correspond to black bars in the bright field TEM (eg dashed black rectangle in Fig
74(c)) According to the generation mechanism of moireacute fringes [33] the on-going
ordering process along the c-axis is related to the increase of number of parallel layers
and evolution (decrease) of the inter plane distance of (002) planes
Figure 76 gives the bright field TEM and HRTEM images showing the
microstructure evolution in a low density PyC coating (C7) Globular growth features
with diameters of about 400 nm were observed in as-deposited C7 as shown in Fig
76(a) and the HRTEM image shows 2-3 layers of parallel planes (Fig 76(b)) In low
density PyC coatings the graphene fringes are longer and less oriented than in high
density coatings (reflected from orientation angle shown in Table 71 and Fig 13 in
Ref [21]]) After thermal treatment the short dark bars andor dots (as indicated by
the white arrows Fig 76(c)) were observed which is due to the moireacute fringes as
shown in Fig 76(d) The number of parallel layer increased up to 8-10 (Fig 76(d))
and it reflects the slight crystallinity after thermal treatment In the other low density
PyC coatings C9-C11 the TEM images are similar with the as-deposited low density
PyC coatings (as shown in Fig 14 and Fig 13(c) in Ref [21]) Furthermore the
orientation angle is almost the same in all low density PyC before and after thermal
treatment
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
185
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
732 Mechanical properties of PyC coatings
7321 Force-displacement curve
Figure 77 gives the force-displacement curve of PyC coatings with different density
under the maximum load of 60 mN and 100 mN by nano-indentation The unloading
curve did not completely retrace the loading curve but still returned to the origin This
process is called anelastic behaviour or hysteresis behaviour and the anelastic
reversible indentation processes with an enclosed loop are found in all the PyC
coatings
(a) (b)
100 nm 5 nm
5 nm
Sphere-like
particle
Tops
Moireacute fringes Sphere-like
particle
Top (d)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
186
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
The maximum indentation depth in low density PyC (C6-C11 lt 19 gcm3) is deeper
than in high density PyC coatings (C1-C5 gt 19 gcm3) under the same load and the
low density PyC also shows larger hysteresis loop area The ratio of the hysteresis
energy (area within the loading-unloading loop) to total loading energy (area under
loading curve) in high density PyC is lower than in low density PyC coatings For
example the ratios of sample C3 C9 and C11 are 0243 0270 and 0292 respectively
Furthermore the deformation behaviour of all PyC coatings showed the hysteresis
behaviour after thermal treatment up to 2000 ordmC The high density PyC after thermal
treatment at 1800 ordmC (red curve in Fig 77) shows anelasticity however the ratio of
its hysteresis energy (0249) is much higher than in as-deposited coating (0174)
According to previous studies [10 34] the low ratio obtained in high density PyC
coatings under pyramidal indenter corresponds to high elasticity while low density
exhibits high hysteresis (anelasticity high viscosity))
Under indentation the hardness is defined as the mean pressure the material will
support under load according to Oliver and Pharrrsquos study [24] This pressure is equal
to the load at maximum load divided by the contact area (according to eqs (7 10 11)
hc
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
187
in Chapter 2) However the residual depth hf is zero and no pleastic deformation is
observed after unloading The hardness obtained by Oliver and Pharr method does not
reflect the resistance of plastic deformation of material but it could represent the
degree of unelastic deformation qualitatively Therefore the mean pressure (P) value is
used which could reflect the anelastic properties of PyC coatings
7322 Youngrsquos modulus and the mean pressure
Figure 78 gives the Youngrsquos modulus (E) and the mean pressue (P) of as-deposited
PyC coatings as a function of density For low density PyC coatings (C6-C11 lt 19
gcm3) Youngrsquos modulus and the mean pressure increase almost linearly with the
density For high density PyC coatings (C1-C5 gt 19 gcm3) both Youngrsquos modulus
and the mean pressure reach plateaus which are independent of density It indicates
that mechanical properties of high PyC coatings are dominated by other factors
which are discussed in session 744
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
Table 73 shows the Youngrsquos modulus and the mean pressure of PyC coatings with
different density before and after thermal treatment at 1800 and 2000 ordmC After
thermal treatment at 1800 ordmC Youngrsquos modulus decreased by around 50 and the the
mean pressure is reduced by around 69 in high density PyC coatings (C1-C5 gt19
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
188
gcm3) whereas minor change is observed when thermal treatment temperature
further increased to 2000 ordmC Previous study [20] showed similar results about
changes of mechanical properties in high density PyC after thermal treatment at
different temperature In low density PyC coatings C6-C8 (164-186 gcm3) the
mean pressure and Youngrsquos modulus decreased by about 23 and 8 after thermal
treatment at 1800 ordmC respectively which is consistent with Rooyen et alrsquos results
[19] and further decreased by 18 and 15 by increasing thermal treatment
temperature to 2000 ordmC In low density coatings C9-C11 (140-160 gcm3) little
change in mechanical properties after thermal treatment up to 2000 ordmC was found and
it is similar as the isotropic low density PyC [20] Mechanical properties and their
change after thermal treatment in PyC coatings are different with different density
Table 73 Changes of mechanical properties of PyC coatings after thermal treatment
Sample As deposited Thermal treated at 1800 Thermal treated at 2000
P (GPa) E (GPa) P (GPa) E (GPa) P (GPa) E (GPa)
High density
C1 468plusmn025 2670plusmn119 103plusmn018 1482plusmn131 090plusmn013 1337plusmn093
C2 435plusmn048 2513plusmn117 132plusmn019 1091plusmn069 076plusmn021 1204plusmn126
C3 490plusmn036 2878plusmn117 -- -- 091plusmn026 1271plusmn125
C4 397plusmn019 2291plusmn076 171plusmn010 1313plusmn034 110plusmn010 1370plusmn051
C5 456plusmn010 2610plusmn036 132plusmn015 1177plusmn051 177plusmn025 1361plusmn101
Low density
C6 388plusmn035 2165plusmn191 296plusmn022 1912plusmn113 244plusmn023 1647plusmn088
C7 395plusmn053 2149plusmn200 292plusmn036 1934plusmn114 232plusmn033 1568plusmn182
C8 354plusmn027 1945plusmn070 292plusmn036 1904plusmn113 232plusmn063 1678plusmn240
C9 284plusmn040 1938plusmn094 226plusmn057 1677plusmn178 263plusmn042 1733plusmn151
C10 189plusmn009 1266plusmn035 213plusmn019 1363plusmn076 188plusmn023 1381plusmn087
C11 168plusmn017 1166plusmn082 178plusmn034 1284plusmn106 086plusmn014 1167plusmn151
74 Discussions
The main findings of this study can be summarised as follows 1) PyC with different
density show different full width at half maximum (FWHM) of the D band and
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
189
concentration of the Drsquorsquo band which suggests that they have different types of disorder
TEM observation shows longer graphene fringes with lower density PyC (Fig 13 in
Ref [21]) thermal treatments decrease the degree of disorder while PyC with higher
density (gt19 gcm3) shows higher degree of decrease 3) initial increase in PyC
density until 19 gcm3 lead to proportional increase in Youngrsquos modulus (E) and the
mean pressure (P) while further increase in density has no effect on E and P 4)
hysteresis occurred after nano-indentation of PyC while the degree of hysteresis is
controlled by the PyC density and heat treatments
741 Disorders and their changes after thermal treatment
High density PyC Coatings (C1-C5 gt 19 cmg3) The dominant in-plane disorders
are domain boundaries according to a previous study [21] which generates high
FWHM of the D band due to the low energetic disorientations (eg domains andor
graphene layers) [25 28] The Drsquorsquo band (interstitial defects) is due to the amorphous
carbon structure which is composed of mainly disordered sp2 atoms and a low
amount of sp3 atoms [27 28 35] Particularly the sp3 lines are out of plane defects
which could be formed in high density PyC coatings [36] Therefore it is assumed
that the microstructure in high density PyC is composed of disoriented nano-size
graphite domains connected by amorphous carbon
After thermal treatment the reductions of the out-of-plane defects and the tilt and
twist in graphite planes are observed which could contribute to the increase of Lc
(out-of-plane domain size) as shown in HRTEM image (Fig 75) It was supposed
that the equilibrium shear stress were generated by in-plane defects and out-of-plane
defects in PyC coatings [25] once the out-of-plane defects was reduced the in-plane
stress would tend to straighten the graphite planes Furthermore the decreases of
FWHM of the D band and the orientation angle (Fig 72 and 4) show the ordering
arrangement of graphite layers is due to the healing of in-plane disorientations The
unchanged domain size Lc could be a result of a combination of increased number of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
190
parallel graphene layers and decreased inter distance of (002) plane As a conclusion
the increase of domain size Lc could be due to the coalescence of domain size andor
graphene layers through reorientation and remove of interstitial defects which
usually started at temperature of about 900-1200 ordmC [17 25] No La (in-plane domain
size) value was obtained in as-deposited PyC and the overlap of the G and the Drsquo
bands indicates it is below 4 nm above which two bands split [37] After thermal
treatment at 1800 ordmC the La is about 6 nm in high density PyC coatings (Table 72
and splitting of G and Drsquo bands was shown in Fig 72) which demonstrates the
slightly increase of La It is attributed to the annihilation of low energetic in-plane
disorientations which could usually be removed at temperature above 1500 ordmC [25]
Since the high temperature above 2000 ordmC is needed to remove the rest high energetic
in-plane defects for high density PyC according to previously study [25 28] it could
explain the La remained nearly constant after thermal treatment further increased to
2000 ordmC The ordering of graphite layers is responsible for the formation of voids (Fig
74(c)) since the ordering could reduce the volume and increase the density of PyC
coatings after thermal treatment [38]
Low density PyC Coatings (C6-C11 lt 19 cmg3) The main defect is the
5-memebered rings in coatings C9-C11 by comparing the Raman spectroscopy (Fig
73(a)) with a previous study [21] In low density coatings C6-C8 (164-186 gcm3)
the degree of in-plane disorder is less than in high density coatings but higher than
coatings C9-C11 (140-160 gcm3 indicated by the FWHM of the D band) and the
out-of-plane defects are much higher than low density PyC coatings (Fig 73) After
thermal treatment the in-plane disorder is similar as in coatings C9-C11 Therefore
the dominant in-plane defects are supposed to be a combination of domain boundaries
and 5-membered rings The slightly increase of domain size Lc in low density PyC
coatings is due to the decrease of interfacial defects through reorientation of domains
However they have much lower degree of increase of Lc than high density coatings
this could be due to low anisotropy in low density PyC coatings which makes it
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
191
difficult to reorient domains and remove the weak defects [17 25] The domain size
La was assumed to be unchanged since ordering in-plane disorders took place at
temperature above 2400 ordmC in low density PyC due to presence of 5-member rings
[17] It is worth to notice that the graphene fringes do not represent the in-plane
domain size in low density PyC due to the curvature caused by 5-memebered rings
[21] Due to the exist of 5-membered rings in low density PyC coatings the
microstructure is lightly affected by thermal treatment
742 Hysteresis after indentation
The increase in density of PyC leads to decrease in hysteresis after indentation and
density of PyC also dominate types and degree of disorders During indentation of
PyC hysteresis is caused by the slip of graphene planes whereas the disorders such as
interstitial defects or 5-memebered rings are supposed to be responsible for the
reversible deformation The hysteresis was also observed in other carbon materials
such as single crystal graphite [15] polycrystalline graphite [15] glassy carbon [9
10] Similar explanations about the effect of slip of graphene layers on the hysteresis
behaviour under indentation were given and it suggests that the deformation
mechanism is related to a common structure in different carbon materials which are
graphene planes
The slip of graphene planes has been demonstrated available The shear modulus (micro)
of graphite is 23 GPa (between graphene layers) [39] Based on the relation of τth= micro
30 [39 40] the theoretical shear stress (τth) of graphite is estimated to be 0077 GPa
This shear stress is much lower than the yield stress under Berkovich indenter for
graphite (03-05 GPa) [15] Under indentation the slip of graphene planes consumes
energy but recovers to the original shape after unload Lower density PyC has longer
fringes than that in higher density PyC (Fig 13 Ref [21]) therefore the panes can
slip for a longer distance under shear stresses generated by nano-indentation
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
192
Reversible deformation is due to presence of interstitial defects or highly curved
5-memebered rings For indentation of crystallite graphite the kink band could be
generated during the initial indentation process then reviersible deformation occurs
under further indentation [15] similar as that shown in Fig 77 In our PyC coatings
disorder in the PyC plays a similar role as the kink band in the crystallite graphite
The slip direction is parallel to the graphene planes so the in-plane defects presents at
the tilt and twist of two adjacent domains could not stop and reflect the slip Only
those defects perpendicular to the slip direction can contribute to the reversible
deformation such as interstitial defects or the highly curved 5-memebered rings
(caused fibrous graphene planes as shown in Fig 13(c) Ref [21])
After heat treatment the growths of the in-plane fringes increase the degree of the
hysteresis in PyC coatings For example the straightened graphene fringes (Fig 75)
caused by reorientation and removes of interstitials facilitate the hysteresis
significantly (the ratio of hysteresis energy to total loading energy increased from
0174 to 0249 Fig 77)
743 Mechanical property of low density PyC coatings
In as deposited low density PyC (C6-C11 gt 19 gcm3) Youngrsquos modulus and the
mean pressure are dominated by the density which is consistent with previous studies
[3 7 41] because of the effect of porous structure [3 21] As discussed in session
741 the disorders in low density PyC coatings play an important part on the stability
of microstructure which could reflect changes of mechanical properties After thermal
treatment the mechanical properties remained almost unchanged in PyC coatings
C9-C11 (140-160 gcm3) and this could be explained by the insignificant change of
microstructures at the presence of 5-membered rings The slightly decrease of
mechanical properties were found in coatings C6-C8 (164-186 gcm3) which is due
to the ordering of graphene planes through reduction of interstitial defects which
could enhance hysteresis and decrease the mean pressure No voids and change of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
193
orientation was observed after thermal treatment in coatings C6-C8 so Youngrsquos
modulus is slightly affected It is concluded that the mean pressure and Youngrsquos
modulus are functions of density in as-deposited low density coatings and their
evolution after thermal treatment is controlled by disorders such as interstitials andor
5-membered rings
744 Mechanical Property of high density PyC coatings
In high density PyC coatings (C1-C5 gt 19 gcm3) Youngrsquos modulus and the mean
pressure are independent of density so they are discussed regarding to variation of
texture domain size and concentration of interstitial defects (the area ratio of the 1500
cm-1
peak to the sum of four peaks shown in Fig 71) Table 74 summarises
microstructure parameters and mechanical properties of high density PyC coatings
Mechanical properties are not controlled by domain size and orientation angle which
is converse to the previous study [41] It is found that Youngrsquos modulus and the mean
pressure in high density PyC coatings decrease with the reduction of concentration of
interstitial defects (as shown in Table 74)
Table 74 The parameters used to explain different mechanical properties of high
density PyC (C1-C5 gt 19 gcm3)
Sample Density
(gcm3)
Texture
OA (deg)
Domain
size (nm)
IinterstialAll Pressure
(GPa)
Modulus
(GPa)
C3 2047 plusmn0030 60 22 013955plusmn000374 490plusmn036 2878plusmn117
C1 2122 plusmn0059 58 21 013513plusmn000399 468plusmn025 2670plusmn119
C5 2000 plusmn0061 43 20 013456plusmn000561 456plusmn010 2610plusmn036
C2 2087 plusmn0183 37 21 013036plusmn000433 435plusmn048 2513plusmn117
C4 2029 plusmn0015 43 24 011823plusmn001628 397plusmn019 2291plusmn076
The physical meaning of the above observation can be explained by the effect of
interstitial defects on the deformation mechanism in high density PyC coatings First
the high concentration of interstitial defects could reduce the energy consumption by
the reversible slip of graphene planes (eg in Fig 77) and it corresponds to high the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
194
mean pressure in high density PyC coatings Second in-plane Youngrsquos modulus is
much higher than out-of plane Youngrsquos modulus in graphite so the bonding between
graphene planes becomes important when the orientation effect could be neglected in
high density PyC (Table 74) For example in sample C4 and C5 the high Youngrsquos
modulus was obtained in C5 which have high amount of covalent band (interstitial
defects sp2 and sp3 in Fig 71) in the direction perpendicular to graphene planes The
high concentration of interstitial defects in high density PyC could also reduce the
influences of orientation angle on the high Youngrsquos modulus This could explain the
similar Youngrsquos modulus in C1 and C5 which have different orientation angles
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
After thermal treatment at temperature range of 1300-1800 ordmC in C5 (about 200
gcm3) the effect of concentration of interstitial defects on mechanical properties was
again demonstrated as given in Table 75 The mechanical properties decrease
gradually with the increase of thermal treatment temperature until 1600 ordmC and then a
dramatic decrease at 1800 ordmC The decrease is related to the reduction of content of
interstitial defects (Table 75) Furthermore no other relationship between mechanical
properties and microstructural features such as FWHM of the D band intensity of D
band and G band in Raman spectroscopy is found in the current work Therefore the
concentration of interstitial defects is proposed to dominant mechanical properties of
high density PyC coatings This idea about effect of interstitial defects on mechanical
properties is similar as the cross-link theory [8] which suggested that the mechanical
properties is related to the length and number of links between domains Furthermore
Temperature (ordmC) IinterstialAll Pressure (GPa) Youngrsquos modulus (GPa)
0 013456plusmn 000561 456plusmn010 2610plusmn 036
1300 011882plusmn000906 430plusmn010 2519plusmn060
1400 011045plusmn000278 413plusmn010 2407plusmn070
1500 009598plusmn000034 406plusmn022 2439plusmn070
1600 009469plusmn000219 391plusmn016 2344plusmn036
1800 007756plusmn000199 132plusmn015 1177plusmn051
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
195
the significant decrease of the the mean pressure and Youngrsquos modulus after 1800 ordmC
could be due to the straightening of graphene layers and formation of voids (Fig
74(c)) respectively To conclude the mechanical properties in high density PyC
coatings before and after thermal treatment from 1300 to 1800 ordmC decrease with the
reduction of concentration of interstitial defects
74 Conclusions
Disorders in PyC coatings was characterised by Raman spectroscopy A
combination of high degree of in-plane (domain boundaries) and out-of plane
defects (interstitial defects) prevail in high density PyC while the 5-membered
rings are dominant defects in low density PyC coatings
In high density PyC coatings the significant increase of domain size Lc is
attributed to the coalescence of domainsgraphene layers through reorientation and
reduction of interstitial defects During this process the graphene planes were
straightened resulting in slightly increase of La
In low density PyC coatings the microstructure remained almost unchanged after
thermal treatment due to the presence of the 5-membered rings which need high
temperature to be reduced
The hysteresis deformation behaviour was found in all PyC coatings before and
after thermal treatment under nano-indentation The nature of hysteresis is
suggested to be Slip of graphene planes consumes energy (hysteresis loop) and
disorders (interstitial defects and highly curved 5-memebered rings in high density
and low density PyC coatings respectively) are responsible for the reversible
deformation (unloading curve back to origin)
The mean pressure and Youngrsquos modulus are functions of density in low density
PyC coatings and their changes after thermal treatment are insignificant which
are due to the almost unchanged microstructure
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
196
In high density PyC coatings the mean pressure and Youngrsquos modulus are
independent of density orientation angle and domain size but they are related to
the concentration of interstitial defects After thermal treatment the decrease of
mechanical properties is attributed to the reduction of interstitial defects leading
to the straightening of graphene planes and formation of voids
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
197
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CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
198
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CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
199
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200
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[35] T Jawhari A Roid J Casado Raman spectroscopic characterization of some
commercially available carbon black materials Carbon 33 (1995) 1561-5
[36] G L Dong K J Huumlttinger Consideration of reaction mechanisms leading to
pyrolytic carbon of different textures Carbon 40 (2002) 2515-28
[37] A Jorio E H Martins Ferreira M V O Moutinho F Stavale C A Achete R
B Capaz Measuring disorder in graphene with the G and D bands Phys Status
Solidi B 247 (2010) 2980-82
[38] R Piat Y Lapusta T Boumlhlke M Guellali BReznik D Gerthsen TChen R
Oberacker M J Hoffmann Microstructure-induced thermal stresses in pyrolytic
carbon matrices at temperatures up to 2900 ordmC J Eur Ceram Soc 27 (2007)
4813-20
[39] J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[40] A H Cottrell Dislocations and plastic flow in crystals Clarendon Press Oxford
1972 p 162
[41] J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
CHAPTER 8 Conclusions and Future Works
201
CHAPTER 8 Conclusions and Future Works
This work provides both fundamental understanding and techniqual guidance on the
mechanical properties and their relationship with microstructures of SiC and PyC
coatings in TRISO fuel particles The measurement of hardness and Youngrsquos modulus
of SiC coatings could be used in the modelling work to study the peroperty of the
failure of the fuel particlues and these results have been published The measurement
of the fracture toughness of SiC in TRISO fuel particle has solved one of the
techniqual problems in field and the study contributes to the study of the fracture
behaviour of SiC coatings The fracture strength measurement has enriched the
strength data of SiC coatings before and after thermal treatment (related paper is
under revision) The characterisation of the interfacial roughness has provided a direct
method to correlate the relationship between fracture strength and interfacial
roughness The mechanical properties of PyC coatings provide foundamental
understanding about the deformation mechanism of the PyC coatings under
indentation The effect of thermal treatment on the mechanical properties has given a
preguidance about the behaviour of the PyC coatings at high temperature
81 Conclusions
(1) In SiC coatings deposited at 1300 ordmC by fluidised bed chemical vapour deposition
the Youngrsquos modulus was an exponential function of the porosity and the high
hardness was attributed to the high density of dislocations and their interactions
The initiation and propagation of micro cracks under the confined shear stress was
found to be responsible for the mechanism of plastic deformation Based on this
hardness-related plastic deformation mechanism the variation of hardness in the
three types of SiC coating was due to different grain morphologies
CHAPTER 8 Conclusions and Future Works
202
(2) The fracture beneath the Vickers indenter consists of Palmqvist cracks as
observed using SEM in above SiC coatings Based on this crack mode Vickers
indentation fracture toughness values of 351-493 MPa m12
were obtained It was
found that stress-induced micro-cracks seem to be a mechanism for the fracture
behaviour The presence of defects such as nano-pores and less constraint grain
boundaries could generate more micro cracks which dissipated energy from the
main cracks
(3) Fracture strength measured by modified crush test give less scattered values
within a given sample by distributing the load under a contact area It has been
found that Weibull modulus and fracture strength of the full shell were
significantly affected by the ratio of radius to thickness of the coating and both of
them decrease linearly with the increase of this ratio
(4) The numericalstatistical analysis was able to characterize the interfacial
roughness of different coatings and the roughness ratio representing the
irregularities was proposed to be a unique parameter for this description The
difference of the local (intrinsic) fracture strength was dominated by the
roughness ratio and it decrease linearly with the increase of the roughness ratio
The roughness ratio has the similar effect on the difference of fracture strength of
the full shell
(5) After heat treatment at 2000 degC the local fracture strength was reduced due to the
formation of pores in the coatings which could act as the enlarged critical flaw
size The Weibull modulus decreased when the pores in SiC coatings became
critical flaws while it increased once more uniformly distributed critical flaws
along the IPyCSiC interface were formed The formation of pores was mainly
related to the annihilation of stacking faults and diffusion of intrinsic defects such
as vacancies interstitials and antisites
CHAPTER 8 Conclusions and Future Works
203
(6) The hysteresis deformation mechanism was proposed to be due to the slip of
graphene planes which constraint by interstitial defects and highly curved
5-membered rings in high density and low density PyC coatings respectively
(7) The hardness and Youngrsquos modulus were related to the concentration of
interstitial defects and density in high density and low density PyC coatings
respectively Their changes in high density PyC is more significant than in low
density PyC coatings after heat treatment over 1800 ordmC due to the annihilation of
interstitial defects and reorientation of graphene layers
82 Suggestions for future work
(1) According to current study high amount of native defects were found in SiC
deposited at low temperature and it would be interesting to study their effects on
the thermal stability in a certain range of temperature such as from 1200-2000 ordmC
The study of the diffusion of native defects in SiC could also assist the study of
diffusion behaviour of fission products because these defects are more active and
they tend to reach the equilibrium during annealing process Due to different
deposition conditions the dominant species of native defects could be different in
different coatings therefore it is also important to study the deposition effect on
thermal stability of SiC coatings
(2) Itrsquos important to know how the microstructure change of SiC coatings deposited at
low temperature after irradiation because they showed robust mechanical
properties and high resistance to fission products It has been found they have high
amount of dislocations and stacking faults which accompanied by interstitials and
vacancies as reflected from the enlarged lattice constant According to this it is
supposed that after irradiation the volume change of SiC will be small because of
the pre-exist lattice defects Therefore study of the irradiation effect (at different
operational temperature) on SiC deposited at low temperature would be
promising
CHAPTER 8 Conclusions and Future Works
204
(3) Although current study has proposed to use self-affine theory to characterize the
interfacial roughness more work about their effects on fracture strength need to
be explored For example find out if the derived linear function between
roughness ratio and fracture strength in the current study could be used to explain
the differences of fracture strength in other tests To do further demonstration it is
necessary to reduce the geometrical influence and choose SiC coatings has
similar microstructure but different IPyCSiC interface These samples could be
prepared by just changing the deposition condition of IPyC while keep it same for
SiC coatings
List of Contents
2
List of Contents
List of Contents 2
Abstract 6
Declaration 7
Copyright Statement 8
Acknowledgement 9
List of Figures 10
List of Tables 17
CHAPTER 1 Introduction 19
11 TRI-Isotropic (TRISO) fuel particles 19
12 Failure mechanism 21
121 Traditional pressure vessel failure mode 21
122 Stress concentration mode 22
13 Goals of dissertation 24
14 References 26
CHAPTER 2 Literature Review 28
21 Introduction 28
22 Microstructure of silicon carbide 29
221 Atomic structure 29
222 Defects in SiC 31
2221 Stacking faults and dislocations 31
2222 Non-stoichiometric and point defects 36
23 Properties of silicon carbide 41
231 Youngrsquos modulus 41
232 Hardness 45
233 Fracture toughness 52
234 Fracture strength 55
235 Effect of thermal treatment on SiC 59
24 Microstructure and properties of pyrolytic carbon 60
241 Microstructure of pyrolytic carbon 61
242 Mechanical properties of pyrolytic carbon 65
List of Contents
3
2421 Youngrsquos modulus and hardness 65
2422 Deformation mechanism 67
2423 Effect of thermal treatment on properties of PyC 70
25 Summary 70
26 References 72
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Coatings Measured by
Indentation 83
31 Introduction 83
32 Experimental details 85
33 Results 88
331 Hardness and Youngrsquos modulus 88
332 Microstructure of low temperature FBCVD SiC 91
333 Deformation behaviour under the indentation 97
34 Discussion 100
341 Influence of porosity on Youngrsquos modulus 101
342 Mechanism for High hardness 102
343 Deformation mechanism under nano-indentation 104
35 Conclusions 105
36 References 107
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC Coatings 112
41 Introduction 112
42 Experimental details 113
43 Results and discussion 117
431 VIF fracture toughness study 117
432 Influence of non-stoichiometries on the VIF fracture toughness 121
433 Microstructural analysis of fracture behaviour under the indenter 122
44 Conclusions 126
45 References 127
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings 131
51 Introduction 131
52 Experimental details 132
List of Contents
4
521 Materials 132
522 Test method and analysis 133
523 Characterisation methods 135
53 Results and discussions 136
531 Fracture strength and dimensional effect 136
532 Observe and qualify the effect of interfacial roughness on fracture strength
140
533 Characterise and quantify the interfacial roughness 143
5331 Self-affine theory introduction and experimental setup 143
5332 Results of self-affine theory 144
534 Quantify the influence of interface roughness on fracture strength 146
54 Conclusions 149
55 References 150
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings 154
61 Introduction 154
62 Experimental details 155
63 Results 156
631 Fracture strength of SiC coatings 156
632 Change in morphologies 160
633 Evolution in microstructure 163
64 Discussion 167
641 Influence of interfacial roughness and pores on fracture strength 167
642 Mechanism of microstructural change 169
65 Conclusions 171
66 References 172
CHAPTER 7 Microstructure and Mechanical Properties of Pyrolytic Carbon
Coatings 175
71 Introduction 175
72 Experimental details 176
73 Results 178
731 Microstructure of PyC coatings 178
7311 Raman spectroscopy 178
7312 Domain sizes 181
List of Contents
5
7313 Evolution of crystallinity 182
732 Mechanical properties of PyC coatings 185
7321 Force-displacement curve 185
7322 Youngrsquos modulus and the mean pressure 187
74 Discussions 188
741 Disorders and their changes after thermal treatment 189
742 Hysteresis after indentation 191
743 Mechanical property of low density PyC coatings 192
744 Mechanical Property of high density PyC coatings 193
74 Conclusions 195
75 References 197
CHAPTER 8 Conclusions and Future Works 201
81 Conclusions 201
82 Suggestions for future work 203
Abstract
6
Abstract
Mechanical and Microstructural Study of Silicon carbide and Pyrolytic Carbon
Coatings in TRISO Fuel Particles
The University of Manchester
Huixing Zhang
Doctor of Philosophy in Materials Science
TRISO fuel particles have been developed as nuclear fuels used for a generation IV
nuclear reactor high temperature reactor Such particle consists of a fuel kernel
pyrolytic carbon (PyC) and silicon carbide (SiC) coatings This study has been carried
out to establish a relationship between mechanical properties and microstructures of
SiC coating and PyC coatings produced by fluidized bed chemical vapour deposition
Indentations were used to measure hardness Youngrsquos modulus and fracture behaviour
of SiC and PyC coatings Fracture strength of SiC coatings was measured by crush
test Microstructure of SiC and PyC was mainly characterised by transmission
scanning electron microscopy and Raman spectroscopy
For SiC coatings produced at 1300 ordmC Youngrsquos modulus is an exponential function of
relative density Hardness of SiC coatings is higher than the bulk SiC produced by
CVD and it is attributed to the high density of dislocations and their interactions The
deformation mechanism of SiC coatings under indentation is explained by presence of
defects such as grain boundaries and nano-pores The fracture of these coatings
beneath the Vickers indentation is the Palmqvist cracks and indentation fracture
toughness was in the range of 35-49 MPa m12
The stress-induced micro-cracks are
assumed to be the mechanism for the high indentation fracture toughness Different
hardness and fracture toughness in these SiC coatings are attributed to influences of
defects and grain morphology
Measurement of fracture strength was carried out on SiC coatings deposited at
1300-1500 ordmC Weibull modulus and fracture strength of the full shell are dominated
by the ratio of radius to thickness of coatings and decrease linearly with the increase
of this ratio The influence of SiCPyC interfacial roughness on fracture strength of
the SiC was quantified by self-affine theory The fracture strength decreases linearly
with the increase of the roughness ratio which is the long-wavelength roughness
characteristic After thermal treatment at 2000 ordmC fracture strength decreased in SiC
coatings due to the formation of pores which are results of diffusion of native defects
in as-deposited SiC coatings and the change of Weibull modulus is related to the size
and distribution of pores
For low density PyC coatings Youngrsquos modulus and the mean pressure increase with
the increase of the density however for high density PyC coatings they are
determined by interstitial defects The hysteresis deformation behaviour under
nano-indenation has been found be affected by density variation and thermal
treatment which is proposed to be due to the disorder structure in PyC coatings
Declaration
7
Declaration
No Portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Copyright Statment
8
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this thesis)
owns any copyright in it (the lsquolsquoCopyrightrsquorsquo) and she has given the University of
Manchester certain rights to use such Copyright including for administrative
purposes
ii Copies of this thesis either in full or in extracts and whether in hard or electronic
copy may be made only in accordance with the Copyright Desings and Patents Act
1988 (as amended) and regulations issued under it or where appropriate in
accordance with licensing agreements which the University has from time to time
This page must form part of any such copies made
iii The ownership of certain Copyright patens designs trade marks and other
intellectual property (the lsquolsquoIntellectual Property Rightsrsquorsquo) and any reproductions of
copyright works in the thesis for example graphs and tables (lsquolsquoReproductionsrsquorsquo)
which may be described in this thesis may not be owned by the author and may be
owned by third parties Such intellectual Properties Rights and Reproductions cannot
and must not be made available for use without the prior written permission of the
owner(s) of the relevant Intellectual Property Rights andor Reproductions
iv Further information on the conditions under which disclosure publication and
commercialization of this thesis the Copyright and any Intellectual Property andor
Reproductions described in it may take place is available in the University IP policy
(see httpwwwcampusmanchesteracukmedialibrarypoliciesintellectual-property
Pdf) in any relevant Thesis restriction declarations deposited in the University
Library The University Libraryrsquos regulations (see
httpwwwmanchesteracuklibraryaboutusregulations) and in the Universityrsquos
policy on presentation of Thesis
Acknowledgement
9
Acknowledgement
I will always be appreciative to Professor Ping Xiao for his support and guidance
during this project period and his enthusiasm for work and positive attitude towards
life inspired me I am thankful for what he shared about his own experience doing
research which impressed me and motivated me to make improvement
I would like to thank in particular Dr Eddie Loacutepez-Honorato for his patient guidance
on my experiments and valuable advices on my project His caution on preparing
delicate specimen infected me and helped me through my project He was always
there listening my ideas and discussing with me and he has set an example for being
a good researcher
I give my thanks to all the members in ceramic coating group old and new and I
treasure and appreciate this chance working with you
I would like to give my great gratitude to Dr Alan Harvey for his kind help on
transmission electron microscopy Mr Andrew Forest and Mr Kenneth Gyves on
nano- and micro-indentation Mr Andrew Zadoroshnyj on Raman spectroscopy Dr
Ali Gholinia and Dr Ferridon Azough on TEM sample preparation Dr Judith
Shackleton and Mr Gary Harrison on X-ray diffraction Mr Christopher Wilkins and
Mr Michael Faulkner on scanning electron microscopy and Mr Stuart Mouse on
tensile tests
I am grateful to my dear friends Yola David and Dean and you make my life more
colourful and interesting I would like to thank my beloved parents and brother for
your love care and support and you are great examples of hard work and kindness
My thanks also go to the ORS scheme the CSC grant and the F-BRIDGE for their
financial support during my PhD studies
List of Figures
10
List of Figures
CHAPTER 1 Introduction
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Fig 12 Behaviour of coated layers in fuel a particle [10]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
CHAPTER 2 Literature Review
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
List of Figures
11
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation[62]
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
List of Figures
12
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC coatings Measured by
Indentation
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
List of Figures
13
BF-TEM and (b) DF-TEM
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for extra-Si SiC coatings
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
Fig 45 Cross-sectional SEM image of stoichiometric SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
List of Figures
14
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a)
extra-C SiC (b) extra-Si SiC
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
Fig 58 Log-log representation of the height-height correlation function ∆h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
List of Figures
15
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC coatings
Fig 61 Weibull plots of local fracture strength (L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
Fig 62 Weibull modulus plots of fracture strength of the whole shell (F
f ) before
(black triangle) and after (red circle) thermal treatment
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after thermal treatment (c) and (d) SiC2
before and after thermal treatment (e) and (f) SiC3 before and after thermal treatment
(g) and (h) SiC4 before and after thermal treatment Dashed and solid arrows indicate
growth direction and pores respectively
Fig 64 The IPyCSiC interfacial morphology of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermal treated at 2000 degC (right in
each figure) The white arrow points towards to the interface irregularities (except for
thermal treated SiC4 coating (d)) black circle represents the pores in SiC coatings
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermal treated
at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and SiC2 inset
shows the peak shift of as-deposited (dash line) and after thermal treatment (solid
line) (b) is SiC4 and inset is the high angle diffraction peak after thermal treatment
showing splitting while it is a single peak in as-deposited coating
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
List of Figures
16
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
List of Tables
17
List of Tables
CHAPTER 2 Literature Review
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Table 23 Elastic tensors of 3C-SiC at room-temperature
Table 24 Vickers and nano-indentation hardness of polycrystalline CVD SiC
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Table 26 Summary of the hardness and Youngrsquos modulus for pyrolytic carbon
measured by different methods
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Measured by Indentation
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχv
along the radial and tangential directions
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Table 52 Summary of measured and calculated parameters for all the coatings
List of Tables
18
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Table 54 Results and variations influences on fracture strength for SiC coating
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings
Table 61 Deposition conditions of SiC coatings
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the whole shell before and after thermal
treatment
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
Table 71 PyC coatings deposition conditions and physical properties
Table 72 Domain size (XRD) of as-deposited and thermal treated PyC coatings
Table 73 Changes of mechanical properties after thermal treatment of PyC coatings
Table 74 The parameters used to explain different mechanical properties of high
density PyC
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
CHAPTER 1 Introduction
19
CHAPTER 1 Introduction
11 TRI-Isotropic (TRISO) fuel particles
A fission reaction is about that a large atomic nucleus (such as Uranium-235) is hit by
a neutron and absorbs the neutron forming a larger unstable nucleus The unstable
larger atomic nuclear breaks into two small nuclei and releases a high amount of
energy more neutrons beta and alpha particles and gamma The energy release is
much greater than for traditional fuels eg 1 g Uranium nuclear fuel releases the
same amount of energy as approximately 3 tonne of coal [1] The energy can be
transferred through the cooling system and used to boil the water to make steam to
drive a turbine and electrical generator in a nuclear power station
The high-temperature gas cooled reactor is one of the most promising candidates for
the production of nuclear energy according to its unique features For example it has
high coolant outlet temperature (850-1000 degC) which provides more efficient
electricity production due to the increased difference of the hot and cold coolant
temperatures [2] Furthermore it has the safety advantages due to the enclosure of the
fuel kernel (such as UO2 UC) within few layers of ceramic coatings Currently the
most common technique to fabricate fuels for operating the next generation
high-temperature gas cooled reactors is the TRISO fuel particles coating system [3]
The TRISO system was designed not only to retain all fission products during neutron
irradiation but also to withstand the thermo-mechanical stresses generated during
service [4]
CHAPTER 1 Introduction
20
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Figure 11 is the schematic of TRISO fuel particles embedded in a graphite matrix A
TRISO fuel particle consists of a fuel kernel and coating layers of porous pyrolytic
carbon (PyC) called buffer layer inner dense PyC (IPyC) silicon carbide (SiC) and an
outer dense PyC (OPyC) [5] and these layers were designed to have different
purposes The buffer layer absorbs metallic fission products recoils from kernel and
provides a space for fission product gases It also takes the volume change caused by
the kernel swelling without transmitting forces to outer layers The dense and
isotropic IPyC layer stops the chlorine from reacting with the kernel during deposition
of SiC and provides a firm substrate for the SiC layer Furthermore it protects the
SiC layer from most of the fission products and carbon monoxide during operation
The OPyC layer protects SiC layer during the remainder of the fabrication process
and provides structural stability to the particle during irradiation [3] The high
mechanical properties of SiC are needed to contain the high pressure generated in the
kernel and withstand the stress developed by the dimensional change of IPyC [3]
CHAPTER 1 Introduction
21
12 Failure mechanism
The radiation effects on the performance of the fuel particles such as fundamental
performance characteristics and fission product relsease mechanisms have been well
understood Different testing conditions (eg temperature up to 1300 degC and the does
of neutron) reflected the senariors encountered real applications [6-8]
During irradiation a number of potential failure mechanisms were revealed according
to several tests of coated fuel particles conducted in material test reactors and in
real-time operating HTR reactors [6-8] Chemically the corrosion of SiC by the
fission product palladium has been observed in almost all kinds of fuel compositions
and is considered as one of the key factors influencing the fuel performance However
this could be avoided by limiting the fuel temperature irradiation time or increase the
thickness of SiC layer [9] Mechanically the built up of the internal gas pressure (eg
CO) of irradiated particle and the neutron induced embrittlement of PyC coatings
could promote the failutre of the TRISO fuel particle The primary mechanisms which
may result in mechanical failure of TRISO fuel particles and lead ultimately to fission
product release depends significantly on the magnitude of the de-bonding strength
between IPyC and SiC layers [3 9]
121 Traditional pressure vessel failure mode
In this mode the failure was assumed to occur due to simple overload of the SiC layer
due to internal pressure build-up from fission gas [10] Both IPyC and OPyC layers
shrink during operation because of the irradiation exposure [11] This causes
compression stress in the SiC layer and tensile stress in the PyC layers Failure of the
SiC layer can only occur if the internal gas pressure is high enough to overcome the
compressive stress and critical stress of the SiC layer itself
CHAPTER 1 Introduction
22
Fig 12 Behaviour of coated layers in fuel a particle [10]
Figure 12 shows the basic behaviour modelled in a three layers standard model [10]
It shows that both IPyC and OPyC layers shrink and creep during irradiation but the
SiC layer exhibits only elastic deformation A portion of gas pressure is transmitted
through the IPyC layer to the SiC The pressure continually increases as irradiation of
the particle goes However if the PyC layer could remain in tension the failure by
fracture of SiC layer would be less likely to happen in this mode When the failure of
the PyC layer occurs a tensile hoop stress in the SiC layer is generated This leads to
the development of the stress concentration mode provided by the fracture of the inner
PyC layer
122 Stress concentration mode
In this mode it is been proposed that there is a point at which the fracture strength of
the IPyC would be exceeded during exposure When this occurs a radial crack will
form in the IPyC layer The crack could either penetrate through the SiC layer or
partially de-bonding the IPyCSiC interface This would lead to severe stress
concentration near the crack tip and it could reach the maximum of 440 MPa
according to previous simulation work [10] Once de-bonding goes through the whole
interface the source of stress in the SiC layer would be fission product gas build-up
CHAPTER 1 Introduction
23
and this case has similar failure mechanism of traditional pressure vessel failure mode
Although this process could decrease the probability of failure compared with the
stress concentration case the probability of failure may be higher than the traditional
failure mode Because the stress generated in the SiC layer after de-bonding would
increase [3]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
All these behaviours make it easier for the SiC layer to reach its fracture strength and
lead to the radial crack and failure of the SiC results in an instantaneous release of
elastic energy that should be sufficient to cause simultaneous failure of the
pyrocarbon layer Shown in Fig 13 is a photomicrograph illustrating the failure of a
TRISO coating According to the above discussion all the carbon layers are partially
designed to support or protect the SiC layer The SiC layer serves as the main
containment barrier for gas and metallic fission products [3] and high mechanical
properties of the SiC layer are needed However without appropriate microstructure
and mechanical properties of the PyC layer the stresses or structural changes
introduced in this layer during the irradiation process could result in the failure of the
whole particle [9 12] Furthermore mechanical properties such as the hardness (It is
CHAPTER 1 Introduction
24
the resistance to plasticpermanent deformation of materials under constant load from
a sharp object) Youngrsquos modulus (It reflects the resistance to reversible deformation
of a material) fracture toughness (It describes the ability of a material containing a
crack to resist fracture) and fracture strength (It is the maximum stress at which a
specimen fails via fracture) of SiC and PyC coatings are also important factors for the
safety design and evaluation of the TRISO coating system [10]
13 Goals of dissertation
Due to the importance of mechanical properties of SiC and PyC layers in keeping the
integrity of TRISO fuel particles and providing adequate information for modelling
the probability of failure of particles a good understanding of the elastic plastic and
fracture properties and their relation with microstructure is necessary Therefore all
the work carried out in this project is aimed at studying the relationship between
microstructure and mechanical properties of these two layers aiming to provide a
fundamental understanding about the deformation mechanism and solve the practical
issues
Due to small scale of SiC and PyC coatings two main techniques used to measure
mechanical properties are micronano-indenation and crush test Furthermore to study
the effect of microstructures on mechanical properties characterization techniques
such as transmissionscanning electron microscope and Raman spectroscopy are
widely used in the current work
In this thesis Chapter 2 reviews the recent progress in microstructural characterisation
and mechanical properties of SiC and PyC related materials which provides basic
information with regard to future study about hardness Youngrsquos modulus
deformation mechanism and fracture behaviour in these
Chapter 3 studies the influences of microstructure on hardness and Youngrsquos modulus
CHAPTER 1 Introduction
25
of SiC coatings and focuses on understanding the deformation mechanism of SiC
under nano-indentation The fracture toughness of these SiC coatings is measured by
Vickers-indentation and the importance of crack modes is discussed in Chapter 4
In Chapter 5 the fracture strength of SiC coatings in TRISO fuel particles is measured
and influence of the IPyCSiC interface on fracture strength is discussed Effect of
thermal treatment on fracture strength and microstructure of SiC coatings deposited at
different conditions are introduced in Chapter 6
Chapter 7 investigates the microstructure and mechanical properties of PyC coatings
with focus on deformation mechanism under indentation and the effect of density and
disorders on mechanical properties before and after thermal treatment
At last the main results and conclusions together with suggestions on future work are
given in Chapter 8
CHAPTER 1 Introduction
26
14 References
[1] httpnuclearinfonetNuclearpowerTheScienceOfNuclearPower
[2] J J Powers Fuel performance modelling of high burnup transuranic TRISO fuels
Disertation of Master University of California Berkeley 2009
[3] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[4] D L Hanson J J Saurwein D W McEachern A S Shoeny Development plan
for advanced high temperature coated-particle fuels Report Nopc000513
[5] httpwwwmpafrprocessphp
[6] W Burck H Nabielek A Christ H Ragos AW Mehner HTR coated particle
fuel irradiation behaviour and performance prediction Specialists meeting on
gas-cooled reactor fuel development and spent fuel treatment IWGGCR-8 1983
174-88
[7] H Nickel H Nabielek G Pott A W Mehner Long-time experience with the
development of HTR fuel elements in Germany Nucl Eng Des 217 (2002)
141-51
[8] H Nabielek W Kuhnlein W Schenk W Heit A Christ and H Ragoss
Development of advanced HTR fuel elements Nucl Eng Des 121 (1990)
199-210
[9] K G Miller D A Petti J Varacalle T Maki Consideration of the effects on
fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[10] A C Kadak R G Ballinger M JDriscoll et al Modular pebble bed reactor
project university research consortium Annual report INEELEXT-2000-01034
MIT-ANP-PR-075
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
CHAPTER 1 Introduction
27
treatment J Nucl Mater 374 (2008) 445-52
[12] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
CHAPTER 2 Literature Review
28
CHAPTER 2 Literature Review
21 Introduction
To model the probability of failure of fuel particles a number of key mechanical
properties of silicon carbide (SiC) are needed such as Youngrsquos modulus hardness
fracture toughness and fracture strength [1 2] These properties could be affected by
the microstructure of SiC coatings such as orientation porosities grain size and
defects [1-5] The small dimensions of the SiC coating limits the techniques available
to measure its mechanical properties However the development of the
nano-indentation has provided an important tool for probing the mechanical properties
of small volumes of material From the load ndash displacement data many mechanical
properties such as hardness Youngrsquos modulus and even fracture behaviour can be
determined [6] When an indentation system is used in conjunction with a focused ion
beam system and a transmission electron microscope images of deformation under
the nano-indentation can be obtained and the 3-D crack morphology can even be
reconstructed [7] Since there is a need to explain the high mechanical properties of
SiC deposited at temperature of 1300 ordmC by fluidized-bed chemical vapour deposition
[8] this combination of techniques could provide fundamental understanding of the
deformation mechanisms during indentation Another important parameter is fracture
strength and there have always been efforts to establish one method to characterise
fracture strength of SiC for example by brittle-ring test [9] whole particle crush test
[10] and modified crush test [5] Furthermore the high temperature application of SiC
and the compact of fuel pellet could affect the microstructure of SiC [2] which would
lead to the changes of mechanical properties
CHAPTER 2 Literature Review
29
The pyrolytic carbon (PyC) has been introduced by previous studies [11-14] and is
important in helping the SiC act as the main loading bearing layer The high
mechanical properties such as Youngrsquos modulus and anelasticity of PyC are necessary
to protect from damage caused by internal stresses and by external mechanical
interactions [12] However cracking and debonding between the SiC and inner PyC
layers could increase the probability of failure of TRISO fuel particles [13 14] It was
shown that without appropriate microstructure and mechanical properties of PyC the
structural or stress changes introduced in the coating during irradiation process could
result in total failure of the particle [11 13] The microstructure of PyC varied under
different deposition conditions [15] and it dominates the mechanical properties of
PyC coatings Therefore in this Chapter we review both the microstructure of SiC
and PyC including atomic structure morphology and defects and their mechanical
properties eg hardness Youngrsquos modulus deformation behaviour etc
22 Microstructure of silicon carbide
221 Atomic structure
The basic structural unit in SiC is a covalently bonded tetrahedron a carbon atom is at
the centre of four silicon atoms (C-Si4) and vice versa (Si-C4) The length of each
bond and the local atomic environment are nearly identical while the stacking
sequence of the tetrahedral bonded Si-C bilayers could be different The different
stacking sequences give SiC more than 250 polytypes [16] of which the 3C 4H 6H
and 15R are the most common The leading number of polytypes shows the repetition
of the SindashC pair and the letter C H and R represents the cubic hexagonal and
rhombohedral crystals respectively The 3C is the only cubic polytype in which the
stacking sequence of the planar unit of Si and C in tetrahedral coordination is depicted
as ABCABC in the lt111gt direction The cubic SiC crystal is called β-SiC and all
the other polytypes are α-SiC The crystal structures of 3C- 4H- 6H- and 15R-SiC
are schematically illustrated in Fig 21(a) [17] and corresponding XRD images were
CHAPTER 2 Literature Review
30
shown in Fig 21(b) [18]
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Although the transformation of SiC polytypes is primarily dependent on temperature
it could be affected by purity of the pre-existing phase pressure andor stacking faults
[19-22] The cubic form of SiC (β -SiC) is believed to be more stable than the
hexagonal structure (α-SiC eg 6H-SiC) below 2100 ordmC [19] However the polytype
of 2H-SiC which has the simplest stacking sequence is rarely observed at higher
temperature Krishna et al [20] reported that single crystals of 2H-SiC can be easily
transformed to 3C-SiC on annealing in argon at temperatures above 1400 ordmC It was
CHAPTER 2 Literature Review
31
found that the pre-existence of α-SiC (except 2H-SiC) could promote β-SiC
transformation to α-SiC while the transformation from α-SiC (6H-SiC) back to β-SiC
(3C-SiC) needs high temperature and pressure [21]
It has also been shown that the phase transformation could be closely related to
pre-existing defects such as stacking faults and their distribution [18] of which the
concentration is high even in single crystal SiC [22] Furthermore due to their low
formation energy the other intrinsic defects such as vacancies interstitials and
antisites were found to be common in SiC [23] These defects could affect mechanical
properties of SiC [8] so it is important to review their structure and properties
222 Defects in SiC
2221 Stacking faults and dislocations
A stacking fault is a disordered part of the ordered sequence in fcc crystal and the
most common stacking faults in cubic SiC are intrinsic and extrinsic stacking faults
(ISF and ESF) [24] For ISF the resulting stacking sequence is ABCACABC
if a double layer B is removed (condensation of vacancies) as for instance shown in
Fig 22[24] The ESF could be thought of as adding a double layer to the stacking
sequence (condensation of interstitials) resulting stacking sequence of
ABCACBCABChellip
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
CHAPTER 2 Literature Review
32
Another interpretation of the stacking faults is related to a twist of the three equivalent
bonds between two bilayers by 180deg [24] There may be an intrinsic shear stress
which could promote the glide of partial dislocations and thereby result in a faulted
crystal containing an error in stacking sequence so itrsquos reasonable to interpret
stacking faults in this way [25] Compared with dislocations and vacancies no bonds
are broken by stacking faults leading to a small energy difference between faulty and
perfect structures [26]
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
[27] [28] [24] [29] [30] [31] [32]
ESF (mJ m-1
) -15 -- -28 -6 -61 -154 -323
ISF (mJ m-1
) 12 34 -34 14 138 111 -71
Table 21 lists the formation energy of stacking faults in SiC and it shows that
extrinsic stacking faults have much lower formation energy than intrinsic stacking
faults in fact the values become negative The negative formation energy of stacking
faults in 3C-SiC means they can be formed very easily even more easily than perfect
3C-SiC As a result the stacking faults in 3C-SiC are spontaneously formed and most
likely in the form of extrinsic faults in the lt111gt direction Furthermore due to the
low energy of formation the length of a stacking fault can only be limited by the size
of the crystal or the presence of other defects that act as obstacles [33]
CHAPTER 2 Literature Review
33
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
The morphology of stacking faults in SiC observed by TEM is given in Fig 23 It
shows that the stacking faults could form a small domain (around 1 nm thick in Fig
23(a)) with different distances between small domains When a large concentration of
stacking faults exists in SiC it has been claimed that a conversion of cubic SiC to
hexagonal SiC on the nano-scale could happen by twinning [35] Furthermore the
stacking sequence of the faulted 3C-SiC was previously treated as random mixing of
α-type unit structures such as 6H and 4H in the 3C structure [36] Therefore it is
important to identify the properties and the microstructure of stacking faults of SiC
layers in TRISO fuel particles because the presence of α-SiC could result in reduction
of strength under irradiation which was due to enhanced possibility of anisotropic
swelling of α-SiC under irradiation compared to β-SiC [37]
(a) (b)
(c)
CHAPTER 2 Literature Review
34
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Figure 24 gives the XRD images of SiC in TRISO fuel particle deposited by fluidized
bed chemical vapour deposition showing the extra peak at 2θ~335ordm a high
background intensity at the peak at 2θ~353ordm and the broadening of the 3C peaks [8]
This is different from the perfect atomic structure of 3C-SiC as shown in Fig 21(b)
According to a previous simulation study [18] this kind of XRD diffraction pattern
could be caused by the existence of a high density of stacking faults and twins in the
regular cubic sequences It was demonstrated that it was unlikely to be due to the
presence of 2H-SiC or other polytypes [18] and two possible explanations were given
First two types of crystalline 3C-SiC with different populations of faults and twins
and second one type of crystal having clusters of faulted regions In SiC single
crystals although the concentration of stacking faults and twins is high the density of
dislocations is low (102-10
5cm
2) compared with metallic materials [22]
Figure 25 shows schematic images of the dislocations in face centred cubic (fcc)
crystals (β-SiC) The perfect dislocation is the (111) lt110gt system with burgers
vector of b=a2[110] (0308 nm) in SiC as shown in Fig 25(a) The perfect
dislocation could be easily dissociated into two partial dislocations of a6[121] and a6
CHAPTER 2 Literature Review
35
[21-1] as shown in Fig5 (a) and (b) because this reduces the total energy As a result
of this split a stacking fault must also be produced between the two partial
dislocations [38] Figure 25 (c) and (d) are lt110gt projections showing the Shockley
and Frank partial dislocations and their formation all related to the formation of
stacking faults
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
(a)
(b)
(c) (d)
CHAPTER 2 Literature Review
36
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
By comparing with previous studies [39-41] it is found that the relationship between
dislocation and stacking faults is complex The stacking faults have influences on the
mechanical properties for example enhancing the mobility of dislocations [39]
Different roles of stacking faults in II-VI heterostructures and devices have been
observed and results indicate that the stacking faults serve as the sources of misfit
dislocations [40] It is necessary to study the propagation of stacking faults or the
formation of stacking faults under stress and their influence on the properties of SiC
For example generation of stacking faults is shown to have occurred during the
fracture process together with the corresponding partial dislocation Furthermore
Agarwal et al [41] observed the growth of stacking faults from certain basal plane
dislocation within the base layer of the SiC
2222 Non-stoichiometric and point defects
Another common class of defects in SiC are non-stoichiometric (excess silicon or
carbon) and point defects [23 41 42] The purity of SiC may have effect on the
crystal structure strength corrosion resistance thermal conductivity diffusion
coefficient and other coating properties depending on its amount [43] The purity
could also affect defects in SiC eg if the stoichiometry deviates (even less than 1)
the concentrations of point defects in cubic SiC were found to be elevated [23]
Although the effect of point defects on general behaviour of nuclear fuel during
application process is not clear but their effect on microstructure evolution during
thermal treatment could be significant [44]
Silicon in SiC Stoichiometric 3C-SiC has generally been obtained at temperatures
between 1500 and 1600 [45] with carbon and silicon codeposited above and below
this temperature range By adding propylene as another carbon source the deposition
temperature of stoichiometric SiC could be reduced to about 1300 [8] The extra-Si
CHAPTER 2 Literature Review
37
SiC is less commonly investigated compared with the extra-C SiC because it has
been found that during the irradiation process the extra-Si plays a negative role in
material properties due to its low melting point [1] It has been found that the effect of
excess-Si on the Youngrsquos modulus and hardness it is more likely depending on its
amount and location [8 46]
Raman spectroscopy is an effective way to identify free Si both in amorphous and
crystalline phases eg it detected excess-Si when the XRD result showed the SiC was
stoichiometric [8] If the extra-Si is high (could be detected by XRD) TEM could be
used to detect its location and characterise the Si lattice contrast For example TEM
was carried out using both high resolution [35 47] and dark field imaging modes [48]
The HRTEM images in Fig 26 show the 3C-SiC crystallite with Si inclusions in
which nano-crystalline 3C-SiC and Si are separated by a weakly crystallized
interphase
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
(a)
(b) (c)
β-SiC
β-SiC
β-SiC
β-SiC
Si
Si
025 nm
025 nm
025 nm
0 312 nm
0312 nm
CHAPTER 2 Literature Review
38
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
Figure 27 shows bright-field and dark-field images of extra-Si SiC It shows the
crystalline Si as bright points in the dark background located at the grain boundaries
[48] The above observations were carried out in SiC with more than 1 at excess Si
(by comparing the intensity of Si Raman peak) as such observations are difficult
when the amount of excess Si is low Since the Youngrsquos modulus in SiC with low
amount of excess Si was comparable to that of stoichiometric SiC[8 46] it may have
unique properties that are worth further exploitation
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Carbon in SiC Excess C can also be identified by Raman spectroscopy but it is more
difficult to quantify its content and observe where this extra carbon exists due to its
small atomic number A comparative method was used to measure the content of
excess carbon by combining Raman spectroscopy auger electron spectroscopy
electron probe microanalysisand X-ray photoelectron spectroscopy [49] Once the
carbon concentration was measured (by above methods) the ratio of free excess to
SiC peak intensity (I796I1600) of Raman spectroscopy could be obtained as shown in
Fig 28 and the excess carbon concentration in the nearly stoichiometric SiC could
(a) (b)
CHAPTER 2 Literature Review
39
be estimated [49]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
There are few reports regarding the location of excess C in SiC The research carried
out by KKaneko et al [50] in carbon-doped hot pressed szlig-SiC showed that grain
boundaries were found to be free of any second phase by HRTEM although excess C
is found to form the second graphite phase Mykhaylyk and Gadzira revealed that
extra-C atoms are located as planar defects [51] The C atoms in the β-SiC structure
were supposed to arrange either as diamond-like carbon interlayers or as
non-correlated point defects after sintering of the as-synthesized powder at high
pressures and high temperature Since it showed that the presence of excess C atoms
in SiC crystal structure changes the local atomic environment [52] they may exist
within the SiC crystal and be correlated with other defects
The above discussion about the excess Si and C indicates that their influences on
properties of SiC depend on their content and that they could be discussed together
with the other point defects when their amount is low (less than 1 at ) [23]
Point defects in SiC SiC has eight kinds of point defects which keep the tetrahedral
symmetry of the perfect SiC crystal [23] They are carbon vacancies (Vc) silicon
vacancies (VSi ) carbon antisites (CSi) silicon antisite (Sic) a tetrahedral interstitial
silicon atom surrounded by four Si atoms (SiTSi) a tetrahedral interstitial silicon atom
CHAPTER 2 Literature Review
40
surrounded by four C atoms (SiTC) a tetrahedral interstitial carbon atom surrounded
by four Si atoms (CTSi) and a tetrahedral interstitial carbon atom surrounded by four
C atoms (CTC) [23] The formation energies for these defects are listed in Table 22
Due to their low formation energies the individual antisites and vacancies
particularly CSi were expected to appear even in as-deposited coatings [53 54]
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Vc VSi Sic CSi SiTSi SiTC CTSi CTC
Ef (eV) 59 68 73 11 150 147 86 110
The importance of point defects for different applications of SiC was studied and
these properties were studied in the relation to the properties of the point defects
including their formation annealing and interaction with each other [53] According
to Raulsrsquos study [54] the actual results of diffusion of CSi are more likely to be the
formation of CSi clusters which could be promoted by the diffusion of vacancies For
the coexistence of self-interstitials and vacancies (eg in irradiated material) it has
been found that the annealing temperature for VSi and Vc by recombination in β-SiC
were about 500 ordmC and 750 ordmC respectively [55] For as-deposited β-SiC without
interstitials the annealing process was only dominated by the out-diffusion of
vacancies the disappearances of VSi and Vc were found at temperature of 1400 ordmC and
1600 ordmC respectively [54] It is also been found that the migration of silicon vacancies
is easier than carbon vacancies due to its lower migration energy barrier Furthermore
in the case of excess carbon inside SiC the carbon clusters may form in SiC after
annealing and the size of the cluster depends on the content of interstitial carbon [56]
The general atomic-scale microstructure of SiC was reviewed above which showed
high degree of defects such as stacking faults dislocations vacancies and antisites
CHAPTER 2 Literature Review
41
The kind and concentration of these defects could affect the mechanical properties
such as hardness Youngrsquos modulus and fracture behaviour of SiC Since variation of
mechanical properties could also be due to other microstructural factors such as grain
size and density the relationship between microstructure and mechanical properties
are further reviewed in the following session
23 Properties of silicon carbide
231 Youngrsquos modulus
Youngrsquos modulus is physically related to the atomic spacing atomic bond strength
and bond density It is accepted that high-purity SiC material eg CVD SiC exhibits
the highest elastic modulus and that a porous microstructure with a high
concentration of impurities could decrease the elastic modulus [1 57] In contrast
neither grain size nor polytype was recognized as having a significant effect on the
elastic modulus of SiC in coated fuel [1 58]
Table 23 Elastic tensors of 3C-SiC at room-temperature
C11 (GPa) C12 (GPa) C44 (GPa) Z Ref
3C-SiC a 3523 1404 2329 18196 [59]
3C-SiC b 511 128 191 10026 [1]
3C-SiC c 390 142 256 -- [60]
3C-SiC a 420 126 287 19503 [61]
a Theoretical calculations
b Sonic resonance measurement
c Raman Spectroscopy
According to the definition of Youngrsquos modulus an important factor which could
affect its value for SiC material is the texture which is the degree of anisotropy (lack
of randomness with regard to the orientation) of SiC crystals The Youngrsquos modulus is
different by a combining of elastic tensors for deformation of the crystal in different
CHAPTER 2 Literature Review
42
orientation The elastic tensors or the stiffness tensors reflect the linear stress-strain
relation of a material There are 81 elastic tensors because the stresses and strains
have 9 components each However due to the symmetries of the SiC the tensors were
reduced to 3 unknown values They could be measured by sonic resonant method [1]
and Raman spectroscopy [60] based on vibrational theory of the crystal lattice They
are defined for SiC in Table 23 and will cause the variation of Youngrsquos modulus for
anisotropic materials The elastic tensors for 3C-SiC identified by previous theoretical
and experimental results [59-61] are substantially different from the current updates
of sonic resonance data The difference could be caused by the difference of the size
of SiC mateirals which could introduce the influences of defects such as grain
boundaries and stacking faults It was proposed to be more reasonable estimation for
SiC in TRISO fuel particle [1]
A measurement of the anisotropy in β-SiC (faced centre cubic crystals) is the ratio of
the two shear moduli [3] 100 shear modulus and 110 shear modulus μ0 and μ1
respectively which is
0 44
1 11 12
2CZ
C C
(1)
the parameter Z is known as the Zener ratio or elastic anisotropy factor (given for
different elastic tensor Table 23) When Zgt1 the Youngrsquos modulus is minimum
along lt100gt and a maximum along lt111gt and the representational surfaces for
Youngrsquos modulus in cubic crystals is shown in Fig 29 For the case when Z=1 the
cubic crystal would also be isotropic and the representation surface would be
spherical
CHAPTER 2 Literature Review
43
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
If the samples were random polycrystals which means samples are isotropic the
theoretical Youngrsquos modulus can be unambiguously given by [3]
3
[1 ( 3 )]E
B
(2)
While bulk modulus and shear modulus are
11 122
3
C CB
(3)
1
0 1
1 0
52( 6 )
(4)
where 0 44C 1 11 12( ) 2C C and
01
0 0
3( 2 )
5 (3 4 )
B
B
(5)
The theoretical value can be gained when the elastic constants are known Using the
Eqs (2-5) the theoretical Youngrsquos modulus E was calculated to be 496 GPa for
isotropic SiC materials when the elastic tensor obtained by Lambrecht et al was used
The calculated value is close to the Youngrsquos modulus measured by nano-indentation
(about 527 GPa) of isotropic bulk CVD SiC [62] But this value is higher than the
Youngrsquos modulus measured by nano-indentation of SiC in TRISO fuel particle which
is about 450 GPa [8 46]
By using the elastic tensors measured by sonic resonance in Snead et alrsquos study [1]
CHAPTER 2 Literature Review
44
the calculated Z (10026) is very close to 1 and it means the Youngrsquos modulus in
TRISO coated fuel particle may show no orientation effect According to Eqs (2-5)
the calculated Youngrsquos modulus is about 459 GPa under the elastic tensors given in
Ref [1] This value is close to the Youngrsquos modulus measured by nano-indentation in
TRISO fuel particle regardless of the orientation effect [1 8 46] Therefore for
TRISO fuel particle the recommended elastic tensors measured by sonic resonances
were supposed to be appreciable due to the scale and the microstructure similarities of
SiC materials [1]
Another significant factor which affects the Youngrsquos modulus is the density The
elastic modulus E at room temperature can be empirically expressed in an exponential
function of porosity pV as [63]
0 exp( )pE E CV (6)
where 0E is the elastic modulus and C is a constant of 357 for a pore-free bulk CVD
SiC pV is the ratio of the relative density difference to the theoretical density of SiC
(322 gcm3)
The relationship between density and Youngrsquos modulus of different kinds of SiC
materials measured by different methods were summarised in a previous study [1] as
shown in Fig 210 It has been found that the standard deviation of elastic modulus of
SiC is about plusmn 10 when the density is higher than 99 and increased to plusmn 15 for
porosity higher than 1
CHAPTER 2 Literature Review
45
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
232 Hardness
In a brittle material indentation hardness is defined as the mean pressure the material
will support under load and it is a complex property which could involve crack
initiation and propagation and the development of new surfaces during the
indentation process [1] Furthermore the value of hardness measured by indentation
also depends on external factors Due to the difference in dimensions of materials
such as the bulk small scale and thin film materials indentation on the nano- micro-
and even macro-scale have been used to measure the hardness [64] The hardness of
β-SiC related material has mainly been investigated by Vickers and nano-indentation
techniques (introduced in the later part of this session according to Ref [65]) as
summarized in Table 24 Reviews have found that the nano-hardness is generally
higher than Vickers hardness [1] which was attributed to the indentation size effect
Although few hardness values of β-SiC are available to be compared (given in Table
24) it shows the difference of hardness within a given sample Regardless of external
influences on the measurement of hardness generally it can be affected by grain size
or grain morphology [46] density composition and defects [1 8 66] To identify the
CHAPTER 2 Literature Review
46
controlling factor for hardness it is necessary to understand the deformation
mechanism of SiC under indentation
Table 24 Vickers and nano-indentation hardness of β-SiC related materials
Deformation mechanism Research into the deformation mechanism of SiC have
shown the availability of dislocation related plasticity [70] phase transformation
(cubic phase to amorphous) [71 72] fracture mechanisms [73] and also the
combination of any two or three [62 73]
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
First the dislocation related plastic deformation was found in single crystal 6H-SiC
[70] and the propagation morphology of dislocations was observed after indentation
as shown in Fig 211 This observation confirmes that the dislocation slip is a
Materials Vickers hardness (GPa) Nano-hardness (GPa) Ref
Single β-SiC (001) 28 -- [67]
CVD β-SiC 207-32 325-406 [466668]
FBCVD β-SiC -- 36-42 [8]
Sintered β-SiC 211-239 -- [69]
500 nm
CHAPTER 2 Literature Review
47
mechanism of plastic deformation from nucleation of a few dislocation loops (at or
near the theoretical strength) to extensive dislocation plasticity
Furthermore the dislocation related plastic deformation in polycrystalline CVD β-SiC
(with micro meters grain size) was first observed by Zhao et al [62] It was found that
the initiation of the plastic deformation was reflected by the burst (pop-in) of the
force-displacement curve which is similar as the initiation of plastic deformation in
metallic materials as shown in Fig 212(a)
According to the Hertzian contact theory [74] the burst was attributed to initiation of
the dislocation glide by comparing the shear stress generated under the indentation at
that load with the theoretical shear stress in β-SiC [62] During the whole indentation
process it was shown that shear slip is the predominant deformation mechanism and
that cracks were associated with the shear faults Figure 212(b) is one of the TEM
images showing the microstructure under indentation and it shows the dislocation
induced shear bands at one side of indent [62] which depend on the orientation of
grains
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation [62]
Second following the observations of phase transformation under indentation in
silicon [75] and the formation of SiC amorphous phase during high speed machining
(a) (b)
CHAPTER 2 Literature Review
48
process [71] the investigation of phase transformation under indentation was carried
out in SiC [7274] It has been demonstrated thermodynamically that the direct
amorphization is less likely to happen under nano-indentation [76] The
amorphization observed in single crystal SiC was attributed to the formation
propagation and accumulation of dislocations which formed the disordered phase at
the maximum stress region under a punch indentation [71] In SiC with nanometers
grain size the molecular dynamic study indicated thedominated deformation under
nano-indenation is a crossover of the indentation-induced crystallization to
disordering leading to amorphization [72] as shown in Fig 213
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Further studies demonstrated that the phase transformation from β-SiC to α-SiC is not
possible under nano-indentation because a pressure of nearly 100 GPa is needed [76]
even when assisted by high dislocation density shear stress and temperature This
simulation work concluded that the primary response of β-SiC to nano-indentation is
dislocation nucleation and propagation which has been confirmed by experimental
observations [62]
Third the plastic deformation of β-SiC under indentation was divided into two parts
CHAPTER 2 Literature Review
49
which are primary dislocation initiation and propagation and the formation of micro
cracks [73] The former contributes to 13 of plastic deformation under indentation
while the later provides 23 of total deformation The hardness related plastic
deformation could be explained well by this mechanism which included above two
process as discussed in previous studies [1 46 62] Moreover considering the effect
of micro cracks the deformation mechanism under indentation could be related to
other factors which could contribute to the formation of micro cracks such as
porosity grain boundaries and stacking faults in SiC [3]
Youngrsquos modulus and hardness of coatings in TRISO fuel particle can be measured by
nanoindentation due to the limitation of small dimension A typical
load-displacement curve and the deformation pattern under nanoindentation of an
elastic-plastic sample during and after indentation are shown in Fig 214 in which the
hc is contact indentation depth and hs is the displacement of the surface at the perimeter
of the contact [65] The peak load and displacement are Pmax and hmax respectively
and the diameter of the contact circle is 2a During unloading process the elastic
displacements are recovered and when the indenter is fully withdrawn the final depth
of the residual hardness impression is hf [65]
Nanoindentation hardness is the ratio of the load to the projected contact area of the
indentation The mean pressure that the material can support under indentation is
defined as the hardness From the loadndashdisplacement curve as in Fig 214(a) hardness
can be gain when the load is at the maximum value
A
PH max (7)
where A is the projected contact area
CHAPTER 2 Literature Review
50
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
The elastic modulus of the indented sample can be inferred from the initial unloading
contact stiffness S=dPdh ie the slope of the initial portion of the unloading curve A
geometry-independent relation involving contact stiffness contact area and elastic
modulus can be derived as follows
2A
S E
(8)
where szlig is a constant that depends on the geometry of the indenter (szlig=1034 for a
Berkovich indenter) [65] and Er is the reduced elastic modulus which accounts for the
fact that elastic deformation occurs in both the sample and the indenter Er is given by
CHAPTER 2 Literature Review
51
22 11 1 i
r i
vv
E E E
(9)
where E and υ are the elastic modulus and Poissonrsquos ratio for the sample respectively
and Ei and υi are the same quantities for the indenter For diamond Ei=1141 GPa and
υi=007[65]
For an indenter with a known geometry the projected contact area is a function of the
contact depth The area function for a perfect Berkovich indenter is given
by 2245 cA h Indenters used in practical nanoindentation testing are not ideally sharp
Therefore tip geometry calibration or area function calibration is needed A series of
indentations is made on fused quartz at depths of interest A plot of A versus hc can be
curve fit according to the following functional form
11 12 1 1282 4
1 2 3 8245 c c c c cA h C h C h C h C h (10)
where C1 through C8 are constants In some cases only the first three constants were
considered
The contact depth can be estimated from the load-displacement data using
maxmaxc
Ph h
S (11)
Where ε is a constant that depends on the indenter geometry (ε=075 for a Berkovich
indenter)
It is worth noting that high Youngrsquos modulus and hardness does not gurantee the
suitability of ceramic material to an engineering application because of the
importance of other mechanical properties such as fracture toughness and fracture
strength
CHAPTER 2 Literature Review
52
233 Fracture toughness
The definition of fracture toughness from Munz and Fett is [77] if a component or a
test specimen with a crack is loaded the stress intensity K1 increases with increasing
load until unstable crack propagation occurs at a critical value of K1 This critical
value is the fracture toughness (KIC) Therefore the measurement of fracture
toughness should be made on sample with a pre-crack however due to the small size
of SiC coating methods could be used are limited Although the most recently
developed micro-beam bending test could measure the fracture toughness of SiC in
TRISO fuel particles [78] this process is costly and time consuming because it
involves the preparation of micro-beams and notched cantilevers by focused ion beam
milling which limites the application of this technique
Indentation is now one of the most commonly used techniques to evaluate the fracture
toughness of ceramics and coating systems because it is easy to perform does not
need special samples and causes only negligible surface damage However some
researchers have declared that the indentation method is not suitable for the
measurement of fracture toughness [79 80] They concluded that the indentation
method does appear to represent some form of a complex crack arrest phenomenon
but that this occurrs in the presence of a multiple-crack path and a highly complex
residual stress field
Despite of these considerations the indentation method is an effective way to
compare the fracture behaviour of materials [80] particularly for small size specimens
and it provides information about the crack initiation and propagation Figure 215 is
the most typical characterization of the crack system generated by Vickers indentation
[81] This crack system is termed as median-radial cracking and consists of
approximately semi-circular cracks
CHAPTER 2 Literature Review
53
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
The mode of crack initiation and propagation under an indenter proposed by Chiang
et al explains many of the features observed in indentation crack patterns and is the
most recent advance [82] It was found that radial cracks are the first to initiate
trigged by a combination of the highly tensile surface stress field and the availability
of surface flaws [74 82] These cracks grow on unloading and can either propagate
into the plastic zone (half penny cracks) or terminate in the elastic zone (Palmqvist
cracks) [83] depending on the microstructure of the material
For different types of crack modes such as half-penny and Palmqvist cracks different
equations were developed based on theoretical analysis of stress field and empirically
calibrations to calculate the fracture toughness under indentation For example in the
half penny crack model the Vickers indentation fracture toughness was most
frequently determined using the relationship proposed by Anstis et al [84] This
equation was first inferred based on isotropic materials and it is suitable for general
application to well-developed cracks [84]
1 2
3 2( )IC
E PK
H c (12)
Where P is the indentation load c is the radial crack length from indentation centre to
crack tip E and H are the Youngrsquos Modulus and hardness of the materialand χ
denoted as the geometrical constant which is independent of the materials The Eq
CHAPTER 2 Literature Review
54
(12) was developed on the basis of half penny cracking in homogeneous brittle
materials under high load for example in glasses [84]
The above information shows that it is possible to compare fracture toughness under
indentation in SiC coatings with different microstructures The fracture toughness of
SiC could depend on a large number of factors such as grain size porosity micro
cracks and inclusions which could dissipate the fracture energy from the main crack
[3] According to a previous review [1] fracture toughness of SiC peaks at the grain
size range of 1-5 microm So fracture toughness of SiC in TRISO fuel particle is likely to
be influenced by the grain size due to the similar range of grain size Although micro
cracks and pores could improve fracture toughness they would decrease the strength
[3] which is detrimental for the safe design of fuel particles Over several decades
studies have worked to improve the fracture toughness by introducing a
heterogeneous microstructure such as weak grain boundary phases [85] In the
heterogeneous phase toughening mechanism the cracks could initiate in or be
reflected into weak defects and thereby dissipate the fracture energy for the main
crack propagation Furthermore the distribution of grain boundary character (the
crystallagraphic type and frequency of grain boundaries) and morphology could
influence the fracture toughness [85 86] Different grain boundary orientations and
their frequency were found to affect the fracture toughness by controlling the
intergranular fracture of materials [86] Different grain morphologies such as
elongated grains could increase the fracture toughness by crack bridging or by
generating micro cracks along grain boundaries or triple junctions [85] No
heterogeneous phase is supposed to exist in SiC in TRISO fuel particles so the
fracture toughness is most likely to be affected by grain morphologies or as-deposited
defects
According to the Griffth fracture theory once the size of the critical flaw is the same
the fracture toughness is propotional to the fracture strength which is another
CHAPTER 2 Literature Review
55
parameter used in modelling of the probability of the failure of fuel particle
234 Fracture strength
For brittle materials the fracture strength is best considered as a distribution rather
than a fixed value as the flaws (such as surface cracks pores and inclusions) from
which fracture initiates vary in size and type (result in different frature strength value)
between nominally identical samples [3] The Weibull approach is a commonly used
empirical method to characterise the strength of a brittle material It assumes a simple
power-law stress function (eg in Eqs (18-20)) for the survival of the elements
which is integrated over the body volumesurface area (as shown in Eqs (19) and
(21)) In many cases this function gives results in the form of Weibull modulus (m in
Eq (19)) and characterstic strength which describe the width and magnitude of the
strength distribution [3] The Weibull modulus is the slope of Log-Log distribution
function of the survival of elements and strength (Eq (19)) For engineering
application the high Weibull modulus represents the small variation of the fracture
strengthes for a given material
Higher Weibull modulus reflects lower variability of the strength and it is typically in
the range of 5-20 [3] The commonly used strength test methods for bulk ceramics are
uniaxial tension three- and four-point bending However the small dimensions of
TRISO fuel particles make it difficult to measure the strength by those conventional
methods As a consequence some specific methods were developed in the last few
decades such as O-ring test [87 88] C-ring test [88] hemisphere bending [10]
internal pressurization [89] and crush test [5 89 90] The schematic of easily
repetitive fracture strength test geometries are given in Fig 216 and the obtained
fracture strength by different methods was shown in Table 25
CHAPTER 2 Literature Review
56
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Methods L
f (MPa) Weibull Modulus F
f (MPa) Ref
O-ring compression 596-1412 41-66 -- 87
O-ring compression 1050-1890 48-94 -- 88
C-ring Compression 980-2200 40-90 -- 88
Semi-spherical bend 720-1350 70-80 340-620 10
Inner pressurization -- 43-62 222-448 89
Crush test -- 58-75 356-427 89
Crush test 770-1324 40-73 330-647 5
Crush test 1484-1721 135-183 1045-1091 90
L
f Local fracture strength F
f Fracture strength of the full particle
The local fracture strength is in the range of 596-2200 MPa and the fracture strength
of the whole particle varies from 222 MPa to 1091 MPa Such significant variation is
tought to be caused by the differences in specimen size and loading mode which were
related to the nature of the Weibull distribution [1 3] It has been demonstrated that
specimens with larger volumesurface area (under the same loading mode) have lower
strength because there is an increased probability that a larger flaw exists in a larger
body Similarly when there is no volume difference the loading mode which stresses
larger area has lower local fracture strength [3] These discussions show the
importance of regulating the fracture strength test method and producing specimens
with regular shape and size
CHAPTER 2 Literature Review
57
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
The modified crush test developed by Byun et al [5] is recommended for the fracture
strength measurement of SiC in TRISO fuel particles because it considered the effect
of contacting area between SiC shell and plunger which reduced the variation and
uncertainty of the stress distribution under tensile stress
Modified crush test When a partial spherical shell is diametrically loaded by an
external load F concentrated on a small circular contact area of radius 0 the
maximum membrane stress and bending stress are given by [91]
2
1 2
1membrane
FC
t
(13)
CHAPTER 2 Literature Review
58
2 2
1bending
FC
t
(14)
where ν is the Poisson ratio t is the thickness of shell and C1 and C2 were defined as
2
1 0115004022050 C (15)
)27031exp(204412 C (16)
2 2 2 1 4
0[12(1 ) ( )]r R t (17)
max membrane bending (18)
where max (L
f ) is the fracture strength for locally loaded specimens R is the outer
diameter of shell t is the thickness of the SiC shell The distribution of local fracture
strength is analysed by the Weibull distribution function which presents the
cumulative probability of failure P as [5]
mL
f
E
m
s
F
fSdAP
00
exp1exp1
(19)
where L
f m 0 and ES are the local fracture strength the Weibull modulus the
characteristic sterngth and the size effect factor respectively The size effect factor is
dAS
m
s L
f
F
f
E
Byun et al [5] used the probability estimator as follows
1
N
iPi (20)
where iP is the probability of failure for the i th-ranked strength and N is the
CHAPTER 2 Literature Review
59
sample size The increased probability that the full SiC shell has more critical flaws
compared with the stress-weighted surface is corrected by the size effect and the
fracture strength of the full shell (F
f ) is given
L
f
m
L
f
m
F
E
L
EF
ftR
r
S
S
1
2
2
0
1
)(4
(21)
After adjusting the size effect the fracture strength of the full particl of different SiC
coatings could be compared In a previou study [87] the difference of the fracture
strength was attributed to the microstructural variations which were determined by
deposition conditions [87] More detailed analysis [510] showed that the variation of
fracture strength was due to factors such as porosity roughness of the IPyCSiC
interface and grain size For example Evans et al [10] observed that the surface
roughness influenced the failure of the particle withstrength improved by reducing
the inner surface roughness According to above discussion the variation of Weibull
modulus could be attributed to the different test methods flaw distribution and sample
size [3 5]
Micostructure and mechanical properties of as-deposited SiC are reviewed above
which may change after high temperature treatment and the degree of evolution could
be different due to variational deposition conditions of SiC coatings As summarized
in a previous study [92] one of the critical properties for SiC layers in TRISO fuel
particle is that the microstructure remains unchanged after thermal treatment at 2000
ordmC for 1 hour in an inert atmosphere as determined by electron microscopy and X-ray
diffraction
235 Effect of thermal treatment on SiC
The SiC with perfect crystal structure tends to have good high temperature thermal
stability however due to the concentration and type of imperfections generated
CHAPTER 2 Literature Review
60
during deposoition process its thermal stability could be affected Defects such as
stacking faults vacancies and interstitials in as-deposited SiC coatings affect the
microstructural change after thermal treatment [93-96] For example the phase
transformation from β- to α-SiC generally happened at temperatures above 2100 ordmC
[19] but it could take place at lower temperature (gt 1700 ordmC) in special cases (eg
CVD β-SiC deposited on Si substrate with high amount of stacking faults) [93]
During high temperature thermal treatment (about 2000 ordmC) of CVD β-SiC one
significant microstructural change would be the annihilation of stacking faults [94
95] A thermodynamics study [94] has shown that the mechanism of reduction of the
stacking faults was due to the diffusion of Si or C atoms and it also demonstrated that
the migration energy of Si atoms was smaller than C atoms Considering the
abundance of intrinsic defects (section 222) there has been little investigation of
their effects on microstructure change of β-SiC after thermal treatment Furthermore
the effects of high temperature thermal treatment on mechanical properties such as
the hardness Youngrsquos modulus [97] and strength [98] have been carried out Their
results showed that mechanical properties showed little change when the treatment
temperature was lower than 2000 ordmC while there was decrease in the strength after
thermal treatment at 2100 ordmC
24 Microstructure and properties of pyrolytic carbon
In this part the microstructure of carbon related material is reviewed first which is
followed by the measurement of Youngrsquos modulus and hardness Furthermore to
know the controlling factor on mechanical properties of PyC coatings different
deformation mechanisms under indentation are introduced A brief review about effect
of thermal treatment on properties of PyC coatings is given
CHAPTER 2 Literature Review
61
241 Microstructure of pyrolytic carbon
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
The graphite structure consists of graphene sheets having localized in-plane σ (sp2)
hybrids bonds and delocalized out of plane π (pz) orbital bonds connecting graphene
sheets The out-of-plane bond is a van der Waals interaction which is much weaker
than sp2 and sp
3 hybrids Pyrolytic carbon is a material with some covalent bonding
between its graphene layers as a result of imperfections (defects) in its structure [99]
Figure 217 gives schematics and TEM images showing different microstructures of
PyC with different densities The growth features are polyhedral or conical shape in
high density pyrolytic carbon (Fig 217 (ab)) but are globular in low density
pyrolytic carbon (Fig 217(cd)) [15] It shows that the microstructure of pyrolytic
carbon consists of growth features between 200 nm- 1000 nm in size (Fig 217 (b)
and (d)) [15] Pores were formed at the boundaries or triple junctions between growth
(a) (b)
(c) (d)
CHAPTER 2 Literature Review
62
features
According to previous studies [15101] individual growth features contain crystallites
(domains) as shown schematically in Fig 218(a) They are composed of a series of
curved graphene layers randomly rotated with respect to each other along the c-axis
[101] The dimensions of the crystal were described by La (diameter of crystal along
the χ direction) and Lc (height of the crystal perpendicular to χy plane) as shown in
Fig 218(a) Regarding the definition of the PyC there are defects within the growth
features together with crystallites A local atomic structure of less ordered graphene
layers is shown in Fig 218(b) which could reflect the plane defects in graphene
layers [102]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
A high density of defects such as dislocation loops and kink bands were observed in
ball milled graphite by HRTEM as shown in Fig 219(a) The distorted
microstructure of graphite was also inferred from the striped diffraction points in
selected area electron diffraction image (Fig 219(b)) [103] since the diffraction
pattern gives information on orientation of crystal planes Compared with ball milled
graphite the HRTEM image of pyrolytic carbon has higher amount of defects as
shown in Fig 19(c) which is reflected from the highly distorted lattice planes and low
texture The selected area electron diffraction image of pyrolytic carbon (Fig 219(d)
with eperture diameter of 200 nm) showed arc shaped diffraction patterns [15 104]
The arc represents the overlap of diffraction patterns from different graphite domains
CHAPTER 2 Literature Review
63
with different orientations and this indicats that the microstructure is more distorted
eg smaller domain size and increased random orientation of domains In heavily
disordered PyC it is not possible to observe the individual dislocations or other
defects which is thought to be due to the numerous defects such as tilt boundaries
which obscure individual defects as described in Ref [105]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
Raman spectroscopy is one of the most effective techniques to characterise the defects
in carbon materials and has previously been used to characterise the microstructure of
PyC [15 106] These spectra can identify even quantify the microstructure such as
crystallite boundaries and size disorders (5-memebered rings) and chemical bonding
type Figure 220 shows the evolution of the Raman spectra with the change of the
CHAPTER 2 Literature Review
64
in-plane defect types The carbon spectra of Fig 220(a-c) showed increased and
broadened D signal and the main in-plane defects observed in these structures were
supposed to be domain boundaries [15] In Fig 220(d-e) the D signal became shaper
which was attributed to the formation of five-member rings [15]
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
The high density of disorders such as in-plane domain boundaries makes the Raman
bands become broder and overlapped with each other as shown in Fig 220(c) which
inferred the structure of turbostratic or high density PyC [10 15] According to
previous studies [106 107] the broadened Raman bonds could be deconvoluted into a
number of peaks which correspond to different types of disordered structure in
carbon materials Figure 221 is an example of a first order Raman spectra fitted with
Lorentzian and Gaussian functions and it includs I (~1170 cm-1
) D (~1330 cm-1
) Drdquo
(~1500 cm-1
) G (~1580 cm-1
) and Drsquo(~1618 cm-1
) bands [106] The Drdquo peak was
CHAPTER 2 Literature Review
65
attributed to amorphous carbon with a certain amount of sp3 carbon [106108] which
could reflect the interstitial defects coupling to the graphene layers or adjacent
domains [109]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
242 Mechanical properties of pyrolytic carbon
The different deformation mechanism of carbon materials compared to ceramic
materials results in distinct force-displacement curves which show the complete
recovery of the unloading curve [110 111] Therefore we describe the mechanical
properties of PyC coatings and deformation mechanism of carbon materials
2421 Youngrsquos modulus and hardness
Due to the importance of PyC in the nuclear industry mechanical properties were
measured by three-point bending [102 112] and nano-indentation [113-115] Table
26 gives the Youngrsquos modulus and hardness of PyC measured by different methods
In three-point bending tests the mechanical properties were functions of density
orientation angle and domain size No individual factor could clearly explain the
variation in Youngrsquos modulus strength or fracture toughness [112116] In previous
nano-indentation tests the low density PyC was found to have low hardness and
Youngrsquos modulus [114] whereas the influence on mechanical properties was
CHAPTER 2 Literature Review
66
uncertain which could be due to lack of investigation about the deformation
mechanisms
Table 26 Summary of the hardness and Youngrsquos modulus for PyC measured by
different methods
Methods Density range
(gcm3)
Youngrsquos modulus
(GPa)
Hardness
(GPa)
Ref
3-point-bending 150-212 310-427 -- 112
137-206 165-281 -- 116
Nano-indentation 185-190 255 + 2 -- 114
165-203 235-270 30-44 115
155-187 70-150 05-18 115
135-212 125-346 15-48 113
Youngrsquos modulus was changed from PSI to GPa
Figure 222 is a schematic of the typical force-displacement curve of different kinds
of materials under indentation [65110111] The curve of carbon materials shows a
completely recovery and no net displacement after unloading as shown in Fig
222(a) In carbon materials the force-displacement curve formed a closed loop and
this phenomenon was called anelastic deformation behaviour [14 117] This was
related to the internal friction of materials but there is controversy regarding the
sources of the internal friction [14105111] Since the force-displacement curve gives
information about the energy change during indentation the deformation behaviour of
carbon material can be analysed by the energy method
The energy distribution under indentation is shown in Fig 222 which includs the
hysteresis energy (Uh) and unloading energy (Uunloading) and the total energy (loading
energy Uloading) is the sum of the above two energies [110] As shown in Fig 222 the
ratio of the hysteresis energy to total loading energy could be different for different
microstructure of carbon materials [118] The ratio could be used to estimate the
CHAPTER 2 Literature Review
67
flexibility of elasticityductility [110119] For example a low ratio corresponds to
higher elasticity whist a high ratio meants higher ductility
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
The different force-displacement curve of carbon materials was compared with the
irreversible deformation behaviour of materials with linear elasticity such as SiC as
shown in Fig 214(a) [65] In linear elastic deformation the final displacement of hf
was left after complete unloading and the unloading curve nearly followed the linear
relationship Furthermore the area between the loading and unloading curves
represents the energy consumed by the plastic deformation which could be due to the
movement of dislocations and formation of micro cracks [1 62]
2422 Deformation mechanism
Reversible slip and sliding friction theory In this theory the complete recovery of
strain was due to the reversible slip of graphene planes and the energy loss was
attributed to the friction during the slip which was caused by a compressive stress on
the graphene layers [110111] The theory was obtained by considering an arbitrary
grain located at some position in a radially declining hydrostatic stress field below a
spherical indenter as shown in Fig 223 [110111] The force was resolved into
CHAPTER 2 Literature Review
68
compressive stress perpendicular to and shear stress parallel to the slip plane By
using the equation proposed by Kelly [120] the shear component (τ τ0 shear stress
with and without friction respectively) may be expressed as τ= τ0 +μσ where μ is a
friction coefficient and σ is normal stress component To initiate slip between
graphene layers the shear stress needs to exceed some critical value Therefore the
inter-layer slip with friction was supposed to be the mechanism of anelastic
deformation The authors [110111] also concluded that the hysteresis during
unloading appeared to be a natural result of friction between the graphene layers but
additional mechanisms were supposed to be operating in the different forms of
graphitic materials Furthermore the study did not give a clear explanation about how
the reversibility of the basal plane slip was realized
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Dislocation pileup theory This idea was derived from isotropic carbon after thermal
treatment at the temperature range of 880-2600 ordmC by using micro indentation [121]
The authors attributed the unique unloadingreloading behaviour of the
well-graphitized carbons to the slip of dislocation networks on graphitic basal planes
which is partially or fully reversible It is supposed that the dislocations could pile up
at grain boundaries as in metals The stress at grain boundaries due to dislocation pile
ups could reverse the dislocation movement during indentation unloading but it did
CHAPTER 2 Literature Review
69
not explain why deformation behaviour of PyC is unlike that of metals This is also
the reason that other researches [105] doubt this theory because it fails to explain the
nature of the reversible behaviour [121]
Kink band theory It was suggested that the origin of the loops obtained in single
polycrystalline and porous carbons is the formation of incipient kink band and kink
bands [105] The kink band model was proposed by Frank and Stroh [122] as
shown in Fig 224 which showed pairs of dislocations of opposite sign nucleate and
grow at the tip of a thin elliptical kink (not clear about the nature) The stability of
kink bands depended on a shear stress [122]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
In this theory since the dislocations were confined to the basal plane the hysteresis
process was attributed to the reversible movement of the dislocation along a long
distance The same mechanism was used to explain the deformation behaviour of the
bulk polycrystalline graphite The microstructural change under indentation should
first be related to the kink band initiation and then further microstructure change
could be reflected in the accumulation of other chemical bonds which could resist
dislocation glide
CHAPTER 2 Literature Review
70
2423 Effect of thermal treatment on properties of PyC
The effect of thermal treatment on the microstructure of carbon materials has been
widely studied [112 123 124] The change of the microstructure of carbon materials
during thermal treatment mainly involves the growth of the domain size (in-plane
crystal size along a axis) La and (along c axis crystal size) Lc with the increase of
temperature For different kinds of carbon materials these evolutions started at
different temperatures For example the crystal growth in-plane happened at 400-600
ordmC for graphitisable carbon and could continue up to high temperature the
coalescence of crystallites along the c-axis started above 1000-1200 ordmC the
coalescence of crystallites along ab direction occurred at temperature above 1400 ordmC
[124] For carbons with strong cross-linking (non-graphitisable) the coalescence of
domains usually happened at temperatures higher than 2400 ordmC [124] Although the
increase in anisotropy and density during processing of coated particle fuel was
reported by Hunn et al [11] no change in texture was identified on PyC due to the
post deposition of SiC shown in Lopeacutez-Honorato et alrsquos study [125] Furthermore no
significant change of mechanical properties was obtained after thermal treatment at
temperatures in the range 1000-1980 ordmC in PyC coatings with density of about 19
gcm3 [97] however a decrease of Youngrsquos modulus was observed in high density
(above 2 gcm3) PyC coatings [125] It was assumed that certain microstructures of
PyC would be less affected by thermal treatment
25 Summary
The microstructure and mechanical properties of SiC and PyC were reviewed in this
Chapter and the information obtained is summarized below
(1) It is common for SiC to have defects such as stacking fautls and dislocations
non-stoichiometry and point defects due to their low formation energy
particularly in SiC deposited by chemical vapour deposition
CHAPTER 2 Literature Review
71
(2) Defects interact with each other Stacking faults could be the result of gliding
of partial dislocations Vacancies promoted diffusion of antisites forming
antisite clusters
(3) The Youngrsquos modulus of SiC coatings in TRISO fuel particle is affected
mainly by texture and porosity
(4) Hardness related plastic deformation in single and polycrystalline (nano-meter
or micro-meter grain size) SiC is related to dislocation propagation fracture
of crystallites or phase transformation
(5) A combination of indentation together with electron microscopy is an
effective way to study the fracture behaviour of SiC coatings in TRISO fuel
particle
(6) Fracture strength of SiC coating in TRISO fuel particle varies significantly in
different measurements and the modified crush test is recommended The
interface roughness and porosity are found to be main factors controlling
fracture strength of SiC coatings
(7) The typical change of microstructure after thermal treatment in SiC is the
annihilation of stacking faults through the diffusion of vacancies
(8) The disorder in PyC coatings could be significant such as domain boundaries
and 5-membered rings Raman spectroscopy together with transmission
electron microscopy are important techniques to characterize these disorders
(9) Carbon related materials show hysteretic deformation behaviour under
indentation Different deformation mechanisms are proposed which all relate
to the slip of graphene layers
CHAPTER 2 Literature Review
72
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[4] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
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[8] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
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74
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[62] X Zhao R M Langford I P Shapiro P Xiao Onset plastic deformation and
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[68] S Nagappa M Zupan CA Zorman Mechanical characterization of
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[79] G D Quinn RC Bradt On the Vickers indentation fracture toughness test J
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[100]J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
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[112]J C Bokros R J Price Deformation and fracture of pyrolytic carbons
deposited in a fluidized bed Carbon 3 (1966) 503-19
[113]E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure
and mechanical properties of pyrolytic carbon produced by fluidized bed
chemical vapour deposition Nucl Eng Des 238 (2008) 3121-28
[114]C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by
different techniques Thin solid films 469-70 (2004) 214-20
[115]G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
CHAPTER 2 Literature Review
82
[116]J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[117]L M Brown In H Libelt R Talreja Fatigue and creep of composites
materials Riskilde Denmark Riso National Laboratory 1982 p 1-18
[118]M Skai The Meyer hardness A measure for plasticity J Mater Res 14 (1999)
3630-39
[119]M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics ndash adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[120]B T Kelly The physics of graphite Applied Science Publications London
1981
[121]M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated
carbons J Am Ceram Soc 85 (2002) 1522-28
[122]F C Frank A N Stroh On the theory of kinking Proc Phys Soc 65 (1952)
811-21
[123]R F Franklin Royal Society London A London 1951 209 196
[124]F G Emmerich Evolution with heat treatment of crystallinity in carbons
Carbon 33 (1995) 1709-15
[125]E Loacutepez-Honorato P J Meadows R A Shatwell P Xiao Characterization
of the anisotropy of pyrolytic carbon by Raman spectroscopy Carbon 48 (2010)
881-90
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
83
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC
Coatings Measured by Indentation
31 Introduction
The silicon carbide (SiC) coating is the most important component for structural
integrity of Tri-isotropic (TRISO) fuel particles as it sustains most of the internal
pressure produced by the fission gases produced in the kernel [1-3] Youngrsquos modulus
and hardness are mechanical properties used in modeling to estimate the failure
probability of TRISO fuel particles [4] The values at room temperature are used due
to the fact that the Youngrsquos modulus slightly decreased at elevated temperature in SiC
material and the higher value could be kept until the temperature reached 2000 degC [1]
It was also found that SiC material with higher hardness at room temperature
maintains higher hardness values at temperatures up to 1600 degC [1] To achieve a
reliable fuel design a better understanding of the mechanical properties of the SiC
layer at room temperature needs to be established
It is difficult to use traditional methods to measure hardness and Youngrsquos modulus
due to the small dimension of the TRISO fuel particles (~1 mm) Nano-indentation
has made it possible to measure the hardness and Youngrsquos modulus accurately [5 6]
for a coating of such a small dimension Furthermore this method also offers the
ability to study the deformation behaviour under the indentation [7-12] as the
indentation stress field is of a localized character
Loacutepez-Honorato et alrsquos [5] study of SiC deposited at 1300 degC by fluidized bed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
84
chemical vapour deposition (FBCVD) showed that the SiC coatings produced under
those conditions had high hardness (gt 42 GPa) and Youngrsquos modulus (~455 GPa)
They found that even samples with the composition of SiC+C or SiC+Si showed high
mechanical properties It was shown that the coatings had sub-micrometer (lt1 μm
diameter) grain size but due to the complex microstructure the mechanism controlling
the hardness and Youngrsquos modulus was unknown Researchers [10 11 13-16] have
made efforts to study the deformation mechanism under indentation in SiC single
crystals and polycrystals (with a grain size lt 100 nm or grain size gt 1μm) Szlufarska
et al [15] suggested a crossover mechanism from indentation-induced crystallization
to deformation-dominated amorphization in nano-crystalline SiC
From the work reported [11 16 17] it is clear that dislocation initiation and
propagation is the primary response for the plastic deformation under an indentation
in single crystal and polycrystalline (gt 1μm) SiC Further it has also been found
while studying the microstructure [11 16 17] that defects such as stacking faults and
dislocations were present in these polycrystalline (gt 1 μm) SiC materials
(nano-indentation hardness less than 36 GPa) However the amount of defects were
lower compared to the low temperature (ie 1300 o
C vs 1500 o
C) FBCVD SiC [5]
The discrepancies in the microstructure and mechanical properties still demand
further explanation on the deformation mechanism of low temperature FBCVD SiC
This chapter focus on the fundamental study on the mechanical properties of SiC we
have investigated the Youngrsquos modulus and hardness of three sub-micrometer FBCVD
SiC coatings using the indentation method The microstructure and mechanical
properties are explained on the basis of defects observed with a transmission electron
microscope (TEM) The deformation behaviour underneath a nano-indentation is
discussed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
85
32 Experimental details
Silicon carbide (SiC) coatings were produced on top of highly-dense pyrolytic carbon
coatings using fluidized-bed chemical vapour deposition (FBCVD) method The SiC
coatings with varied stoichiometry and deposited at low temperature of 1300 oC by
Loacutepez-Honorato et alrsquos [5] were chosen and studied in this Chapter Table 1 gives the
deposition conditions of these coatings which were found and demonstrated to give
superberb mechanical properties in prevous studies [5] Figure 31(a) and (b) show the
polished cross-section (x-y plane) and (b) polished external surface section (x-z plane)
of TRISO fuel particles (defining the directions used in the later part of this Chapter)
Densities were measured by the Archimedes method in ethanol (density is the mean
value of three tests the weight of SiC shells is 01-03 g) Composition was measured
by Raman spectroscopy (Renishaw 1000 Raman system with a 514 nm argon laser
source) with a single spot measurements of around 1 microm diameter through an times50
objective lens as shown in Fig 31 (c) Two peaks at around 794 and 970 cm-1
are for
SiC and the asymmetric peaks around 200-500 cm-1
and 1500 cm-1
are acoustic SiC
and second order SiC respectively (S1 coating) [5] Carbon peaks are around 1360
and 1600 cm-1
(S2 coating) and the peak at 520 cm-1
represents silicon (S3 coating)
[5] It was estimated that the excess C amount is less than 1 at in S2 by measuring
the intensity ratios of I1600I794 and compared to previous study [18] where Raman
spectroscopy and elemental analysis (EPMA AES and XPS) were used
The phase and composition were also analysed using X-ray diffraction (XRD PW
1830 Philips Eindhoven The Netherlands) with Cu Kα1 radiation Figure 31(d)
shows the XRD spectra of the three types of SiC coatings All three coatings exhibit
the β-SiC phase A very small shoulder peak around 2θ=345deg was also obtained from
the coatings which indicated the presence of stacking faults No evidence of a Si or C
peak was found in the XRD result This was probably due to the fact that the
additional levels of Si and C were very small (le 1at ) and it would be difficult to
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
86
identify these traces using XRD [5 19]
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
Codes H2MTCS (volvol) Additives Temperature Density (gcm3)
S1 (SiC) 10 01vol Propylene 1300 o
C 3173 + 0029
S2 (SiC+C) 10 10 vol Propylene 1300 o
C 3135 + 0034
S3 (SiC+Si) 10 -- 1300 o
C 3188 + 0002
SiC+C or SiC+Si means that nearly stoichiometric SiC with low excess C or Si less than 1 at
Productions of samples are contributed by Dr Eddie Loacutepez-Honorato
SiC coated fuel particles were hot mounted in copper-loaded conductive resin To
reduce the influence of the surface roughness the FBCVD SiC coatings were first
ground down to obtain a flat surface where the nano-indentation could be carried out
The flat surface was further polished using increasingly finer diamond suspensions
until frac14 μm and finally polished using a 003 μm colloidal silica suspension The
thickness of the coating after final polishing was estimated to be around 60 μm A
final surface roughness of lt 5 nm was detected by atomic force microscopy (AFM)
Youngrsquos modulus and hardness were measured using a nano-indenterTM
XP (MTS
System Corp USA) and a micro-indenter (CSM Instruments Switzerland)
Nano-indentation was made using a Berkovich indenter calibrated with a standard
silica specimen Before the measurement the initial contact of the indenter with the
specimen surface was checked and the compliance of the loading column was
corrected Arrays of indentations were performed on each specimen with an interval
of 20 times the indentation depth between each indentation The penetration depth for
the measurement of Youngrsquos modulus and hardness was 500 nm All data were
analysed using the Oliver and Pharr method [7] Micro-indentation was made using a
Vickers indenter at a maximum load of 3 N and the interval between each indentation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
87
was also kept to 20 times the indentation depth of ~26 μm
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
(c)
(d)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
88
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Moreover a high purity (gt999995) and fully dense polycrystalline 3C-SiC bulk
(diameter 3 cm thickness 15 cm) sample fabricated by static CVD (Rohm amp Haas
Ltd UK) was used as a reference sample in order to confirm the accurate mechanical
property measurements for FBCVD SiC coatings The Raman spectroscopy of bulk
CVD SiC was the inset in Fig 31(b) and no excess C or Si was found in it
To observe the grain morphology more clearly the finely polished (no scratch could
be seen under optical microscopes times50) cross-section (Fig 1(a)) of the coatings were
chemically etched using Murakamirsquos solution (10 g sodium hydroxide and 10 g
potassium ferricyanide in 100 ml of boiling water) The surface morphology of
coatings was characterized using scanning electron microscopy (Field emission gun
Philips XL30 FEG-SEM) A transmission electron microscope TEM (FEG-TEM
Tecnai TM
G2 F30 U-TWIN 300KV) was used to study the microstructure of the
coating layer before and after indentation For cross-sectional analysis of indentations
TEM samples were made from thin plates which are parallel to one edge and through
the center of Berkovich indentation using a focused ion beam (FIB FEI Nova 600
Dual Beam system) milling For high resolution TEM (HRTEM) the samples were
prepared using an ion beam milling method
33 Results
331 Hardness and Youngrsquos modulus
Figure 32 shows the typicl load-displacement curve of SiC coatings and the hardness
(H) and Youngrsquos modulus (E) as a function of composition of the three types of
coatings The load-displacment curve (Fig 32(a)) shows a smooth character of the
deformation process during nanoindentation There is multiple mini lsquopop-inrsquo events
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
89
reflected on the hardness curve which started at the beginning from the low
indentation load These mini lsquopop-inrsquo can not provide enough consumption of the
internal stresses induced by indenter as it was needed for the initiation and
propagation of dislocations so no well-pronounced lsquopop-inrsquo effect was observed from
the load-displacement curve
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Measurements were made on the x-z plane of SiC coatings (Fig 31(b)) and static
bulk CVD SiC for both micro- and nano-indentation to give reliable comparison with
previous studies [20-23] In the reference material the nano-hardness (36 GPa) and
Youngrsquos modulus (496 GPa) of bulk CVD SiC are nearly the same as in a previous
(c) (b)
(a)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
90
study [20] namely 36 GPa and 503 GPa respectively From Fig 32(b) it can be seen
that S1 has a higher hardness compared with S2 and S3 Further the values of
hardness obtained by nano-indentation (Fig 32(b)) are higher than by
micro-indentation for all samples
For low temperature FBCVD coatings the nano-hardness varies in the range 39 GPa
to 44 GPa whereas the micro-hardness varies between 36 GPa - 42 GPa These values
are at least 8 higher than the bulk static CVD SiC which has a nano-hardness ~36
GPa and a micro-hardness ~32 GPa (see Fig 32(b)) Moreover the low temperature
FBCVD SiC coatings have higher hardness as compared to a previous study of CVD
SiC for which the hardness values varied in the range of 25-39 GPa as measured by
nano-indentation under the similar experimental conditions [20-23]
In FBCVD SiC coatings Youngrsquos modulus of all three coatings is lower than the bulk
CVD SiC (see Fig 32(c)) which is an average Youngrsquos modulus (438 GPa) of
polycrystalline CVD SiC reported by Roy et al[24] The difference in hardness and
Youngrsquos modulus data could not be simply explained by the existence of C or Si due
to their low concentration (lt 1 at ) and location in the coatings which has been
addressed in detail in previous study [25] Therefore the difference of hardness and
modulus could be related to other microstructure such as pores which could vary
from atomic scale to micrometres which is discussed in the following session
Both nano- and micro-hardness results (Fig 32(b)) are higher than the available data
for polycrystalline CVD SiC [20-23] as discussed above and the correct measurement
of SiC coatings with small dimensions was ensured by comparing with the bulk CVD
SiC As mentioned the hardness and Youngrsquos modulus measured by
micro-indentation are slightly lower than the values measured by nano-indentation
because cracks were formed under micro-indentation due to the higher indentation
load
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
91
332 Microstructure of low temperature FBCVD SiC
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Figure 33 shows SEM images of the three etched FBCVD SiC coatings In all three
coatings the width and length of columnar grains were found to be approximately 200
nm and 1-2 μm respectively These are found to be much smaller than the SiC coating
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
92
produced at a temperature of 1500 degC which had width ~1μm and length ~4-5 μm
[17] They are also smaller than the SiC showing dislocation movement under the
indentation deformation zone which was produced at temperature of 1500-1600 degC
by FBCVD and 1500 degC by static CVD with grain size of 1-5 μm and 5-10 μm
respectively [11 16]
Although the grain size is in a similar range for three coatings (as mentioned above)
due to different deposition conditions the grain morphologies of three coatings vary
First a less laminar structure was observed in the S1 coating (see Fig 33 (a)) as
compared to the coatings with excess C or Si (Fig 33 (c) and (e)) Fig 33 (b) shows
the existence of triple junctions (dashed circle) that could resist the movement of
grain boundaries and dislocation slip [12] Pores were also observed along the laminar
structure after etching In the S2 coating it has a large amount of a laminar structure
running through a single grain (laminar structure parallel to growh direction) as
illustrated in Fig3 (d) The information of grain morphology in S2 was mostly a
laminar structure perpendicular to the growth direction after etching (Fig 33(d))
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
To get more information about the grains morphology in S2 coating a TEM image
05 μm
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
93
was taken and shown in Fig 34 Figure 34 shows that grains in S2 coating interact
(branch-like grain growth pattern on the lower-left part of Fig 34) with each other
which is similar as in sample S1 (Fig 33(b)) and grains form branch like structures
In the S3 coating (as can be seen in Fig 33 (f)) a parallel growth of grains with less
interaction among grains was observed
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
According to a previous study [25] about definition of grain boundary the grain
boundary in the S3 coating is smooth while in the S1 and S2 coating the grain
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
94
boundaries are rough which could result in branch-like grain growth pattern It could
be attributed to the different CSi ratio in reaction gas which produce SiC with
different morphologies on the (111) crystal plane which may have three different
morphologies rough smooth and pyramidal defect [26] Grains with differently
finished surfaces could lead to different grain growth morphologies because of
different surface energy For example in rough grain boundaries of S1 and S2
coatings branch like crystals were found as in Fig 33(b) and Fig 34
Figure 35 shows bright field TEM images of the S1 coating S2 and S3 coatings The
columnar grains were observed to grow perpendicular to the coating surface which
was consistent with the SEM results Further nano porous layers normal to the
coating growth direction are observed in the S2 coating (see Fig5 (b)) The formation
of porosity in thin films could be due to differences in diffusion of growth species the
incident molecule direction and deposition of secondary phases such as excess Si or C
[27]
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
BF-TEM and (b) DF-TEM
At low deposition temperatures the probability of a precursor reaching the edge of the
nucleus is considerably lower compared with that of arriving on the top due to a low
surface diffusion As these nuclei grow the areas immediately around them will suffer
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
95
from a shadowing effect blocking the arrival of new molecules and the formation of
new nuclei Since the diffusivity of atoms is low and no new nuclei are formed in
those regions gaps will be formed among grains A wrinkled like defect layer was
seen in the S3 coating (Fig 35 (c)) which could be attributed to the interruption of
the SiC crystallization growth during the deposition process such as crystal lattice
misorientation as seen in Fig 36
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
No obvious laminar defect was observed in the S1 coating by TEM this could be due
5 nm
(a) (b)
5 nm
5 nm
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
96
to less interruption during deposition process According to above observation it was
proposed that the laminar structure observed in SEM images indicates some
instability during the fabrication process resulting in the deposition of the nano- and
micro-pores and misorientation This was attributed the variations in circulation and
deposition occurring close to the nozzle or at the hot zone [5]
Stacking faults were observed for all three types of samples as shown in Fig 35 with
a higher density than for the SiC deposited at a temperature of 1500 C [11 16 17]
These stacking faults could cause an intrinsic residual stress due to the coexistence of
the partial dislocations This was supported by the high resolution TEM images
(shown in Fig 37) exhibiting wave pattern fringes and they could only be observed
in one direction which is determined by the intrinsic stress
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Since the dislocation mobility under nano-indentation deformation has not been fully
understood in hard ceramic materials therefore it is significant to study this
behaviour in FBCVD SiC coatings with a sub-micrometer grain size However it is
difficult to observe the dislocations under the two-beam or weak beam dark field
2 nm
(a)
(111)
[110]
(111)
Sessile
dislocations
(b)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
97
conditions due to the high density of defects In the present study the reversed fast
Fourier transform (FFT) images of the corresponding high resolution TEM images
was used to obtain information about the dislocations This method has been used in
many cases for dislocation observations [28]
Figure 38(a) shows a high resolution TEM image of a S1 coating which was taken as
a representative image to compare the atomic structure of all three coatings Figure
38(b) is the reverse FFT image using the marked inset diffraction pattern of Fig
37(a) in which sessile and glide dislocations can be observed The dislocation
density was calculated from the total number of glide dislocations divided by the area
in the image [29 30] From the analysis of images shown in Fig 38 the dislocation
density in S1 coatings was found to be 1013
cm2 The same magnitude of dislocations
density was found in the S2 and S3 coatings as shown in Fig 37 (three HRTEM
images were analysed for each coating)
333 Deformation behaviour under the indentation
The deformation zone under the indentation was investigated through the images of
FIB milled TEM samples in order to study the deformation mechanism of the low
temperature FBCVD SiC coatings Figure 39 shows the bright field TEM images
showing the mechanical behaviour of a S1 coating under nano-indentation on the x-z
plane (Fig 31(b)) at a maximum indentation depth of 500 nm
Figure 39(a) is an overview of the deformation area under an indentation A median
crack has formed just underneath the surface and has a direction aligned with the
indenter tip impression A higher magnification image around the elastic and plastic
interface is shown in Fig 39(b) It can be seen that a large amount of inter-granular
and trans-granular micro cracks were produced around the median crack initiation
zone This is substantially different from the dislocation-related plastic deformation
behaviour [10 11 16 31] which usually has a severe plastically deformed region
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
98
with few or no cracks Moreover the micro cracks were also observed in the C and D
zones under the indentation
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Figure 39(c) shows that micro cracks that are formed along the grain boundaries
which tend to follow the shear band direction with the formation of a few
trans-granular cracks In Fig 39(d) it can be seen that shear band micro cracks were
formed in one single grain (see inset in the left bottom corner of Fig 39(d)) This
single grain has a large amount of defects which are supposed to be the as-deposited
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
99
defects as shown in Fig 35(a) Shear band cracks were also observed just underneath
the indenter tip (right top inset in Fig 39(d)) As a result a shear band dominated
deformation zone can be seen in Fig 39(c d) under the indentation in a S1 coating
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
The S2 and S3 coatings only show a micro crack pattern which is different from S1
coating Figure 310 gives the TEM images of the S2 and S3 coatings showing the
mechanical reaction underneath the indentation It can be seen from Fig 310(a) and
Fig 310(c) that the median cracks are not always produced under the indentation for
S2 and S3 coatings However some irregular cracks in S3 coatings and lateral cracks
in S2 were produced In particular in the S3 coating (Fig 310(b)) more micro cracks
either intragrain or transgrain were found than in the S1 and S2 coatings This is due
to the fact that the most micro cracks propagate along the grain boundaries in S1 and
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
100
S2 coatings (Fig 39(b) and Fig 310(d)) A careful analysis of the TEM images
shows that only micro cracks were found under the indentation and no
dislocation-induced shear band was observed This is different from previous studies
on the deformation behaviour of polycrystalline SiC [11 16 31] For example in bulk
polycrystalline CVD SiC [11] it was found that it has more dislocation slip bands
rather than micro cracks either in grains or along grain boundaries even though the
indentation load is higher than the load used in the FBCVD SiC based materials The
possible reason of this discrepancy is discussed later Moreover no amorphous phase
and α-SiC phase was formed under the indentation observed by diffraction and bright
field TEM images which is consistent with the work of Mishra and Szlufarska [32]
34 Discussion
High hardness and Youngrsquos modulus were obtained in the sub-micrometer grain size
coatings produced at a low temperature by FBCVD In the S1 coatings the
nano-hardness is ~22 higher while the micro-hardness is ~31 higher compared to
a commercial CVD SiC The higher hardness was also obtained in S2 and S3 coatings
All the coatings retained a higher Youngrsquos modulus than those SiC materials having
high hardness in previous study (equal or higher than 40 GPa nano-hardness) [33]
making these coatings unique among polycrystalline phase brittle ceramic material
Under nano-indentation only micro cracks were found in the deformation zone The
results seem to be consistent with the conventional view of the failure mechanism of
brittle ceramics at room temperature [34] The lack of dislocation and the high Peierls
force are reasons for fracture to occur in brittle materials However
dislocation-related plastic deformation routinely occurred in hardness testing because
the indentation stress field offers conditions of stress conductive to plastic
deformation [11 13 16 34] Molecular dynamic simulations even demonstrate that
13 of the hardness-related deformation is from dislocation-related plastic deformation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
101
while 23 comes from fracture in SiC [31] It is rare to see a deformation zone
dominated by micro cracks in polycrystalline SiC such as in FBCVD SiC coatings
(Fig9 and Fig10 and see for example Ref [11 16 31]) With the above questions
we first estimated the factors controlling Youngrsquos modulus in FBCVD SiC coatings
followed by a study of the mechanism of superior hardness and deformation under an
indentation which influence the hardness in the three coatings
341 Influence of porosity on Youngrsquos modulus
Youngrsquos modulus presents a material constant for uniaxial tensile deformation which
is physically related to the atomic spacing inter atomic bond strength and bond
density In a low temperature FBCVD SiC coating it was shown from XRD
measurements that a shoulder peak was observed in addition to the β-SiC (111)
diffraction peak which corresponded to a crystal plane spacing of ~0266 nm (Fig
31(c)) Moreover we found that the XRD peak shifted to a lower diffraction angle
compared with the bulk CVD SiC According to the XRD pattern in Fig 31(c) the
crystal lattice constants of about 04366 04368 and 04368 nm for S1 S2 and S3
coatings were obtained respectively However the crystal lattice constant for bulk
CVD SiC is ~04359 nm (XRD pattern obtained by the same condition was shown in
Ref 25)
Further crystal orientation impurities and porosity may affect the Youngrsquos modulus
As the Youngrsquos modulus on the x-z plane (Fig 31(b)) was similar to the value
obtained along the cross-section (Fig 31(a)) [5 25] which meant that the orientation
has no effect on Youngrsquos modulus Moreover as discussed before the effect of C or Si
in S2 was found to have no effect on the difference of hardness and Youngrsquos modulus
Excluding these two factors (orientation and impurities) the effect of porosity on
variation of the elastic properties in three coatings was investigated The presence of
nano-pores in S2 coating as in Fig 35(b) results in a lower density Although no
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
102
pores were directly observed by TEM in the S1 and S3 coatings their density is lower
than the theoretical density of SiC Thus the elastic modulus E at room temperature
can be expressed in an exponential function of porosity pV [35] as
0 exp( )pE E CV (1)
where 0E = 496 GPa is the elastic modulus and C = 357 is a constant for a pore-free
bulk CVD SiC pV is the ratio of the relative density difference to the theoretical
density of SiC (322 gcm3)
The calculated Youngrsquos modulus for S1 S2 and S3 coatings is 465 plusmn 15 446 plusmn 17 and
473 plusmn 1 GPa respectively which follows a trend similar to the experimental data
presented in Fig 32 It was concluded that the different Youngrsquos modulus in the three
low temperature FBCVD SiC coatings is attributed to porosity although the
experimental Youngrsquos modulus data of FBCVD SiC coatings is slightly lower than the
values calculated using the Eq(1) The difference between calculated and measured
value of FBCVD SiC coatings is due to the fact that the 0E from pore-free bulk
CVD SiC instead of pore-free FBCVD SiC coatings (not available) FBCVD SiC
coatings have larger crystal lattice constant (~0437 nm) than bulk CVD SiC (~04359
nm) as discussed above Since the expanded lattice constant leads to a decrease of the
Youngrsquos modulus according to a previous study [20] the 0E of pore-free FBCVD SiC
coating is expected to be lower than bulk CVD SiC
342 Mechanism for High hardness
From previous studies [10 11 16 31] dislocation nucleation and glide is the primary
response of SiC under nano-indentation Formation of shear bands due to dislocations
has also been reported [11] which were found under the plastic deformation zone
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
103
when indentations were made on a particular grain in polycrystalline SiC and at the
grain boundaries Moreover dislocation nucleation is also correlated with the discrete
pop-ins observed in the force-displacement curve [32] No pop-ins was found due to
the presence of a large amount of dislocations in the present study Dislocation
mobility can be estimated similar to the case of a metallic material having intrinsic
dislocations Mishra and Szlufarska [32] worked on the dislocation mobility in
3C-SiC using large-scale molecular dynamics simulations The results indicated that
dislocation mobility decreased by dislocation interaction as its density reached a
saturation value This is similar to the work hardening effect in a metallic material [34]
We estimated the stress ( ) needed for dislocation to move using Taylorrsquos work
hardening equation [34] given by
1 2
0 Gb (2)
where 0 is the shear stress for a dislocation to move without any obstacle and the
value of 0 taken was 75 GPa [13] is a numerical constant depending on the
locking strength of a nod The value of taken was 8 [36] b is Burgers vector
where b = 0178 nm for a Shockley partial dislocation in SiC initiated and gliding on a
close packed (111) plane and is the density of glide dislocations G is the shear
modulus which can be written as
2(1 )
EG
(3)
where is the Poissonrsquos ratio and E is the Youngrsquos modulus The dislocation density
was ~03times1012
cm2 The calculated shear stress according to Eq (2) was ~52 GPa and
this value is much higher than the theoretical shear stress which is in the range of
295-4312 GPa obtained from previous reports [37-39] The theoretical shear stress is
the maximum stress provided for the dislocation nucleation and propagation in SiC
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
104
crystals Therefore the dislocation-related yield behaviour could not occur under the
plastic deformation zone in sub-micrometer FBCVD SiC coatings
The superior hardness value in FBCVD SiC coatings is attributed to the immobility of
the dislocations In the case of the SiC-C solid solution [40] the occurrence of a high
density of dislocations causes a strain-hardening effect Furthermore given that
dislocations could be motivated by the shear stress a phase transformation from a
crystalline phase to an amorphous could occur [32] However no amorphous phase
was observed under the nano-indentation (Fig 37 and 8) nor was dislocation
movement band observed in this study This suggests that the dislocation-related
phase transformation did not occur under the indentation
343 Deformation mechanism under nano-indentation
The hardness-related plastic deformation which occurs due to the nucleation and
propagation of micro cracks in FBCVD SiC coatings can be explained as follows
(i) The onset of plastic deformation under the indentation occurs as the maximum
shear stress approaches the yield stress [41] According to 15H Y (Y is the yield
stress H is the hardness) the yield stress in FBCVD SiC coatings is around 26 GPa
The yield stress is lower than the stress needed for the movement of dislocations and
the theoretical shear stress [37-39] This indicates that the hardness-related plastic
deformation first occurred by the nucleation of defect-induced cracks which
propagated to the indented surface (see inset (top right) in Fig 39(d)) The
deformation impression was accommodated by the densification of defects such as
the pores dislocation pile ups and grain boundaries as in Fig 33(b)
(ii) The shear stress was used to promote the movement of dislocations under the
indentation and form slip bands in previous studies [10 11 42] The highest amount
of micro cracks were observed in FBCVD SiC coatings contrary to plastic
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
105
deformation under the indentation found in previous studies [10 11 42] The micro
cracks formed in the hardness-related plastic deformation zone is the Mode-II crack)
[43] as shown in Fig 39(c) and (d) Unlike Mode-I which is dominated by the tensile
stress a Mode-II crack is the consequence of a confined shear stress [34] At the
interface of the elasticplastic deformation branch-like micro cracks were observed
as in Fig 39(b) The above discussions distinguish the hardness-related plastic
deformation mechanism in FBCVD from previous studies on ceramics which showed
dislocations are the main deformation mechanism underneath the indentation [31 44]
A unique hardness-related plastic deformation mechanism was used to explain the
difference in hardness of all three types of FBCVD SiC coatings According to Qian
et al [45] the hardness could reach an asymptotic value with the saturation of the
micro cracks growth population In three FBCVD SiC coatings studied here different
amounts of micro cracks were found (Fig 39(b) and Fig 310(b d)) and micro cracks
nucleated at stress concentration zones such as the grain boundaries or defects within
the grains Thus the difference in hardness was attributed to the grain morphologies
as shown in Fig 33 which gives different degree of resistance to the initiation and
propagation of micro cracks In the S1 coating triple junctions hamper grain
boundary shear by forming interlocks [12] which could resist and deflect the initiation
and propagation of micro cracks In the S2 coating elongated grains interact with the
surrounding small grains which could also provide interlocks (Fig 33(d) and Fig
34) The slightly lower hardness of the S2 coating as compared to the S1 coating is
due to the nano pores as seen in Fig 35(b) A lack of triple junctions and grain
interactions could be the reason for the lower hardness in the S3 coating as it has a
parallel crystalline morphology which has less constraint towards the initiation and
propagation of cracks
35 Conclusions
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
106
The microstructure and mechanical properties of three types of FBCVD SiC coatings
(SiC SiC+C and SiC+Si) were studied FBCVD SiC coatings with a sub-micrometer
grain size were deposited on simulated TRISO fuel particles by FBCVD at a low
temperature (1300 oC) The mechanical properties were studied using micro and
nano-indention The microstructures were studied using SEM and TEM It was
found that the Youngrsquos modulus of all three coatings differ which was attributed due
to the presence of nano-pores The high hardness of FBCVD SiC coatings was due to
the large amount of defects particularly the high density of dislocations It is found
that the interactions between dislocations reduced their mobility and make
dislocation-related plastic deformation unavailable We suggest that the work
hardening effect is the reason for the high hardness in the sub-micrometer grain size
FBCVD SiC coatings A hardness related-deformation mechanism was attributed to
the initiation and propagation of micro cracks The nano-indentation indent volume is
most likely be accommodated by the densification of defects such as the pores As a
result the hardness difference in FBCVD SiC coatings is due to the different grain
morphologies producing different amounts of micro cracks
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
107
36 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[2] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[3] D A Petti J Buongiorno J T Maki R R Hobbins G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[4] A C Kadak R Gnallinger M J Driscoll S Yip D G Wilson H C No J
Wang H Maclean T Galen C Wang J Lebenhaft T Zhai D A Petti W K
Terry H D Gougar A M Ougouag C H Oh R L Morre G K Miller J T
Maki G R Smolik D J Varacalle Modular pebble bed reactor Modular pebble
bed reactor project University research consortium annual report Beijing 2000
[5] E Lopez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[6] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram P Xiao Youngs modulus measurements of SiC coatings on spherical
particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[7] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[8] C H Chien S R Jian C T Wang J Y Juang J C Huang Y S Lai
Cross-sectional transmission electron microscopy observations on the Berkovich
indentation-induced deformation microstructures in GaN thin films J Phys D
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
108
Appl Phys 40 (2007) 3985-90
[9] T C Tan C A Merrill J B Orton A K Cheetham Anisotropic mechanical
properties of polymorphic hybrid inorganic-organic framework materials with
different dimensionalities Acta Mater 57 (2009) 3481-96
[10] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
related isostructural materials to nanoindentation Slip vs densification Mater
Res Soc Symp P 522 (1998) 113-18
[11] X Zhao X R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of 3C-SiC upon indentation at room temperature J Am
Ceram Soc 94 (2011) 3509-14
[12] D Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
mechanism of plastic deformation in macro- micro- and nanoindentation
processes J Phys D Appl Phys 41 (2008) 074016-24
[13] H P Chen R K Kalia A Nakano P Vashishta I Szlufarska
Multimillion-atom nanoindentation simulation of crystalline silicon carbide
Orientation dependence and anisotropic pileup J Appl Phys 102 (2007)
063514-22
[14] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[15] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[16] G Chollon J M Vallerot D Helary S Jouannigot Structural and textural
changes of CVD-SiC to indentation high temperature creep and irradiation J Eu
Ceram Soc 27 (2007) 1503-11
[17] D Heacutelary X Bourrat ODugne G Maveyraud M Peacuterez O Guillermier
Microstructures of silicon carbide and pyrocarbon coatings for fuel particles for
high temperature reactors 2nd international topical meeting on high temperature
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
109
reactor technology Beijing China 2004
[18] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[19] T Fukuzaki K Tanaka K Nishimoto Y Mur K Nishio and R Tamura
Magnetic property and microstructure of Nd-Fe-B-M (M=Si C) bulk
pnanocomposite magnets prepared by spark plasma sintering method - art no
012015 J Phys Conf Ser 106 (2008) 12015-124
[20] M C Osborne J C Hay L L Snead D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[21] K H Park S Kondo Y Katoh A Kohyama Mechanical properties of beta-SiC
after Si- and dual Si plus He-ion irradiation at various temperatures Fusion Sci
Technol 44 (2003) 455-59
[22] S Nagappa M Zupan C A Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
Mater 59 (2008) 995-98
[23] C Bellan J Dhers Evaluation of young modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[24] S Roy C Zorman M Mehregany R Deanna C Deeb The mechanical
properties of polycrystalline 3C-SiC films grown on polysilicon substrates by
atmospheric pressure chemical-vapor deposition J Appl Phys 99 (2006)
044108-20
[25] J Tan Mechanical properties of SiC in TRISO fuel particle Thesis University of
Manchester 2010
[26] M J Hernandez G Ferro T Chassagne J Dazord Y Monteil Study of surface
defects on 3C-SiC films grown on Si (111) by CVD J Cryst Growth 253 (2003)
95-101
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
110
[27] E S Machlin Materials science in microelectronics I The relationships between
thin film processing and structure 2nd
ed Oxford Elsevier Science 2005
p206-47
[28] A Nakamura T Yamamoto Y Ikuhara Direct observation of basal dislocation
in sapphire by HRTEM Acta Mater 50 (2002) 101-08
[29] H Y Shin S K Kwon Y I Chang M J Cho K H Park Reducing
dislocation density in GaN films using a cone-shaped patterned sapphire substrate
J Cryst Growth 311 (2009) 4167-70
[30] W D Callister Materials science and engineering An introduction 7th ed
Australia John Wiley amp Sons Australia Limited 2006 p191-99
[31] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
materials with a density functional theory J Appl Phys 104 (2008) 053508-16
[32] M Mishra I Szlufarska Possibility of high-pressure transformation during
nanoindentation of SiC Acta Mater 57 (2009) 6156-65
[33] A R Beaber L J Qi J Hafiz P H Mcmurry J V R Heberlein W W
Gerberich S L Girshick Nanostructured SiC by chemical vapor deposition and
nanoparticle impaction Surf Coat Tech 202 (2007) 871-75
[34] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
p162-91
[35] R W Rice Mechanical properties of ceramics and composites 1st ed New
York Marcel Dekker 2000 p457-534
[36] U Messerschmidt Dislocation dynamics during plastic deformation Part 2
Ceramic Single Crystals Springer Series in Materials Science On line 2010
p264
[37] S Ogata J Li N Hirosaki Y Shibutani S Yip Ideal shear strain of metals and
ceramics Phys Rev B 70 (2004) 104104-10
[38] Y Umeno Y Kinoshita T Kitamura Ab initio DFT study of ideal shear
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
111
strength of polytypes of silicon carbide Strength Mater 40 (2008) 2-6
[39] Y Umeno M Cerny Effect of normal stress on the ideal shear strength in
covalent crystals Phys Rev B 77 (2008) 100101-04
[40] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[41] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000 p139-77
[42] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[43] A A Wereszczak K E Johanns O M Jadaan Hertzian Ring Crack Initiation
in Hot-Pressed Silicon Carbides J Am Ceram Soc 92 (2009) 1788-95
[44] S L Lloyd A Castellero F Giuliani Y Long K K Mclaughlin J M
Molina-Aldareguia N A Stelmashenko L J Vandeperre W J Clegg
Observations of nanoindents via cross-sectional transmission electron microscopy
a survey of deformation mechanisms P Roy Soc a-Math Phy 461 (2005)
2521-43
[45] J Qian L L Daemen Y Zhao Hardness and fracture toughness of moissanite
Diam Relat Mater 14 (2005) 1669-72
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
112
CHAPTER 4 Vickers Indentation Fracture Toughness of
SiC Coatings
41 Introduction
Silicon carbide (SiC) layer is considered to be the most important component for
structural integrity as during the operation of a nuclear reactor it has the ability to
sustain most of the internal pressure caused by gaseous fission products produced in
the kernel and retain most of the fission products [1-4] Previous work was focused on
the investigation of mechanical properties (Youngrsquos modulus and fracture strength) of
SiC coatings on TRISO particles using different techniques such as a ring test [5 6]
a crush test [7 8] a micro-cantilever test [9] and indentation [10 11] However few
reports exist on the measurement of the fracture toughness of SiC coatings even
though it is a property used in modeling to estimate the failure probability of TRISO
fuel particles [12] For example Kadak et al [12] used a fracture toughness value of
33 plusmn 053 MPa m12
This value was obtained from bulk SiC produced by a static
CVD method The fracture toughness value may well differ for SiC coatings produced
by fluidized bed chemical vapour deposition (FBCVD) on TRISO fuel particles [10]
Because microstructure of SiC produced by static CVD and FBCVD methods could
vary significantly For example the static CVD SiC usually has larger grain size and
high density while FBCVD SiC with large grain size is usually accompanied with
porosity [13] Different grain size range and porosity fraction can lead to variation of
fracture toughness [1 2] Therefore the fracture toughness value of bulk SiC may not
be truly representative of SiC coatings used in nuclear fuel applications To our
knowledge the only available data on the fracture toughness of a SiC layer on TRISO
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
113
fuel particle is reported by Zhao et al[9] where the fracture toughness was measured
by the micro-beam method However this method is time consuming and expensive
restricting its implementation as a standard characterization technique where
repetitive measurements are required to confirm the reproducibility of experimental
data
In this Chapter micro-indentation is used to investigate the fracture behaviour of
different SiC coatings produced (on TRISO fuel particles) by FBCVD due to its
capacity to measure the mechanical properties in a small area and produce visible
cracks [14-16] The fracture behaviour under an indenter is also studied using a
transmission electron microscope (TEM) in order to give better understanding of the
fracture mechanism The characteristics of the SiC microstructures are then correlated
with their fracture behaviour
42 Experimental details
The SiC coatings used are the same as the ones in Chapter 3 and the deposition
conditions were shown in Table 31 Chapter 3
For the micro-indentation study SiC coated fuel particles were hot mounted in
copper-loaded conductive resin (to get better SEM images) and then ground to a
cross-section (as shown in Fig 31(a)) or polished a flat external surface (as shown in
Fig 31(b)) In this Chapter the y direction is called radial direction x is called
tangential direction according to Fig 31(a) and (b) The samples were then polished
using increasingly fine diamond suspensions to 14 μm Indentation fracture
toughness measurements were performed using a Vickers diamond indenter (CSM
Instruments Switzerland) Due to the through-thickness (in the radial direction)
failure behaviour of a SiC coating in a TRISO fuel particle under tensile stresses
generated from gases due to nuclear reactions similar tensile stresses could be
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
114
generated from indentation of polished external surface of TRISO particles which
could generate cracks along the radial direction (y direction in Fig 31(b)) of the
TRISO particles as well The indentations were carried out under a maximum load of
3 N (corresponding to a maximum indentation depth of ~26 μm) To avoid PyC
influence the thickness of SiC coatings (in the section as shown in Fig 31(b)) were
kept to ~60 μm after polishing which is more than 20 times the indentation depth
In this case the elastic zone has not expanded to the substrate according to the
criterion that indentation depth is less than 10 of coating thickness [17] For each
sample six indents were made on the polished external surface of SiC perpendicular
to the radial direction with a separation of 70 μm between each indent
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference [25]
The calculation of the VIF fracture toughness must account for the crack profile under
the indenter whether the cracks are of the Palmqvist mode or half-penny mode which
are illustrated in Fig 41 The halfpenny crack system is formed by the joining of
radial cracks as shown in Fig 41(a) while the Palmqvist crack system is always
shallow as shown in Fig 41(b)
To observe the crack impression under the indenter on the polished external surface
an indentation (as in Fig 42(a)) with a final indentation depth of 26 μm was
sequentially polished with 6 μm diamond suspensions The surface was polished until
the plastic deformation zone was exposed together with the radial cracks (as shown in
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
115
Fig 42(b) Afterwards polishing continued until the removal of the plastic
deformation zone (as shown in Fig 42(c)) The surface showed no cross-over
cracking present as illustrated in Fig 41(a) and this confirms the presence of the
Palmqvist mode cracks on the polished external surface of SiC coatings under the
Vickers indenter The three polished samples showed the same crack propagation
mode and this is consistent with previous reports [18 19] where a Palmqvist crack
system has been observed in SiC at low loads (lt 10 N)
The Palmqvist crack mode allows the VIF fracture toughness to be calculated using
the equation proposed by Laugier [15 16] given as
1 2 23
3 2( ) ( )IC v
a E PK
l H c
(1)
In Eq (1) the geometrical constant v is a calibrated value using the already known
fracture toughness due to the variation in use of the Vickers hardness or the
nano-hardness [14 16 20 21] The 2a and l are the lengthes of diagonal and radial
crack length of Vickers indentation (as shown later in Fig 43) respectively c=a+l
the E and H are Youngrsquos modulus and hardness measured by nano-indentation P is
the load of Vickers indentation Therefore this geometrical constant was calibrated
before it was used to calculate the VIF fracture toughness of SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
116
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
117
The only already known fracture toughness was measured on the cross-section of
extra-Si SiC coatings using a micro-beam bending method [9] so the calibration of
v was carried out on the cross section (as in Fig 31(a)) of the same coating
According to Eq(1) the hardness (H ) and Youngrsquos modulus (E) are nano-hardness
and Youngrsquos modulus as measured in a previous study [22] P is the load a is the
impression half diagonal l is the crack length and c is the half diagonal crack length
(see later in Fig 43) To get the load and dimensional values of indentations a total
of 8 indentations at different loads (3 35 and 4 N) were applied on the cross-section
of the extra-Si SiC coating
The crack lengths were measured using a scanning electron microscope (Philips XL30
FEG-SEM) FEG-TEM (Tecnai TM
G2 F30 U-TWIN 300KV) which was used to
study the fracture behaviour under the indenter For the TEM study the cross
sectional specimens for the indents were prepared using focused ion beam milling
(FIB FEI Nova 600 Dual Beam system) Note that due to the large deformation zone
(gt10 μm diameter) and radial crack length (gt15 μm) observed from micro-indent
impression it was not possible to produce a sufficiently large TEM sample by the FIB
technique This limitation restricted us to study the fracture behaviour under a sharper
indenter (Berkovich) with lower load
43 Results and discussion
431 VIF fracture toughness study
Figure 43 is the crack morphology observed in S3 (SiC + Si) coating cross-section It
shows that the fracture resistance is different in the tangential and radial directions of
the cross-section which is consistent with the previous measurements along these
directions measured by the micro beam method [9] Different crack lengths along the
tangential and radial directions observed from 8 indentations are illustrated in Table
41 Correspondingly fracture toughness values of 347 MPa m12
and 672 MPa m12
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
118
taken from Ref [9] were used as the standard values for the tangential and radial
directions of the SiC coating respectively According to Eq (1) taking into account
observed and measured parameters (KIC a c l H and E) the geometric constant
value v was calculated in each indentation for each direction (Table 41)
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for S3 SiC coatings
Table 41 illustrates the indentation parameters and the calibrated geometrical
constant v for the Palmqvist crack mode According to the results shown in Table
41 the calibrated mean value of v is 002008plusmn000273 and this value is within
the range of the geometrical constant value (0014-0023) from previous theoretical
studies [14 23] By using nano-indentation hardness and Youngrsquos modulus v was
taken as 002 for the calculation of the VIF fracture toughness in SiC layers in this
study which is the upper limit of 0016plusmn0004 used for previous studies of bulk
CVD SiC using the HE from micro-indentation [14 24-27]
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
119
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχ
v along the radial and tangential directions
Load Radial direction
Tangential direction
a (μm) c (μm) l (μm) χv a (μm) c (μm) l (μm) χv
3 N 6650 13125 6475 0020368 6685 18285 11600 0023088
6900 13090 6190 0019473 6995 15470 8475 0015013
6675 11895 5220 0015749 6120 16615 10495 0019880
6695 13130 6435 0020249 6555 15935 9380 0017057
6790 12610 5820 0017997 6425 18275 11850 0023783
35 N 7195 14970 7775 0022404 7235 20790 13555 0024930
6670 14080 7410 0020721 6715 18160 11445 0019412
4 N 7770 15855 8085 0020967 7390 20240 12850 0020187
χv 002008 plusmn 000273
Note The geometrical constantsχv presented in Table 41 were calculated using Eq(1) The fracture
toughness along the radial (672 MPa m12
) and tangential directions (347 MPa m12
) were taken from
Ref 9
Although the Vickers indentation method for fracture toughness measurement has
been discredited as a mean to obtain true fracture toughness [28] and always gives a
lower fracture toughness value than that obtained using the standard methods (such as
single edge V-norched bending)[1] the values obtained can be compared with each
other This is particular important for small samples and thin coatings since Vickers
indentation provides a method to quantify fracture behaviour when it is not feasible to
obtain true fracture toughness However to get reasonable comparison of Vickers
indentation fracture toughness in SiC coatings the following conditions should be
met
(1) SiC materials produced four regular radial cracks along the corners of the
Vickers indenter For indentation at the polished external surface of SiC
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
120
coatings deposited by FBCVD similar fracture resistance along different
orientation at the surface should be obtained
(2) The calibration of the geometrical constant should be made v was obtained
as 002 based on previous experimental results (see above)
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
Sample Grain size range (μm) Vickers toughness (MPa m12
)
S1 (SiC) 02-2 351plusmn042
S2 (SiC + C) 02-2 403plusmn043
S3 (SiC + Si) 02-2 493plusmn016
Table 42 presents the measured VIF fracture toughness on the polished external
surface using equation (1) for the SiC coatings in which the deposition conditions and
grain size were given It can be seen that the SiC coating with excess Si (S3) has
highest indentation fracture toughness followed by SiC with excess carbon (S2) and
stoichiometric SiC coatings (S1)
Vickers indentation fracture toughness values obtained in this study are slightly higher
than that of commercial CVD β-SiC which has been reported to vary from 24 to 33
MPa m12
measured by the same method [24 26 27] The VIF fracture toughness of
49 MPa m12
for extra-Si SiC measured on a polished external surface is between
347 and 672 MPa m12
when measured on a cross section by micro-beam method [9]
This is consistent with the observation of radial crack length differences ndash the crack
length on the polished external surface is between those in the tangential and radial
direction on the cross-section It is suggested that Vickers indentation is an effective
method for the characterization of fracture behaviour of FBCVD SiC coatings
Moreover the high hardness and Youngrsquos modulus of these three coatings [22] do not
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
121
cause a decrease in fracture toughness which is explained in the later part of this
paper
432 Influence of non-stoichiometries on the VIF fracture toughness
The VIF fracture toughness in S2 SiC coating is ~14 higher than the value for S1
SiC coatings and this can not be attributed to heterogeneous toughening due to the
excess carbon being at the grain boundaries Due to the low content of excess C it is
difficult to identify such an excess at the grain boundaries [29] Previous work
reported in Ref[30] showed that there was no presence of carbon at the grain
boundaries for a concentration up to 1 wt excess C In our case a similar situation
was found in S3 SiC coating where excess Si has not been found along the grain
boundaries Previous studies had [31 32] shown that excess Si in SiC was observed in
grains or near the grain boundaries by TEM only when the amount of excess Si is
high enough (such that it could be detected by XRD or a much higher Raman
spectroscopic intensity)Thus it is assumed that the excess Si could not be considered
as giving heterogeneous toughening which caused a ~43 higher VIF fracture
toughness in the S3 SiC than the S1 SiC coatings As a result the small amount of
excess carbon or silicon in SiC coatings does not seem to have influence on the VIF
fracture toughness through serving as the heterogeneous phase along the grain
boundary
The excess Si or C could be related to different grain morphologies according to
previous study [33] where it was observed that different SiC ratios in the reaction
gas produced rough smooth and irregular pyramid-like grain surfaces This further
affects the growth morphology and cohesion stress between grains For example the
smooth grain surface favours the parallel grain growth The weak grain boundary
cohesion could be the micro crack initiation zone while the strong grain boundary
could transfer the stress to stress concentration zone Here the role of grain
morphology is studied later in terms of stress concentration zone under indentation
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
122
433 Microstructural analysis of fracture behaviour under the indenter
SiC coating under nano-indentation on the polished external surface at a maximum
indentation load of 160 mN It can be seen that the median crack propagation root
deflected slightly and changed from intergranular to transgranular fracture as shown
in Fig 44(a) It is worth noticing that the median crack observed under
nano-indentation was not found under indentation because the indentation cracking
mode depends on the condition of the indenter tip [34] Higher magnification images
(Fig 44(b)) show that a large number of micro cracks were produced at the
elasticplastic interface
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
123
Both intergranular and transgranular cracks were observed near the median crack
initiation zone These cracks are under a tensile stress dominated by Mode I cracks as
the elastic-plastic stress field gives the highest tensile stress around this interface
according to a previous report (see Ref [35]) Moreover micro-cracks were observed
surrounding the median crack and also at the median crack tip as shown in Fig 44(c)
and Fig 44(d) respectively Figure 44(c) illustrates that the micro-cracks are along
the grain boundaries while the micro-cracks around the crack tip were found to both
pass through the grains and along grain boundaries (Fig 44(d))
Non-stoichiometric SiC coatings (S2 and S3) show quite different crack morphologies
under the indenter from that in the stoichiometric SiC (S1) coating as shown in Fig
310 in chapter 3 It can be seen that the propagation root of median cracks in S3 SiC
and S2 SiC coatings were affected by the microstructures as in Fig 310(a) and (c) in
chapter 3 Moreover a lateral crack was found in the S2 SiC coating The irregular
median crack propagation route in non-stoichiometric SiC coatings seems to be
related to the laminar structure
Fig 45 Cross-sectional SEM image of the S1 SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
Figure 45 shows the cross section of S1 SiC coating and the laminar structure (as
indicated by the dashed lines) is perpendicular to the grain growth direction It was
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
124
discussed in chapter 3 that the laminar structure is due to either nano-pores or a high
concentration of stacking faults and it is much less evident in the stoichiometric SiC
coating as compared to the coatings with impurities [22] In the S3 SiC coating (Fig
310(b) in chapter 3) a larger amount of micro cracks either intergranular or
transgranular were found under the indenter than in the S1 and S2 SiC coatings
The fracture mechanism of materials is influenced by their microstructure and the
fracture toughness could be enhanced by changing it For example ceramics
containing micro-cracks during fabrication could be associated with good fracture
behaviour but low strength and hardness since the micro-cracks usually serve as the
failure origins A better solution is to fabricate materials with microstructures that can
form stress induced micro-cracks under an external force [36] In FBCVD SiC a
number of micro cracks were observed under the indenter (Fig 44(b) Fig 310(b)
and (d) in chapter 3) from where the main cracks initiated and propagated away from
this zone According to a previous study although the tip of the main crack leaves the
micro-cracked zone under the indenter the wake region can provide stress shielding
against some further crack extension [37]
Thus the micro-cracks under the indentation (Fig 44(b) Fig 310(a) and (c) in
chapter 3) seem to be a mechanism for the toughening behaviour of FBCVD SiC by
dissipating the fracture energy for brittle fracture Micro-cracks were also found near
the main crack tip and surrounding the main crack for example in the stoichiometric
SiC coating (Fig 44(c) and (d)) This further confirms the toughening behaviour
through micro-cracking In CVD SiC which has a slightly lower fracture toughness
(around 33 MPa m12
) only a few micro-cracks were observed under the indentation
[38] which could be caused by indentation-induced slip bands As a result the
micro-cracks formed under the indentation near the main crack seem to be the reason
for the high VIF fracture toughness in SiC coatings when a high hardness is obtained
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
125
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a) S2
SiC (b) S3 SiC
Stress concentration zones are known to facilitate the nucleation of micro-cracks so a
large amount of micro-faults (eg pores) and weak grain boundaries (inducing the
micro-cracks under an external stress) could increase the VIF fracture toughness A
higher VIF fracture toughness in the extra-C SiC than in stoichiometric SiC coatings
may be due to the presence of the nano-pores (as shown in Fig 35(b) in chapter 3)
The S3 SiC has an even higher VIF fracture toughness than the S2 SiC coating and
this may correspond to a larger number of micro-cracks under the indentation We
assume this difference is due to their varied grain boundary morphologies as shown
in Fig 46 For example we observed different length of cracks on the cross section
(Fig 43) with cracks parallel to the grain growth direction shorter than cracks
perpendicular to the grain growth direction This is because along grain growth
direction itrsquos more likely to produce micro-cracks along the grain boundary As we see
in Fig 46 grains interact with each other in extra-C SiC (Fig 46(a)) forming branch
grains while in S3 SiC grains grow parallel (Fig 46(b)) According to a previous
study it is easier for parallel grains to form a transgranular fracture when the grain
boundaries are along the loading axis [39] This can explain the larger number of
transgranular micro-cracks under the indentation in the extra-Si SiC compared to the
extra-C coatings (Fig 310(b) in chapter 3) which caused different VIF fracture
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
126
toughness This different grain morphology could be caused by the
non-stoichiometries and further work needs to be done to study how excess C or Si
affects the microstructure of the SiC
44 Conclusions
In summary micro-indentation on the polished external surface of the SiC coating in
TRISO particles has been successfully applied to measure the VIF fracture toughness
of the silicon carbide (SiC) Three different types of SiC coatings (stoichiometric SiC
SiC with excess silicon and SiC with excess carbon) produced on spherical particles
by FBCVD were analysed The VIF fracture toughness (measured on the polished
external surface) in these three coatings investigated in this study was observed to
vary between 35 and 49 MPa m12
The results have shown that the VIF fracture
toughness is influenced by the microstructure and non-stoichiometry of SiC coatings
For FBCVD SiC coatings a high VIF fracture toughness accompanied with superior
hardness was attributed to the formation of micro-cracks The difference in VIF
fracture toughness was proposed to be dominated by the laminar defects and grain
morphologies in the SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
127
45 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo and D A Petti
Handbook of SiC properties for fuel performance modeling J Nucl Mater 371
(2007) 329-77
[2] N Swaminathan P J Kamenski D Morgan and I Szlufarska Effects of grain
size and grain boundaries on defect production in nanocrystalline 3C-SiC Acta
Mater 58 (2010) 2843-53
[3] G K Miller D A Petti D J Varacalle and J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[4] D A Petti J Buongiorno J T Maki R R Hobbins and G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[5] K Bongartz E Gyarmati H Schuster and K Tauber Brittle Ring Test - Method
for Measuring Strength and Youngs Modulus on Coatings of Htr Fuel Particles J
Nucl Mater 62 (1976) 123-37
[6] K Bongartz E Gyarmati H Nickel H Schuster and W Winter Measurement of
Youngs Modulus and Fracture Stress on Htr Particle Coatings by Brittle Ring Test
J Nucl Mater 45 (1972) 261-64
[7] M W Kim J H Kim H K Lee J Y Park W J Kim and D K Kim Strength
of chemical vapor deposited silicon carbide films using an internal pressurization
test J Ceram Process Res 10 (2009) 373-77
[8] T S Byun J D Hunn J H Miller L L Snead and J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[9] X Zhao R M Langford J Tan and P Xiao Mechanical properties of SiC
coatings on spherical particles measured using the micro-beam method Scripta
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
128
Mater 59 (2008) 39-42
[10] E Lopez-Honorato P J Meadows J Tan and P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[11] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram and P Xiao Youngs modulus measurements of SiC coatings on
spherical particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[12] ACKadak RGNallinger MJDriscoll SYip DGWilson HCNo JWang
HMaclean TGalen and CWang et al Modular Pebble Bed Reactor Project
University Research Consortium Annual Report Beijing 2000
[13] J I Federer Parametric Study of Silicon-Carbide Coatings Deposited in a
Fluidized-Bed Thin Solid Films 40 (1977) 89-96
[14] G R Anstis P Chantikul B R Lawn and D B Marshall A Critical-Evaluation
of Indentation Techniques for Measuring Fracture-Toughness 1 Direct Crack
Measurements J Am CeramSoc 64 (1981) 533-38
[15] M T Laugier Palmqvist Toughness in Wc-Co Composites Viewed as a Ductile
Brittle Transition J Mater Sci Lett 6 (1987) 768-70
[16] M T Laugier Palmqvist Indentation Toughness in Wc-Co Composites J Mater
Sci Lett 6 (1987) 897-900
[17] W D Nix and R Saha Effects of the substrate on the determination of thin film
mechanical properties by nanoindentation Acta Mater 50 (2002) 23-38
[18] J Lankford and D L Davidson Crack-Initiation Threshold in Ceramic Materials
Subject to Elastic-Plastic Indentation J Mater Sci 14 (1979) 1662-68
[19] Z Li A Ghosh A S Kobayashi and R C Bradt Indentation
Fracture-Toughness of Sintered Silicon-Carbide in the Palmqvist Crack Regime J
Am CeramSoc 72 (1989) 904-11
[20] H Hatta M Zoguchi M Koyama Y Furukawa and T Sugibayashi
Micro-indentation method for evaluation of fracture toughness and thermal
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
129
residual stresses of SiC coating on carboncarbon composite Adv Compos Mater
12 (2003) 155
[21] C B Ponton and R D Rawlings Vickers Indentation Fracture-Toughness Test 1
Review of Literature and Formulation of Standardized Indentation Toughness
Equations Mater Sci Tech Ser 5 (1989) 865-72
[22] H Zhang E Lopez-Honorato A Javed X Zhao and P Xiao Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc In Press (2011)
[23] A Leonardi F Furgiuele S Syngellakis and R J K Wood Analytical
Approaches to Stress Intensity Factor Evaluation for Indentation Cracks J Am
Ceram Soc 92 (2009) 1093-97
[24] M C Osborne J C Hay L L Snead and D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[25] R D Dukino and M V Swain Comparative Measurement of Indentation
Fracture-Toughness with Berkovich and Vickers Indenters J Am CeramSoc 75
(1992) 3299-304
[26] K H Park S Kondo Y Katoh and A Kohyama Mechanical properties of
beta-SiC after Si- and dual Si plus He-ion irradiation at various temperatures
Fusion Sci Technol 44 (2003) 455-59
[27] S Nogami S Ohtsuka M B Toloczko A Hasegawa and K Abe Deformation
during surface modification of silicon carbide using rare-gas ion-beam irradiation
Pricm 4 Forth Pacific Rim International Conference on Advanced Materials and
Processing Vols I and Ii 1367-70 3028 (2001)
[28] G D Quinn and R C Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[29] J Tan Mechanical properties of SiC in TRISO fuel particle PhDThesis
University of Manchester Manchester 2010
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
130
[30] K Kaneko M Kawasaki T Nagano N Tamari and S Tsurekawa
Determination of the chemical width of grain boundaries of boron- and
carbon-doped hot-pressed beta-SiC by HAADF imaging and ELNES line-profile
Acta Mater 48 (2000) 903-10
[31] B Reznik D Gerthsen W G Zhang and K J Huttinger Microstructure of SiC
deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499-508
[32] R A Shatwell K L Dyos C Prentice Y Ward and R J Young Microstructural
analysis of silicon carbide monofilaments J Microsc-Oxford 201 (2001) 179-88
[33] M J Hernandez G Ferro T Chassagne J Dazord and Y Monteil Study of
surface defects on 3C-SiC films grown on Si(111) by CVD J Cryst Growth 253
(2003) 95-101
[34] D S Harding W C Oliver and G M Pharr Cracking during nanoindentation
and its use in the measurement of fracture toughness Thin Films Stresses and
Mechanical Properties V 356 (1995) 663-68
[35] ACFischer-Cripps Introduction to contact mechanics Springer New York
2000
[36] DJGreen An introduction to the mechanical properties of ceramics Cambridge
University Press Cambridge 1998
[37] S B Biner A Numerical-analysis of crack-growth in microcracking brittle solids
Acta Metall Mater 42 (1994) 3643-51
[38] K H Park T Hinoki and A Kohyama Influence of irradiation-induced defects
on fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[39] H Horii and S Nematnasser Brittle failure in compression - splitting faulting
and brittle-ductile transition Philos T Roy Soc A 319 (1986) 337-74
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
131
CHAPTER 5 Influence of Interfacial Roughness on Fracture
Strength of SiC Coatings
51 Introduction
During the irradiation process of TRI-Isotropic (TRISO) fuel particles the high
tensile stress could be accumulated at crack tips These tips were due to direct
penetration of the cracks formed in the PyC layer or the high stress concentration as a
result of the debonding of IPyCSiC interface [1 2] When the tensile stress inside of
the particle exceeded the critical fracture stress of the SiC coating it caused the
failure of the whole particle [3] Furthermore the fracture strength is a main
parameter used in modeling the probability of failure of fuel particles so it is
important to measure the fracture strength of SiC to determine their performance
which is determined from the maximum tensile stress
Different methods such as hemi-spherical bending [4] crush test [5 6] and inner
pressure [6] were introduced to measure the fracture strength of SiC coating in
TRISO fuel particle The fracture strength was in a range and could be characterised
by the Weibull distribution function [4-6] The common vague conclusion derived
from previous results is the significant effect of the IPyCSiC interface on the fracture
strength [4-6] The interface was also found to affect the primary failure mechanism
by determining if the load can transmit through the SiC [6] Previous analyses are
consistent with the well-known prescription that the fracture strength of ceramic
materials varies largely and it is dependent on the size and surface condition of the
specimen [7-9] Among these methods the latest modified crush test proposed by
Byun et al[510] showed a well controlled scatter of the fracture strength in a given
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
132
sample
Although the importance of the interface has been noticed the lack of an accurate and
scientific description of the interface has limited the further study about its
relationship with the fracture strength Roughness is a commonly used terminology to
describe the interface and it could be measured by atomic force microscope and
characterised by the standard deviation of the vertical features [11 12] However
roughness is not enough to describe the interface and to relate it to fracture strength
[13] Due to the importance of the statistical analysis for ceramic materials the
self-affine theory was used to characterise the complex interface numerically
according to previous studies [14-17] A self-affine interface is characterised by a
correlation length the saturation roughness and the roughness exponent [18] A
similarly straightforward approach was applied to demonstrate the importance of the
interfacial roughness on the mechanical properties [19] showing that interfaces with
big and sharp irregularity fail first
In this work the modified crush test was used to measure the fracture strength of a
SiC layer deposited at different temperatures The IPyCSiC interface was well
described by self-affine theory Therefore the effect of the IPyCSiC interface and
dimension of particles together with other possible influences such as porosity and
grain size on the fracture strength were discussed The improvement of this work is
being able to do statistical analysis on the interfacial roughness
52 Experimental details
521 Materials
In this Chapter the buffer pyrolytic carbon and dense pyrolytic carbon coatings were
deposited on the top of ZrO2 kernel (~ Φ500 μm) by fluidized bed chemical vapour
deposition Thirteen SiC coatings were deposited at different temperature flow rate
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
133
MTS concentration and added gas as shown in Table 51 The deposition conditions
were chosen according to previous studies to get different microstructures and more
deposition mechanisms of SiC coating can be found in Ref [20] For fracture strength
measurement the SiC particles were mounted with thermoplastic resin and ground to
about 55 portion of the sphere and polished using increasingly fine diamond
suspensions until frac14 μm SiC shells were released from surrounded PyC layers by
oxidizing at 700 ordmC for 8 hours and further washed in an ultrasonic bath with acetone
for 5 minutes
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Sample Temperature
(ordmC)
MTS
(vol )
Added gas concentration Flow rate
(LMin)
Radius
Thickness (~)
S1 1300 91 05vol C3H
6 600 72
S2 1300 91 01vol C3H
6 600 76
S3 1280 91 01vol C3H
6 600 83
S4 1300 91 -- 600 85
S5 1400 19 57vol Ar 778 87
S6 1500 22 82vol Ar 700 90
S7 1500 19 89vol Ar 778 101
S8 1500 22 79vol Ar 700 112
S9 1400 19 57vol Ar 777 117
S10 1300 19 57vol Ar 778 129
S11 1500 19 89vol Ar 777 151
S12 1500 22 76vol Ar 700 158
S13 1500 19 57vol Ar 778 190
The difference between sample S5 and S9 S7 and S11 is the thickness of the PyC layer MTS
methyltrichlorosilane Lmin the flow rate measured in liter per minute To produce SiC coatings with
particular microstructures and compositions different deposition conditions were chosen which were
contributed to Dr Eddie Lopez-Honorator
522 Test method and analysis
The crush test taking the contact area into consideration was used in this study [2 5
21] and the loading profile of the crush system is shown in Fig 51 When a partial
spherical shell (Radius R thickness t) was diametrically loaded by an external load F
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
134
concentrated on a small circular area (radius 0 ) the maximum membrane stress and
bending stress could be calculated by the equations developed by Roark and Young
[21] The combination of the maximum bending and membrane stress (Local fracture
strengthL
f ) in the inner side of the shell was the maximum fracture strength for
partially loaded shell (around 55 of the sphere)
The fracture strength of brittle SiC coating is best considered as a distribution rather
than a fixed number and the most widely used expression for characterisation is the
cumulative distribution functionmdashWeibull distribution function [7 22] In the current
study the distribution of local fracture strength and fracture strength for a full
spherical shell were characterised by the Weibull distribution The Weibull modulus m
is derived from the local fracture strength (Eq 14 in Chapter 2) The calculation of the
fracture strength for the full spherical shell (F
f ) is based on the size effect (scaling
factor mtRr 122
0 ))(4( R radius of the particle t thickness of SiC shell 0
radius of residual impression after loading) which is equal to the partial strength
divided by the scaling factor [5 7] More details about fracture strength calculation
are available in Ref [5]
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
According to a previous study [5] one reason for the difference of local fracture
10 ordm
t
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
135
strength in a given batch of coating is due to different sizes of residual impression
( 0 ) under which the distribution of defects could be different To reduce the
influence of the 0 the radius (R) at the edge of the residual impression was kept at
an angle of around 10ordm (as shown in Fig 51) from the loading axis by inserting
different kind of soft metal It varied slightly (the ratio of standard deviation to mean
value is around 10) in each batch of SiC
The crush test was carried out in a universal tensile machine INSTRON 5569
(INSTRON High Wycombe Bucks) with a 100 N maximum load cell For each batch
of SiC shell (except for S13) at least 30 specimens were tested at room temperature
with a crosshead speed of 0005 mms The failure load recorded by the tensile
machine was used as the fracture load The individual impression left on the soft
metal (Nickel alloy cold worked copper or brass) was marked under corresponding
load and its diameter was measured by optical microscope (times100 ZESIS Company
German)
523 Characterisation methods
A Philips XL30 FEG-SEM (Philips Eindhoven Netherlands) was used to characterise
IPyCSiC interfacial roughness grain size and porosity from the finely polished cross
section of SiC coatings Characterisation of the IPyCSiC interfacial roughness was
realized by editing the SEM images (in the magnification of times1600) with the Image J
software and extracted it as a line from the background SEM image The interfacial
roughness could be described by a series of pairs of x (distance tangential to the
interface) and y (distance normal to the interface) coordinates assuming the interface
is flat at a scale of 70 microm
Porosity was measured by controlling the threshold of SEM images (times1600 TIF) at a
gray level and adjusted to distinguish pores from grains with the Image J software
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
136
Pore fraction was defined as the ratio of the pores and the total area of the SEM image
Grain size of FBCVD SiC coatings varied in a range and in a columnar shape It was
characterised by measuring mean width and length of single crystals from SEM
images (times6400) and the grain size of the coatings is represented by the mean width
timeing the length of grains A FEG-TEM (TecnaiTM G2
F30 U-TWIN) was used to
observe the IPyCSiC interfacial roughness and TEM samples were prepared by
focused ion beam milling The linear regression method was used to analyze and
quantify the influences of parameters on the fracture strength and Weibull modulus
53 Results and discussions
531 Fracture strength and dimensional effect
Table 52 gives the summary of the measured and calculated parameters for all the
coatings It includes the diameter of impression (mean value 2 0 ) force (mean value
F) Weibull modulus (derived from local fracture strength m) local fracture strength
(L
fmean value) and fracture strength for the full spherical shell (
F
fmean value)
Table 52 Summary of measured and calculated parameters for all the coatings
Sample 2 0 μm F N L
f MPa Modulus (m) Scaling Factor
For Size Effect
F
f MPa
S 1 15239 2235 1784 7397 185 963
S 2 15043 1999 1599 7687 183 872
S 3 14898 1540 1446 7459 187 774
S 4 16052 2042 1620 8261 178 908
S 5 17018 2573 1810 7927 178 1018
S 6 16220 1885 1648 6953 193 855
S 7 14662 1691 1974 7755 190 1019
S 8 14905 1336 1717 7102 198 868
S 9 13040 1088 1825 6495 223 820
S10 16410 1215 1472 6801 204 722
S11 16165 1006 1430 6104 219 652
S12 14677 903 1512 6616 205 737
S13 11586 489 1762 4912 300 587
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
137
As given in Table 52 a significant difference (49-257 N) of the load among SiC
coatings was obtained According to a previous study [5] the variation is mainly
caused by different thicknesses (varied from 30 μm to 60 μm) of SiC coatings
because the relatively thin coating tends to reach higher strength concentration at
fracture
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
The Weibull modulus derived from the local fracture strength (as given in Fig 52) is
in the range of 49-86 (as shown in Table 52) and it falls into the category of moduli
for ceramics materials (from 5 to 30) This range of Weibull modulus is similar to the
values obtained from the brittle ring tests which also gave a similar range of the local
fracture strength [23 24] In different batches of SiC coatings it was found that the
Weibull modulus decreases linearly with the increase of the ratio of outer radius (R) to
the thickness of SiC coatings ( tR ) as shown in Fig 53 The ratio of Rt accounts
for up to 778 (2R from linear regression) of differences of the modulus This is
because the tR ratio is a critical dimension value for the strength distribution of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
138
SiC shell and it represents the relative thickness of SiC coating The higher the ratio
is the thinner the SiC coating So it corresponds to the larger inner surface area
resulting in larger scattering sizes of the critical flaws This observation is consistent
with the previous finite element modeling results showing that the Weibull modulus is
related to the sample dimension [10]
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
As given in Table 52 the scaling factor (effective area-parameter based on the local
fracture strength) between the local fracture strength and the fracture strength of the
full shell are in the range of 18-30 The results are consistent with Byun et alrsquos study
(19-31) [5] and it indicated the importance of the size effect on the fracture strength
of the full shell
The fracture strength for the full spherical shell of thirteen SiC coatings were given in
the form of Weibull plots as shown in Fig 54 The mean fracture strength for the full
spherical shell was in the range of 587-1019 MPa (as given in Table 52) which is
higher than the range of 330-650 MPa obtained by Byun et al [5] This is because the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
139
Rt ratio (above 11) in Ref [5] falls into the higher value categary in current work as
shown in Fig 53
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Because the Weibull modulus is dominated by the tR ratio (Fig 53) its influence on
fracture strength for a full spherical shell could also be from this ratio as shown in
Fig 55 It shows that the fracture strength for the full shell decreases nearly linearly
with the increase of the tR ratio which produces a difference of 6528 (2R derived
from linear curve fit which represents fair agreement) of differences In this work the
similar range of Rt ratio (above 11) corresponds to the fracture strength lower than
850 MPa (as shown in Fig 55) which reduced the difference from previous results
[5] Furthermore the fracture strength of about 1000 MPa was obtained when the Rt
was about 8 [25] and it is similar as the result given in Fig 55 This again
demonstrated the importance of the geometry on the fracture strength of SiC coating
Therefore it is important to eliminate the external influence and study the influences
of microstructures such as interfacial roughness porosity and grain size on fracture
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
140
strength which are discussed in the following parts
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
532 Observe and qualify the effect of interfacial roughness on fracture strength
According to Griffith fracture theory the fracture strength (L
f ) is a function of the
critical flaw size (C) and the fracture toughness ( ICK ) as shown in the following
equation [26]
12( )
L ICf
K Z
Yc (1)
Y is a loading geometrical parameter Z is the flaw size parameter The magnitude of
the critical flaw size could be related to the IPyCSiC interfacial irregularities
The interfacial flaw shape of SiC coatings is modeled from the surface morphology of
PyC coating during deposition process as shown in Fig 56(a) The crack was taken
as a semi-circular surface crack as given in Fig 56(b) where Y is 2 and Z is 16 (Y
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
141
Z are geometrical constants introduced in Eq (1) [26] The fracture toughness of SiC
coatings in TRISO fuel particle was taken to be 33 MPamiddotm12
according to previous
report [27] Taking the result of the local fracture strength from individual SiC coating
into Eq (1) the magnitude of the critical flaw size C could be obtained
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Figure 46 shows the redraws of the IPyCSiC interfacial roughness from SEM images
and the calculated critical flaw sizes according to Eq (1) (range and mean values) for
all specimens are given in the right columns If the fracture initiated at the IPyCSiC
interface as proposed in previous studies [4-6] the calculated critical flaw size range
of each type of SiC coating was expected to match the size range of the interfacial
irregularities
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
142
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
In Fig 57 most of the calculated critical flaw sizes according to Eq (1) are in the
same magnitude as the flaw size observed directly from the interfacial profile images
and this indicates that the dominant effect of the surface roughness on the local
fracture strength For example the direct observation of the biggest flaw size from the
profile is about 43 μm and 26 μm in sample S9 and S13 respectively and they are in
the range of the calculated defect sizes of 09-65 μm and 17-47 μm for S9 and S13
respectively However exceptions were found such as specimens S1 and S2 which
show slightly higher calculated surface flaw size than the observation from SEM
images Furthermore it is difficult to accurately characterise the difference of the
interfacial roughness by observing the converted images and give specific
information (such as shape) of single profile (shown in Fig 57) The estimation of
the shape of surface irregularities to be half-circular could also result in the error on
the critical flaw size calculation [7] To give a direct estimation about the influence of
interfacial roughness on local fracture strength the scaling behavior of IPyCSiC
interface need to be characterised by a statisticalnumerical method
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
143
533 Characterise and quantify the interfacial roughness
Self-affine theory has become a standard tool in the study of various rough interfaces
[18 28 29] Here it was the first time being proposed to describe the IPyCSiC
interfacial roughness accurately and scientifically and then was used to quantify the
relationship between interfacial roughness and local (intrinsic) fracture strength and
fracture strength of the full shell
5331 Self-affine theory introduction and experimental setup
In order to describe the IPyCSiC interfacial roughness with specific parameters an
easy way is using a height-height function [29 30]
2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)
where the x axis is along the IPyCSiC interface and ( )h x is the surface height profile
The amplitude of the roughness ( )h x is correlated with the length scale x and
lt gt denotes the spatial average over ( )h x in a planar reference surface If the
interfacial roughness of IPyCSiC were self-affine the correlation of x and
h should follow the power law relationship (Eq (2)) and it could be obtained by the
log-log plot of x and h The (for self-affine surface 0lt lt1) is the roughness
exponent and it describes the degree of surface roughness at short length scales [31]
This short length scale is shorter than correlation length ξ which is another parameter
used to describe the self-affine surface (besides the surface roughness h and
roughness exponent ) It is the average distance between the features in the surface
profiles within which the surface variations are correlated [28] Therefore the small
(close to 0) characterises extremely jagged or irregular interfaces while large
value characterise interface with smooth hills and valleys [32]
For all the samples the scaling properties of IPyCSiC interface (as shown in Fig 57)
are characterised by their one-dimensional height-height correlation function Eq (2)
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
144
The characteristic parameters of the digitalized IPyCSiC interfacial roughness are as
follows The resolution between two points along x axis is 020833 μm and x
changes by timing the resolution with integer (1 2 3hellip15) According to previous
self-affine theory study [16] the number of recorded points along the x axis was
taken in the range of 250-400 in this work corresponding to the length of 50-70 μm
for different IPyCSiC interfaces
5332 Results of self-affine theory
Figure 58 is a log-log plot showing the variation of h as a function of the distance
x for three SiC coatings The h varied as a power law of x (solid line ) when
x ltξ while remained nearly constant ˗ saturation roughness (σ0 dashed parallel
lines) for x gtξThese results indicated that these three IPyCSiC interfacial
roughness were self-affine with the roughness exponent of around 063-067 For the
rest of the samples the same scaling characterisation method was used Theξ σ0 and
are given in Table 53
Fig 58 Log-log representation of the height-height correlation function h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
ξ3 ξ12 ξ6
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
145
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Sample σ0 (μm) ζ ξ(μm) σ0ξ
S 1 02378 05903 06250 03804
S 2 04142 06950 08333 04971
S 3 06701 06673 16666 04021
S 4 06825 05244 14583 04680
S 5 05271 06308 14581 03615
S 6 08500 06343 20833 04080
S 7 04293 05162 14583 02944
S 8 07452 05107 14583 05110
S 9 05453 06099 12500 04362
S10 06953 05490 13044 05330
S11 05806 04949 10417 05574
S12 07584 06899 16666 04550
S13 05522 02971 18750 02945
The roughness exponent values for the 93 of IPyCSiC interface were in the range
of 05-07 (as shown in Table 53) This indicated the self-affine measurement is
reliable according to Schmittbuhl and Vilottersquos review [14] which showed that this
range of roughness exponents could have the minimum characterisation errors
Furthermore these roughness exponents are comparable except specimen S13 and it
was consistent with the observation of the interfacial roughness (Fig 57) in which
only specimen S13 showed the high degree of high frequency and short wavelength
irregularities (the dark pits in S13 profile) According to previous study [31] the
concentration of the roughness exponent values could be attributed to the same
original mechanism of the IPyCSiC interface which was produced by the FBCVD
under different conditions As a result the different roughness exponent value could
not describe the difference of the IPyCSiC interface
As shown in Table 53 the saturation roughness (σ0) and correlation length (ξ) are in
the range of 024-085 μm 063-208 μm respectively (Table 53) According to
previous studies [16 17 30] the σ0 and ξ couldnrsquot represent the interfacial
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
146
irregularities correlated with the critical flaw size Because the σ0 value range was
nearly one magnitude lower than the calculated critical flow size (mean value range of
2-4 μm) and the dimension of ξ was perpendicular to the calculated critical flaw size
direction Furthermore it was found that σ0 and ξ values were correlated to the sample
size (recorded points) [16] With the increase of the sample size for the same profile
both the ξ and the σ0 values increased and indicated these two parameters may not be
intrinsic properties of the samples However the roughness ratio σ0ξ is constant
which was found in both the current work and previous study [16]
As a result of above discussions the roughness ratio of σ0ξ was proposed to
characterise the interfacial roughness which could represent the sharpness of the
interfacial irregularities according to Ref [30] For example the low ξ value
corresponded to narrow surface irregularity when the σ0 and values were the same
With the increase of the σ0 value the surface irregularity became deep and narrow
which was hazard to the mechanical properties according to previous simulation work
on the fracture strength of SiC coatings [22] The above observations and analysis
results are supported by previous study [31] when length scale x gt ξ (shown in
Fig 58) the roughness ratio σ0ξ describes mainly the long-wavelength roughness
characteristics which could be statistically equal to the effect of the critical flaw size
on fracture strength
534 Quantify the influence of interface roughness on fracture strength
Figure 59 gives the influence of roughness ratio on the local fracture strength and it
contributes to nearly 50 (R2 from linear regression) of variation of the local fracture
strength It shows that the local fracture strength decrease linearly with the increase of
the roughness ratio This result approves previous findings about the importance of
the interfacial roughness [4-6] and is correlated with the Griffth fracture theory (Eq
(1)) about the importance of the shape and dimension of critical flaws Furthermore
the relation between interfacial roughness has been characterised quantitatively and a
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
147
linear relationship between roughness ratio and local fracture strength is proposed
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Except for the interfacial roughness the local fracture strength could also be affected
by the fracture toughness as shown in Eq (1) Although Vickers-indentation fracture
behavior of SiC coatings was different due to the laminar defects and grain
morphology [33] the fracture toughness of SiC was found to be insensitive to the
microstructure of materials [34] This could be attributed to the fact that
Vickers-indentation provided a static propagation of the crack while the real fracture
toughness was measured dynamically In this work the fast fracture process could
overtake the effect of microstructure on the different static fracture behaviour [5 25]
Since porosity and grain size were main microstructural variations in SiC coatings [1]
their effects on fracture strength were estimated
The characterisation and quantification of grain size and porosity were shown in Table
54 The grain size was found to have no effect on fracture strength according to
previous studies [5] which was also indicated from the regress analysis (R2 is close to
0) No influence was found by regressing the local fracture strength on pores
Therefore the dominant influence on the local fracture strength is from the roughness
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
148
ratio
Table 54 Results and variations influences on fracture strength for SiC coating
Specimen S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S10 S11 S12 S13
Grain size
(μm2)
04 06 06 08 20 20 20 28 20 08 20 28 25
Porosity
(Area )
0 0 0 0 05 04 12 09 03 0 08 21 20
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
Because the fracture strength for a full spherical shell is a function of the Weibull
modulus and local fracture strength [5] it was affected by factors such as the
dimension ratio of thickness to radius of the coating (as shown in Fig 55) the
roughness ratio (as shown in Fig 510) Figure 510 shows the influence of roughness
ratio on fracture strength of the full shell The linear relationship was found in 12
samples as indicated by the dashed line in Fig 510 and it could explain about 68
(2R from linear regression) of difference in fracture strength of the full particle The
high roughness ratio would decrease the fracture strength of the full shell linearly The
deviated point of sample S13 could be due to its largest Rt ratio (as shown in Fig
55) which may have over taken the effect of the roughness ratio (Work about the size
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
149
effect on the fracture strength has being carried out)
54 Conclusions
The fracture strength of SiC coatings deposited under different conditions were
measured by the modified crush test and analyzed by the statistical analysis (Weibull
function and Self-affine theory) The influences on fracture strength were studied
such as the IPyCSiC interfacial roughness specimen size and porosities Following
results were obtained
(1) Weibull modulus and fracture strength of the full shell were significantly affected
by the ratio of radius to thickness of SiC coating and both of them decrease
linearly with the increase of the ratio
(2) The dominant effect of the IPyCSiC interfacial roughness on intrinsic fracture
strength was found by matching the SEM images with the calculated critical flaw
size based on the Griffith fracture theory
(3) The interfacial roughness were successfully characterised by a
numericalstatistical method and the roughness ratio representing the shape of the
irregularities was proposed to be a unique parameter among different coatings
(4) The difference of the local fracture strength was dominated by the roughness ratio
and it decreased linearly with the increase of the roughness ratio It is been the
first time that the interfacial roughness was numerically related to the fracture
strength
(5) Microstructures such as grain boundaries and porosity were found to have
neglectable influence on fracture strength
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
150
55 References
[1] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[2] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the tri-isotropic-coated fuel particle J
Am Ceram Soc 90 (2007) 184-91
[3] T Nozawa L L Snead Y Katoh J H Miller E Lara-Curzio Determining the
shear properties of the PyCSiC interface for a model TRISO fuel J Nucl Mater
350 (2006) 182-94
[4] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
Fuel Particles for High-Temperature Gas-Cooled Reactors J Am Ceram Soc 56
(1973) 36-41
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[6] S G Hong T S Byun RA Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the TRI-Isotropic-coated fuel particle
J Am Ceram Soc 90 (2007) 184-91
[7] D J Green An introduction to the mechanical properties of ceramics Cambridge
solid state science series Cambridge Cambridge University press 1998
[8] R Danzer Some notes on the correlation between fracture and defect statistics
Are Weibull statistics valid for very small specimens J Eur Ceram Soc 26
(2006) 3043-49
[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
Transgranular Cleavage J Mech Phys Solids 34 (1986) 477-97
[10] J W Kim T S Byun Y Katoh Optimization of fracture strength tests for the
TRISO layers of coated fuel particles by finite element analysis 33rd international
conference on advanced ceramics and composites Daytona Beach FL2009
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
151
[11] W N W Chen X Nie A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
Ceram Soc 92 (2009) 1287-95
[12] R T Wu X Wang A Atkinson On the interfacial degradation mechanisms of
thermal barrier coating systems Effects of bond coat composition Acta Mater 58
(2010) 5578-85
[13] X Nie W N W Chen A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
Ceram Soc 92 (2009) 1287-95
[14] J Schmittbuhl J P Vilotte S Roux Reliability of Self-Affine Measurements
Phys Rev E 51 (1995) 131-47
[15] J T M De Hosson G Palasantzas Roughness effect on the measurement of
interface stress Acta Mater 48 (2000) 3641-45
[16] L Ponson H Auradou M Pessel V Lazarus J P Hulin Failure mechanisms
and surface roughness statistics of fractured Fontainebleau sandstone Phys Rev
E 76 (2007) 036108-14
[17] L Ponson H Auradou P Vie J P Hulin Low self-affine exponents of
fractured glass ceramics surfaces Phys Rev Lett 97 (2006) 125501-4
[18] F Spaepen Interfaces and stresses in thin films Acta Mater 48 (2000) 31-42
[19] W G Sloof T S Hille T J Nijdam A S J Suiker S Turteltaub Damage
growth triggered by interface irregularities in thermal barrier coatings Acta Mater
57 (2009) 2624-30
[20] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[21] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[22] G K Miller D A Petti J T Maki D L Knudson An evaluation of the effects
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
152
of SiC layer thinning on failure of TRISO-coated fuel particles J Nucl Mater
355 (2006) 150-62
[23] K Bongartz E Gyarmati H Schuster KTauber The brittle ring test A method
for measuring strength and Youngrsquos modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[24] K Minato K Fukuda K Ikawa Strength of silicon-carbide coating layers of
fuel Pparticles for high-temperature gas-cooled reactors J Nucl Sci Tech 19
(1982) 69-77
[25] J W Kim T S Byun Y T Katoh Optimization of fracture tests for the SiC
layer of coated fuel particles by finite element analysis Ceram Nucl Appl DOI
1010029780470584002 ch13 2010
[26] S Gonzalez B Ferrari R Moreno C Baudin Strength analysis of
self-supported films produced by aqueous electrophoretic deposition J Am
Ceram Soc 88 (2005) 2645-48
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] B N Dev A Roy K Bhattacharjee H P Lenka D P Mahapatra Ge growth
on self-affine fractal Si surfaces influence of surface roughness J Phys D Appl
Phys 42 (2009) 145303-10
[29] J Feder Fractals Plenum New York 1988
[30] J T M De Hosson R Van Tijum Effects of self-affine surface roughness on the
adhesion of metal-polymer interfaces J Mater Sci 40 (2005) 3503-08
[31] G Palasantzas Roughness spectrum and surface width of self-affine fractal
surfaces via the K-correlation model Phys Rev B 48 (1993) 14472-78
[32] P Meakin Fractals scaling and growth far from equilibrium Cambridge
Cambridge University Press 1998
[33] H Zhang E Loacutepez-Honorato A Javed I Shapiro and P Xiao A study of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
153
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc 95 (2012) 1086-92
[34] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany and A H
Heuer Fracture toughness of polycrystalline silicon carbide thin films Apply
Phys Lett 86 (2005) 071920-22
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
154
CHAPTER 6 Effect of Thermal Treatment on
Microstructure and Fracture Strength of SiC Coatings
61 Introduction
The mechanical properties of the as-deposited SiC coatings have been widely studied
eg Youngrsquos modulus and hardness [1-3] fracture toughness [4] and fracture strength
[5] etc However after it experiences the high temperature the composition and the
microstructure of the SiC coating may change which consequently influences the
mechanical properties It has been found that mechanical properties of SiC such as
Youngrsquos modulus and hardness are less affected when experiencing the current fuel
operation temperature (less than 1600 ordmC) [1 6] even after thermal treatment
temperatures of 1980 ordmC [7] To enhance the operational temperature of the high
temperature reactor in the future design it would be necessary to understand the
evolution of microstructure and mechanical properties of SiC coatings at even higher
temperature Some research [8-10] has been carried out to study the effect of high
temperature (more than 2000 ordmC) thermal treatment on the density and microstructure
of the fuel particle Itrsquos concluded that fuel failure and fission product release
dependent on SiC thermal stability at high temperature [9] Rooyen et al[11]
measured the annealing temperature effect on the fracture strength of SiC coatings It
is found that the fracture strength increases after thermal treatment at temperature up
to 2000 ordmC decreases in strength after thermal treatment at 2100 ordmC However no
clear explanation was given on this result
Due to the importance of the SiC on the safety of this fuel it is necessary to study the
thermal stability of SiC and characterise any change in microstructure and mechanical
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
155
properties It has been previously found that SiC deposited at 1300 ordmC with the
addition of propylene and methyltrichlorosilane as gas precursors not only have good
mechanical properties such as hardness and Youngrsquos modulus [3] fracture toughness
[4] but also have high silver and palladium diffusion resistance [12 13] Therefore in
this Chapter we thermally treated SiC coatings deposited at a range of temperature
(1300-1500 ordmC) at 2000 ordmC for 1 hour in argon atmosphere The change of fracture
strength and thermal stability of SiC coating were studied in terms of composition and
microstructural change of the coatings after thermal treatment
62 Experimental details
Four batches of SiC coatings (with nearly stoichiometry) deposited by Fluidized bed
chemical vapour deposition at different tempearure were chosen to study the thermal
treatment effect on the evolution of the microstructure and fracture strength Table 61
gives the deposition conditions of coatings studied and symbols used to describe each
sample The stoichiometry was measured by the Raman spectroscopy (Renishaw 1000
Raman microprobe system with 514 nm Argon laser) The laser beam was focused on
the surface of the cross section through a times50 objective lens
Table 61 Deposition conditions of SiC coatings
Sample Temperature
(oC)
MTS concentration
(vol)
Added gas
concentration
Stoichiometry
SiC1 1280 91 01vol C3H6 SiC
SiC2 1300 91 01vol C3H6 SiC+C
SiC3 1400 19 57vol Ar SiC
SiC4 1500 22 79vol Ar SiC+C
The inner side of the coating is stoichiometric (23 of the thickness) while outside of the coating is
SiC with excess C The microstructure characterization was done in the inner side coating while the
fracture strength measurement is related to the full coating SiC+C means that the C peak around
1300-1500 cm-1
was observed in SiC coating Chosen of deposition conditions was contributed to Dr
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
156
Eddie Lopez-Honorato
The sample preparation for fracture strengths measurement is the same as described in
Chapter 5 As introduced before thermal treatment was carried out at 2000 ordmC for 1
hour in argon protected atmosphere on SiC half shells The same fracture strength test
and equipment settings as described in Chapter 5 were used in this Chapter
In addition to Raman spectroscopy the microstructure of SiC coatings before and
after thermal treatment was also characterised using X-ray diffraction (PW 1830
Philips) with a Cu Kα1 radiation source The XRD samples were the SiC segments
(fractured SiC shells without external residual stress) Scanning electron microscopy
(Philips XL30 FEG-SEM) was used to characterise the change in morphologies of
SiC coatings Porosity was measured by setting a threshold of the SEM images
(times1600 TIF) at a gray level and adjusted to distinguish pores from grains with Image
J software Three SEM images were measured for each SiC coating Average pore size
(diameter nm) and the pore fraction (area ratio of pores to the total area as observed
by SEM) were obtained For transmission electron microscopy (TEM) the specimens
were prepared by crushing the SiC shell and dispersing the fragments on a carbon
holy film copper grid and crystal structures were characterised using an FEG-TEM
(TecnaiTM G2
F30 U-TWIN)
63 Results
631 Fracture strength of SiC coatings
Figure 61 shows the Weibull distribution of the local fracture strength ( L
f ) in SiC
coatings before and after thermal treatment at 2000 ordmC It gives a direct observation on
the decrease of the local fracture strength in coating SiC2 SiC3 and SiC4 after
thermal treatment while the local fracture strength of coating SiC1 is nearly
overlapped with the as-deposited coating The magnitude of the mean local fracture
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
157
strength (as summarised in Table 62) could represent the decrease trend of the full
batch of the coating in current study
Fig 61 Weibull plots of local fracture strength ( L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
The Weibull modulus (m) was obtained by linearly fitting the curves shown in Fig 61
It shows that the Weibull modulus decreased by 14 07 and 21 in coating SiC1 SiC3
and SiC4 respectively however it increased slightly (by 12) in SiC2 after heat
treatment As shown in Fig 61 the Weibull modulus derived from linear fitting is
affected by the deviation of few points from the linear distribution of the local fracture
strength (as shown in Fig 61) For example in sample SiC3 the slightly decrease
could be attributed to the deviation of the lowest points According to previous study
[14] the slight decrease (07) of Weibull modulus in SiC3 could be neglected since
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
158
the deviated points could be caused by different failure mechanisms involved in the
fracture process [14]
Fig 62 Weibull modulus plots of fracture strength of the full shell ( F
f ) before
(black triangle) and after (red circle) thermal treatment
Figure 62 shows the Weibull plots of fracture strength of the full shell ( F
f ) before
and after thermal treatment at 2000 degC In the same batch of coatings (the same size
effect) the fracture strength of the full shell increase with the increase of the Weibull
modulus and local fracture strength according to previous study [5] Therefore the
decrease of local fracture strength and increase of the modulus in SiC2 could explain
the slight change (decreased 25 MPa obtained from Table 62) of the fracture strength
of the full shell after thermal treatment In the other three samples the fracture
strength of the full shell decreased significantly (more than 110 MPa obtained from
Table 62) after thermal treatment due to the decrease of local fracture strength and
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
159
unchanged modulus)
Table 62 summarized the results of the fracture strength measured before and after
thermal treatment at 2000 degC including the Weibull modulus (m) derived from the
distribution of the local fracture strength ( L
f ) the mean local fracture strength and
fracture strength of the full shell ( F
f ) After thermal treatment the mean local
fracture strength of coatings decreased significantly except SiC1 coating which
retained the same level as in as-deposited coating The mean fracture strength of the
full shell was reduced after thermal treatment in a different degree but the change of
Weibull modulus is more complex which shows both decreased and increased values
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the full shell before and after thermal
treatment
Sample m (from
L
f )
as deposited 2000degC
L
f MPa
as deposited 2000degC
F
f MPa
as deposited 2000degC
SiC1 75 61 1445 1421 774 660
SiC2 77 89 1599 1395 872 847
SiC3 65 58 1824 1333 820 548
SiC4 74 53 1717 1443 858 587
As concluded from Fig 61 Fig 62 and Table 62 the fracture strength decreases
less in coatings deposited at lower temperature (about 1300 degC) than those deposited
at higher temperature (1400-1500 degC) This is consistent with previous study about
high properties of SiC coatings deposited at low temperature such as the hardness
Youngrsquos modulus and resistance to the fission products [12 13 15]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
160
632 Change in morphologies
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after (c) and (d) SiC2 before and after
(e) and (f) SiC3 before and after (g) and (h) SiC4 before and after thermal treatment
Dashed and solid arrows indicate growth direction and pores respectively
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
161
Figure 63 gives the SEM images showing the microstructure of SiC coatings before
and after thermal treatment at 2000 ordmC Before thermal treatment no pores were found
in SiC1 and SiC2 coatings (Fig 63(a) and (c)) while nano-pores were found in SiC3
coating (Fig 63(e)) and even bigger (micrometres) pores were occasionally found in
SiC4 coating (Fig 63(g)) Among four as-deposited coatings SiC4 has highest area
fraction of pores (~09) followed by SiC3 (~03) coating (Fig 63 (a) (c) (e) and
(g) summarized in Table 63)
After thermal treatment at 2000 ordmC pores with different size and area fraction were
observed in all the coatings even though as-deposited SiC1 and SiC2 were free of
pores as shown in Fig 63(b) (d) (f) and (h) The amount of pores formed in treated
SiC1 coating (area fraction of ~05 ) is lower than the other three coatings which
have similar area fraction of pores (~14 ~13 and ~15 for SiC2 SiC3 and
SiC4 respectively given in Table 63) Similar to the content of the pores the pore
size (mean size of ~50 nm) in SiC1 is smaller than in the other coatings (gt 100 nm)
Among coatings SiC2 SiC3 and SiC4 much larger pores (micro-meter sized as in
Fig 63(f) and (h)) were produced in SiC3 and SiC4 coatings after thermal treatment
compared with nano-sized pores in SiC2 Furthermore it is found that most of pores
in coatings SiC2 SiC3 and SiC4 were formed along the grain boundaries and triple
junctions as we can see from Fig 63(d) (f) and (h)
The pores are uniformly distributed through the coatings and no area free of pores or
area with highly concentrated pores is observed However there are connections of
pores (2 or 3 pores formed closely) in SiC2 SiC3 and SiC4 as indicated by solid
arrows in Fig 63(d) (f) and (h) and the diameter of the porous connection zone
(black circle in Fig 63(d) (f) and (h)) could be in the magnitude of few micrometres
The connection of pores could easily become larger pores of few micrometres
diameter under external tensile strength due to the high strength concentration [14]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
162
Fig 64 The IPyCSiC interfacial roughness of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermally treated at 2000 degC (right
in each figure) The white arrow points towards to the interface irregularities (except
for thermally treated SiC4 coating (d)) black circle represents the pores in SiC
coatings
Figure 64 gives the evolution of interfacial roughness in different coatings after
thermal treatment at 2000 ordmC to study their influence on the change of fracture
strength Compared with the as-deposited coating the changes of the interfacial
roughness in SiC1 are similar to SiC3 which show the smoother interface with
interval of irregularities were observed Fig 64(a) and (c) However different from
as-deposited coatings with defects mainly at the interface defects (pores) are also
observed through the coating after thermal treatment (as seen in Fig 61(b) (f) and
Fig 64(a) (c)) Furthermore the size of pores is in the same magnitude as their
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
163
interfacial roughness (shown in Fig 64(a) and (c))
The change of the interfacial roughness in SiC2 is more significant than SiC1 and
SiC3 since pores formed as part of the interface (indicated by arrows in Fig 64(b))
and they are larger than the pores formed in the coating (circle in Fig 64(b))
Different from others three coatings the IPyCSiC interface of SiC4 becomes
smoother (Fig 64(e)) after thermal treatment compared with as-deposited coating so
the defects (pores) within the coating are bigger than surface irregularities
633 Evolution in microstructure
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermally
treated at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and
SiC2 inset shows the peak shift of as-deposited (dash line) and after thermal
treatment (solid line) (b) is SiC4 and inset is the high angle diffraction peak after
thermal treatment showing splitting while it is a single peak in as-deposited coating
Figure 65 gives XRD results of the as-deposited and thermally treated samples
which show the presence of the β-SiC in coatings The peak presents at 2θ~335ordm is
from the crystallographic errors which could either be due to the stacking faults or
the disordered α-SiC according to previous descriptions [16 17] It is found that the
intensity ratio of the 2θ~335ordm peak to the (111) plane peak (2θ~356ordm) decreased after
thermal treatment in all the coatings The coating SiC4 also shows the split of high
angle diffraction peaks (inset of the Fig 65(b) 2θ~613ordm and 713ordm) which is
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
164
attributed to the X-ray double diffraction and this implies the high crystallites after
thermal treatment
Figure 66 is the HRTEM image of sample SiC4 after thermal treatment in which the
stacking faults and micro twins could still be seen The stacking sequence of
ABCACBACBACB was observed as shown in the dashed square zone in Fig 66
According to study about crystal structure [18] this stacking sequence is supposed to
be the micro twins compared with the rest 3C stacking sequence rather than the
6H-SiC domain Furthermore the (111) peak shifted to the high angle after thermal
treatment in all the coatings as shown in the inset of Fig 65(a) which corresponded
to the decrease of the crystal constant
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Figure 67 gives the Raman spectroscopic results of SiC coatings before and after
thermal treatment The carbon peak at 1300-1600 cm-1
was found in the as-deposited
SiC2 and SiC4 coatings According to previous studies [4 19] the intensity ratio of
I1600I796 indicated that the estimated amount of excess C was less than 05 at in
this study The peak between TO and LO peaks (around 882 cm-1
) was attributed to
the stacking faults or highly disordered stacking faults cluster [3 15 20-22]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
165
After thermal treatment the weak carbon related peaks appeared at around 1395 cm-1
and 1600 cm-1
(G band) in sample SiC1 SiC2 and SiC4 The peak around 1395 cm-1
could represent the methyl group and amorphous carbon structures and G band is due
to the stretching mode of all pairs of sp2 atoms in chains and rings [23] The arising of
the 2D peak (also called G peak 2715 cm-1
) after thermal treatment was observed in
sample SiC2 SiC3 and SiC4 which is the second order of zone-boundary phonons
[24]Considering the amount of excess carbon in SiC coatings the symmetry of the
2D peak indicates that the carbon after treatment is more likely to be graphene rather
than graphite [24] which means the concentration of excess C is low in SiC coatings
It is also found that the intensity ratio of the disordered stacking faults (around 882
cm-1
) to the TO peak decreases in all samples after thermal treatment (shown in Fig
67)
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings The lower line is before thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
166
treatment and the upper line is after thermal treatment at 2000 degC in individual
sample
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
Sample Porosity ()
As 2000degC
Stoichiometry
As 2000degC
Critical Defects
As 2000degC
SiC1 0 05 0 C clusters Inter Inter+ Pore
SiC2 0 14 C clusters Ordered C Inter Inter
SiC3 03 13 0 Ordered C Inter Inter+ Pore
SiC4 09 15 C cluster Ordered C Inter Pore
First order Raman spectroscopy (1200-1600 cm-1
) Represents the carbon structure related to the
methyl group or amorphous carbon structures (contains SP2 and SP
3) [23] Second order (2700 cm
-1)
single layer grapheme related carbon materials [24]
Represents the interface irregularities
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
Furthermore the narrowing of the TO peak was found (the inset in Fig 67 (b)) in the
Raman spectroscopy Although it could be an overlap of two peaks at around 796 cm-1
and 789 cm-1
in coatings before and after thermal treatment the peak at 789 cm-1
corresponding to the stacking sequence of ABCACBhellip [25] is more likely to be
micro-twins in current study(as shown in Fig 66) Table 63 summarized the main
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
167
morphological and microstructural change of SiC coatings before and after thermal
treatment
Particularly for sample SiC3 except for the appearance of weak 2D peak after thermal
treatment without visible first order carbon peaks in the sample SiC3 the precipitates
were also observed from both inner and outside of the shell These precipitates were
demonstrated to be the single 3C-SiC crystal by Raman spectroscopy as shown in Fig
68 Raman spectra of precipitates represents the incident direction of the laser is
perpendicular to the SiC single crystal (111) plane which the LO mode at around 970
cm-1
is forbidden when Raman spectra were obtained in a backscattering geometry
[22] (The appearance of the forbidden LO band might be due to to finite collecting
angle of the spectrometer)
64 Discussion
641 Influence of interfacial roughness and pores on fracture strength
To evaluate the critical flaw size we used the equation 1
2( )
L ICf
K Z
Yc for tensile
strength (local fracture strength) and the case for the semi-circular surface crack
(Y=125 [26]) of radius c and inside holes (Y= π12
[14]) of diameter 2a When the
fracture toughness ( ICK ) of the SiC coating was taken as 33 MPa m-12
[27] the
critical surface defect radius and the diameter of the inside pores were calculated to be
in the range of 15 ndash 78 microm obtained from all the coatings The mean critical flaw
size is in the range of 30 ndash 40 microm after thermal treatment The calculated critical
flaw sizes are in the same magnitude as the defects observed at the IPyCSiC interface
and the pores in the SiC coatings after thermal treatment (see in Fig 63 and Fig 64)
Therefore the decrease of the local fracture strength after thermal treatment could be
related to the formation of these defects in SiC coatings Accordingly the sources of
critical defects were summarized in Table 63 for coatings before and after thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
168
treatment The interfacial roughness and pores within the coating compete to be the
critical flaws Once the size of interfacial irregularities is lower than critical flaw size
and rarely distributed their effect on fracture strength could be decreased or even
excluded according to previous study [14] Therefore the pores inside the coating
with the diameter of 2a would be considered as the main failure origins [14] These
could explain the decrease of local fracture strength in coatings SiC2 SiC3 and SiC4
which have micrometer pores formed within the coatings andor at the interface while
the local fracture strength is less affected in coating SiC1 due to formation of
nanometer pores
The Weibull modulus is related to the specimen size loading method and defects
distribution [5 14] In this study the specimen size and the loading morphology could
be excluded for one kind of SiC coating so the change of the modulus is due to the
degree of the scattering of the critical flaw size under the tensile strength The
interfacial irregularities in SiC2 became narrower and deeper (about 4 microm of depth as
shown in Fig 64(c)) after thermal treatment and they are also bigger than the pores
generated within the coating So the critical flaw in SiC2 after thermal treatments is
due to the interfacial irregularities (Table 62) with less scattered size under the
loading area than as-deposited coating which increased the Weibull modulus
However the critical defects in the other coatings include pores within the coatings
(shown in Fig 64 and Table 62) For example in SiC4 the critical flaw is only from
pores within the coating after thermal treatment due to the lack of interstitial
irregularities (Fig 64(h)) This enlarged the distribution of critical flaws after thermal
treatment which leads to the decrease of the Weibull modulus in different degree The
change of the fracture strength of the full shell depends on both Weibull modulus and
local fracture strength as discussed before [5] Our result showed that the SiC coating
deposited at low temperature of 1300 ordmC produced less critical flaws and smaller
decrease of the fracture strength of the full shell (see Table 63)
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
169
642 Mechanism of microstructural change
Changes in SiC coatings after thermal treatment include the formation of pores the
decreased intensity of the 2θ~335 ordm peak (crystallographic errors) in XRD the arising
of Raman peaks around 1395 cm-1
and 2715 cm-1
According to previous studies [8
10 21 25 28 29] we propose that these changes after thermal treatment could be
attributed to phase transformation or the diffusion of defects such as vacancies and
interstitials
If the 2θ~335ordm peak is from amorphous α-SiC its intensity ratio to (111) diffraction
peak would increase after heat treatment Because the presence of α-SiC phase in
β-SiC could promote the transformation of β-SiC into α-SiC [29] Conversely the
intensity of 2θ~335ordm peak decreased after thermal treatment in this work as observed
in Fig 65 and no α-SiC phase segregation (Fig 66) was found by HRTEM after
thermal treatment Furthermore the transformation from disordered α-SiC into β-SiC
after thermal treatment is also excluded because high pressure and high temperature
are needed for this process to happen [29] Therefore it is concluded that the 2θ~335ordm
peak derived from stacking faults and they could be annihilated at current
environment according to previous studies [8 28 30]
Stacking faults were surrounded by defects such as dislocations vacancies and
interstitials [10 15 31] so the high density of stacking faults in this work
corresponded to the high amount of native defects The annihilation of stacking faults
after thermal treatment indicated the reduction of these defects and it could reduce
the lattice constant In this work the decrease of the lattice constant was found after
thermal treatment as indicated by the peak shift of (111) plane in XRD results (Fig
65) and the crystallisation (ordering) was also reflected from the decreased intensity
of the 2θ~335ordm peak (Fig 65) and Raman defect peak (around 882 cm-1
) (Fig 67)
Therefore the formation of pores is due to the annealing of defects through the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
170
diffusion of vacancies or interstitials which are common even in high-purity CVD
SiC [32] However diffusion of native defects depended on their concentration which
was constrained by different composition of SiC (deviation from stoichiometry) [31]
For example for the C-rich cubic SiC the dominant defect is the CSi antisite (Si atom
site was occupied by C atom in tetrahedral structure) [31]
According to above analysis the formation mechanism of pores could be governed by
different kinds of defects In SiC1 coating the smallest and least content of pores
formed after thermal treatment is most likely caused by the annealing of stacking
faults surrounded by the dislocations and vacancies which is consistent with previous
study about the thermal treatment effect on stoichiometric SiC [28] In SiC coating
with excess carbon the microstructure evolution could be more complex as
demonstrated by the presence of the graphene layer (Raman peak at 2700 cm-1
)
According to previous studies [31 33] this is attributed to the existence of the CSi
antisite and vacancies which form the vacancy cluster and antisite clusters after
thermal treatment at 2000 degC
The microstructure change in SiC3 coating is different from SiC1 The diffusion
mechanism in SiC3 was supposed to be involved with the interstitials since the single
SiC crystal precipitate was found out of the coating(Fig 68) This also resulted in
higher amount of the pores in SiC3 than in SiC1 after thermal treatment It is
proposed that the different diffusion mechanism found in stoichiometric SiC1 (Si and
C vacancies) and SiC3 (tetragonal interstitials) could be due to different deposition
conditions which produced different kinds of dominant native defects The larger
pores formed in SiC3 and SiC4 could be due to larger grain size than SiC1 and SiC2
(different deposition temperature) because most of pores were near to the grain
boundaries and triple junctions (as shown in Fig 63(d) (f) and (h)) The diffusion of
native defects also affects the interfacial irregularities and the diffusion mechanism in
SiC coatings is being studied in our research group
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
171
65 Conclusions
The SiC coatings deposited at temperature range of 1300-1500 degC with composition
near-to the stoichiometry were thermally treated at 2000 degC in Ar atmosphere for 1
hour to study the effect of thermal treatment on microstructure and fracture strength
The following conclusions were obtained
(1) The local (intrinsic) fracture strength decreased in a varied degree after
thermal treatment and it was due to the formation of pores along the IPyCSiC
interface and in the coatings
(2) The Weibull modulus decreased once the pores have similarbigger size
asthan interfacial irregularities and distribute uniformly within coatings while
it increased with the size of pores much smaller than interfacial irregularities
after thermal treatment
(3) After thermal treatment no phase transformation was found in SiC coatings
and the crystallographic error (2θ~335 ordm) detected by XRD was demonstrated
to be stacking faults which were annihilated during this process
(4) The formation of pores after thermal treatment was attributed to the diffusion
of intrinsic defects such as vacancies interstitials and antisites Different
content and size of pores were observed in different coatings which are
presumed to have different kinds of native defects in as-deposited coatings
produced at different conditions
(5) The vacancies are supposed to be the dominant defects in stoichiometric SiC
deposited at 1280 ordmC however in other coatings the dominant defects could
be a combination of vacancies antisites and interstitials based on Raman
results before and after thermal treatment Furthermore the diffusion of native
defects also affects interfacial roughness after thermal treatment which needs
further study
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
172
66 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook of
SiC properties for fuel performance modeling J Nucl Mater 371 (2007) 329-77
[2] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[3] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidised
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
[4] H Zhang E Loacutepez-Honorato A Javed I Shapiro P Xiao A study of the
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc (2011) DOI
101111j1551-2916201105044x
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of fracture
stress for the SiC Layer of TRISO-Coated fuel particles using a modified crush
test method Int J Appl Ceram Tech 7 (2010) 327-37
[6] G H Lohnert H Nabielek W Schenk The fuel-element of the Htr-module a
prerequisite of an inherently safe reactor Nucl Eng Des 109 (1988) 257-63
[7] I J Van Rooyen J H Neethling J Mahlangu Influence of temperature on the
micro-and nanostructures of experimental PBMR TRISO coated particles A
comparative study Proceedings of the 4th
international topical meeting on high
temperature reactor technology HTR 2008 September 28-October 1 2008
Washington DC USA HTR 2008-58189
[8] Y Kurata K Ikawa K Iwamoto The effect of heat-treatment on density and
structure of SiC J Nucl Mater 92 (1980) 351-53
[9] D T Goodin Accident condition performance of fuels for high-temperature
gas-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[10] N Shirahata K Kijima A Nakahira K Tanaka Thermal stability of stacking
faults in Beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
173
[11] J van Rooyen J H Neethling P M van Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[12] E Loacutepez-Honorato K Fu P J Meadows J Tan and P Xiao Silicon carbide
coatings resistant to attack by palladium J Am Ceram Soc 93 (2010) 4135-41
[13] E Loacutepez-Honorato H Zhang D X Yang P Xiao Silver diffusion in silicon
carbide J Am Ceram Soc 94 (2011) 3064-71
[14] D J Green An Introduction to the Mechanical Properties of Ceramics
Cambridge University Press Cambridge 1998
[15] H Zhang E Loacutepez-Honorato A Javed X Zhao J Tan P Xiao A Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc (2012) DOI101016jjeurceramsoc201112014
[16] H Tateyama H Noma Y Adachi M Komatsu Prediction of stacking faults in
βndashSilicon carbide X-Ray and NMR studies Chem Mater 9 (1997) 766- 72
[17] K R Carduner S S Shinozaki M J Okosz C R Peters T J Whalen
Characterization of β-Silicon carbide by silicon-29 solid-state NMR transmission
electron microscopy and powder X-ray diffraction J Am Ceram Soc 73 (1990)
2281-86
[18] httptfuni-kieldematwisamatdef_enkap_6advancedt6_3_2html
[19] S M Dong G Chollon C Larbrugere M Lahaye A Guette J L Brunee M
Couzi R Naslain and D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[20] M Havel D BaronL Mazerolles P Colomban Phonon confinement in SiC
nanocrystals comparison of the size determination using transmission electron
microscopy and Raman spectroscopy Appl Spet 61 (2007) 855-59
[21] V V Pujar J D Cawley Effect of stacking faults on the X-Ray diffraction
profiles of 3C-SiC powder J Am Ceram Soc 78 (1995) 774-82
[22] Y L Ward R J Young R A Shatwell Effect of excitation wavelength on the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
174
Raman scattering from optical phonons in silicon carbide monofilaments J Appl
Phys 102 (2007) 023512 -17
[23] X J Li J Hayashi C Z Li FT-Raman spectroscopic study of the evolution of
char structure during the prolysis of a victorian brown coal Fuel 85 (2006)
1700-07
[24] A C Ferrari J C Meyer V Scardaci C Casiraghi M Lazzeri F Mauri S
Piscanec D Jiang K S Novoselov S Roth A K Geim Raman spectrum of
graphene and graphene layers Phys Rev Lett 97 (2006) 187401-04
[25] S Nakashima H Harima Raman investigation of SiC polytypes Phys Stat Sol
A-Appl Res 162 (1997) 39-64
[26] GKBasal Effect of flaw shape on strength of seramics J Am Ceram Soc 59
(1976) 87-8
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] K Koumoto S Takeda CH Pai High-resolution electron microscopy
observation of stacking faults in βndashSiC J Am Ceram Soc 72 (1989) 1985-87
[29] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J Am Ceram Soc 84 (2001) 3013-16
[30] K Koumoto S Takeda C H Pai T Sato H Yanagida High-resolution electron
microscopy observations of stacking faults in β-SiC J Am Ceram Soc 72 (1989)
1985-87
[31] C Wang J Bernholc Formation energies abundances and the electronic
structure of native defects in cubic SiC Phys Rev B 38 (1998) 12752-55
[32] E Janzen N T Son B Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[33] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-09
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
175
CHAPTER 7 Microstructure and Mechanical Properties of
Pyrolytic Carbon Coatings
71 Introduction
Pyrolytic carbon (PyC) coatings forming part of the TRI-Isotropic (TRISO) fuel
particle are important for the stability of this type of nuclear fuel Without appropriate
microstructure and mechanical properties of PyC coatings the stress generated inside
the particle due to internal gas pressure andor the dimensional change (anisotropic
shrinkage or creep) introduced in this layer during irradiation process could result in
the failure of the full particle [1-5] Fundamental understanding about relationship
between mechanical properties and microstructure of PyC coatings could help to
analyse the failure mechanism and model the probability of failure of TRISO fuel
particles [1 5] However their relations in PyC are complex [3 6-8] Kaae [7] found
that mechanical properties were related to the density crystal size and anisotropy but
they are not controlled by a single variable For example Youngrsquos modulus increased
with density for isotropic carbons with constant crystallite size but decreased with
increasing anisotropy for carbon with constant density and crystalline size In a
separate work [3] density had a dominant effect on the hardness and Youngrsquos
modulus in relative low density PyC coatings whereas no controlling factor was
given for high density PyC coatings
Nano-indentation is an effective way to study microstructural effects on mechanical
properties of PyC coatings because it could help with the understanding of the
deformation mechanism and measure Youngrsquos modulus and hardness spontaneously
Among studies on mechanical properties in carbon related materials under
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
176
depth-sensing indentation [3 9-15] few explanations about the nature of their
deformation mechanism have been discussed [9 10 13 15] First the hysteresis was
assumed to due to the slip of graphene layers in nano-meter grains and the energy
loss was attributed to the friction between graphene layers under compression stress
[9 10] Second the dislocation pileups were assumed to be responsible for energy
loss [13] but this idea failed to account for the reversible deformation [15] The most
recent theory suggested that the origin of the hysteresis was due to the formation of
(incipient) kink bands [15] This theory was found to be a universal explanation for
most laminar structured materials but the nature of initial kink band was not clear
[15]
During pressing process of TRISO fuel particles into fuel elements they experience a
final thermal treatment of 1 h above 1800 ordmC to drive off any residual impurities and
improve thermal conductivity of the fuel compact [16] The evolution of
microstructure of carbon related materials have been widely studied [17-20] Few
researches measured changes of mechanical properties after thermal treatment [19
20] but there is a lack of understanding about effect of microstructural evolution on
mechanical properties in PyC coatings Therefore in this Chapter together with the
microstructural properties the deformation mechanism under indentation influences
on mechanical properties and their change after thermal treatment in PyC coatings are
studied
72 Experimental details
Pyrolytic carbon (PyC) was coated on alumina particles (Φ 500 μm) by fluidised bed
chemical vapour deposition by Dr Eddie Loacutepez-Honorato and PyC coatings with
different density was chosen to study the mechanical properties Table 61 gives the
density and texture (orientation angle) of PyC coatings and more about deposition
mechanism could be found in Ref [21] The number of sample sequence Ci (i=1
2hellip11) starts from highest density to lowest density with density of 19 gcm3 as
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
177
border line to distinguish highlow density PyC which was measured by the
Archimedes method in ethanol For thermal treatment the coatings were first
grounded into fragments and then removed the alumina kernel The fragments of PyC
were then thermal treated at 1800 degC and 2000 degC for 1 hour in argon atmosphere For
further understanding of microstructural evolution during thermal treatment sample
C5 was thermal treated at 1300 1400 1500 and 1600 degC for 1 hour
Table 71 PyC coatings with different density and orientation angle
PyC
(High density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
PyC
(Low density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
C1 2122plusmn0059 58 C6 1855plusmn0050 63
C2 2087plusmn0183 37 C7 1738plusmn0013 73
C3 2047plusmn0030 60 C8 1635plusmn0008 71
C4 2029plusmn0015 43 C9 1603plusmn0024 71
C5 2000plusmn0061 43 C10 1414plusmn0002 85
C11 1400plusmn0024 81
Orientation angle was obtained from the full width of half maximum of azimuthal intensity scan of
SAED pattern for more information in Ref [22] Productions of PyC coatings measurement of
orientation and density measurement are contributed by Dr Eddie Loacutepez-Honorato et al
The selected area electron diffraction (SAED) patterns were obtained with the use of a
FEG-TEM (see Chapter 3) and orientation angle was measured by the azimuthal
intensity scans of SAED pattern (selected aperture diameter of 200 nm) Further
details about this measurement were shown in a previous study [22] Transmission
electron microscopy (TEM) samples were obtained by focus ion beam milling High
resolution TEM samples were prepared by dispersing the fragments on a carbon holey
film copper grid X-ray diffraction (see Chapter 3) was used to obtain domain sizes of
PyC coatings After correction of intrinsic instrumental effect the out of plane and
in-plane domain sizes (along c-axis and a-axis in graphite crystal structure) Lc and La
were qualitatively estimated from XRD data by applying the Scherrer equation to the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
178
(002) and (110) reflections respectively [23] In as-deposited PyC coatings the (110)
peak was too weak to estimate accurately on the La Raman spectroscopy (633 nm
Helium ion laser source) was performed by single spot measurements (spot size was
carefully controlled to be the same for each test) of around 2 μm diameter using a times50
objective lens The laser power of less than 05 mW (10) was used with the step
size of 60 seconds and twice accumulations For each sample 5 different positions
were measured The band fitting of the first order spectra was carried out with
GRAMS32 software
To reduce the influence of surface roughness on indentation test the PyC coatings
were ground with successive finer grades of SiC paper and polished down to a 1 microm
grid diamond paste The same nano-indentation as in Chapter 3 was used The
measurements were performed at fixed loading rate of 1 mNS reaching the
maximum load of 100 mN For each coating at least 25 indentations were conducted
on the sample surface to increase the reliability of the results The Olive and Pharr
method [24] was used to analyse all the data
73 Results
731 Microstructure of PyC coatings
In order to study the influences of microstructure on mechanical properties it is
necessary to know the nature of structure which makes one sample from another eg
disorders domain size crystallinity etc and their evolution after thermal treatment
7311 Raman spectroscopy
Figure 71 is a Raman spectroscopy for an as-deposited high density PyC coating (C5
200 gcm3) which exhibits two relatively broad Raman bands at around 1335 cm
-1
and 1600 cm-1
The first band corresponds to the D band which is attributed to double
resonant Raman scattering and represents the in-plane defects [21 25 26] The
second band is an overlap of broadened G (1580 cm-1
) and D (1620 cm-1
) bands due
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
179
to high disordered pyrolytic carbon [27] The G band is due to the stretching modes of
pairs of sp2 atoms in graphene planes whereas D represents the similar defects
structure as the D band [18 27] It is convenient to consider 1600 cm-1
band a single
G peak for practical purposes when comparing different samples or the overall
structural evolution of a given PyC coating [27]
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
According to previous studies [25-32] on fitting similar Raman spectra shown in Fig
71 a simple two-symmetric-line fit (D and G bands) could not fit it well Therefore
the Raman spectra of high density PyC coatings (C1-C5 gt 19 gcm3) were
deconvoluted into above peaks at about 1220 cm-1
1335 cm-1
1500 cm-1
and 1600
cm-1
( Fig 71) The band at about 1500 cm-1
(Drsquorsquo) is attributed to interstitial defects
which could act as coupling (covalent band) between two graphene layers or adjacent
overlapped domains [25 28] The I band at around 1220 cm-1
is due to C-C on hydro
aromatic rings [28] The Raman spectra mean the high degree of in-plane andor
out-of-plane disorders in high density PyC coatings represented mainly by the full
width at half maximum (FWHM) of the D band [28] and intensity ratio (the area ratio
of the 1500 cm-1
peak to the sum of four peaks shown in Fig 71) of the Drdquo bands
[25] respectively
D
I
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
180
Figure 72 is the Raman spectra of high density PyC coating C5 after thermal
treatment at temperature of 1300 1400 1600 and 1800 ordmC The FWHM of the D band
decreased significantly from about 150 cm-1
(as-deposited) to about 106 cm-1
(1400
ordmC) and then to about 40 cm-1
(1800 ordmC) Similarly the intensity ratio of the Drdquo was
reduced from about 0135 (as-deposited) to about 0110 (1400 ordmC) and then to about
0078 (1800 ordmC) Another change is the split of G and D bands after thermal treatment
at 1800 ordmC (Fig 72) The above changes indicate that disorders in high density PyC
coatings are low energy structural defects ie degree of disorder is low according to a
previous study [28]
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
181
After thermal treatment the degree of microstructural changes of low density PyC
coatings C6-C8 (164-186 gcm3) is slightly different from even lower density
coatings C9-C11 (140-160 gcm3) so they are described separately Figure 73 shows
Raman spectra of low density PyC coatings (a) C7 and (b) C10 before and after
thermal treatment at 1800 ordmC Similar to high density PyC the as-deposited coatings
C6-C8 contains four Raman bands After thermal treatment the FWHM of the D peak
in C7 decreased from about 120 cm-1
to 57 cm-1
and the intensity ratio of interstitial
defects was also reduced (from 0116 to 0042 Fig 73(b)) In coating C10 only
slightly decrease of FWHM of the D peak (from about 83 cm-1
to 57 cm-1
) was found
after thermal treatment at 1800 ordmC (Fig 73(b)) No split of the G and D bands was
observed in low density PyC coatings
With increase in density of PyC the FWHM of the D band the concentration of the
Drdquo band and the degree of their changes after thermal treatment increase considerably
which suggest that the disorder defects in PyC are different with variation of density
and thermal treatments change the degree of the disorder
7312 Domain sizes
Table 72 summarises the out-of-plane domain size (crystallite size perpendicular to
the graphene plane Lc) and in-plane domain size (crystallite size along the graphene
plane La) measured by XRD in PyC coatings before and after thermal treatment The
Lc is in the range of 1-3 nm in all the as-deposited coatings and it is slightly bigger in
high density (about 2-3 nm) coatings than low density (about 1-2 nm) coatings After
thermal treatment at 1800 ordmC the Lc increased significantly which is about 5 times
and 2-3 times larger than in as-deposited high density and low density PyC coatings
respectively It is 2-4 times larger in high density PyC than low density PyC coatings
The La in high density (about 6 nm) is larger than low density PyC coatings (3-4 nm)
after thermal treatment at 1800 ordmC Both Lc and La remained unchanged after thermal
treatment at 2000 ordmC in all PyC coatings (This is explained in section 741) The
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
182
increase of domain size indicated the ordering process in PyC coatings after thermal
treatment which may involve annealing of different kinds of disorders
Table 72 Domain size of as-deposited and thermal treated PyC coatings
Sample As deposited 1800 2000
Lc (nm) La (nm) Lc (nm) La (nm) Lc (nm) La (nm)
High density (gt19 gcm3)
C1 21 -- 112 -- 116 53
C2 21 -- 132 63 154 69
C3 22 -- 98 66 111 63
C4 24 -- 95 57 118 63
C5 20 -- 120 60 152 73
Low density (lt 19 gcm3)
C6 22 -- 50 42 56 44
C7 18 -- 38 36 50 34
C8 14 -- 31 33 27 39
C9 11 -- 27 32 31 34
C10 17 -- 24 33 27 35
C11 11 -- 27 35 27 33
7313 Evolution of crystallinity
Figure 74 is the TEM images of high density PyC (C5) before and after thermal
treatment The dark field TEM show bright areas (Fig 74(a) and (b)) that represent
graphene layers with similar orientation in the selected direction of the diffraction
pattern A decrease of the orientation angle from 43 ordm to 25 ordm is found after thermal
treatment at 1800 ordmC which is obtained from the full width at half maximum of
azimuthal intensity scan of SAED pattern (insets in Fig4(a) and (b)) A bright field
TEM image of a conical microstructure after thermal treatment (Fig 74(c) dashed
rectangle in Fig 74(b)) which shows the voids at the top of conical structures The
above observations show that thermal treatment increases anisotropy and results in the
volume shrinkage and generation of voids in high density PyC coatings
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
183
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Figure 75 is the typical HRTEM away from the top of conical growth feature (eg
OA=43 ordm
OA=25 ordm
Top
Voids
100 nm
(c)
(a) (b)
5 nm
Moireacute
fringes
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
184
white circle in Fig 74(c)) in high density PyC coatings (C1) before and after thermal
treatment at 1800 ordmC The wrinkled short graphene fringes in as deposited high
density PyC (Fig 75(a)) were replaced by distorted planes in a larger scale with a
bigger radius of curvature (white arrow in Fig 75(b)) The common number of
parallel layers (Fig 75(a) (002) plane white parallel lines) is 2-4 in as-deposited C1
which increased to about 30 (Fig 75(b) between white parallel lines) The moireacute
fringes were observed after thermal treatment (black arrow in Fig 75(b)) which
correspond to black bars in the bright field TEM (eg dashed black rectangle in Fig
74(c)) According to the generation mechanism of moireacute fringes [33] the on-going
ordering process along the c-axis is related to the increase of number of parallel layers
and evolution (decrease) of the inter plane distance of (002) planes
Figure 76 gives the bright field TEM and HRTEM images showing the
microstructure evolution in a low density PyC coating (C7) Globular growth features
with diameters of about 400 nm were observed in as-deposited C7 as shown in Fig
76(a) and the HRTEM image shows 2-3 layers of parallel planes (Fig 76(b)) In low
density PyC coatings the graphene fringes are longer and less oriented than in high
density coatings (reflected from orientation angle shown in Table 71 and Fig 13 in
Ref [21]]) After thermal treatment the short dark bars andor dots (as indicated by
the white arrows Fig 76(c)) were observed which is due to the moireacute fringes as
shown in Fig 76(d) The number of parallel layer increased up to 8-10 (Fig 76(d))
and it reflects the slight crystallinity after thermal treatment In the other low density
PyC coatings C9-C11 the TEM images are similar with the as-deposited low density
PyC coatings (as shown in Fig 14 and Fig 13(c) in Ref [21]) Furthermore the
orientation angle is almost the same in all low density PyC before and after thermal
treatment
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
185
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
732 Mechanical properties of PyC coatings
7321 Force-displacement curve
Figure 77 gives the force-displacement curve of PyC coatings with different density
under the maximum load of 60 mN and 100 mN by nano-indentation The unloading
curve did not completely retrace the loading curve but still returned to the origin This
process is called anelastic behaviour or hysteresis behaviour and the anelastic
reversible indentation processes with an enclosed loop are found in all the PyC
coatings
(a) (b)
100 nm 5 nm
5 nm
Sphere-like
particle
Tops
Moireacute fringes Sphere-like
particle
Top (d)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
186
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
The maximum indentation depth in low density PyC (C6-C11 lt 19 gcm3) is deeper
than in high density PyC coatings (C1-C5 gt 19 gcm3) under the same load and the
low density PyC also shows larger hysteresis loop area The ratio of the hysteresis
energy (area within the loading-unloading loop) to total loading energy (area under
loading curve) in high density PyC is lower than in low density PyC coatings For
example the ratios of sample C3 C9 and C11 are 0243 0270 and 0292 respectively
Furthermore the deformation behaviour of all PyC coatings showed the hysteresis
behaviour after thermal treatment up to 2000 ordmC The high density PyC after thermal
treatment at 1800 ordmC (red curve in Fig 77) shows anelasticity however the ratio of
its hysteresis energy (0249) is much higher than in as-deposited coating (0174)
According to previous studies [10 34] the low ratio obtained in high density PyC
coatings under pyramidal indenter corresponds to high elasticity while low density
exhibits high hysteresis (anelasticity high viscosity))
Under indentation the hardness is defined as the mean pressure the material will
support under load according to Oliver and Pharrrsquos study [24] This pressure is equal
to the load at maximum load divided by the contact area (according to eqs (7 10 11)
hc
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
187
in Chapter 2) However the residual depth hf is zero and no pleastic deformation is
observed after unloading The hardness obtained by Oliver and Pharr method does not
reflect the resistance of plastic deformation of material but it could represent the
degree of unelastic deformation qualitatively Therefore the mean pressure (P) value is
used which could reflect the anelastic properties of PyC coatings
7322 Youngrsquos modulus and the mean pressure
Figure 78 gives the Youngrsquos modulus (E) and the mean pressue (P) of as-deposited
PyC coatings as a function of density For low density PyC coatings (C6-C11 lt 19
gcm3) Youngrsquos modulus and the mean pressure increase almost linearly with the
density For high density PyC coatings (C1-C5 gt 19 gcm3) both Youngrsquos modulus
and the mean pressure reach plateaus which are independent of density It indicates
that mechanical properties of high PyC coatings are dominated by other factors
which are discussed in session 744
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
Table 73 shows the Youngrsquos modulus and the mean pressure of PyC coatings with
different density before and after thermal treatment at 1800 and 2000 ordmC After
thermal treatment at 1800 ordmC Youngrsquos modulus decreased by around 50 and the the
mean pressure is reduced by around 69 in high density PyC coatings (C1-C5 gt19
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
188
gcm3) whereas minor change is observed when thermal treatment temperature
further increased to 2000 ordmC Previous study [20] showed similar results about
changes of mechanical properties in high density PyC after thermal treatment at
different temperature In low density PyC coatings C6-C8 (164-186 gcm3) the
mean pressure and Youngrsquos modulus decreased by about 23 and 8 after thermal
treatment at 1800 ordmC respectively which is consistent with Rooyen et alrsquos results
[19] and further decreased by 18 and 15 by increasing thermal treatment
temperature to 2000 ordmC In low density coatings C9-C11 (140-160 gcm3) little
change in mechanical properties after thermal treatment up to 2000 ordmC was found and
it is similar as the isotropic low density PyC [20] Mechanical properties and their
change after thermal treatment in PyC coatings are different with different density
Table 73 Changes of mechanical properties of PyC coatings after thermal treatment
Sample As deposited Thermal treated at 1800 Thermal treated at 2000
P (GPa) E (GPa) P (GPa) E (GPa) P (GPa) E (GPa)
High density
C1 468plusmn025 2670plusmn119 103plusmn018 1482plusmn131 090plusmn013 1337plusmn093
C2 435plusmn048 2513plusmn117 132plusmn019 1091plusmn069 076plusmn021 1204plusmn126
C3 490plusmn036 2878plusmn117 -- -- 091plusmn026 1271plusmn125
C4 397plusmn019 2291plusmn076 171plusmn010 1313plusmn034 110plusmn010 1370plusmn051
C5 456plusmn010 2610plusmn036 132plusmn015 1177plusmn051 177plusmn025 1361plusmn101
Low density
C6 388plusmn035 2165plusmn191 296plusmn022 1912plusmn113 244plusmn023 1647plusmn088
C7 395plusmn053 2149plusmn200 292plusmn036 1934plusmn114 232plusmn033 1568plusmn182
C8 354plusmn027 1945plusmn070 292plusmn036 1904plusmn113 232plusmn063 1678plusmn240
C9 284plusmn040 1938plusmn094 226plusmn057 1677plusmn178 263plusmn042 1733plusmn151
C10 189plusmn009 1266plusmn035 213plusmn019 1363plusmn076 188plusmn023 1381plusmn087
C11 168plusmn017 1166plusmn082 178plusmn034 1284plusmn106 086plusmn014 1167plusmn151
74 Discussions
The main findings of this study can be summarised as follows 1) PyC with different
density show different full width at half maximum (FWHM) of the D band and
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
189
concentration of the Drsquorsquo band which suggests that they have different types of disorder
TEM observation shows longer graphene fringes with lower density PyC (Fig 13 in
Ref [21]) thermal treatments decrease the degree of disorder while PyC with higher
density (gt19 gcm3) shows higher degree of decrease 3) initial increase in PyC
density until 19 gcm3 lead to proportional increase in Youngrsquos modulus (E) and the
mean pressure (P) while further increase in density has no effect on E and P 4)
hysteresis occurred after nano-indentation of PyC while the degree of hysteresis is
controlled by the PyC density and heat treatments
741 Disorders and their changes after thermal treatment
High density PyC Coatings (C1-C5 gt 19 cmg3) The dominant in-plane disorders
are domain boundaries according to a previous study [21] which generates high
FWHM of the D band due to the low energetic disorientations (eg domains andor
graphene layers) [25 28] The Drsquorsquo band (interstitial defects) is due to the amorphous
carbon structure which is composed of mainly disordered sp2 atoms and a low
amount of sp3 atoms [27 28 35] Particularly the sp3 lines are out of plane defects
which could be formed in high density PyC coatings [36] Therefore it is assumed
that the microstructure in high density PyC is composed of disoriented nano-size
graphite domains connected by amorphous carbon
After thermal treatment the reductions of the out-of-plane defects and the tilt and
twist in graphite planes are observed which could contribute to the increase of Lc
(out-of-plane domain size) as shown in HRTEM image (Fig 75) It was supposed
that the equilibrium shear stress were generated by in-plane defects and out-of-plane
defects in PyC coatings [25] once the out-of-plane defects was reduced the in-plane
stress would tend to straighten the graphite planes Furthermore the decreases of
FWHM of the D band and the orientation angle (Fig 72 and 4) show the ordering
arrangement of graphite layers is due to the healing of in-plane disorientations The
unchanged domain size Lc could be a result of a combination of increased number of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
190
parallel graphene layers and decreased inter distance of (002) plane As a conclusion
the increase of domain size Lc could be due to the coalescence of domain size andor
graphene layers through reorientation and remove of interstitial defects which
usually started at temperature of about 900-1200 ordmC [17 25] No La (in-plane domain
size) value was obtained in as-deposited PyC and the overlap of the G and the Drsquo
bands indicates it is below 4 nm above which two bands split [37] After thermal
treatment at 1800 ordmC the La is about 6 nm in high density PyC coatings (Table 72
and splitting of G and Drsquo bands was shown in Fig 72) which demonstrates the
slightly increase of La It is attributed to the annihilation of low energetic in-plane
disorientations which could usually be removed at temperature above 1500 ordmC [25]
Since the high temperature above 2000 ordmC is needed to remove the rest high energetic
in-plane defects for high density PyC according to previously study [25 28] it could
explain the La remained nearly constant after thermal treatment further increased to
2000 ordmC The ordering of graphite layers is responsible for the formation of voids (Fig
74(c)) since the ordering could reduce the volume and increase the density of PyC
coatings after thermal treatment [38]
Low density PyC Coatings (C6-C11 lt 19 cmg3) The main defect is the
5-memebered rings in coatings C9-C11 by comparing the Raman spectroscopy (Fig
73(a)) with a previous study [21] In low density coatings C6-C8 (164-186 gcm3)
the degree of in-plane disorder is less than in high density coatings but higher than
coatings C9-C11 (140-160 gcm3 indicated by the FWHM of the D band) and the
out-of-plane defects are much higher than low density PyC coatings (Fig 73) After
thermal treatment the in-plane disorder is similar as in coatings C9-C11 Therefore
the dominant in-plane defects are supposed to be a combination of domain boundaries
and 5-membered rings The slightly increase of domain size Lc in low density PyC
coatings is due to the decrease of interfacial defects through reorientation of domains
However they have much lower degree of increase of Lc than high density coatings
this could be due to low anisotropy in low density PyC coatings which makes it
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
191
difficult to reorient domains and remove the weak defects [17 25] The domain size
La was assumed to be unchanged since ordering in-plane disorders took place at
temperature above 2400 ordmC in low density PyC due to presence of 5-member rings
[17] It is worth to notice that the graphene fringes do not represent the in-plane
domain size in low density PyC due to the curvature caused by 5-memebered rings
[21] Due to the exist of 5-membered rings in low density PyC coatings the
microstructure is lightly affected by thermal treatment
742 Hysteresis after indentation
The increase in density of PyC leads to decrease in hysteresis after indentation and
density of PyC also dominate types and degree of disorders During indentation of
PyC hysteresis is caused by the slip of graphene planes whereas the disorders such as
interstitial defects or 5-memebered rings are supposed to be responsible for the
reversible deformation The hysteresis was also observed in other carbon materials
such as single crystal graphite [15] polycrystalline graphite [15] glassy carbon [9
10] Similar explanations about the effect of slip of graphene layers on the hysteresis
behaviour under indentation were given and it suggests that the deformation
mechanism is related to a common structure in different carbon materials which are
graphene planes
The slip of graphene planes has been demonstrated available The shear modulus (micro)
of graphite is 23 GPa (between graphene layers) [39] Based on the relation of τth= micro
30 [39 40] the theoretical shear stress (τth) of graphite is estimated to be 0077 GPa
This shear stress is much lower than the yield stress under Berkovich indenter for
graphite (03-05 GPa) [15] Under indentation the slip of graphene planes consumes
energy but recovers to the original shape after unload Lower density PyC has longer
fringes than that in higher density PyC (Fig 13 Ref [21]) therefore the panes can
slip for a longer distance under shear stresses generated by nano-indentation
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
192
Reversible deformation is due to presence of interstitial defects or highly curved
5-memebered rings For indentation of crystallite graphite the kink band could be
generated during the initial indentation process then reviersible deformation occurs
under further indentation [15] similar as that shown in Fig 77 In our PyC coatings
disorder in the PyC plays a similar role as the kink band in the crystallite graphite
The slip direction is parallel to the graphene planes so the in-plane defects presents at
the tilt and twist of two adjacent domains could not stop and reflect the slip Only
those defects perpendicular to the slip direction can contribute to the reversible
deformation such as interstitial defects or the highly curved 5-memebered rings
(caused fibrous graphene planes as shown in Fig 13(c) Ref [21])
After heat treatment the growths of the in-plane fringes increase the degree of the
hysteresis in PyC coatings For example the straightened graphene fringes (Fig 75)
caused by reorientation and removes of interstitials facilitate the hysteresis
significantly (the ratio of hysteresis energy to total loading energy increased from
0174 to 0249 Fig 77)
743 Mechanical property of low density PyC coatings
In as deposited low density PyC (C6-C11 gt 19 gcm3) Youngrsquos modulus and the
mean pressure are dominated by the density which is consistent with previous studies
[3 7 41] because of the effect of porous structure [3 21] As discussed in session
741 the disorders in low density PyC coatings play an important part on the stability
of microstructure which could reflect changes of mechanical properties After thermal
treatment the mechanical properties remained almost unchanged in PyC coatings
C9-C11 (140-160 gcm3) and this could be explained by the insignificant change of
microstructures at the presence of 5-membered rings The slightly decrease of
mechanical properties were found in coatings C6-C8 (164-186 gcm3) which is due
to the ordering of graphene planes through reduction of interstitial defects which
could enhance hysteresis and decrease the mean pressure No voids and change of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
193
orientation was observed after thermal treatment in coatings C6-C8 so Youngrsquos
modulus is slightly affected It is concluded that the mean pressure and Youngrsquos
modulus are functions of density in as-deposited low density coatings and their
evolution after thermal treatment is controlled by disorders such as interstitials andor
5-membered rings
744 Mechanical Property of high density PyC coatings
In high density PyC coatings (C1-C5 gt 19 gcm3) Youngrsquos modulus and the mean
pressure are independent of density so they are discussed regarding to variation of
texture domain size and concentration of interstitial defects (the area ratio of the 1500
cm-1
peak to the sum of four peaks shown in Fig 71) Table 74 summarises
microstructure parameters and mechanical properties of high density PyC coatings
Mechanical properties are not controlled by domain size and orientation angle which
is converse to the previous study [41] It is found that Youngrsquos modulus and the mean
pressure in high density PyC coatings decrease with the reduction of concentration of
interstitial defects (as shown in Table 74)
Table 74 The parameters used to explain different mechanical properties of high
density PyC (C1-C5 gt 19 gcm3)
Sample Density
(gcm3)
Texture
OA (deg)
Domain
size (nm)
IinterstialAll Pressure
(GPa)
Modulus
(GPa)
C3 2047 plusmn0030 60 22 013955plusmn000374 490plusmn036 2878plusmn117
C1 2122 plusmn0059 58 21 013513plusmn000399 468plusmn025 2670plusmn119
C5 2000 plusmn0061 43 20 013456plusmn000561 456plusmn010 2610plusmn036
C2 2087 plusmn0183 37 21 013036plusmn000433 435plusmn048 2513plusmn117
C4 2029 plusmn0015 43 24 011823plusmn001628 397plusmn019 2291plusmn076
The physical meaning of the above observation can be explained by the effect of
interstitial defects on the deformation mechanism in high density PyC coatings First
the high concentration of interstitial defects could reduce the energy consumption by
the reversible slip of graphene planes (eg in Fig 77) and it corresponds to high the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
194
mean pressure in high density PyC coatings Second in-plane Youngrsquos modulus is
much higher than out-of plane Youngrsquos modulus in graphite so the bonding between
graphene planes becomes important when the orientation effect could be neglected in
high density PyC (Table 74) For example in sample C4 and C5 the high Youngrsquos
modulus was obtained in C5 which have high amount of covalent band (interstitial
defects sp2 and sp3 in Fig 71) in the direction perpendicular to graphene planes The
high concentration of interstitial defects in high density PyC could also reduce the
influences of orientation angle on the high Youngrsquos modulus This could explain the
similar Youngrsquos modulus in C1 and C5 which have different orientation angles
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
After thermal treatment at temperature range of 1300-1800 ordmC in C5 (about 200
gcm3) the effect of concentration of interstitial defects on mechanical properties was
again demonstrated as given in Table 75 The mechanical properties decrease
gradually with the increase of thermal treatment temperature until 1600 ordmC and then a
dramatic decrease at 1800 ordmC The decrease is related to the reduction of content of
interstitial defects (Table 75) Furthermore no other relationship between mechanical
properties and microstructural features such as FWHM of the D band intensity of D
band and G band in Raman spectroscopy is found in the current work Therefore the
concentration of interstitial defects is proposed to dominant mechanical properties of
high density PyC coatings This idea about effect of interstitial defects on mechanical
properties is similar as the cross-link theory [8] which suggested that the mechanical
properties is related to the length and number of links between domains Furthermore
Temperature (ordmC) IinterstialAll Pressure (GPa) Youngrsquos modulus (GPa)
0 013456plusmn 000561 456plusmn010 2610plusmn 036
1300 011882plusmn000906 430plusmn010 2519plusmn060
1400 011045plusmn000278 413plusmn010 2407plusmn070
1500 009598plusmn000034 406plusmn022 2439plusmn070
1600 009469plusmn000219 391plusmn016 2344plusmn036
1800 007756plusmn000199 132plusmn015 1177plusmn051
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
195
the significant decrease of the the mean pressure and Youngrsquos modulus after 1800 ordmC
could be due to the straightening of graphene layers and formation of voids (Fig
74(c)) respectively To conclude the mechanical properties in high density PyC
coatings before and after thermal treatment from 1300 to 1800 ordmC decrease with the
reduction of concentration of interstitial defects
74 Conclusions
Disorders in PyC coatings was characterised by Raman spectroscopy A
combination of high degree of in-plane (domain boundaries) and out-of plane
defects (interstitial defects) prevail in high density PyC while the 5-membered
rings are dominant defects in low density PyC coatings
In high density PyC coatings the significant increase of domain size Lc is
attributed to the coalescence of domainsgraphene layers through reorientation and
reduction of interstitial defects During this process the graphene planes were
straightened resulting in slightly increase of La
In low density PyC coatings the microstructure remained almost unchanged after
thermal treatment due to the presence of the 5-membered rings which need high
temperature to be reduced
The hysteresis deformation behaviour was found in all PyC coatings before and
after thermal treatment under nano-indentation The nature of hysteresis is
suggested to be Slip of graphene planes consumes energy (hysteresis loop) and
disorders (interstitial defects and highly curved 5-memebered rings in high density
and low density PyC coatings respectively) are responsible for the reversible
deformation (unloading curve back to origin)
The mean pressure and Youngrsquos modulus are functions of density in low density
PyC coatings and their changes after thermal treatment are insignificant which
are due to the almost unchanged microstructure
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
196
In high density PyC coatings the mean pressure and Youngrsquos modulus are
independent of density orientation angle and domain size but they are related to
the concentration of interstitial defects After thermal treatment the decrease of
mechanical properties is attributed to the reduction of interstitial defects leading
to the straightening of graphene planes and formation of voids
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
197
75 References
[1] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques thin solid films 469-70 (2004) 214-20
[2] D G Martin Considerations pertaining to the achievement of high burn-ups in
HTR fuel Nucl Eng Des 213 (2002) 241-58
[3] E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure and
mechanical properties of pyrolytic carbon produced by fluidized bed chemical
vapour deposition Nucl Eng Des 238 (2008) 3121-28
[4] G K Miller D A Petti A J Varacalle J T Maki Consideration of the effects
on fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[5] A C Kada R Gnallinger M J Driscoll S Yip D G Wilson H C No et al
Modular pebble bed reactor In Modular pebble bed reactor project University
research consortium annual report 2000
[6] G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
[7] J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[8] F G Emmerich C A Luengo Youngrsquos modulus of heat-treated carbons A
theory for nongraphitizing carbons Carbon 31 (1993) 333-39
[9] J S Field MVSwain The indentation characterisation of mechanical properties
of various carbon materials Glassy carbon coke and pyrolytic graphite Carbon
34 (1996) 1357-66
[10] N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[11] M V Swain J S Field Investigation of the mechanical properties of two glassy
carbon materials using pointed indetners Philos Mag A 74 (1996) 1085-96
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
198
[12] N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philos Mag A 82 (2002) 1873-81
[13] M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated carbons
J Am Ceram Soc 85 (2002) 1522-28
[14] A Richter R Ries R Smith MHenkel B Wolf Nanoindentation of diamond
graphite and fullerene films Diamond Relat Mater 9 (2000) 170-84
[15] MW Barsoum A Murugaiah S R Kalidindi T Zhen Y Gogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[16] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
treatment J Nucl Mater 374 (2008) 445-52
[17] F G Emmerich Evolution with heat treatment of crystallinity in carbons Carbon
33 (1995) 1709-15
[18] M A Pimenta G Dresselhaus M S Dresselhaus L G Cancado A Jorio R
Saito Studying disorder in graphite-based systems by Raman spectroscopy Phys
Chem Chem Phys 9 (2007) 1276-91
[19] I J Van Rooyen J H Neethling J Mahlangu Influence of Temperature on the
Micro-and Nanostructures of Experimental PBMR TRISO Coated Particles A
Comparative Study Proceedings of the 4th
international topical meeting on high
temperature reactor technology Washington DC USA HTR 2008-58189
[20] J C Bokros R J Price Deformation and fracture of pyrolytic carbons deposited
in a fluidized bed Carbon 3 (1966) 503-19
[21] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-I Effect of deposition conditions on microstructure
Carbon 47 (2009) 396-10
[22] P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
199
[23] S Bernard O Beyssac K Benzerara N Findling G Tzvetkov G E Brown Jr
XANES raman and XRD study of anthracene-based coke and saccharose-based
chars submitted to high-temperature pyrolysis Carbon 48 (2010) 2506-16
[24] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[25] J N Rouzaud A Oberlin C Beny-bassez Carbon films structure and
microstructure (optical and electron microscopy Raman spectroscopy) Thin solid
film 105 (1983) 75-96
[26] S Potgieter-Vermaak N Maledi N Wagner J H P Van Heerden R Van
Grieken J HPotgieter Raman spectroscopy for the analysis of coal a review J
Raman Spectrosc 42 (2011) 123-29
[27] A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-photon coupling doping and nonadiabatic effects Solid state commun
143 (2007) 47-57
[28] J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy electron
diffraction and few other techniques Carbon 44(2006) 1833-44
[29] G A Zickler B Smarsly NGierlinger H Peterlik O Paris A reconsideration
of the relationship between the crystallite size La of carbons determined by X-ray
diffraction and Raman spectroscopy Carbon 44 (2006) 3239-46
[30] A Cuesta P Dhamelincourt J Laureyns A Martinez-Alonso JMD Tascon
Raman microprobe studies on carbon materials Carbon 32 (1994) 1523-32
[31] A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
200
[32] S Yamauchi Y Kurimoto Raman spectroscopic study on pyrolyzed wood and
bark of Japanese cedar temperature dependence of Raman parameters J Wood
Sci 49 (2003) 235-40
[33] D B Williams C B Carter Transmission electron microscopy A textbook for
materials science Springer New York p 392-97
[34] M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[35] T Jawhari A Roid J Casado Raman spectroscopic characterization of some
commercially available carbon black materials Carbon 33 (1995) 1561-5
[36] G L Dong K J Huumlttinger Consideration of reaction mechanisms leading to
pyrolytic carbon of different textures Carbon 40 (2002) 2515-28
[37] A Jorio E H Martins Ferreira M V O Moutinho F Stavale C A Achete R
B Capaz Measuring disorder in graphene with the G and D bands Phys Status
Solidi B 247 (2010) 2980-82
[38] R Piat Y Lapusta T Boumlhlke M Guellali BReznik D Gerthsen TChen R
Oberacker M J Hoffmann Microstructure-induced thermal stresses in pyrolytic
carbon matrices at temperatures up to 2900 ordmC J Eur Ceram Soc 27 (2007)
4813-20
[39] J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[40] A H Cottrell Dislocations and plastic flow in crystals Clarendon Press Oxford
1972 p 162
[41] J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
CHAPTER 8 Conclusions and Future Works
201
CHAPTER 8 Conclusions and Future Works
This work provides both fundamental understanding and techniqual guidance on the
mechanical properties and their relationship with microstructures of SiC and PyC
coatings in TRISO fuel particles The measurement of hardness and Youngrsquos modulus
of SiC coatings could be used in the modelling work to study the peroperty of the
failure of the fuel particlues and these results have been published The measurement
of the fracture toughness of SiC in TRISO fuel particle has solved one of the
techniqual problems in field and the study contributes to the study of the fracture
behaviour of SiC coatings The fracture strength measurement has enriched the
strength data of SiC coatings before and after thermal treatment (related paper is
under revision) The characterisation of the interfacial roughness has provided a direct
method to correlate the relationship between fracture strength and interfacial
roughness The mechanical properties of PyC coatings provide foundamental
understanding about the deformation mechanism of the PyC coatings under
indentation The effect of thermal treatment on the mechanical properties has given a
preguidance about the behaviour of the PyC coatings at high temperature
81 Conclusions
(1) In SiC coatings deposited at 1300 ordmC by fluidised bed chemical vapour deposition
the Youngrsquos modulus was an exponential function of the porosity and the high
hardness was attributed to the high density of dislocations and their interactions
The initiation and propagation of micro cracks under the confined shear stress was
found to be responsible for the mechanism of plastic deformation Based on this
hardness-related plastic deformation mechanism the variation of hardness in the
three types of SiC coating was due to different grain morphologies
CHAPTER 8 Conclusions and Future Works
202
(2) The fracture beneath the Vickers indenter consists of Palmqvist cracks as
observed using SEM in above SiC coatings Based on this crack mode Vickers
indentation fracture toughness values of 351-493 MPa m12
were obtained It was
found that stress-induced micro-cracks seem to be a mechanism for the fracture
behaviour The presence of defects such as nano-pores and less constraint grain
boundaries could generate more micro cracks which dissipated energy from the
main cracks
(3) Fracture strength measured by modified crush test give less scattered values
within a given sample by distributing the load under a contact area It has been
found that Weibull modulus and fracture strength of the full shell were
significantly affected by the ratio of radius to thickness of the coating and both of
them decrease linearly with the increase of this ratio
(4) The numericalstatistical analysis was able to characterize the interfacial
roughness of different coatings and the roughness ratio representing the
irregularities was proposed to be a unique parameter for this description The
difference of the local (intrinsic) fracture strength was dominated by the
roughness ratio and it decrease linearly with the increase of the roughness ratio
The roughness ratio has the similar effect on the difference of fracture strength of
the full shell
(5) After heat treatment at 2000 degC the local fracture strength was reduced due to the
formation of pores in the coatings which could act as the enlarged critical flaw
size The Weibull modulus decreased when the pores in SiC coatings became
critical flaws while it increased once more uniformly distributed critical flaws
along the IPyCSiC interface were formed The formation of pores was mainly
related to the annihilation of stacking faults and diffusion of intrinsic defects such
as vacancies interstitials and antisites
CHAPTER 8 Conclusions and Future Works
203
(6) The hysteresis deformation mechanism was proposed to be due to the slip of
graphene planes which constraint by interstitial defects and highly curved
5-membered rings in high density and low density PyC coatings respectively
(7) The hardness and Youngrsquos modulus were related to the concentration of
interstitial defects and density in high density and low density PyC coatings
respectively Their changes in high density PyC is more significant than in low
density PyC coatings after heat treatment over 1800 ordmC due to the annihilation of
interstitial defects and reorientation of graphene layers
82 Suggestions for future work
(1) According to current study high amount of native defects were found in SiC
deposited at low temperature and it would be interesting to study their effects on
the thermal stability in a certain range of temperature such as from 1200-2000 ordmC
The study of the diffusion of native defects in SiC could also assist the study of
diffusion behaviour of fission products because these defects are more active and
they tend to reach the equilibrium during annealing process Due to different
deposition conditions the dominant species of native defects could be different in
different coatings therefore it is also important to study the deposition effect on
thermal stability of SiC coatings
(2) Itrsquos important to know how the microstructure change of SiC coatings deposited at
low temperature after irradiation because they showed robust mechanical
properties and high resistance to fission products It has been found they have high
amount of dislocations and stacking faults which accompanied by interstitials and
vacancies as reflected from the enlarged lattice constant According to this it is
supposed that after irradiation the volume change of SiC will be small because of
the pre-exist lattice defects Therefore study of the irradiation effect (at different
operational temperature) on SiC deposited at low temperature would be
promising
CHAPTER 8 Conclusions and Future Works
204
(3) Although current study has proposed to use self-affine theory to characterize the
interfacial roughness more work about their effects on fracture strength need to
be explored For example find out if the derived linear function between
roughness ratio and fracture strength in the current study could be used to explain
the differences of fracture strength in other tests To do further demonstration it is
necessary to reduce the geometrical influence and choose SiC coatings has
similar microstructure but different IPyCSiC interface These samples could be
prepared by just changing the deposition condition of IPyC while keep it same for
SiC coatings
List of Contents
3
2421 Youngrsquos modulus and hardness 65
2422 Deformation mechanism 67
2423 Effect of thermal treatment on properties of PyC 70
25 Summary 70
26 References 72
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Coatings Measured by
Indentation 83
31 Introduction 83
32 Experimental details 85
33 Results 88
331 Hardness and Youngrsquos modulus 88
332 Microstructure of low temperature FBCVD SiC 91
333 Deformation behaviour under the indentation 97
34 Discussion 100
341 Influence of porosity on Youngrsquos modulus 101
342 Mechanism for High hardness 102
343 Deformation mechanism under nano-indentation 104
35 Conclusions 105
36 References 107
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC Coatings 112
41 Introduction 112
42 Experimental details 113
43 Results and discussion 117
431 VIF fracture toughness study 117
432 Influence of non-stoichiometries on the VIF fracture toughness 121
433 Microstructural analysis of fracture behaviour under the indenter 122
44 Conclusions 126
45 References 127
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings 131
51 Introduction 131
52 Experimental details 132
List of Contents
4
521 Materials 132
522 Test method and analysis 133
523 Characterisation methods 135
53 Results and discussions 136
531 Fracture strength and dimensional effect 136
532 Observe and qualify the effect of interfacial roughness on fracture strength
140
533 Characterise and quantify the interfacial roughness 143
5331 Self-affine theory introduction and experimental setup 143
5332 Results of self-affine theory 144
534 Quantify the influence of interface roughness on fracture strength 146
54 Conclusions 149
55 References 150
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings 154
61 Introduction 154
62 Experimental details 155
63 Results 156
631 Fracture strength of SiC coatings 156
632 Change in morphologies 160
633 Evolution in microstructure 163
64 Discussion 167
641 Influence of interfacial roughness and pores on fracture strength 167
642 Mechanism of microstructural change 169
65 Conclusions 171
66 References 172
CHAPTER 7 Microstructure and Mechanical Properties of Pyrolytic Carbon
Coatings 175
71 Introduction 175
72 Experimental details 176
73 Results 178
731 Microstructure of PyC coatings 178
7311 Raman spectroscopy 178
7312 Domain sizes 181
List of Contents
5
7313 Evolution of crystallinity 182
732 Mechanical properties of PyC coatings 185
7321 Force-displacement curve 185
7322 Youngrsquos modulus and the mean pressure 187
74 Discussions 188
741 Disorders and their changes after thermal treatment 189
742 Hysteresis after indentation 191
743 Mechanical property of low density PyC coatings 192
744 Mechanical Property of high density PyC coatings 193
74 Conclusions 195
75 References 197
CHAPTER 8 Conclusions and Future Works 201
81 Conclusions 201
82 Suggestions for future work 203
Abstract
6
Abstract
Mechanical and Microstructural Study of Silicon carbide and Pyrolytic Carbon
Coatings in TRISO Fuel Particles
The University of Manchester
Huixing Zhang
Doctor of Philosophy in Materials Science
TRISO fuel particles have been developed as nuclear fuels used for a generation IV
nuclear reactor high temperature reactor Such particle consists of a fuel kernel
pyrolytic carbon (PyC) and silicon carbide (SiC) coatings This study has been carried
out to establish a relationship between mechanical properties and microstructures of
SiC coating and PyC coatings produced by fluidized bed chemical vapour deposition
Indentations were used to measure hardness Youngrsquos modulus and fracture behaviour
of SiC and PyC coatings Fracture strength of SiC coatings was measured by crush
test Microstructure of SiC and PyC was mainly characterised by transmission
scanning electron microscopy and Raman spectroscopy
For SiC coatings produced at 1300 ordmC Youngrsquos modulus is an exponential function of
relative density Hardness of SiC coatings is higher than the bulk SiC produced by
CVD and it is attributed to the high density of dislocations and their interactions The
deformation mechanism of SiC coatings under indentation is explained by presence of
defects such as grain boundaries and nano-pores The fracture of these coatings
beneath the Vickers indentation is the Palmqvist cracks and indentation fracture
toughness was in the range of 35-49 MPa m12
The stress-induced micro-cracks are
assumed to be the mechanism for the high indentation fracture toughness Different
hardness and fracture toughness in these SiC coatings are attributed to influences of
defects and grain morphology
Measurement of fracture strength was carried out on SiC coatings deposited at
1300-1500 ordmC Weibull modulus and fracture strength of the full shell are dominated
by the ratio of radius to thickness of coatings and decrease linearly with the increase
of this ratio The influence of SiCPyC interfacial roughness on fracture strength of
the SiC was quantified by self-affine theory The fracture strength decreases linearly
with the increase of the roughness ratio which is the long-wavelength roughness
characteristic After thermal treatment at 2000 ordmC fracture strength decreased in SiC
coatings due to the formation of pores which are results of diffusion of native defects
in as-deposited SiC coatings and the change of Weibull modulus is related to the size
and distribution of pores
For low density PyC coatings Youngrsquos modulus and the mean pressure increase with
the increase of the density however for high density PyC coatings they are
determined by interstitial defects The hysteresis deformation behaviour under
nano-indenation has been found be affected by density variation and thermal
treatment which is proposed to be due to the disorder structure in PyC coatings
Declaration
7
Declaration
No Portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Copyright Statment
8
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this thesis)
owns any copyright in it (the lsquolsquoCopyrightrsquorsquo) and she has given the University of
Manchester certain rights to use such Copyright including for administrative
purposes
ii Copies of this thesis either in full or in extracts and whether in hard or electronic
copy may be made only in accordance with the Copyright Desings and Patents Act
1988 (as amended) and regulations issued under it or where appropriate in
accordance with licensing agreements which the University has from time to time
This page must form part of any such copies made
iii The ownership of certain Copyright patens designs trade marks and other
intellectual property (the lsquolsquoIntellectual Property Rightsrsquorsquo) and any reproductions of
copyright works in the thesis for example graphs and tables (lsquolsquoReproductionsrsquorsquo)
which may be described in this thesis may not be owned by the author and may be
owned by third parties Such intellectual Properties Rights and Reproductions cannot
and must not be made available for use without the prior written permission of the
owner(s) of the relevant Intellectual Property Rights andor Reproductions
iv Further information on the conditions under which disclosure publication and
commercialization of this thesis the Copyright and any Intellectual Property andor
Reproductions described in it may take place is available in the University IP policy
(see httpwwwcampusmanchesteracukmedialibrarypoliciesintellectual-property
Pdf) in any relevant Thesis restriction declarations deposited in the University
Library The University Libraryrsquos regulations (see
httpwwwmanchesteracuklibraryaboutusregulations) and in the Universityrsquos
policy on presentation of Thesis
Acknowledgement
9
Acknowledgement
I will always be appreciative to Professor Ping Xiao for his support and guidance
during this project period and his enthusiasm for work and positive attitude towards
life inspired me I am thankful for what he shared about his own experience doing
research which impressed me and motivated me to make improvement
I would like to thank in particular Dr Eddie Loacutepez-Honorato for his patient guidance
on my experiments and valuable advices on my project His caution on preparing
delicate specimen infected me and helped me through my project He was always
there listening my ideas and discussing with me and he has set an example for being
a good researcher
I give my thanks to all the members in ceramic coating group old and new and I
treasure and appreciate this chance working with you
I would like to give my great gratitude to Dr Alan Harvey for his kind help on
transmission electron microscopy Mr Andrew Forest and Mr Kenneth Gyves on
nano- and micro-indentation Mr Andrew Zadoroshnyj on Raman spectroscopy Dr
Ali Gholinia and Dr Ferridon Azough on TEM sample preparation Dr Judith
Shackleton and Mr Gary Harrison on X-ray diffraction Mr Christopher Wilkins and
Mr Michael Faulkner on scanning electron microscopy and Mr Stuart Mouse on
tensile tests
I am grateful to my dear friends Yola David and Dean and you make my life more
colourful and interesting I would like to thank my beloved parents and brother for
your love care and support and you are great examples of hard work and kindness
My thanks also go to the ORS scheme the CSC grant and the F-BRIDGE for their
financial support during my PhD studies
List of Figures
10
List of Figures
CHAPTER 1 Introduction
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Fig 12 Behaviour of coated layers in fuel a particle [10]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
CHAPTER 2 Literature Review
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
List of Figures
11
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation[62]
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
List of Figures
12
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC coatings Measured by
Indentation
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
List of Figures
13
BF-TEM and (b) DF-TEM
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for extra-Si SiC coatings
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
Fig 45 Cross-sectional SEM image of stoichiometric SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
List of Figures
14
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a)
extra-C SiC (b) extra-Si SiC
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
Fig 58 Log-log representation of the height-height correlation function ∆h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
List of Figures
15
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC coatings
Fig 61 Weibull plots of local fracture strength (L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
Fig 62 Weibull modulus plots of fracture strength of the whole shell (F
f ) before
(black triangle) and after (red circle) thermal treatment
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after thermal treatment (c) and (d) SiC2
before and after thermal treatment (e) and (f) SiC3 before and after thermal treatment
(g) and (h) SiC4 before and after thermal treatment Dashed and solid arrows indicate
growth direction and pores respectively
Fig 64 The IPyCSiC interfacial morphology of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermal treated at 2000 degC (right in
each figure) The white arrow points towards to the interface irregularities (except for
thermal treated SiC4 coating (d)) black circle represents the pores in SiC coatings
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermal treated
at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and SiC2 inset
shows the peak shift of as-deposited (dash line) and after thermal treatment (solid
line) (b) is SiC4 and inset is the high angle diffraction peak after thermal treatment
showing splitting while it is a single peak in as-deposited coating
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
List of Figures
16
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
List of Tables
17
List of Tables
CHAPTER 2 Literature Review
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Table 23 Elastic tensors of 3C-SiC at room-temperature
Table 24 Vickers and nano-indentation hardness of polycrystalline CVD SiC
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Table 26 Summary of the hardness and Youngrsquos modulus for pyrolytic carbon
measured by different methods
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Measured by Indentation
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχv
along the radial and tangential directions
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Table 52 Summary of measured and calculated parameters for all the coatings
List of Tables
18
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Table 54 Results and variations influences on fracture strength for SiC coating
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings
Table 61 Deposition conditions of SiC coatings
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the whole shell before and after thermal
treatment
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
Table 71 PyC coatings deposition conditions and physical properties
Table 72 Domain size (XRD) of as-deposited and thermal treated PyC coatings
Table 73 Changes of mechanical properties after thermal treatment of PyC coatings
Table 74 The parameters used to explain different mechanical properties of high
density PyC
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
CHAPTER 1 Introduction
19
CHAPTER 1 Introduction
11 TRI-Isotropic (TRISO) fuel particles
A fission reaction is about that a large atomic nucleus (such as Uranium-235) is hit by
a neutron and absorbs the neutron forming a larger unstable nucleus The unstable
larger atomic nuclear breaks into two small nuclei and releases a high amount of
energy more neutrons beta and alpha particles and gamma The energy release is
much greater than for traditional fuels eg 1 g Uranium nuclear fuel releases the
same amount of energy as approximately 3 tonne of coal [1] The energy can be
transferred through the cooling system and used to boil the water to make steam to
drive a turbine and electrical generator in a nuclear power station
The high-temperature gas cooled reactor is one of the most promising candidates for
the production of nuclear energy according to its unique features For example it has
high coolant outlet temperature (850-1000 degC) which provides more efficient
electricity production due to the increased difference of the hot and cold coolant
temperatures [2] Furthermore it has the safety advantages due to the enclosure of the
fuel kernel (such as UO2 UC) within few layers of ceramic coatings Currently the
most common technique to fabricate fuels for operating the next generation
high-temperature gas cooled reactors is the TRISO fuel particles coating system [3]
The TRISO system was designed not only to retain all fission products during neutron
irradiation but also to withstand the thermo-mechanical stresses generated during
service [4]
CHAPTER 1 Introduction
20
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Figure 11 is the schematic of TRISO fuel particles embedded in a graphite matrix A
TRISO fuel particle consists of a fuel kernel and coating layers of porous pyrolytic
carbon (PyC) called buffer layer inner dense PyC (IPyC) silicon carbide (SiC) and an
outer dense PyC (OPyC) [5] and these layers were designed to have different
purposes The buffer layer absorbs metallic fission products recoils from kernel and
provides a space for fission product gases It also takes the volume change caused by
the kernel swelling without transmitting forces to outer layers The dense and
isotropic IPyC layer stops the chlorine from reacting with the kernel during deposition
of SiC and provides a firm substrate for the SiC layer Furthermore it protects the
SiC layer from most of the fission products and carbon monoxide during operation
The OPyC layer protects SiC layer during the remainder of the fabrication process
and provides structural stability to the particle during irradiation [3] The high
mechanical properties of SiC are needed to contain the high pressure generated in the
kernel and withstand the stress developed by the dimensional change of IPyC [3]
CHAPTER 1 Introduction
21
12 Failure mechanism
The radiation effects on the performance of the fuel particles such as fundamental
performance characteristics and fission product relsease mechanisms have been well
understood Different testing conditions (eg temperature up to 1300 degC and the does
of neutron) reflected the senariors encountered real applications [6-8]
During irradiation a number of potential failure mechanisms were revealed according
to several tests of coated fuel particles conducted in material test reactors and in
real-time operating HTR reactors [6-8] Chemically the corrosion of SiC by the
fission product palladium has been observed in almost all kinds of fuel compositions
and is considered as one of the key factors influencing the fuel performance However
this could be avoided by limiting the fuel temperature irradiation time or increase the
thickness of SiC layer [9] Mechanically the built up of the internal gas pressure (eg
CO) of irradiated particle and the neutron induced embrittlement of PyC coatings
could promote the failutre of the TRISO fuel particle The primary mechanisms which
may result in mechanical failure of TRISO fuel particles and lead ultimately to fission
product release depends significantly on the magnitude of the de-bonding strength
between IPyC and SiC layers [3 9]
121 Traditional pressure vessel failure mode
In this mode the failure was assumed to occur due to simple overload of the SiC layer
due to internal pressure build-up from fission gas [10] Both IPyC and OPyC layers
shrink during operation because of the irradiation exposure [11] This causes
compression stress in the SiC layer and tensile stress in the PyC layers Failure of the
SiC layer can only occur if the internal gas pressure is high enough to overcome the
compressive stress and critical stress of the SiC layer itself
CHAPTER 1 Introduction
22
Fig 12 Behaviour of coated layers in fuel a particle [10]
Figure 12 shows the basic behaviour modelled in a three layers standard model [10]
It shows that both IPyC and OPyC layers shrink and creep during irradiation but the
SiC layer exhibits only elastic deformation A portion of gas pressure is transmitted
through the IPyC layer to the SiC The pressure continually increases as irradiation of
the particle goes However if the PyC layer could remain in tension the failure by
fracture of SiC layer would be less likely to happen in this mode When the failure of
the PyC layer occurs a tensile hoop stress in the SiC layer is generated This leads to
the development of the stress concentration mode provided by the fracture of the inner
PyC layer
122 Stress concentration mode
In this mode it is been proposed that there is a point at which the fracture strength of
the IPyC would be exceeded during exposure When this occurs a radial crack will
form in the IPyC layer The crack could either penetrate through the SiC layer or
partially de-bonding the IPyCSiC interface This would lead to severe stress
concentration near the crack tip and it could reach the maximum of 440 MPa
according to previous simulation work [10] Once de-bonding goes through the whole
interface the source of stress in the SiC layer would be fission product gas build-up
CHAPTER 1 Introduction
23
and this case has similar failure mechanism of traditional pressure vessel failure mode
Although this process could decrease the probability of failure compared with the
stress concentration case the probability of failure may be higher than the traditional
failure mode Because the stress generated in the SiC layer after de-bonding would
increase [3]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
All these behaviours make it easier for the SiC layer to reach its fracture strength and
lead to the radial crack and failure of the SiC results in an instantaneous release of
elastic energy that should be sufficient to cause simultaneous failure of the
pyrocarbon layer Shown in Fig 13 is a photomicrograph illustrating the failure of a
TRISO coating According to the above discussion all the carbon layers are partially
designed to support or protect the SiC layer The SiC layer serves as the main
containment barrier for gas and metallic fission products [3] and high mechanical
properties of the SiC layer are needed However without appropriate microstructure
and mechanical properties of the PyC layer the stresses or structural changes
introduced in this layer during the irradiation process could result in the failure of the
whole particle [9 12] Furthermore mechanical properties such as the hardness (It is
CHAPTER 1 Introduction
24
the resistance to plasticpermanent deformation of materials under constant load from
a sharp object) Youngrsquos modulus (It reflects the resistance to reversible deformation
of a material) fracture toughness (It describes the ability of a material containing a
crack to resist fracture) and fracture strength (It is the maximum stress at which a
specimen fails via fracture) of SiC and PyC coatings are also important factors for the
safety design and evaluation of the TRISO coating system [10]
13 Goals of dissertation
Due to the importance of mechanical properties of SiC and PyC layers in keeping the
integrity of TRISO fuel particles and providing adequate information for modelling
the probability of failure of particles a good understanding of the elastic plastic and
fracture properties and their relation with microstructure is necessary Therefore all
the work carried out in this project is aimed at studying the relationship between
microstructure and mechanical properties of these two layers aiming to provide a
fundamental understanding about the deformation mechanism and solve the practical
issues
Due to small scale of SiC and PyC coatings two main techniques used to measure
mechanical properties are micronano-indenation and crush test Furthermore to study
the effect of microstructures on mechanical properties characterization techniques
such as transmissionscanning electron microscope and Raman spectroscopy are
widely used in the current work
In this thesis Chapter 2 reviews the recent progress in microstructural characterisation
and mechanical properties of SiC and PyC related materials which provides basic
information with regard to future study about hardness Youngrsquos modulus
deformation mechanism and fracture behaviour in these
Chapter 3 studies the influences of microstructure on hardness and Youngrsquos modulus
CHAPTER 1 Introduction
25
of SiC coatings and focuses on understanding the deformation mechanism of SiC
under nano-indentation The fracture toughness of these SiC coatings is measured by
Vickers-indentation and the importance of crack modes is discussed in Chapter 4
In Chapter 5 the fracture strength of SiC coatings in TRISO fuel particles is measured
and influence of the IPyCSiC interface on fracture strength is discussed Effect of
thermal treatment on fracture strength and microstructure of SiC coatings deposited at
different conditions are introduced in Chapter 6
Chapter 7 investigates the microstructure and mechanical properties of PyC coatings
with focus on deformation mechanism under indentation and the effect of density and
disorders on mechanical properties before and after thermal treatment
At last the main results and conclusions together with suggestions on future work are
given in Chapter 8
CHAPTER 1 Introduction
26
14 References
[1] httpnuclearinfonetNuclearpowerTheScienceOfNuclearPower
[2] J J Powers Fuel performance modelling of high burnup transuranic TRISO fuels
Disertation of Master University of California Berkeley 2009
[3] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[4] D L Hanson J J Saurwein D W McEachern A S Shoeny Development plan
for advanced high temperature coated-particle fuels Report Nopc000513
[5] httpwwwmpafrprocessphp
[6] W Burck H Nabielek A Christ H Ragos AW Mehner HTR coated particle
fuel irradiation behaviour and performance prediction Specialists meeting on
gas-cooled reactor fuel development and spent fuel treatment IWGGCR-8 1983
174-88
[7] H Nickel H Nabielek G Pott A W Mehner Long-time experience with the
development of HTR fuel elements in Germany Nucl Eng Des 217 (2002)
141-51
[8] H Nabielek W Kuhnlein W Schenk W Heit A Christ and H Ragoss
Development of advanced HTR fuel elements Nucl Eng Des 121 (1990)
199-210
[9] K G Miller D A Petti J Varacalle T Maki Consideration of the effects on
fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[10] A C Kadak R G Ballinger M JDriscoll et al Modular pebble bed reactor
project university research consortium Annual report INEELEXT-2000-01034
MIT-ANP-PR-075
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
CHAPTER 1 Introduction
27
treatment J Nucl Mater 374 (2008) 445-52
[12] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
CHAPTER 2 Literature Review
28
CHAPTER 2 Literature Review
21 Introduction
To model the probability of failure of fuel particles a number of key mechanical
properties of silicon carbide (SiC) are needed such as Youngrsquos modulus hardness
fracture toughness and fracture strength [1 2] These properties could be affected by
the microstructure of SiC coatings such as orientation porosities grain size and
defects [1-5] The small dimensions of the SiC coating limits the techniques available
to measure its mechanical properties However the development of the
nano-indentation has provided an important tool for probing the mechanical properties
of small volumes of material From the load ndash displacement data many mechanical
properties such as hardness Youngrsquos modulus and even fracture behaviour can be
determined [6] When an indentation system is used in conjunction with a focused ion
beam system and a transmission electron microscope images of deformation under
the nano-indentation can be obtained and the 3-D crack morphology can even be
reconstructed [7] Since there is a need to explain the high mechanical properties of
SiC deposited at temperature of 1300 ordmC by fluidized-bed chemical vapour deposition
[8] this combination of techniques could provide fundamental understanding of the
deformation mechanisms during indentation Another important parameter is fracture
strength and there have always been efforts to establish one method to characterise
fracture strength of SiC for example by brittle-ring test [9] whole particle crush test
[10] and modified crush test [5] Furthermore the high temperature application of SiC
and the compact of fuel pellet could affect the microstructure of SiC [2] which would
lead to the changes of mechanical properties
CHAPTER 2 Literature Review
29
The pyrolytic carbon (PyC) has been introduced by previous studies [11-14] and is
important in helping the SiC act as the main loading bearing layer The high
mechanical properties such as Youngrsquos modulus and anelasticity of PyC are necessary
to protect from damage caused by internal stresses and by external mechanical
interactions [12] However cracking and debonding between the SiC and inner PyC
layers could increase the probability of failure of TRISO fuel particles [13 14] It was
shown that without appropriate microstructure and mechanical properties of PyC the
structural or stress changes introduced in the coating during irradiation process could
result in total failure of the particle [11 13] The microstructure of PyC varied under
different deposition conditions [15] and it dominates the mechanical properties of
PyC coatings Therefore in this Chapter we review both the microstructure of SiC
and PyC including atomic structure morphology and defects and their mechanical
properties eg hardness Youngrsquos modulus deformation behaviour etc
22 Microstructure of silicon carbide
221 Atomic structure
The basic structural unit in SiC is a covalently bonded tetrahedron a carbon atom is at
the centre of four silicon atoms (C-Si4) and vice versa (Si-C4) The length of each
bond and the local atomic environment are nearly identical while the stacking
sequence of the tetrahedral bonded Si-C bilayers could be different The different
stacking sequences give SiC more than 250 polytypes [16] of which the 3C 4H 6H
and 15R are the most common The leading number of polytypes shows the repetition
of the SindashC pair and the letter C H and R represents the cubic hexagonal and
rhombohedral crystals respectively The 3C is the only cubic polytype in which the
stacking sequence of the planar unit of Si and C in tetrahedral coordination is depicted
as ABCABC in the lt111gt direction The cubic SiC crystal is called β-SiC and all
the other polytypes are α-SiC The crystal structures of 3C- 4H- 6H- and 15R-SiC
are schematically illustrated in Fig 21(a) [17] and corresponding XRD images were
CHAPTER 2 Literature Review
30
shown in Fig 21(b) [18]
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Although the transformation of SiC polytypes is primarily dependent on temperature
it could be affected by purity of the pre-existing phase pressure andor stacking faults
[19-22] The cubic form of SiC (β -SiC) is believed to be more stable than the
hexagonal structure (α-SiC eg 6H-SiC) below 2100 ordmC [19] However the polytype
of 2H-SiC which has the simplest stacking sequence is rarely observed at higher
temperature Krishna et al [20] reported that single crystals of 2H-SiC can be easily
transformed to 3C-SiC on annealing in argon at temperatures above 1400 ordmC It was
CHAPTER 2 Literature Review
31
found that the pre-existence of α-SiC (except 2H-SiC) could promote β-SiC
transformation to α-SiC while the transformation from α-SiC (6H-SiC) back to β-SiC
(3C-SiC) needs high temperature and pressure [21]
It has also been shown that the phase transformation could be closely related to
pre-existing defects such as stacking faults and their distribution [18] of which the
concentration is high even in single crystal SiC [22] Furthermore due to their low
formation energy the other intrinsic defects such as vacancies interstitials and
antisites were found to be common in SiC [23] These defects could affect mechanical
properties of SiC [8] so it is important to review their structure and properties
222 Defects in SiC
2221 Stacking faults and dislocations
A stacking fault is a disordered part of the ordered sequence in fcc crystal and the
most common stacking faults in cubic SiC are intrinsic and extrinsic stacking faults
(ISF and ESF) [24] For ISF the resulting stacking sequence is ABCACABC
if a double layer B is removed (condensation of vacancies) as for instance shown in
Fig 22[24] The ESF could be thought of as adding a double layer to the stacking
sequence (condensation of interstitials) resulting stacking sequence of
ABCACBCABChellip
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
CHAPTER 2 Literature Review
32
Another interpretation of the stacking faults is related to a twist of the three equivalent
bonds between two bilayers by 180deg [24] There may be an intrinsic shear stress
which could promote the glide of partial dislocations and thereby result in a faulted
crystal containing an error in stacking sequence so itrsquos reasonable to interpret
stacking faults in this way [25] Compared with dislocations and vacancies no bonds
are broken by stacking faults leading to a small energy difference between faulty and
perfect structures [26]
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
[27] [28] [24] [29] [30] [31] [32]
ESF (mJ m-1
) -15 -- -28 -6 -61 -154 -323
ISF (mJ m-1
) 12 34 -34 14 138 111 -71
Table 21 lists the formation energy of stacking faults in SiC and it shows that
extrinsic stacking faults have much lower formation energy than intrinsic stacking
faults in fact the values become negative The negative formation energy of stacking
faults in 3C-SiC means they can be formed very easily even more easily than perfect
3C-SiC As a result the stacking faults in 3C-SiC are spontaneously formed and most
likely in the form of extrinsic faults in the lt111gt direction Furthermore due to the
low energy of formation the length of a stacking fault can only be limited by the size
of the crystal or the presence of other defects that act as obstacles [33]
CHAPTER 2 Literature Review
33
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
The morphology of stacking faults in SiC observed by TEM is given in Fig 23 It
shows that the stacking faults could form a small domain (around 1 nm thick in Fig
23(a)) with different distances between small domains When a large concentration of
stacking faults exists in SiC it has been claimed that a conversion of cubic SiC to
hexagonal SiC on the nano-scale could happen by twinning [35] Furthermore the
stacking sequence of the faulted 3C-SiC was previously treated as random mixing of
α-type unit structures such as 6H and 4H in the 3C structure [36] Therefore it is
important to identify the properties and the microstructure of stacking faults of SiC
layers in TRISO fuel particles because the presence of α-SiC could result in reduction
of strength under irradiation which was due to enhanced possibility of anisotropic
swelling of α-SiC under irradiation compared to β-SiC [37]
(a) (b)
(c)
CHAPTER 2 Literature Review
34
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Figure 24 gives the XRD images of SiC in TRISO fuel particle deposited by fluidized
bed chemical vapour deposition showing the extra peak at 2θ~335ordm a high
background intensity at the peak at 2θ~353ordm and the broadening of the 3C peaks [8]
This is different from the perfect atomic structure of 3C-SiC as shown in Fig 21(b)
According to a previous simulation study [18] this kind of XRD diffraction pattern
could be caused by the existence of a high density of stacking faults and twins in the
regular cubic sequences It was demonstrated that it was unlikely to be due to the
presence of 2H-SiC or other polytypes [18] and two possible explanations were given
First two types of crystalline 3C-SiC with different populations of faults and twins
and second one type of crystal having clusters of faulted regions In SiC single
crystals although the concentration of stacking faults and twins is high the density of
dislocations is low (102-10
5cm
2) compared with metallic materials [22]
Figure 25 shows schematic images of the dislocations in face centred cubic (fcc)
crystals (β-SiC) The perfect dislocation is the (111) lt110gt system with burgers
vector of b=a2[110] (0308 nm) in SiC as shown in Fig 25(a) The perfect
dislocation could be easily dissociated into two partial dislocations of a6[121] and a6
CHAPTER 2 Literature Review
35
[21-1] as shown in Fig5 (a) and (b) because this reduces the total energy As a result
of this split a stacking fault must also be produced between the two partial
dislocations [38] Figure 25 (c) and (d) are lt110gt projections showing the Shockley
and Frank partial dislocations and their formation all related to the formation of
stacking faults
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
(a)
(b)
(c) (d)
CHAPTER 2 Literature Review
36
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
By comparing with previous studies [39-41] it is found that the relationship between
dislocation and stacking faults is complex The stacking faults have influences on the
mechanical properties for example enhancing the mobility of dislocations [39]
Different roles of stacking faults in II-VI heterostructures and devices have been
observed and results indicate that the stacking faults serve as the sources of misfit
dislocations [40] It is necessary to study the propagation of stacking faults or the
formation of stacking faults under stress and their influence on the properties of SiC
For example generation of stacking faults is shown to have occurred during the
fracture process together with the corresponding partial dislocation Furthermore
Agarwal et al [41] observed the growth of stacking faults from certain basal plane
dislocation within the base layer of the SiC
2222 Non-stoichiometric and point defects
Another common class of defects in SiC are non-stoichiometric (excess silicon or
carbon) and point defects [23 41 42] The purity of SiC may have effect on the
crystal structure strength corrosion resistance thermal conductivity diffusion
coefficient and other coating properties depending on its amount [43] The purity
could also affect defects in SiC eg if the stoichiometry deviates (even less than 1)
the concentrations of point defects in cubic SiC were found to be elevated [23]
Although the effect of point defects on general behaviour of nuclear fuel during
application process is not clear but their effect on microstructure evolution during
thermal treatment could be significant [44]
Silicon in SiC Stoichiometric 3C-SiC has generally been obtained at temperatures
between 1500 and 1600 [45] with carbon and silicon codeposited above and below
this temperature range By adding propylene as another carbon source the deposition
temperature of stoichiometric SiC could be reduced to about 1300 [8] The extra-Si
CHAPTER 2 Literature Review
37
SiC is less commonly investigated compared with the extra-C SiC because it has
been found that during the irradiation process the extra-Si plays a negative role in
material properties due to its low melting point [1] It has been found that the effect of
excess-Si on the Youngrsquos modulus and hardness it is more likely depending on its
amount and location [8 46]
Raman spectroscopy is an effective way to identify free Si both in amorphous and
crystalline phases eg it detected excess-Si when the XRD result showed the SiC was
stoichiometric [8] If the extra-Si is high (could be detected by XRD) TEM could be
used to detect its location and characterise the Si lattice contrast For example TEM
was carried out using both high resolution [35 47] and dark field imaging modes [48]
The HRTEM images in Fig 26 show the 3C-SiC crystallite with Si inclusions in
which nano-crystalline 3C-SiC and Si are separated by a weakly crystallized
interphase
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
(a)
(b) (c)
β-SiC
β-SiC
β-SiC
β-SiC
Si
Si
025 nm
025 nm
025 nm
0 312 nm
0312 nm
CHAPTER 2 Literature Review
38
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
Figure 27 shows bright-field and dark-field images of extra-Si SiC It shows the
crystalline Si as bright points in the dark background located at the grain boundaries
[48] The above observations were carried out in SiC with more than 1 at excess Si
(by comparing the intensity of Si Raman peak) as such observations are difficult
when the amount of excess Si is low Since the Youngrsquos modulus in SiC with low
amount of excess Si was comparable to that of stoichiometric SiC[8 46] it may have
unique properties that are worth further exploitation
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Carbon in SiC Excess C can also be identified by Raman spectroscopy but it is more
difficult to quantify its content and observe where this extra carbon exists due to its
small atomic number A comparative method was used to measure the content of
excess carbon by combining Raman spectroscopy auger electron spectroscopy
electron probe microanalysisand X-ray photoelectron spectroscopy [49] Once the
carbon concentration was measured (by above methods) the ratio of free excess to
SiC peak intensity (I796I1600) of Raman spectroscopy could be obtained as shown in
Fig 28 and the excess carbon concentration in the nearly stoichiometric SiC could
(a) (b)
CHAPTER 2 Literature Review
39
be estimated [49]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
There are few reports regarding the location of excess C in SiC The research carried
out by KKaneko et al [50] in carbon-doped hot pressed szlig-SiC showed that grain
boundaries were found to be free of any second phase by HRTEM although excess C
is found to form the second graphite phase Mykhaylyk and Gadzira revealed that
extra-C atoms are located as planar defects [51] The C atoms in the β-SiC structure
were supposed to arrange either as diamond-like carbon interlayers or as
non-correlated point defects after sintering of the as-synthesized powder at high
pressures and high temperature Since it showed that the presence of excess C atoms
in SiC crystal structure changes the local atomic environment [52] they may exist
within the SiC crystal and be correlated with other defects
The above discussion about the excess Si and C indicates that their influences on
properties of SiC depend on their content and that they could be discussed together
with the other point defects when their amount is low (less than 1 at ) [23]
Point defects in SiC SiC has eight kinds of point defects which keep the tetrahedral
symmetry of the perfect SiC crystal [23] They are carbon vacancies (Vc) silicon
vacancies (VSi ) carbon antisites (CSi) silicon antisite (Sic) a tetrahedral interstitial
silicon atom surrounded by four Si atoms (SiTSi) a tetrahedral interstitial silicon atom
CHAPTER 2 Literature Review
40
surrounded by four C atoms (SiTC) a tetrahedral interstitial carbon atom surrounded
by four Si atoms (CTSi) and a tetrahedral interstitial carbon atom surrounded by four
C atoms (CTC) [23] The formation energies for these defects are listed in Table 22
Due to their low formation energies the individual antisites and vacancies
particularly CSi were expected to appear even in as-deposited coatings [53 54]
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Vc VSi Sic CSi SiTSi SiTC CTSi CTC
Ef (eV) 59 68 73 11 150 147 86 110
The importance of point defects for different applications of SiC was studied and
these properties were studied in the relation to the properties of the point defects
including their formation annealing and interaction with each other [53] According
to Raulsrsquos study [54] the actual results of diffusion of CSi are more likely to be the
formation of CSi clusters which could be promoted by the diffusion of vacancies For
the coexistence of self-interstitials and vacancies (eg in irradiated material) it has
been found that the annealing temperature for VSi and Vc by recombination in β-SiC
were about 500 ordmC and 750 ordmC respectively [55] For as-deposited β-SiC without
interstitials the annealing process was only dominated by the out-diffusion of
vacancies the disappearances of VSi and Vc were found at temperature of 1400 ordmC and
1600 ordmC respectively [54] It is also been found that the migration of silicon vacancies
is easier than carbon vacancies due to its lower migration energy barrier Furthermore
in the case of excess carbon inside SiC the carbon clusters may form in SiC after
annealing and the size of the cluster depends on the content of interstitial carbon [56]
The general atomic-scale microstructure of SiC was reviewed above which showed
high degree of defects such as stacking faults dislocations vacancies and antisites
CHAPTER 2 Literature Review
41
The kind and concentration of these defects could affect the mechanical properties
such as hardness Youngrsquos modulus and fracture behaviour of SiC Since variation of
mechanical properties could also be due to other microstructural factors such as grain
size and density the relationship between microstructure and mechanical properties
are further reviewed in the following session
23 Properties of silicon carbide
231 Youngrsquos modulus
Youngrsquos modulus is physically related to the atomic spacing atomic bond strength
and bond density It is accepted that high-purity SiC material eg CVD SiC exhibits
the highest elastic modulus and that a porous microstructure with a high
concentration of impurities could decrease the elastic modulus [1 57] In contrast
neither grain size nor polytype was recognized as having a significant effect on the
elastic modulus of SiC in coated fuel [1 58]
Table 23 Elastic tensors of 3C-SiC at room-temperature
C11 (GPa) C12 (GPa) C44 (GPa) Z Ref
3C-SiC a 3523 1404 2329 18196 [59]
3C-SiC b 511 128 191 10026 [1]
3C-SiC c 390 142 256 -- [60]
3C-SiC a 420 126 287 19503 [61]
a Theoretical calculations
b Sonic resonance measurement
c Raman Spectroscopy
According to the definition of Youngrsquos modulus an important factor which could
affect its value for SiC material is the texture which is the degree of anisotropy (lack
of randomness with regard to the orientation) of SiC crystals The Youngrsquos modulus is
different by a combining of elastic tensors for deformation of the crystal in different
CHAPTER 2 Literature Review
42
orientation The elastic tensors or the stiffness tensors reflect the linear stress-strain
relation of a material There are 81 elastic tensors because the stresses and strains
have 9 components each However due to the symmetries of the SiC the tensors were
reduced to 3 unknown values They could be measured by sonic resonant method [1]
and Raman spectroscopy [60] based on vibrational theory of the crystal lattice They
are defined for SiC in Table 23 and will cause the variation of Youngrsquos modulus for
anisotropic materials The elastic tensors for 3C-SiC identified by previous theoretical
and experimental results [59-61] are substantially different from the current updates
of sonic resonance data The difference could be caused by the difference of the size
of SiC mateirals which could introduce the influences of defects such as grain
boundaries and stacking faults It was proposed to be more reasonable estimation for
SiC in TRISO fuel particle [1]
A measurement of the anisotropy in β-SiC (faced centre cubic crystals) is the ratio of
the two shear moduli [3] 100 shear modulus and 110 shear modulus μ0 and μ1
respectively which is
0 44
1 11 12
2CZ
C C
(1)
the parameter Z is known as the Zener ratio or elastic anisotropy factor (given for
different elastic tensor Table 23) When Zgt1 the Youngrsquos modulus is minimum
along lt100gt and a maximum along lt111gt and the representational surfaces for
Youngrsquos modulus in cubic crystals is shown in Fig 29 For the case when Z=1 the
cubic crystal would also be isotropic and the representation surface would be
spherical
CHAPTER 2 Literature Review
43
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
If the samples were random polycrystals which means samples are isotropic the
theoretical Youngrsquos modulus can be unambiguously given by [3]
3
[1 ( 3 )]E
B
(2)
While bulk modulus and shear modulus are
11 122
3
C CB
(3)
1
0 1
1 0
52( 6 )
(4)
where 0 44C 1 11 12( ) 2C C and
01
0 0
3( 2 )
5 (3 4 )
B
B
(5)
The theoretical value can be gained when the elastic constants are known Using the
Eqs (2-5) the theoretical Youngrsquos modulus E was calculated to be 496 GPa for
isotropic SiC materials when the elastic tensor obtained by Lambrecht et al was used
The calculated value is close to the Youngrsquos modulus measured by nano-indentation
(about 527 GPa) of isotropic bulk CVD SiC [62] But this value is higher than the
Youngrsquos modulus measured by nano-indentation of SiC in TRISO fuel particle which
is about 450 GPa [8 46]
By using the elastic tensors measured by sonic resonance in Snead et alrsquos study [1]
CHAPTER 2 Literature Review
44
the calculated Z (10026) is very close to 1 and it means the Youngrsquos modulus in
TRISO coated fuel particle may show no orientation effect According to Eqs (2-5)
the calculated Youngrsquos modulus is about 459 GPa under the elastic tensors given in
Ref [1] This value is close to the Youngrsquos modulus measured by nano-indentation in
TRISO fuel particle regardless of the orientation effect [1 8 46] Therefore for
TRISO fuel particle the recommended elastic tensors measured by sonic resonances
were supposed to be appreciable due to the scale and the microstructure similarities of
SiC materials [1]
Another significant factor which affects the Youngrsquos modulus is the density The
elastic modulus E at room temperature can be empirically expressed in an exponential
function of porosity pV as [63]
0 exp( )pE E CV (6)
where 0E is the elastic modulus and C is a constant of 357 for a pore-free bulk CVD
SiC pV is the ratio of the relative density difference to the theoretical density of SiC
(322 gcm3)
The relationship between density and Youngrsquos modulus of different kinds of SiC
materials measured by different methods were summarised in a previous study [1] as
shown in Fig 210 It has been found that the standard deviation of elastic modulus of
SiC is about plusmn 10 when the density is higher than 99 and increased to plusmn 15 for
porosity higher than 1
CHAPTER 2 Literature Review
45
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
232 Hardness
In a brittle material indentation hardness is defined as the mean pressure the material
will support under load and it is a complex property which could involve crack
initiation and propagation and the development of new surfaces during the
indentation process [1] Furthermore the value of hardness measured by indentation
also depends on external factors Due to the difference in dimensions of materials
such as the bulk small scale and thin film materials indentation on the nano- micro-
and even macro-scale have been used to measure the hardness [64] The hardness of
β-SiC related material has mainly been investigated by Vickers and nano-indentation
techniques (introduced in the later part of this session according to Ref [65]) as
summarized in Table 24 Reviews have found that the nano-hardness is generally
higher than Vickers hardness [1] which was attributed to the indentation size effect
Although few hardness values of β-SiC are available to be compared (given in Table
24) it shows the difference of hardness within a given sample Regardless of external
influences on the measurement of hardness generally it can be affected by grain size
or grain morphology [46] density composition and defects [1 8 66] To identify the
CHAPTER 2 Literature Review
46
controlling factor for hardness it is necessary to understand the deformation
mechanism of SiC under indentation
Table 24 Vickers and nano-indentation hardness of β-SiC related materials
Deformation mechanism Research into the deformation mechanism of SiC have
shown the availability of dislocation related plasticity [70] phase transformation
(cubic phase to amorphous) [71 72] fracture mechanisms [73] and also the
combination of any two or three [62 73]
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
First the dislocation related plastic deformation was found in single crystal 6H-SiC
[70] and the propagation morphology of dislocations was observed after indentation
as shown in Fig 211 This observation confirmes that the dislocation slip is a
Materials Vickers hardness (GPa) Nano-hardness (GPa) Ref
Single β-SiC (001) 28 -- [67]
CVD β-SiC 207-32 325-406 [466668]
FBCVD β-SiC -- 36-42 [8]
Sintered β-SiC 211-239 -- [69]
500 nm
CHAPTER 2 Literature Review
47
mechanism of plastic deformation from nucleation of a few dislocation loops (at or
near the theoretical strength) to extensive dislocation plasticity
Furthermore the dislocation related plastic deformation in polycrystalline CVD β-SiC
(with micro meters grain size) was first observed by Zhao et al [62] It was found that
the initiation of the plastic deformation was reflected by the burst (pop-in) of the
force-displacement curve which is similar as the initiation of plastic deformation in
metallic materials as shown in Fig 212(a)
According to the Hertzian contact theory [74] the burst was attributed to initiation of
the dislocation glide by comparing the shear stress generated under the indentation at
that load with the theoretical shear stress in β-SiC [62] During the whole indentation
process it was shown that shear slip is the predominant deformation mechanism and
that cracks were associated with the shear faults Figure 212(b) is one of the TEM
images showing the microstructure under indentation and it shows the dislocation
induced shear bands at one side of indent [62] which depend on the orientation of
grains
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation [62]
Second following the observations of phase transformation under indentation in
silicon [75] and the formation of SiC amorphous phase during high speed machining
(a) (b)
CHAPTER 2 Literature Review
48
process [71] the investigation of phase transformation under indentation was carried
out in SiC [7274] It has been demonstrated thermodynamically that the direct
amorphization is less likely to happen under nano-indentation [76] The
amorphization observed in single crystal SiC was attributed to the formation
propagation and accumulation of dislocations which formed the disordered phase at
the maximum stress region under a punch indentation [71] In SiC with nanometers
grain size the molecular dynamic study indicated thedominated deformation under
nano-indenation is a crossover of the indentation-induced crystallization to
disordering leading to amorphization [72] as shown in Fig 213
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Further studies demonstrated that the phase transformation from β-SiC to α-SiC is not
possible under nano-indentation because a pressure of nearly 100 GPa is needed [76]
even when assisted by high dislocation density shear stress and temperature This
simulation work concluded that the primary response of β-SiC to nano-indentation is
dislocation nucleation and propagation which has been confirmed by experimental
observations [62]
Third the plastic deformation of β-SiC under indentation was divided into two parts
CHAPTER 2 Literature Review
49
which are primary dislocation initiation and propagation and the formation of micro
cracks [73] The former contributes to 13 of plastic deformation under indentation
while the later provides 23 of total deformation The hardness related plastic
deformation could be explained well by this mechanism which included above two
process as discussed in previous studies [1 46 62] Moreover considering the effect
of micro cracks the deformation mechanism under indentation could be related to
other factors which could contribute to the formation of micro cracks such as
porosity grain boundaries and stacking faults in SiC [3]
Youngrsquos modulus and hardness of coatings in TRISO fuel particle can be measured by
nanoindentation due to the limitation of small dimension A typical
load-displacement curve and the deformation pattern under nanoindentation of an
elastic-plastic sample during and after indentation are shown in Fig 214 in which the
hc is contact indentation depth and hs is the displacement of the surface at the perimeter
of the contact [65] The peak load and displacement are Pmax and hmax respectively
and the diameter of the contact circle is 2a During unloading process the elastic
displacements are recovered and when the indenter is fully withdrawn the final depth
of the residual hardness impression is hf [65]
Nanoindentation hardness is the ratio of the load to the projected contact area of the
indentation The mean pressure that the material can support under indentation is
defined as the hardness From the loadndashdisplacement curve as in Fig 214(a) hardness
can be gain when the load is at the maximum value
A
PH max (7)
where A is the projected contact area
CHAPTER 2 Literature Review
50
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
The elastic modulus of the indented sample can be inferred from the initial unloading
contact stiffness S=dPdh ie the slope of the initial portion of the unloading curve A
geometry-independent relation involving contact stiffness contact area and elastic
modulus can be derived as follows
2A
S E
(8)
where szlig is a constant that depends on the geometry of the indenter (szlig=1034 for a
Berkovich indenter) [65] and Er is the reduced elastic modulus which accounts for the
fact that elastic deformation occurs in both the sample and the indenter Er is given by
CHAPTER 2 Literature Review
51
22 11 1 i
r i
vv
E E E
(9)
where E and υ are the elastic modulus and Poissonrsquos ratio for the sample respectively
and Ei and υi are the same quantities for the indenter For diamond Ei=1141 GPa and
υi=007[65]
For an indenter with a known geometry the projected contact area is a function of the
contact depth The area function for a perfect Berkovich indenter is given
by 2245 cA h Indenters used in practical nanoindentation testing are not ideally sharp
Therefore tip geometry calibration or area function calibration is needed A series of
indentations is made on fused quartz at depths of interest A plot of A versus hc can be
curve fit according to the following functional form
11 12 1 1282 4
1 2 3 8245 c c c c cA h C h C h C h C h (10)
where C1 through C8 are constants In some cases only the first three constants were
considered
The contact depth can be estimated from the load-displacement data using
maxmaxc
Ph h
S (11)
Where ε is a constant that depends on the indenter geometry (ε=075 for a Berkovich
indenter)
It is worth noting that high Youngrsquos modulus and hardness does not gurantee the
suitability of ceramic material to an engineering application because of the
importance of other mechanical properties such as fracture toughness and fracture
strength
CHAPTER 2 Literature Review
52
233 Fracture toughness
The definition of fracture toughness from Munz and Fett is [77] if a component or a
test specimen with a crack is loaded the stress intensity K1 increases with increasing
load until unstable crack propagation occurs at a critical value of K1 This critical
value is the fracture toughness (KIC) Therefore the measurement of fracture
toughness should be made on sample with a pre-crack however due to the small size
of SiC coating methods could be used are limited Although the most recently
developed micro-beam bending test could measure the fracture toughness of SiC in
TRISO fuel particles [78] this process is costly and time consuming because it
involves the preparation of micro-beams and notched cantilevers by focused ion beam
milling which limites the application of this technique
Indentation is now one of the most commonly used techniques to evaluate the fracture
toughness of ceramics and coating systems because it is easy to perform does not
need special samples and causes only negligible surface damage However some
researchers have declared that the indentation method is not suitable for the
measurement of fracture toughness [79 80] They concluded that the indentation
method does appear to represent some form of a complex crack arrest phenomenon
but that this occurrs in the presence of a multiple-crack path and a highly complex
residual stress field
Despite of these considerations the indentation method is an effective way to
compare the fracture behaviour of materials [80] particularly for small size specimens
and it provides information about the crack initiation and propagation Figure 215 is
the most typical characterization of the crack system generated by Vickers indentation
[81] This crack system is termed as median-radial cracking and consists of
approximately semi-circular cracks
CHAPTER 2 Literature Review
53
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
The mode of crack initiation and propagation under an indenter proposed by Chiang
et al explains many of the features observed in indentation crack patterns and is the
most recent advance [82] It was found that radial cracks are the first to initiate
trigged by a combination of the highly tensile surface stress field and the availability
of surface flaws [74 82] These cracks grow on unloading and can either propagate
into the plastic zone (half penny cracks) or terminate in the elastic zone (Palmqvist
cracks) [83] depending on the microstructure of the material
For different types of crack modes such as half-penny and Palmqvist cracks different
equations were developed based on theoretical analysis of stress field and empirically
calibrations to calculate the fracture toughness under indentation For example in the
half penny crack model the Vickers indentation fracture toughness was most
frequently determined using the relationship proposed by Anstis et al [84] This
equation was first inferred based on isotropic materials and it is suitable for general
application to well-developed cracks [84]
1 2
3 2( )IC
E PK
H c (12)
Where P is the indentation load c is the radial crack length from indentation centre to
crack tip E and H are the Youngrsquos Modulus and hardness of the materialand χ
denoted as the geometrical constant which is independent of the materials The Eq
CHAPTER 2 Literature Review
54
(12) was developed on the basis of half penny cracking in homogeneous brittle
materials under high load for example in glasses [84]
The above information shows that it is possible to compare fracture toughness under
indentation in SiC coatings with different microstructures The fracture toughness of
SiC could depend on a large number of factors such as grain size porosity micro
cracks and inclusions which could dissipate the fracture energy from the main crack
[3] According to a previous review [1] fracture toughness of SiC peaks at the grain
size range of 1-5 microm So fracture toughness of SiC in TRISO fuel particle is likely to
be influenced by the grain size due to the similar range of grain size Although micro
cracks and pores could improve fracture toughness they would decrease the strength
[3] which is detrimental for the safe design of fuel particles Over several decades
studies have worked to improve the fracture toughness by introducing a
heterogeneous microstructure such as weak grain boundary phases [85] In the
heterogeneous phase toughening mechanism the cracks could initiate in or be
reflected into weak defects and thereby dissipate the fracture energy for the main
crack propagation Furthermore the distribution of grain boundary character (the
crystallagraphic type and frequency of grain boundaries) and morphology could
influence the fracture toughness [85 86] Different grain boundary orientations and
their frequency were found to affect the fracture toughness by controlling the
intergranular fracture of materials [86] Different grain morphologies such as
elongated grains could increase the fracture toughness by crack bridging or by
generating micro cracks along grain boundaries or triple junctions [85] No
heterogeneous phase is supposed to exist in SiC in TRISO fuel particles so the
fracture toughness is most likely to be affected by grain morphologies or as-deposited
defects
According to the Griffth fracture theory once the size of the critical flaw is the same
the fracture toughness is propotional to the fracture strength which is another
CHAPTER 2 Literature Review
55
parameter used in modelling of the probability of the failure of fuel particle
234 Fracture strength
For brittle materials the fracture strength is best considered as a distribution rather
than a fixed value as the flaws (such as surface cracks pores and inclusions) from
which fracture initiates vary in size and type (result in different frature strength value)
between nominally identical samples [3] The Weibull approach is a commonly used
empirical method to characterise the strength of a brittle material It assumes a simple
power-law stress function (eg in Eqs (18-20)) for the survival of the elements
which is integrated over the body volumesurface area (as shown in Eqs (19) and
(21)) In many cases this function gives results in the form of Weibull modulus (m in
Eq (19)) and characterstic strength which describe the width and magnitude of the
strength distribution [3] The Weibull modulus is the slope of Log-Log distribution
function of the survival of elements and strength (Eq (19)) For engineering
application the high Weibull modulus represents the small variation of the fracture
strengthes for a given material
Higher Weibull modulus reflects lower variability of the strength and it is typically in
the range of 5-20 [3] The commonly used strength test methods for bulk ceramics are
uniaxial tension three- and four-point bending However the small dimensions of
TRISO fuel particles make it difficult to measure the strength by those conventional
methods As a consequence some specific methods were developed in the last few
decades such as O-ring test [87 88] C-ring test [88] hemisphere bending [10]
internal pressurization [89] and crush test [5 89 90] The schematic of easily
repetitive fracture strength test geometries are given in Fig 216 and the obtained
fracture strength by different methods was shown in Table 25
CHAPTER 2 Literature Review
56
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Methods L
f (MPa) Weibull Modulus F
f (MPa) Ref
O-ring compression 596-1412 41-66 -- 87
O-ring compression 1050-1890 48-94 -- 88
C-ring Compression 980-2200 40-90 -- 88
Semi-spherical bend 720-1350 70-80 340-620 10
Inner pressurization -- 43-62 222-448 89
Crush test -- 58-75 356-427 89
Crush test 770-1324 40-73 330-647 5
Crush test 1484-1721 135-183 1045-1091 90
L
f Local fracture strength F
f Fracture strength of the full particle
The local fracture strength is in the range of 596-2200 MPa and the fracture strength
of the whole particle varies from 222 MPa to 1091 MPa Such significant variation is
tought to be caused by the differences in specimen size and loading mode which were
related to the nature of the Weibull distribution [1 3] It has been demonstrated that
specimens with larger volumesurface area (under the same loading mode) have lower
strength because there is an increased probability that a larger flaw exists in a larger
body Similarly when there is no volume difference the loading mode which stresses
larger area has lower local fracture strength [3] These discussions show the
importance of regulating the fracture strength test method and producing specimens
with regular shape and size
CHAPTER 2 Literature Review
57
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
The modified crush test developed by Byun et al [5] is recommended for the fracture
strength measurement of SiC in TRISO fuel particles because it considered the effect
of contacting area between SiC shell and plunger which reduced the variation and
uncertainty of the stress distribution under tensile stress
Modified crush test When a partial spherical shell is diametrically loaded by an
external load F concentrated on a small circular contact area of radius 0 the
maximum membrane stress and bending stress are given by [91]
2
1 2
1membrane
FC
t
(13)
CHAPTER 2 Literature Review
58
2 2
1bending
FC
t
(14)
where ν is the Poisson ratio t is the thickness of shell and C1 and C2 were defined as
2
1 0115004022050 C (15)
)27031exp(204412 C (16)
2 2 2 1 4
0[12(1 ) ( )]r R t (17)
max membrane bending (18)
where max (L
f ) is the fracture strength for locally loaded specimens R is the outer
diameter of shell t is the thickness of the SiC shell The distribution of local fracture
strength is analysed by the Weibull distribution function which presents the
cumulative probability of failure P as [5]
mL
f
E
m
s
F
fSdAP
00
exp1exp1
(19)
where L
f m 0 and ES are the local fracture strength the Weibull modulus the
characteristic sterngth and the size effect factor respectively The size effect factor is
dAS
m
s L
f
F
f
E
Byun et al [5] used the probability estimator as follows
1
N
iPi (20)
where iP is the probability of failure for the i th-ranked strength and N is the
CHAPTER 2 Literature Review
59
sample size The increased probability that the full SiC shell has more critical flaws
compared with the stress-weighted surface is corrected by the size effect and the
fracture strength of the full shell (F
f ) is given
L
f
m
L
f
m
F
E
L
EF
ftR
r
S
S
1
2
2
0
1
)(4
(21)
After adjusting the size effect the fracture strength of the full particl of different SiC
coatings could be compared In a previou study [87] the difference of the fracture
strength was attributed to the microstructural variations which were determined by
deposition conditions [87] More detailed analysis [510] showed that the variation of
fracture strength was due to factors such as porosity roughness of the IPyCSiC
interface and grain size For example Evans et al [10] observed that the surface
roughness influenced the failure of the particle withstrength improved by reducing
the inner surface roughness According to above discussion the variation of Weibull
modulus could be attributed to the different test methods flaw distribution and sample
size [3 5]
Micostructure and mechanical properties of as-deposited SiC are reviewed above
which may change after high temperature treatment and the degree of evolution could
be different due to variational deposition conditions of SiC coatings As summarized
in a previous study [92] one of the critical properties for SiC layers in TRISO fuel
particle is that the microstructure remains unchanged after thermal treatment at 2000
ordmC for 1 hour in an inert atmosphere as determined by electron microscopy and X-ray
diffraction
235 Effect of thermal treatment on SiC
The SiC with perfect crystal structure tends to have good high temperature thermal
stability however due to the concentration and type of imperfections generated
CHAPTER 2 Literature Review
60
during deposoition process its thermal stability could be affected Defects such as
stacking faults vacancies and interstitials in as-deposited SiC coatings affect the
microstructural change after thermal treatment [93-96] For example the phase
transformation from β- to α-SiC generally happened at temperatures above 2100 ordmC
[19] but it could take place at lower temperature (gt 1700 ordmC) in special cases (eg
CVD β-SiC deposited on Si substrate with high amount of stacking faults) [93]
During high temperature thermal treatment (about 2000 ordmC) of CVD β-SiC one
significant microstructural change would be the annihilation of stacking faults [94
95] A thermodynamics study [94] has shown that the mechanism of reduction of the
stacking faults was due to the diffusion of Si or C atoms and it also demonstrated that
the migration energy of Si atoms was smaller than C atoms Considering the
abundance of intrinsic defects (section 222) there has been little investigation of
their effects on microstructure change of β-SiC after thermal treatment Furthermore
the effects of high temperature thermal treatment on mechanical properties such as
the hardness Youngrsquos modulus [97] and strength [98] have been carried out Their
results showed that mechanical properties showed little change when the treatment
temperature was lower than 2000 ordmC while there was decrease in the strength after
thermal treatment at 2100 ordmC
24 Microstructure and properties of pyrolytic carbon
In this part the microstructure of carbon related material is reviewed first which is
followed by the measurement of Youngrsquos modulus and hardness Furthermore to
know the controlling factor on mechanical properties of PyC coatings different
deformation mechanisms under indentation are introduced A brief review about effect
of thermal treatment on properties of PyC coatings is given
CHAPTER 2 Literature Review
61
241 Microstructure of pyrolytic carbon
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
The graphite structure consists of graphene sheets having localized in-plane σ (sp2)
hybrids bonds and delocalized out of plane π (pz) orbital bonds connecting graphene
sheets The out-of-plane bond is a van der Waals interaction which is much weaker
than sp2 and sp
3 hybrids Pyrolytic carbon is a material with some covalent bonding
between its graphene layers as a result of imperfections (defects) in its structure [99]
Figure 217 gives schematics and TEM images showing different microstructures of
PyC with different densities The growth features are polyhedral or conical shape in
high density pyrolytic carbon (Fig 217 (ab)) but are globular in low density
pyrolytic carbon (Fig 217(cd)) [15] It shows that the microstructure of pyrolytic
carbon consists of growth features between 200 nm- 1000 nm in size (Fig 217 (b)
and (d)) [15] Pores were formed at the boundaries or triple junctions between growth
(a) (b)
(c) (d)
CHAPTER 2 Literature Review
62
features
According to previous studies [15101] individual growth features contain crystallites
(domains) as shown schematically in Fig 218(a) They are composed of a series of
curved graphene layers randomly rotated with respect to each other along the c-axis
[101] The dimensions of the crystal were described by La (diameter of crystal along
the χ direction) and Lc (height of the crystal perpendicular to χy plane) as shown in
Fig 218(a) Regarding the definition of the PyC there are defects within the growth
features together with crystallites A local atomic structure of less ordered graphene
layers is shown in Fig 218(b) which could reflect the plane defects in graphene
layers [102]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
A high density of defects such as dislocation loops and kink bands were observed in
ball milled graphite by HRTEM as shown in Fig 219(a) The distorted
microstructure of graphite was also inferred from the striped diffraction points in
selected area electron diffraction image (Fig 219(b)) [103] since the diffraction
pattern gives information on orientation of crystal planes Compared with ball milled
graphite the HRTEM image of pyrolytic carbon has higher amount of defects as
shown in Fig 19(c) which is reflected from the highly distorted lattice planes and low
texture The selected area electron diffraction image of pyrolytic carbon (Fig 219(d)
with eperture diameter of 200 nm) showed arc shaped diffraction patterns [15 104]
The arc represents the overlap of diffraction patterns from different graphite domains
CHAPTER 2 Literature Review
63
with different orientations and this indicats that the microstructure is more distorted
eg smaller domain size and increased random orientation of domains In heavily
disordered PyC it is not possible to observe the individual dislocations or other
defects which is thought to be due to the numerous defects such as tilt boundaries
which obscure individual defects as described in Ref [105]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
Raman spectroscopy is one of the most effective techniques to characterise the defects
in carbon materials and has previously been used to characterise the microstructure of
PyC [15 106] These spectra can identify even quantify the microstructure such as
crystallite boundaries and size disorders (5-memebered rings) and chemical bonding
type Figure 220 shows the evolution of the Raman spectra with the change of the
CHAPTER 2 Literature Review
64
in-plane defect types The carbon spectra of Fig 220(a-c) showed increased and
broadened D signal and the main in-plane defects observed in these structures were
supposed to be domain boundaries [15] In Fig 220(d-e) the D signal became shaper
which was attributed to the formation of five-member rings [15]
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
The high density of disorders such as in-plane domain boundaries makes the Raman
bands become broder and overlapped with each other as shown in Fig 220(c) which
inferred the structure of turbostratic or high density PyC [10 15] According to
previous studies [106 107] the broadened Raman bonds could be deconvoluted into a
number of peaks which correspond to different types of disordered structure in
carbon materials Figure 221 is an example of a first order Raman spectra fitted with
Lorentzian and Gaussian functions and it includs I (~1170 cm-1
) D (~1330 cm-1
) Drdquo
(~1500 cm-1
) G (~1580 cm-1
) and Drsquo(~1618 cm-1
) bands [106] The Drdquo peak was
CHAPTER 2 Literature Review
65
attributed to amorphous carbon with a certain amount of sp3 carbon [106108] which
could reflect the interstitial defects coupling to the graphene layers or adjacent
domains [109]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
242 Mechanical properties of pyrolytic carbon
The different deformation mechanism of carbon materials compared to ceramic
materials results in distinct force-displacement curves which show the complete
recovery of the unloading curve [110 111] Therefore we describe the mechanical
properties of PyC coatings and deformation mechanism of carbon materials
2421 Youngrsquos modulus and hardness
Due to the importance of PyC in the nuclear industry mechanical properties were
measured by three-point bending [102 112] and nano-indentation [113-115] Table
26 gives the Youngrsquos modulus and hardness of PyC measured by different methods
In three-point bending tests the mechanical properties were functions of density
orientation angle and domain size No individual factor could clearly explain the
variation in Youngrsquos modulus strength or fracture toughness [112116] In previous
nano-indentation tests the low density PyC was found to have low hardness and
Youngrsquos modulus [114] whereas the influence on mechanical properties was
CHAPTER 2 Literature Review
66
uncertain which could be due to lack of investigation about the deformation
mechanisms
Table 26 Summary of the hardness and Youngrsquos modulus for PyC measured by
different methods
Methods Density range
(gcm3)
Youngrsquos modulus
(GPa)
Hardness
(GPa)
Ref
3-point-bending 150-212 310-427 -- 112
137-206 165-281 -- 116
Nano-indentation 185-190 255 + 2 -- 114
165-203 235-270 30-44 115
155-187 70-150 05-18 115
135-212 125-346 15-48 113
Youngrsquos modulus was changed from PSI to GPa
Figure 222 is a schematic of the typical force-displacement curve of different kinds
of materials under indentation [65110111] The curve of carbon materials shows a
completely recovery and no net displacement after unloading as shown in Fig
222(a) In carbon materials the force-displacement curve formed a closed loop and
this phenomenon was called anelastic deformation behaviour [14 117] This was
related to the internal friction of materials but there is controversy regarding the
sources of the internal friction [14105111] Since the force-displacement curve gives
information about the energy change during indentation the deformation behaviour of
carbon material can be analysed by the energy method
The energy distribution under indentation is shown in Fig 222 which includs the
hysteresis energy (Uh) and unloading energy (Uunloading) and the total energy (loading
energy Uloading) is the sum of the above two energies [110] As shown in Fig 222 the
ratio of the hysteresis energy to total loading energy could be different for different
microstructure of carbon materials [118] The ratio could be used to estimate the
CHAPTER 2 Literature Review
67
flexibility of elasticityductility [110119] For example a low ratio corresponds to
higher elasticity whist a high ratio meants higher ductility
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
The different force-displacement curve of carbon materials was compared with the
irreversible deformation behaviour of materials with linear elasticity such as SiC as
shown in Fig 214(a) [65] In linear elastic deformation the final displacement of hf
was left after complete unloading and the unloading curve nearly followed the linear
relationship Furthermore the area between the loading and unloading curves
represents the energy consumed by the plastic deformation which could be due to the
movement of dislocations and formation of micro cracks [1 62]
2422 Deformation mechanism
Reversible slip and sliding friction theory In this theory the complete recovery of
strain was due to the reversible slip of graphene planes and the energy loss was
attributed to the friction during the slip which was caused by a compressive stress on
the graphene layers [110111] The theory was obtained by considering an arbitrary
grain located at some position in a radially declining hydrostatic stress field below a
spherical indenter as shown in Fig 223 [110111] The force was resolved into
CHAPTER 2 Literature Review
68
compressive stress perpendicular to and shear stress parallel to the slip plane By
using the equation proposed by Kelly [120] the shear component (τ τ0 shear stress
with and without friction respectively) may be expressed as τ= τ0 +μσ where μ is a
friction coefficient and σ is normal stress component To initiate slip between
graphene layers the shear stress needs to exceed some critical value Therefore the
inter-layer slip with friction was supposed to be the mechanism of anelastic
deformation The authors [110111] also concluded that the hysteresis during
unloading appeared to be a natural result of friction between the graphene layers but
additional mechanisms were supposed to be operating in the different forms of
graphitic materials Furthermore the study did not give a clear explanation about how
the reversibility of the basal plane slip was realized
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Dislocation pileup theory This idea was derived from isotropic carbon after thermal
treatment at the temperature range of 880-2600 ordmC by using micro indentation [121]
The authors attributed the unique unloadingreloading behaviour of the
well-graphitized carbons to the slip of dislocation networks on graphitic basal planes
which is partially or fully reversible It is supposed that the dislocations could pile up
at grain boundaries as in metals The stress at grain boundaries due to dislocation pile
ups could reverse the dislocation movement during indentation unloading but it did
CHAPTER 2 Literature Review
69
not explain why deformation behaviour of PyC is unlike that of metals This is also
the reason that other researches [105] doubt this theory because it fails to explain the
nature of the reversible behaviour [121]
Kink band theory It was suggested that the origin of the loops obtained in single
polycrystalline and porous carbons is the formation of incipient kink band and kink
bands [105] The kink band model was proposed by Frank and Stroh [122] as
shown in Fig 224 which showed pairs of dislocations of opposite sign nucleate and
grow at the tip of a thin elliptical kink (not clear about the nature) The stability of
kink bands depended on a shear stress [122]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
In this theory since the dislocations were confined to the basal plane the hysteresis
process was attributed to the reversible movement of the dislocation along a long
distance The same mechanism was used to explain the deformation behaviour of the
bulk polycrystalline graphite The microstructural change under indentation should
first be related to the kink band initiation and then further microstructure change
could be reflected in the accumulation of other chemical bonds which could resist
dislocation glide
CHAPTER 2 Literature Review
70
2423 Effect of thermal treatment on properties of PyC
The effect of thermal treatment on the microstructure of carbon materials has been
widely studied [112 123 124] The change of the microstructure of carbon materials
during thermal treatment mainly involves the growth of the domain size (in-plane
crystal size along a axis) La and (along c axis crystal size) Lc with the increase of
temperature For different kinds of carbon materials these evolutions started at
different temperatures For example the crystal growth in-plane happened at 400-600
ordmC for graphitisable carbon and could continue up to high temperature the
coalescence of crystallites along the c-axis started above 1000-1200 ordmC the
coalescence of crystallites along ab direction occurred at temperature above 1400 ordmC
[124] For carbons with strong cross-linking (non-graphitisable) the coalescence of
domains usually happened at temperatures higher than 2400 ordmC [124] Although the
increase in anisotropy and density during processing of coated particle fuel was
reported by Hunn et al [11] no change in texture was identified on PyC due to the
post deposition of SiC shown in Lopeacutez-Honorato et alrsquos study [125] Furthermore no
significant change of mechanical properties was obtained after thermal treatment at
temperatures in the range 1000-1980 ordmC in PyC coatings with density of about 19
gcm3 [97] however a decrease of Youngrsquos modulus was observed in high density
(above 2 gcm3) PyC coatings [125] It was assumed that certain microstructures of
PyC would be less affected by thermal treatment
25 Summary
The microstructure and mechanical properties of SiC and PyC were reviewed in this
Chapter and the information obtained is summarized below
(1) It is common for SiC to have defects such as stacking fautls and dislocations
non-stoichiometry and point defects due to their low formation energy
particularly in SiC deposited by chemical vapour deposition
CHAPTER 2 Literature Review
71
(2) Defects interact with each other Stacking faults could be the result of gliding
of partial dislocations Vacancies promoted diffusion of antisites forming
antisite clusters
(3) The Youngrsquos modulus of SiC coatings in TRISO fuel particle is affected
mainly by texture and porosity
(4) Hardness related plastic deformation in single and polycrystalline (nano-meter
or micro-meter grain size) SiC is related to dislocation propagation fracture
of crystallites or phase transformation
(5) A combination of indentation together with electron microscopy is an
effective way to study the fracture behaviour of SiC coatings in TRISO fuel
particle
(6) Fracture strength of SiC coating in TRISO fuel particle varies significantly in
different measurements and the modified crush test is recommended The
interface roughness and porosity are found to be main factors controlling
fracture strength of SiC coatings
(7) The typical change of microstructure after thermal treatment in SiC is the
annihilation of stacking faults through the diffusion of vacancies
(8) The disorder in PyC coatings could be significant such as domain boundaries
and 5-membered rings Raman spectroscopy together with transmission
electron microscopy are important techniques to characterize these disorders
(9) Carbon related materials show hysteretic deformation behaviour under
indentation Different deformation mechanisms are proposed which all relate
to the slip of graphene layers
CHAPTER 2 Literature Review
72
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[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
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329-77
[2] DT Goodin Accident condition performance of fuels for high-temperature gas
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[3] D J Green An Introduction to the mechanical properties of ceramics 1st ed
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[4] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
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[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
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[6] X Li B Bhushan A review of nanoindentation continuous stiffness
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[7] A Grabulov U Ziese HW Zandbergen TEMSEM investigation of
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[8] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
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[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
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[10] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
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56 (1973) 36-41
CHAPTER 2 Literature Review
73
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
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[12] D G Martin Considerations pertaining to the achievement of high burn-ups in
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[13] G K Miller D A Petti D J Varacalle J T Maki Consideration of the effects
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[14] G K Miller D A Petti J T Maki Consideration of the effects of partial
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[15] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
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[16] R Cheung Silicon carbide microelectromechnical systems for harsh
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[17] M Iwami Silicon carbide fundamentals Nuclear instruments and methods in
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[18] V V Pujar J D Cawley Effect of stacking faults on the X-ray diffraction
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[20] P Krishna RC Marshall CE Ryan The discovery of a 2H-3C solid state
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[22] R Stevens Defects in silicon carbide J Mater Sci 7 (1972) 517-21
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74
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[25] U Lindefelt H Iwata S Oumlberg P R Briddon Stacking faults in 3C- 4H and
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[26] P T B Shaffer A review of the structure of silicon carbide Acta Crystal Sec B
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[27] P J H Denteneer W v Haeringen Stacking-fault energies in semiconductors
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[28] X G Ning H Q Ye Experimental determination of the intrinsic stackingfault
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[29] P J H Denteneer W v Haeringen Ground-state properties of wurtzite silicon
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[30] P J H Denteneer Stacking-fault energies in silicon diamond and silicon
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[31] K Karch G Wellenhofer P Pavone U Roumlssler D Strauch Proceedings of the
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[32] C Cheng V Heine and R J Needs Atomic relaxation in silicon carbide
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[33] M Marinova A Mantzari E K Polychroniadis Some recent results on the
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[34] VV Pujar JD Cawley Computer simulations of diffraction effects due to
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[35] B Reznik DGerthsen W Zhang K J Huumlttinger Microstructure of SiC
deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499ndash508
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[36] T Mitani S Nakashima H Okumura et al Raman Scattering Analyses of
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[37] G Newsome LL Snead T Hinoki et al Evaluation of neutron irradiated
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[38] httpwwwtfuni-kieldematwisamatdef_enkap_5backboner5_4_2html
[39] P Pirouz J W Yang Polytypic transformations in SiC the role of TEM
Ultramicroscopy 51 (1993)189-214
[40] S Guha J M DePuydt J Qiu Role of stacking faults as misfit dislocation
sources and nonradioactive recombination centres in II-VI heterostructures and
devices Appl Phys Lett 63 (1993) 3023-25
[41] AK Agarwal SKrishnaswami JRichmond et al Influence of basal plane
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Forum 527-29 (2006) 1409-12
[42] N W Mueggenburg H M Jaeger S R Nagel Stress transmission through
three-dimensional ordered granular arrays Phys Rev E 66 (2002) 031304
[43] S Somiya Y Inomata Silicon carbide ceramics-2 ceramic research and
development in Japan p1-18
[44] A Gali N T Son E Janzeacuten Electrical characterization of metastable carbon
clusters in SiC A theoretical study Phys Rev B 73 (2006) 033204-08
[45] C Chu Y Luand M Hon Growth characteristics of β-SiC by chemical vapour
deposition J Mater Sci 27 (1992) 3883-88
[46] J Tan Mechanical properties of SiC in TRISO fuel particle PhD Thesis
University of Manchester 2010
[47] Z R Huang B Liang DL Jiang S H Tan Preparation of nanocrystal SiC
powder by chemical vapour deposition J Mater Sci 31 (1996) 4327-32
[48] R A Shatwell K L Dyos C P Rentice Y Ward R J Young
Microstructural analysis of silicon carbide monofilaments J Microscopy 201
(2001) 179-88
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[49] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[50] K Kaneko M Kawasaki T Nagano et al Determination of the chemical width
of grain boundaries of boron- and carbon-doped hot-pressed β-SiC by HAADF
imaging and ELNES line-profile Acta Materialia 48 (2000) 903-10
[51] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[52] O O Mykhaylyk YZ Khimyak JP Attfield Phase Segregation in Silicon
Carbide-Carbon Solid Solutions from XRD and NMR Studies Chem Mater 14
(2002) 1348-35
[53] E Janzeacuten N T Son N Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[54] E Rauls Th Frauenheim A Gali PDeaacutek Theoretical study of vacancy
diffusion and vacancy-assisted clustering of antisites in SiC Phys Rev B 68
(2003) 155208-09
[55] N T Son P N Hai E Janzeacuten Carbon vacancy-related defect in 4H and 6H SiC
Phys Rev B 63 (2001) 201201-04
[56] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-10
[57] J M Grow R A Levy Micromechanical characterization of chemically vapor
deposited ceramic films J Mater Res 9 (1994) 2072-78
[58] T D Guldn H Nickel Coated particle fuels Nucl Technol 35 (1977) 206-35
[59] KB Tolpygo Optical elastic and piezoelectric properties of ionic and valence
crystals with ZnS type lattice Sov Phys Solid State 2 (1961) 2367
[60] D W Feldman J H Parker Jr J W Choyke L Patrick Phonon dispersion
curves by Raman scattering in SiC polytypes 3C 4H 6H 15R and 21R Phys
Rev 173 (1968) 787-93
CHAPTER 2 Literature Review
77
[61] W R L Lambrecht B Segall M Methfessel M van Schilfgaarde Calculated
elastic constants and deformation potentials of cubic SiC Phys Rev B 44
(1991) 3685-94
[62] X Zhao R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of silicon carbide under contact load at room temperature J
Am Ceram Soc 94 (2011) 3509-14
[63] R W Rice Mechanical properties of ceramics and composites 1st ed New
York Marcel Dekker 2000 p 457-534
[64] O Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
mechanism of plastic deformation in macro-micro- and nanoindentation
processes J PhyD Appl Phys 41 (2008) 074016-24
[65]W C Oliver GMPharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7(1992)1564-83
[66] MC Osborne JC Hay LL Snead Mechanical- and physical-property changes
of neutron-irradiated chemical-vapour-deposited silicon carbide J Am Ceram
Soc 82 (1999) 2490-96
[67] D M Teter Computational alchemy the search for new superhard materials
MRS Bull 23 (1995) 22-27
[68] S Nagappa M Zupan CA Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
Materialia 59 (2008) 995 -98
[69] M J Slavin G D Quinn Mechanical property evaluation at elevated
temperature of sintered β-silicon carbide Inter J High Tech Ceram 2 (1986)
47-63
[70] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
related isostructural materials to nanoindentation Slip vs densification Mater
Res Soc Symp P 522 (1998) 113-18
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[71] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[72] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[73] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
materials with a density functional theory J Appl Phys 104 (2008) 053508-16
[74] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000
[75] I Zarudi J Zou L C Zhang Microstructures of phases in indented silicon A
high resolution characterization Appl Phys Lett 82 (2003) 874
[76] M Mishra I Szlufarska Possibility of high-pressure transformation during
nanoindentation of SiC Acta Mater 57 (2009) 6256-6165
[77] D Munz T Fett Ceramics Mechcanical properties failure properties failure
behavior and materials selection Springer Verlag NewYork 1999 p 20
[78] X Zhao RM Langford J Tan P Xiao Mechanical properties of SiC coatings
on spherical particles measured using the micro-beam method Scripta Mater 59
(2008) 39ndash42
[79] G D Quinn RC Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[80] R Morrell Fracture toughness testing for advanced technical ceramics
internationally agreed good practice Adv Appl Ceram 105 (2006)1-11
[81] R E Cook G M Pharr Direct observation and analysis of indentation cracking
in glasses and ceramics J Am Ceram Soc 73 (1990) 787 - 817
[82] S S Chiang D B Marshall AG Evans The response of solids to elasticplastic
indentation I stresses and residual stresses J Appl Phys 53 (1982) 298-311
[83] M T Laugier Palmqvist toughness in Wc-Co composites viewed as a ductile
brittle transition J Mater Sci Lett 6 (1987) 768-70
CHAPTER 2 Literature Review
79
[84] G R Anstis P Chantikul B R Lawn D B Marshall A critical-evaluation of
indentation techniques for measuring fracture-toughness 1 Direct Crack
Measurements J Am CeramSoc 64 (1981) 533-38
[85] X F Zhang Q Yang L C D Jonghe Microstructure development in
hot-pressed silicon carbide effects of aluminium boron and carbon additives
Acta Mater 51 (2003) 3849-60
[86] T Watanabe The impact of grain boundary character distribution on fracture in
polycrystals Mater Sci Eng A 176 (1994) 39-49
[87] S J Xu J G Zhou B Yang B Z Zhang Effect of deposition temperature on
the properties of pyrolytic SiC 224 (1995) 12-16
[88] K Bongartz E Gyarmati H Schuster K Tauber Brittle ring test ndash method for
measuring strength and Youngs modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[89] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the Tri-Isotropic-Coated fuel particle
J Am Ceram Soc 90 (2007) 184-91
[90] J W Kim TSByun YKatoh Optimization of fracture strength tests for the SiC
layer of coated fuel particles by finite element analysis
[91] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[92] SDKurbakov TAMireev Deposition of high-density silicon carbide coatings
by fluidized-bed pyrolysis of chlorinated silane derivatives Solid Fuel Chem 43
(2009) 113-23
[93] M Hundhausen R Puumlsche J Roumlhrl L Ley Characterization of defects in
silicon carbide by Raman spectroscopy Phys Stat Sol 245 (2008) 1356-68
[94] N Shirahata K Kijima A Nakahira and K Tanaka Thermal stability of
stacking faults in beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
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80
[95] W S Seo C H Pai K Koumoto H Yanagida Microstructure development and
stacking fault annihilation in β-SiC powder compact Ceram Soc Jap 99 (1991)
443-47
[96] Z G Cambaz G N Yushin Y Gogotsi K L Vyshnyakova L N
Pereselentseva Formation of carbide-derived carbon on beta-silicon carbide
whiskers J Am Ceram Soc 89 (2006) 509-14
[97] I J V Rooyen J H Neethling J Mahlangu Influence of temperature on the
micro-and nanostructures of experimental PBMR TRISO coated particles A
comparative study Proceedings of the 4th international topical meeting on high
temperature reactor technology HTR 2008 September 28-October 1 2008
Washington DC USA HTR 2008-58189
[98] I J v Rooyen J H Neethling P M v Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[99] httpenwikipediaorgwikiPyrolytic_carbon
[100]J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
[101]Z Q Li C J Lu Z P Xia Y Zhou Z Luo X-ray diffraction patterns of
graphite and turbostratic carbon Carbon 45 (2007) 1686-95
[102]W P Hoffman W C Hurley P M Liu T W Owens The surface topography
of non-shear treated pitch and PAN carbon fibers as viewed by the STM J
Mater Res 6 (1991) 1685-94
[103]J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[104]P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
CHAPTER 2 Literature Review
81
[105]M W Barsoum A Murugaiah S R Kalidindi T Zhen YGogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[106]J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy
electron diffraction and few other techniques Carbon 44 (2006) 1833-44
[107]A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
[108]A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-phonon coupling doping and nonadiabatic defects Solid State
Communic 143 (2007) 47-57
[109]J N Rouzaud A Oberlin Carbon films Structure and microtexture (optical and
electron microscopy Raman spectroscopy) Thin Solid Films 105 (1983) 75-96
[110]N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[111]N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philosophical Magazine A 82 (2002) 1873-81
[112]J C Bokros R J Price Deformation and fracture of pyrolytic carbons
deposited in a fluidized bed Carbon 3 (1966) 503-19
[113]E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure
and mechanical properties of pyrolytic carbon produced by fluidized bed
chemical vapour deposition Nucl Eng Des 238 (2008) 3121-28
[114]C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by
different techniques Thin solid films 469-70 (2004) 214-20
[115]G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
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[116]J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[117]L M Brown In H Libelt R Talreja Fatigue and creep of composites
materials Riskilde Denmark Riso National Laboratory 1982 p 1-18
[118]M Skai The Meyer hardness A measure for plasticity J Mater Res 14 (1999)
3630-39
[119]M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics ndash adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[120]B T Kelly The physics of graphite Applied Science Publications London
1981
[121]M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated
carbons J Am Ceram Soc 85 (2002) 1522-28
[122]F C Frank A N Stroh On the theory of kinking Proc Phys Soc 65 (1952)
811-21
[123]R F Franklin Royal Society London A London 1951 209 196
[124]F G Emmerich Evolution with heat treatment of crystallinity in carbons
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[125]E Loacutepez-Honorato P J Meadows R A Shatwell P Xiao Characterization
of the anisotropy of pyrolytic carbon by Raman spectroscopy Carbon 48 (2010)
881-90
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
83
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC
Coatings Measured by Indentation
31 Introduction
The silicon carbide (SiC) coating is the most important component for structural
integrity of Tri-isotropic (TRISO) fuel particles as it sustains most of the internal
pressure produced by the fission gases produced in the kernel [1-3] Youngrsquos modulus
and hardness are mechanical properties used in modeling to estimate the failure
probability of TRISO fuel particles [4] The values at room temperature are used due
to the fact that the Youngrsquos modulus slightly decreased at elevated temperature in SiC
material and the higher value could be kept until the temperature reached 2000 degC [1]
It was also found that SiC material with higher hardness at room temperature
maintains higher hardness values at temperatures up to 1600 degC [1] To achieve a
reliable fuel design a better understanding of the mechanical properties of the SiC
layer at room temperature needs to be established
It is difficult to use traditional methods to measure hardness and Youngrsquos modulus
due to the small dimension of the TRISO fuel particles (~1 mm) Nano-indentation
has made it possible to measure the hardness and Youngrsquos modulus accurately [5 6]
for a coating of such a small dimension Furthermore this method also offers the
ability to study the deformation behaviour under the indentation [7-12] as the
indentation stress field is of a localized character
Loacutepez-Honorato et alrsquos [5] study of SiC deposited at 1300 degC by fluidized bed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
84
chemical vapour deposition (FBCVD) showed that the SiC coatings produced under
those conditions had high hardness (gt 42 GPa) and Youngrsquos modulus (~455 GPa)
They found that even samples with the composition of SiC+C or SiC+Si showed high
mechanical properties It was shown that the coatings had sub-micrometer (lt1 μm
diameter) grain size but due to the complex microstructure the mechanism controlling
the hardness and Youngrsquos modulus was unknown Researchers [10 11 13-16] have
made efforts to study the deformation mechanism under indentation in SiC single
crystals and polycrystals (with a grain size lt 100 nm or grain size gt 1μm) Szlufarska
et al [15] suggested a crossover mechanism from indentation-induced crystallization
to deformation-dominated amorphization in nano-crystalline SiC
From the work reported [11 16 17] it is clear that dislocation initiation and
propagation is the primary response for the plastic deformation under an indentation
in single crystal and polycrystalline (gt 1μm) SiC Further it has also been found
while studying the microstructure [11 16 17] that defects such as stacking faults and
dislocations were present in these polycrystalline (gt 1 μm) SiC materials
(nano-indentation hardness less than 36 GPa) However the amount of defects were
lower compared to the low temperature (ie 1300 o
C vs 1500 o
C) FBCVD SiC [5]
The discrepancies in the microstructure and mechanical properties still demand
further explanation on the deformation mechanism of low temperature FBCVD SiC
This chapter focus on the fundamental study on the mechanical properties of SiC we
have investigated the Youngrsquos modulus and hardness of three sub-micrometer FBCVD
SiC coatings using the indentation method The microstructure and mechanical
properties are explained on the basis of defects observed with a transmission electron
microscope (TEM) The deformation behaviour underneath a nano-indentation is
discussed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
85
32 Experimental details
Silicon carbide (SiC) coatings were produced on top of highly-dense pyrolytic carbon
coatings using fluidized-bed chemical vapour deposition (FBCVD) method The SiC
coatings with varied stoichiometry and deposited at low temperature of 1300 oC by
Loacutepez-Honorato et alrsquos [5] were chosen and studied in this Chapter Table 1 gives the
deposition conditions of these coatings which were found and demonstrated to give
superberb mechanical properties in prevous studies [5] Figure 31(a) and (b) show the
polished cross-section (x-y plane) and (b) polished external surface section (x-z plane)
of TRISO fuel particles (defining the directions used in the later part of this Chapter)
Densities were measured by the Archimedes method in ethanol (density is the mean
value of three tests the weight of SiC shells is 01-03 g) Composition was measured
by Raman spectroscopy (Renishaw 1000 Raman system with a 514 nm argon laser
source) with a single spot measurements of around 1 microm diameter through an times50
objective lens as shown in Fig 31 (c) Two peaks at around 794 and 970 cm-1
are for
SiC and the asymmetric peaks around 200-500 cm-1
and 1500 cm-1
are acoustic SiC
and second order SiC respectively (S1 coating) [5] Carbon peaks are around 1360
and 1600 cm-1
(S2 coating) and the peak at 520 cm-1
represents silicon (S3 coating)
[5] It was estimated that the excess C amount is less than 1 at in S2 by measuring
the intensity ratios of I1600I794 and compared to previous study [18] where Raman
spectroscopy and elemental analysis (EPMA AES and XPS) were used
The phase and composition were also analysed using X-ray diffraction (XRD PW
1830 Philips Eindhoven The Netherlands) with Cu Kα1 radiation Figure 31(d)
shows the XRD spectra of the three types of SiC coatings All three coatings exhibit
the β-SiC phase A very small shoulder peak around 2θ=345deg was also obtained from
the coatings which indicated the presence of stacking faults No evidence of a Si or C
peak was found in the XRD result This was probably due to the fact that the
additional levels of Si and C were very small (le 1at ) and it would be difficult to
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
86
identify these traces using XRD [5 19]
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
Codes H2MTCS (volvol) Additives Temperature Density (gcm3)
S1 (SiC) 10 01vol Propylene 1300 o
C 3173 + 0029
S2 (SiC+C) 10 10 vol Propylene 1300 o
C 3135 + 0034
S3 (SiC+Si) 10 -- 1300 o
C 3188 + 0002
SiC+C or SiC+Si means that nearly stoichiometric SiC with low excess C or Si less than 1 at
Productions of samples are contributed by Dr Eddie Loacutepez-Honorato
SiC coated fuel particles were hot mounted in copper-loaded conductive resin To
reduce the influence of the surface roughness the FBCVD SiC coatings were first
ground down to obtain a flat surface where the nano-indentation could be carried out
The flat surface was further polished using increasingly finer diamond suspensions
until frac14 μm and finally polished using a 003 μm colloidal silica suspension The
thickness of the coating after final polishing was estimated to be around 60 μm A
final surface roughness of lt 5 nm was detected by atomic force microscopy (AFM)
Youngrsquos modulus and hardness were measured using a nano-indenterTM
XP (MTS
System Corp USA) and a micro-indenter (CSM Instruments Switzerland)
Nano-indentation was made using a Berkovich indenter calibrated with a standard
silica specimen Before the measurement the initial contact of the indenter with the
specimen surface was checked and the compliance of the loading column was
corrected Arrays of indentations were performed on each specimen with an interval
of 20 times the indentation depth between each indentation The penetration depth for
the measurement of Youngrsquos modulus and hardness was 500 nm All data were
analysed using the Oliver and Pharr method [7] Micro-indentation was made using a
Vickers indenter at a maximum load of 3 N and the interval between each indentation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
87
was also kept to 20 times the indentation depth of ~26 μm
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
(c)
(d)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
88
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Moreover a high purity (gt999995) and fully dense polycrystalline 3C-SiC bulk
(diameter 3 cm thickness 15 cm) sample fabricated by static CVD (Rohm amp Haas
Ltd UK) was used as a reference sample in order to confirm the accurate mechanical
property measurements for FBCVD SiC coatings The Raman spectroscopy of bulk
CVD SiC was the inset in Fig 31(b) and no excess C or Si was found in it
To observe the grain morphology more clearly the finely polished (no scratch could
be seen under optical microscopes times50) cross-section (Fig 1(a)) of the coatings were
chemically etched using Murakamirsquos solution (10 g sodium hydroxide and 10 g
potassium ferricyanide in 100 ml of boiling water) The surface morphology of
coatings was characterized using scanning electron microscopy (Field emission gun
Philips XL30 FEG-SEM) A transmission electron microscope TEM (FEG-TEM
Tecnai TM
G2 F30 U-TWIN 300KV) was used to study the microstructure of the
coating layer before and after indentation For cross-sectional analysis of indentations
TEM samples were made from thin plates which are parallel to one edge and through
the center of Berkovich indentation using a focused ion beam (FIB FEI Nova 600
Dual Beam system) milling For high resolution TEM (HRTEM) the samples were
prepared using an ion beam milling method
33 Results
331 Hardness and Youngrsquos modulus
Figure 32 shows the typicl load-displacement curve of SiC coatings and the hardness
(H) and Youngrsquos modulus (E) as a function of composition of the three types of
coatings The load-displacment curve (Fig 32(a)) shows a smooth character of the
deformation process during nanoindentation There is multiple mini lsquopop-inrsquo events
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
89
reflected on the hardness curve which started at the beginning from the low
indentation load These mini lsquopop-inrsquo can not provide enough consumption of the
internal stresses induced by indenter as it was needed for the initiation and
propagation of dislocations so no well-pronounced lsquopop-inrsquo effect was observed from
the load-displacement curve
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Measurements were made on the x-z plane of SiC coatings (Fig 31(b)) and static
bulk CVD SiC for both micro- and nano-indentation to give reliable comparison with
previous studies [20-23] In the reference material the nano-hardness (36 GPa) and
Youngrsquos modulus (496 GPa) of bulk CVD SiC are nearly the same as in a previous
(c) (b)
(a)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
90
study [20] namely 36 GPa and 503 GPa respectively From Fig 32(b) it can be seen
that S1 has a higher hardness compared with S2 and S3 Further the values of
hardness obtained by nano-indentation (Fig 32(b)) are higher than by
micro-indentation for all samples
For low temperature FBCVD coatings the nano-hardness varies in the range 39 GPa
to 44 GPa whereas the micro-hardness varies between 36 GPa - 42 GPa These values
are at least 8 higher than the bulk static CVD SiC which has a nano-hardness ~36
GPa and a micro-hardness ~32 GPa (see Fig 32(b)) Moreover the low temperature
FBCVD SiC coatings have higher hardness as compared to a previous study of CVD
SiC for which the hardness values varied in the range of 25-39 GPa as measured by
nano-indentation under the similar experimental conditions [20-23]
In FBCVD SiC coatings Youngrsquos modulus of all three coatings is lower than the bulk
CVD SiC (see Fig 32(c)) which is an average Youngrsquos modulus (438 GPa) of
polycrystalline CVD SiC reported by Roy et al[24] The difference in hardness and
Youngrsquos modulus data could not be simply explained by the existence of C or Si due
to their low concentration (lt 1 at ) and location in the coatings which has been
addressed in detail in previous study [25] Therefore the difference of hardness and
modulus could be related to other microstructure such as pores which could vary
from atomic scale to micrometres which is discussed in the following session
Both nano- and micro-hardness results (Fig 32(b)) are higher than the available data
for polycrystalline CVD SiC [20-23] as discussed above and the correct measurement
of SiC coatings with small dimensions was ensured by comparing with the bulk CVD
SiC As mentioned the hardness and Youngrsquos modulus measured by
micro-indentation are slightly lower than the values measured by nano-indentation
because cracks were formed under micro-indentation due to the higher indentation
load
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
91
332 Microstructure of low temperature FBCVD SiC
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Figure 33 shows SEM images of the three etched FBCVD SiC coatings In all three
coatings the width and length of columnar grains were found to be approximately 200
nm and 1-2 μm respectively These are found to be much smaller than the SiC coating
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
92
produced at a temperature of 1500 degC which had width ~1μm and length ~4-5 μm
[17] They are also smaller than the SiC showing dislocation movement under the
indentation deformation zone which was produced at temperature of 1500-1600 degC
by FBCVD and 1500 degC by static CVD with grain size of 1-5 μm and 5-10 μm
respectively [11 16]
Although the grain size is in a similar range for three coatings (as mentioned above)
due to different deposition conditions the grain morphologies of three coatings vary
First a less laminar structure was observed in the S1 coating (see Fig 33 (a)) as
compared to the coatings with excess C or Si (Fig 33 (c) and (e)) Fig 33 (b) shows
the existence of triple junctions (dashed circle) that could resist the movement of
grain boundaries and dislocation slip [12] Pores were also observed along the laminar
structure after etching In the S2 coating it has a large amount of a laminar structure
running through a single grain (laminar structure parallel to growh direction) as
illustrated in Fig3 (d) The information of grain morphology in S2 was mostly a
laminar structure perpendicular to the growth direction after etching (Fig 33(d))
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
To get more information about the grains morphology in S2 coating a TEM image
05 μm
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
93
was taken and shown in Fig 34 Figure 34 shows that grains in S2 coating interact
(branch-like grain growth pattern on the lower-left part of Fig 34) with each other
which is similar as in sample S1 (Fig 33(b)) and grains form branch like structures
In the S3 coating (as can be seen in Fig 33 (f)) a parallel growth of grains with less
interaction among grains was observed
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
According to a previous study [25] about definition of grain boundary the grain
boundary in the S3 coating is smooth while in the S1 and S2 coating the grain
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
94
boundaries are rough which could result in branch-like grain growth pattern It could
be attributed to the different CSi ratio in reaction gas which produce SiC with
different morphologies on the (111) crystal plane which may have three different
morphologies rough smooth and pyramidal defect [26] Grains with differently
finished surfaces could lead to different grain growth morphologies because of
different surface energy For example in rough grain boundaries of S1 and S2
coatings branch like crystals were found as in Fig 33(b) and Fig 34
Figure 35 shows bright field TEM images of the S1 coating S2 and S3 coatings The
columnar grains were observed to grow perpendicular to the coating surface which
was consistent with the SEM results Further nano porous layers normal to the
coating growth direction are observed in the S2 coating (see Fig5 (b)) The formation
of porosity in thin films could be due to differences in diffusion of growth species the
incident molecule direction and deposition of secondary phases such as excess Si or C
[27]
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
BF-TEM and (b) DF-TEM
At low deposition temperatures the probability of a precursor reaching the edge of the
nucleus is considerably lower compared with that of arriving on the top due to a low
surface diffusion As these nuclei grow the areas immediately around them will suffer
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
95
from a shadowing effect blocking the arrival of new molecules and the formation of
new nuclei Since the diffusivity of atoms is low and no new nuclei are formed in
those regions gaps will be formed among grains A wrinkled like defect layer was
seen in the S3 coating (Fig 35 (c)) which could be attributed to the interruption of
the SiC crystallization growth during the deposition process such as crystal lattice
misorientation as seen in Fig 36
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
No obvious laminar defect was observed in the S1 coating by TEM this could be due
5 nm
(a) (b)
5 nm
5 nm
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
96
to less interruption during deposition process According to above observation it was
proposed that the laminar structure observed in SEM images indicates some
instability during the fabrication process resulting in the deposition of the nano- and
micro-pores and misorientation This was attributed the variations in circulation and
deposition occurring close to the nozzle or at the hot zone [5]
Stacking faults were observed for all three types of samples as shown in Fig 35 with
a higher density than for the SiC deposited at a temperature of 1500 C [11 16 17]
These stacking faults could cause an intrinsic residual stress due to the coexistence of
the partial dislocations This was supported by the high resolution TEM images
(shown in Fig 37) exhibiting wave pattern fringes and they could only be observed
in one direction which is determined by the intrinsic stress
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Since the dislocation mobility under nano-indentation deformation has not been fully
understood in hard ceramic materials therefore it is significant to study this
behaviour in FBCVD SiC coatings with a sub-micrometer grain size However it is
difficult to observe the dislocations under the two-beam or weak beam dark field
2 nm
(a)
(111)
[110]
(111)
Sessile
dislocations
(b)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
97
conditions due to the high density of defects In the present study the reversed fast
Fourier transform (FFT) images of the corresponding high resolution TEM images
was used to obtain information about the dislocations This method has been used in
many cases for dislocation observations [28]
Figure 38(a) shows a high resolution TEM image of a S1 coating which was taken as
a representative image to compare the atomic structure of all three coatings Figure
38(b) is the reverse FFT image using the marked inset diffraction pattern of Fig
37(a) in which sessile and glide dislocations can be observed The dislocation
density was calculated from the total number of glide dislocations divided by the area
in the image [29 30] From the analysis of images shown in Fig 38 the dislocation
density in S1 coatings was found to be 1013
cm2 The same magnitude of dislocations
density was found in the S2 and S3 coatings as shown in Fig 37 (three HRTEM
images were analysed for each coating)
333 Deformation behaviour under the indentation
The deformation zone under the indentation was investigated through the images of
FIB milled TEM samples in order to study the deformation mechanism of the low
temperature FBCVD SiC coatings Figure 39 shows the bright field TEM images
showing the mechanical behaviour of a S1 coating under nano-indentation on the x-z
plane (Fig 31(b)) at a maximum indentation depth of 500 nm
Figure 39(a) is an overview of the deformation area under an indentation A median
crack has formed just underneath the surface and has a direction aligned with the
indenter tip impression A higher magnification image around the elastic and plastic
interface is shown in Fig 39(b) It can be seen that a large amount of inter-granular
and trans-granular micro cracks were produced around the median crack initiation
zone This is substantially different from the dislocation-related plastic deformation
behaviour [10 11 16 31] which usually has a severe plastically deformed region
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
98
with few or no cracks Moreover the micro cracks were also observed in the C and D
zones under the indentation
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Figure 39(c) shows that micro cracks that are formed along the grain boundaries
which tend to follow the shear band direction with the formation of a few
trans-granular cracks In Fig 39(d) it can be seen that shear band micro cracks were
formed in one single grain (see inset in the left bottom corner of Fig 39(d)) This
single grain has a large amount of defects which are supposed to be the as-deposited
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
99
defects as shown in Fig 35(a) Shear band cracks were also observed just underneath
the indenter tip (right top inset in Fig 39(d)) As a result a shear band dominated
deformation zone can be seen in Fig 39(c d) under the indentation in a S1 coating
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
The S2 and S3 coatings only show a micro crack pattern which is different from S1
coating Figure 310 gives the TEM images of the S2 and S3 coatings showing the
mechanical reaction underneath the indentation It can be seen from Fig 310(a) and
Fig 310(c) that the median cracks are not always produced under the indentation for
S2 and S3 coatings However some irregular cracks in S3 coatings and lateral cracks
in S2 were produced In particular in the S3 coating (Fig 310(b)) more micro cracks
either intragrain or transgrain were found than in the S1 and S2 coatings This is due
to the fact that the most micro cracks propagate along the grain boundaries in S1 and
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
100
S2 coatings (Fig 39(b) and Fig 310(d)) A careful analysis of the TEM images
shows that only micro cracks were found under the indentation and no
dislocation-induced shear band was observed This is different from previous studies
on the deformation behaviour of polycrystalline SiC [11 16 31] For example in bulk
polycrystalline CVD SiC [11] it was found that it has more dislocation slip bands
rather than micro cracks either in grains or along grain boundaries even though the
indentation load is higher than the load used in the FBCVD SiC based materials The
possible reason of this discrepancy is discussed later Moreover no amorphous phase
and α-SiC phase was formed under the indentation observed by diffraction and bright
field TEM images which is consistent with the work of Mishra and Szlufarska [32]
34 Discussion
High hardness and Youngrsquos modulus were obtained in the sub-micrometer grain size
coatings produced at a low temperature by FBCVD In the S1 coatings the
nano-hardness is ~22 higher while the micro-hardness is ~31 higher compared to
a commercial CVD SiC The higher hardness was also obtained in S2 and S3 coatings
All the coatings retained a higher Youngrsquos modulus than those SiC materials having
high hardness in previous study (equal or higher than 40 GPa nano-hardness) [33]
making these coatings unique among polycrystalline phase brittle ceramic material
Under nano-indentation only micro cracks were found in the deformation zone The
results seem to be consistent with the conventional view of the failure mechanism of
brittle ceramics at room temperature [34] The lack of dislocation and the high Peierls
force are reasons for fracture to occur in brittle materials However
dislocation-related plastic deformation routinely occurred in hardness testing because
the indentation stress field offers conditions of stress conductive to plastic
deformation [11 13 16 34] Molecular dynamic simulations even demonstrate that
13 of the hardness-related deformation is from dislocation-related plastic deformation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
101
while 23 comes from fracture in SiC [31] It is rare to see a deformation zone
dominated by micro cracks in polycrystalline SiC such as in FBCVD SiC coatings
(Fig9 and Fig10 and see for example Ref [11 16 31]) With the above questions
we first estimated the factors controlling Youngrsquos modulus in FBCVD SiC coatings
followed by a study of the mechanism of superior hardness and deformation under an
indentation which influence the hardness in the three coatings
341 Influence of porosity on Youngrsquos modulus
Youngrsquos modulus presents a material constant for uniaxial tensile deformation which
is physically related to the atomic spacing inter atomic bond strength and bond
density In a low temperature FBCVD SiC coating it was shown from XRD
measurements that a shoulder peak was observed in addition to the β-SiC (111)
diffraction peak which corresponded to a crystal plane spacing of ~0266 nm (Fig
31(c)) Moreover we found that the XRD peak shifted to a lower diffraction angle
compared with the bulk CVD SiC According to the XRD pattern in Fig 31(c) the
crystal lattice constants of about 04366 04368 and 04368 nm for S1 S2 and S3
coatings were obtained respectively However the crystal lattice constant for bulk
CVD SiC is ~04359 nm (XRD pattern obtained by the same condition was shown in
Ref 25)
Further crystal orientation impurities and porosity may affect the Youngrsquos modulus
As the Youngrsquos modulus on the x-z plane (Fig 31(b)) was similar to the value
obtained along the cross-section (Fig 31(a)) [5 25] which meant that the orientation
has no effect on Youngrsquos modulus Moreover as discussed before the effect of C or Si
in S2 was found to have no effect on the difference of hardness and Youngrsquos modulus
Excluding these two factors (orientation and impurities) the effect of porosity on
variation of the elastic properties in three coatings was investigated The presence of
nano-pores in S2 coating as in Fig 35(b) results in a lower density Although no
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
102
pores were directly observed by TEM in the S1 and S3 coatings their density is lower
than the theoretical density of SiC Thus the elastic modulus E at room temperature
can be expressed in an exponential function of porosity pV [35] as
0 exp( )pE E CV (1)
where 0E = 496 GPa is the elastic modulus and C = 357 is a constant for a pore-free
bulk CVD SiC pV is the ratio of the relative density difference to the theoretical
density of SiC (322 gcm3)
The calculated Youngrsquos modulus for S1 S2 and S3 coatings is 465 plusmn 15 446 plusmn 17 and
473 plusmn 1 GPa respectively which follows a trend similar to the experimental data
presented in Fig 32 It was concluded that the different Youngrsquos modulus in the three
low temperature FBCVD SiC coatings is attributed to porosity although the
experimental Youngrsquos modulus data of FBCVD SiC coatings is slightly lower than the
values calculated using the Eq(1) The difference between calculated and measured
value of FBCVD SiC coatings is due to the fact that the 0E from pore-free bulk
CVD SiC instead of pore-free FBCVD SiC coatings (not available) FBCVD SiC
coatings have larger crystal lattice constant (~0437 nm) than bulk CVD SiC (~04359
nm) as discussed above Since the expanded lattice constant leads to a decrease of the
Youngrsquos modulus according to a previous study [20] the 0E of pore-free FBCVD SiC
coating is expected to be lower than bulk CVD SiC
342 Mechanism for High hardness
From previous studies [10 11 16 31] dislocation nucleation and glide is the primary
response of SiC under nano-indentation Formation of shear bands due to dislocations
has also been reported [11] which were found under the plastic deformation zone
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
103
when indentations were made on a particular grain in polycrystalline SiC and at the
grain boundaries Moreover dislocation nucleation is also correlated with the discrete
pop-ins observed in the force-displacement curve [32] No pop-ins was found due to
the presence of a large amount of dislocations in the present study Dislocation
mobility can be estimated similar to the case of a metallic material having intrinsic
dislocations Mishra and Szlufarska [32] worked on the dislocation mobility in
3C-SiC using large-scale molecular dynamics simulations The results indicated that
dislocation mobility decreased by dislocation interaction as its density reached a
saturation value This is similar to the work hardening effect in a metallic material [34]
We estimated the stress ( ) needed for dislocation to move using Taylorrsquos work
hardening equation [34] given by
1 2
0 Gb (2)
where 0 is the shear stress for a dislocation to move without any obstacle and the
value of 0 taken was 75 GPa [13] is a numerical constant depending on the
locking strength of a nod The value of taken was 8 [36] b is Burgers vector
where b = 0178 nm for a Shockley partial dislocation in SiC initiated and gliding on a
close packed (111) plane and is the density of glide dislocations G is the shear
modulus which can be written as
2(1 )
EG
(3)
where is the Poissonrsquos ratio and E is the Youngrsquos modulus The dislocation density
was ~03times1012
cm2 The calculated shear stress according to Eq (2) was ~52 GPa and
this value is much higher than the theoretical shear stress which is in the range of
295-4312 GPa obtained from previous reports [37-39] The theoretical shear stress is
the maximum stress provided for the dislocation nucleation and propagation in SiC
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
104
crystals Therefore the dislocation-related yield behaviour could not occur under the
plastic deformation zone in sub-micrometer FBCVD SiC coatings
The superior hardness value in FBCVD SiC coatings is attributed to the immobility of
the dislocations In the case of the SiC-C solid solution [40] the occurrence of a high
density of dislocations causes a strain-hardening effect Furthermore given that
dislocations could be motivated by the shear stress a phase transformation from a
crystalline phase to an amorphous could occur [32] However no amorphous phase
was observed under the nano-indentation (Fig 37 and 8) nor was dislocation
movement band observed in this study This suggests that the dislocation-related
phase transformation did not occur under the indentation
343 Deformation mechanism under nano-indentation
The hardness-related plastic deformation which occurs due to the nucleation and
propagation of micro cracks in FBCVD SiC coatings can be explained as follows
(i) The onset of plastic deformation under the indentation occurs as the maximum
shear stress approaches the yield stress [41] According to 15H Y (Y is the yield
stress H is the hardness) the yield stress in FBCVD SiC coatings is around 26 GPa
The yield stress is lower than the stress needed for the movement of dislocations and
the theoretical shear stress [37-39] This indicates that the hardness-related plastic
deformation first occurred by the nucleation of defect-induced cracks which
propagated to the indented surface (see inset (top right) in Fig 39(d)) The
deformation impression was accommodated by the densification of defects such as
the pores dislocation pile ups and grain boundaries as in Fig 33(b)
(ii) The shear stress was used to promote the movement of dislocations under the
indentation and form slip bands in previous studies [10 11 42] The highest amount
of micro cracks were observed in FBCVD SiC coatings contrary to plastic
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
105
deformation under the indentation found in previous studies [10 11 42] The micro
cracks formed in the hardness-related plastic deformation zone is the Mode-II crack)
[43] as shown in Fig 39(c) and (d) Unlike Mode-I which is dominated by the tensile
stress a Mode-II crack is the consequence of a confined shear stress [34] At the
interface of the elasticplastic deformation branch-like micro cracks were observed
as in Fig 39(b) The above discussions distinguish the hardness-related plastic
deformation mechanism in FBCVD from previous studies on ceramics which showed
dislocations are the main deformation mechanism underneath the indentation [31 44]
A unique hardness-related plastic deformation mechanism was used to explain the
difference in hardness of all three types of FBCVD SiC coatings According to Qian
et al [45] the hardness could reach an asymptotic value with the saturation of the
micro cracks growth population In three FBCVD SiC coatings studied here different
amounts of micro cracks were found (Fig 39(b) and Fig 310(b d)) and micro cracks
nucleated at stress concentration zones such as the grain boundaries or defects within
the grains Thus the difference in hardness was attributed to the grain morphologies
as shown in Fig 33 which gives different degree of resistance to the initiation and
propagation of micro cracks In the S1 coating triple junctions hamper grain
boundary shear by forming interlocks [12] which could resist and deflect the initiation
and propagation of micro cracks In the S2 coating elongated grains interact with the
surrounding small grains which could also provide interlocks (Fig 33(d) and Fig
34) The slightly lower hardness of the S2 coating as compared to the S1 coating is
due to the nano pores as seen in Fig 35(b) A lack of triple junctions and grain
interactions could be the reason for the lower hardness in the S3 coating as it has a
parallel crystalline morphology which has less constraint towards the initiation and
propagation of cracks
35 Conclusions
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
106
The microstructure and mechanical properties of three types of FBCVD SiC coatings
(SiC SiC+C and SiC+Si) were studied FBCVD SiC coatings with a sub-micrometer
grain size were deposited on simulated TRISO fuel particles by FBCVD at a low
temperature (1300 oC) The mechanical properties were studied using micro and
nano-indention The microstructures were studied using SEM and TEM It was
found that the Youngrsquos modulus of all three coatings differ which was attributed due
to the presence of nano-pores The high hardness of FBCVD SiC coatings was due to
the large amount of defects particularly the high density of dislocations It is found
that the interactions between dislocations reduced their mobility and make
dislocation-related plastic deformation unavailable We suggest that the work
hardening effect is the reason for the high hardness in the sub-micrometer grain size
FBCVD SiC coatings A hardness related-deformation mechanism was attributed to
the initiation and propagation of micro cracks The nano-indentation indent volume is
most likely be accommodated by the densification of defects such as the pores As a
result the hardness difference in FBCVD SiC coatings is due to the different grain
morphologies producing different amounts of micro cracks
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
107
36 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[2] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[3] D A Petti J Buongiorno J T Maki R R Hobbins G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[4] A C Kadak R Gnallinger M J Driscoll S Yip D G Wilson H C No J
Wang H Maclean T Galen C Wang J Lebenhaft T Zhai D A Petti W K
Terry H D Gougar A M Ougouag C H Oh R L Morre G K Miller J T
Maki G R Smolik D J Varacalle Modular pebble bed reactor Modular pebble
bed reactor project University research consortium annual report Beijing 2000
[5] E Lopez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[6] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram P Xiao Youngs modulus measurements of SiC coatings on spherical
particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[7] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[8] C H Chien S R Jian C T Wang J Y Juang J C Huang Y S Lai
Cross-sectional transmission electron microscopy observations on the Berkovich
indentation-induced deformation microstructures in GaN thin films J Phys D
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
108
Appl Phys 40 (2007) 3985-90
[9] T C Tan C A Merrill J B Orton A K Cheetham Anisotropic mechanical
properties of polymorphic hybrid inorganic-organic framework materials with
different dimensionalities Acta Mater 57 (2009) 3481-96
[10] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
related isostructural materials to nanoindentation Slip vs densification Mater
Res Soc Symp P 522 (1998) 113-18
[11] X Zhao X R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of 3C-SiC upon indentation at room temperature J Am
Ceram Soc 94 (2011) 3509-14
[12] D Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
mechanism of plastic deformation in macro- micro- and nanoindentation
processes J Phys D Appl Phys 41 (2008) 074016-24
[13] H P Chen R K Kalia A Nakano P Vashishta I Szlufarska
Multimillion-atom nanoindentation simulation of crystalline silicon carbide
Orientation dependence and anisotropic pileup J Appl Phys 102 (2007)
063514-22
[14] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[15] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[16] G Chollon J M Vallerot D Helary S Jouannigot Structural and textural
changes of CVD-SiC to indentation high temperature creep and irradiation J Eu
Ceram Soc 27 (2007) 1503-11
[17] D Heacutelary X Bourrat ODugne G Maveyraud M Peacuterez O Guillermier
Microstructures of silicon carbide and pyrocarbon coatings for fuel particles for
high temperature reactors 2nd international topical meeting on high temperature
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
109
reactor technology Beijing China 2004
[18] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[19] T Fukuzaki K Tanaka K Nishimoto Y Mur K Nishio and R Tamura
Magnetic property and microstructure of Nd-Fe-B-M (M=Si C) bulk
pnanocomposite magnets prepared by spark plasma sintering method - art no
012015 J Phys Conf Ser 106 (2008) 12015-124
[20] M C Osborne J C Hay L L Snead D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[21] K H Park S Kondo Y Katoh A Kohyama Mechanical properties of beta-SiC
after Si- and dual Si plus He-ion irradiation at various temperatures Fusion Sci
Technol 44 (2003) 455-59
[22] S Nagappa M Zupan C A Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
Mater 59 (2008) 995-98
[23] C Bellan J Dhers Evaluation of young modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[24] S Roy C Zorman M Mehregany R Deanna C Deeb The mechanical
properties of polycrystalline 3C-SiC films grown on polysilicon substrates by
atmospheric pressure chemical-vapor deposition J Appl Phys 99 (2006)
044108-20
[25] J Tan Mechanical properties of SiC in TRISO fuel particle Thesis University of
Manchester 2010
[26] M J Hernandez G Ferro T Chassagne J Dazord Y Monteil Study of surface
defects on 3C-SiC films grown on Si (111) by CVD J Cryst Growth 253 (2003)
95-101
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
110
[27] E S Machlin Materials science in microelectronics I The relationships between
thin film processing and structure 2nd
ed Oxford Elsevier Science 2005
p206-47
[28] A Nakamura T Yamamoto Y Ikuhara Direct observation of basal dislocation
in sapphire by HRTEM Acta Mater 50 (2002) 101-08
[29] H Y Shin S K Kwon Y I Chang M J Cho K H Park Reducing
dislocation density in GaN films using a cone-shaped patterned sapphire substrate
J Cryst Growth 311 (2009) 4167-70
[30] W D Callister Materials science and engineering An introduction 7th ed
Australia John Wiley amp Sons Australia Limited 2006 p191-99
[31] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
materials with a density functional theory J Appl Phys 104 (2008) 053508-16
[32] M Mishra I Szlufarska Possibility of high-pressure transformation during
nanoindentation of SiC Acta Mater 57 (2009) 6156-65
[33] A R Beaber L J Qi J Hafiz P H Mcmurry J V R Heberlein W W
Gerberich S L Girshick Nanostructured SiC by chemical vapor deposition and
nanoparticle impaction Surf Coat Tech 202 (2007) 871-75
[34] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
p162-91
[35] R W Rice Mechanical properties of ceramics and composites 1st ed New
York Marcel Dekker 2000 p457-534
[36] U Messerschmidt Dislocation dynamics during plastic deformation Part 2
Ceramic Single Crystals Springer Series in Materials Science On line 2010
p264
[37] S Ogata J Li N Hirosaki Y Shibutani S Yip Ideal shear strain of metals and
ceramics Phys Rev B 70 (2004) 104104-10
[38] Y Umeno Y Kinoshita T Kitamura Ab initio DFT study of ideal shear
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
111
strength of polytypes of silicon carbide Strength Mater 40 (2008) 2-6
[39] Y Umeno M Cerny Effect of normal stress on the ideal shear strength in
covalent crystals Phys Rev B 77 (2008) 100101-04
[40] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[41] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000 p139-77
[42] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[43] A A Wereszczak K E Johanns O M Jadaan Hertzian Ring Crack Initiation
in Hot-Pressed Silicon Carbides J Am Ceram Soc 92 (2009) 1788-95
[44] S L Lloyd A Castellero F Giuliani Y Long K K Mclaughlin J M
Molina-Aldareguia N A Stelmashenko L J Vandeperre W J Clegg
Observations of nanoindents via cross-sectional transmission electron microscopy
a survey of deformation mechanisms P Roy Soc a-Math Phy 461 (2005)
2521-43
[45] J Qian L L Daemen Y Zhao Hardness and fracture toughness of moissanite
Diam Relat Mater 14 (2005) 1669-72
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
112
CHAPTER 4 Vickers Indentation Fracture Toughness of
SiC Coatings
41 Introduction
Silicon carbide (SiC) layer is considered to be the most important component for
structural integrity as during the operation of a nuclear reactor it has the ability to
sustain most of the internal pressure caused by gaseous fission products produced in
the kernel and retain most of the fission products [1-4] Previous work was focused on
the investigation of mechanical properties (Youngrsquos modulus and fracture strength) of
SiC coatings on TRISO particles using different techniques such as a ring test [5 6]
a crush test [7 8] a micro-cantilever test [9] and indentation [10 11] However few
reports exist on the measurement of the fracture toughness of SiC coatings even
though it is a property used in modeling to estimate the failure probability of TRISO
fuel particles [12] For example Kadak et al [12] used a fracture toughness value of
33 plusmn 053 MPa m12
This value was obtained from bulk SiC produced by a static
CVD method The fracture toughness value may well differ for SiC coatings produced
by fluidized bed chemical vapour deposition (FBCVD) on TRISO fuel particles [10]
Because microstructure of SiC produced by static CVD and FBCVD methods could
vary significantly For example the static CVD SiC usually has larger grain size and
high density while FBCVD SiC with large grain size is usually accompanied with
porosity [13] Different grain size range and porosity fraction can lead to variation of
fracture toughness [1 2] Therefore the fracture toughness value of bulk SiC may not
be truly representative of SiC coatings used in nuclear fuel applications To our
knowledge the only available data on the fracture toughness of a SiC layer on TRISO
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
113
fuel particle is reported by Zhao et al[9] where the fracture toughness was measured
by the micro-beam method However this method is time consuming and expensive
restricting its implementation as a standard characterization technique where
repetitive measurements are required to confirm the reproducibility of experimental
data
In this Chapter micro-indentation is used to investigate the fracture behaviour of
different SiC coatings produced (on TRISO fuel particles) by FBCVD due to its
capacity to measure the mechanical properties in a small area and produce visible
cracks [14-16] The fracture behaviour under an indenter is also studied using a
transmission electron microscope (TEM) in order to give better understanding of the
fracture mechanism The characteristics of the SiC microstructures are then correlated
with their fracture behaviour
42 Experimental details
The SiC coatings used are the same as the ones in Chapter 3 and the deposition
conditions were shown in Table 31 Chapter 3
For the micro-indentation study SiC coated fuel particles were hot mounted in
copper-loaded conductive resin (to get better SEM images) and then ground to a
cross-section (as shown in Fig 31(a)) or polished a flat external surface (as shown in
Fig 31(b)) In this Chapter the y direction is called radial direction x is called
tangential direction according to Fig 31(a) and (b) The samples were then polished
using increasingly fine diamond suspensions to 14 μm Indentation fracture
toughness measurements were performed using a Vickers diamond indenter (CSM
Instruments Switzerland) Due to the through-thickness (in the radial direction)
failure behaviour of a SiC coating in a TRISO fuel particle under tensile stresses
generated from gases due to nuclear reactions similar tensile stresses could be
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
114
generated from indentation of polished external surface of TRISO particles which
could generate cracks along the radial direction (y direction in Fig 31(b)) of the
TRISO particles as well The indentations were carried out under a maximum load of
3 N (corresponding to a maximum indentation depth of ~26 μm) To avoid PyC
influence the thickness of SiC coatings (in the section as shown in Fig 31(b)) were
kept to ~60 μm after polishing which is more than 20 times the indentation depth
In this case the elastic zone has not expanded to the substrate according to the
criterion that indentation depth is less than 10 of coating thickness [17] For each
sample six indents were made on the polished external surface of SiC perpendicular
to the radial direction with a separation of 70 μm between each indent
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference [25]
The calculation of the VIF fracture toughness must account for the crack profile under
the indenter whether the cracks are of the Palmqvist mode or half-penny mode which
are illustrated in Fig 41 The halfpenny crack system is formed by the joining of
radial cracks as shown in Fig 41(a) while the Palmqvist crack system is always
shallow as shown in Fig 41(b)
To observe the crack impression under the indenter on the polished external surface
an indentation (as in Fig 42(a)) with a final indentation depth of 26 μm was
sequentially polished with 6 μm diamond suspensions The surface was polished until
the plastic deformation zone was exposed together with the radial cracks (as shown in
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
115
Fig 42(b) Afterwards polishing continued until the removal of the plastic
deformation zone (as shown in Fig 42(c)) The surface showed no cross-over
cracking present as illustrated in Fig 41(a) and this confirms the presence of the
Palmqvist mode cracks on the polished external surface of SiC coatings under the
Vickers indenter The three polished samples showed the same crack propagation
mode and this is consistent with previous reports [18 19] where a Palmqvist crack
system has been observed in SiC at low loads (lt 10 N)
The Palmqvist crack mode allows the VIF fracture toughness to be calculated using
the equation proposed by Laugier [15 16] given as
1 2 23
3 2( ) ( )IC v
a E PK
l H c
(1)
In Eq (1) the geometrical constant v is a calibrated value using the already known
fracture toughness due to the variation in use of the Vickers hardness or the
nano-hardness [14 16 20 21] The 2a and l are the lengthes of diagonal and radial
crack length of Vickers indentation (as shown later in Fig 43) respectively c=a+l
the E and H are Youngrsquos modulus and hardness measured by nano-indentation P is
the load of Vickers indentation Therefore this geometrical constant was calibrated
before it was used to calculate the VIF fracture toughness of SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
116
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
117
The only already known fracture toughness was measured on the cross-section of
extra-Si SiC coatings using a micro-beam bending method [9] so the calibration of
v was carried out on the cross section (as in Fig 31(a)) of the same coating
According to Eq(1) the hardness (H ) and Youngrsquos modulus (E) are nano-hardness
and Youngrsquos modulus as measured in a previous study [22] P is the load a is the
impression half diagonal l is the crack length and c is the half diagonal crack length
(see later in Fig 43) To get the load and dimensional values of indentations a total
of 8 indentations at different loads (3 35 and 4 N) were applied on the cross-section
of the extra-Si SiC coating
The crack lengths were measured using a scanning electron microscope (Philips XL30
FEG-SEM) FEG-TEM (Tecnai TM
G2 F30 U-TWIN 300KV) which was used to
study the fracture behaviour under the indenter For the TEM study the cross
sectional specimens for the indents were prepared using focused ion beam milling
(FIB FEI Nova 600 Dual Beam system) Note that due to the large deformation zone
(gt10 μm diameter) and radial crack length (gt15 μm) observed from micro-indent
impression it was not possible to produce a sufficiently large TEM sample by the FIB
technique This limitation restricted us to study the fracture behaviour under a sharper
indenter (Berkovich) with lower load
43 Results and discussion
431 VIF fracture toughness study
Figure 43 is the crack morphology observed in S3 (SiC + Si) coating cross-section It
shows that the fracture resistance is different in the tangential and radial directions of
the cross-section which is consistent with the previous measurements along these
directions measured by the micro beam method [9] Different crack lengths along the
tangential and radial directions observed from 8 indentations are illustrated in Table
41 Correspondingly fracture toughness values of 347 MPa m12
and 672 MPa m12
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
118
taken from Ref [9] were used as the standard values for the tangential and radial
directions of the SiC coating respectively According to Eq (1) taking into account
observed and measured parameters (KIC a c l H and E) the geometric constant
value v was calculated in each indentation for each direction (Table 41)
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for S3 SiC coatings
Table 41 illustrates the indentation parameters and the calibrated geometrical
constant v for the Palmqvist crack mode According to the results shown in Table
41 the calibrated mean value of v is 002008plusmn000273 and this value is within
the range of the geometrical constant value (0014-0023) from previous theoretical
studies [14 23] By using nano-indentation hardness and Youngrsquos modulus v was
taken as 002 for the calculation of the VIF fracture toughness in SiC layers in this
study which is the upper limit of 0016plusmn0004 used for previous studies of bulk
CVD SiC using the HE from micro-indentation [14 24-27]
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
119
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχ
v along the radial and tangential directions
Load Radial direction
Tangential direction
a (μm) c (μm) l (μm) χv a (μm) c (μm) l (μm) χv
3 N 6650 13125 6475 0020368 6685 18285 11600 0023088
6900 13090 6190 0019473 6995 15470 8475 0015013
6675 11895 5220 0015749 6120 16615 10495 0019880
6695 13130 6435 0020249 6555 15935 9380 0017057
6790 12610 5820 0017997 6425 18275 11850 0023783
35 N 7195 14970 7775 0022404 7235 20790 13555 0024930
6670 14080 7410 0020721 6715 18160 11445 0019412
4 N 7770 15855 8085 0020967 7390 20240 12850 0020187
χv 002008 plusmn 000273
Note The geometrical constantsχv presented in Table 41 were calculated using Eq(1) The fracture
toughness along the radial (672 MPa m12
) and tangential directions (347 MPa m12
) were taken from
Ref 9
Although the Vickers indentation method for fracture toughness measurement has
been discredited as a mean to obtain true fracture toughness [28] and always gives a
lower fracture toughness value than that obtained using the standard methods (such as
single edge V-norched bending)[1] the values obtained can be compared with each
other This is particular important for small samples and thin coatings since Vickers
indentation provides a method to quantify fracture behaviour when it is not feasible to
obtain true fracture toughness However to get reasonable comparison of Vickers
indentation fracture toughness in SiC coatings the following conditions should be
met
(1) SiC materials produced four regular radial cracks along the corners of the
Vickers indenter For indentation at the polished external surface of SiC
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
120
coatings deposited by FBCVD similar fracture resistance along different
orientation at the surface should be obtained
(2) The calibration of the geometrical constant should be made v was obtained
as 002 based on previous experimental results (see above)
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
Sample Grain size range (μm) Vickers toughness (MPa m12
)
S1 (SiC) 02-2 351plusmn042
S2 (SiC + C) 02-2 403plusmn043
S3 (SiC + Si) 02-2 493plusmn016
Table 42 presents the measured VIF fracture toughness on the polished external
surface using equation (1) for the SiC coatings in which the deposition conditions and
grain size were given It can be seen that the SiC coating with excess Si (S3) has
highest indentation fracture toughness followed by SiC with excess carbon (S2) and
stoichiometric SiC coatings (S1)
Vickers indentation fracture toughness values obtained in this study are slightly higher
than that of commercial CVD β-SiC which has been reported to vary from 24 to 33
MPa m12
measured by the same method [24 26 27] The VIF fracture toughness of
49 MPa m12
for extra-Si SiC measured on a polished external surface is between
347 and 672 MPa m12
when measured on a cross section by micro-beam method [9]
This is consistent with the observation of radial crack length differences ndash the crack
length on the polished external surface is between those in the tangential and radial
direction on the cross-section It is suggested that Vickers indentation is an effective
method for the characterization of fracture behaviour of FBCVD SiC coatings
Moreover the high hardness and Youngrsquos modulus of these three coatings [22] do not
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
121
cause a decrease in fracture toughness which is explained in the later part of this
paper
432 Influence of non-stoichiometries on the VIF fracture toughness
The VIF fracture toughness in S2 SiC coating is ~14 higher than the value for S1
SiC coatings and this can not be attributed to heterogeneous toughening due to the
excess carbon being at the grain boundaries Due to the low content of excess C it is
difficult to identify such an excess at the grain boundaries [29] Previous work
reported in Ref[30] showed that there was no presence of carbon at the grain
boundaries for a concentration up to 1 wt excess C In our case a similar situation
was found in S3 SiC coating where excess Si has not been found along the grain
boundaries Previous studies had [31 32] shown that excess Si in SiC was observed in
grains or near the grain boundaries by TEM only when the amount of excess Si is
high enough (such that it could be detected by XRD or a much higher Raman
spectroscopic intensity)Thus it is assumed that the excess Si could not be considered
as giving heterogeneous toughening which caused a ~43 higher VIF fracture
toughness in the S3 SiC than the S1 SiC coatings As a result the small amount of
excess carbon or silicon in SiC coatings does not seem to have influence on the VIF
fracture toughness through serving as the heterogeneous phase along the grain
boundary
The excess Si or C could be related to different grain morphologies according to
previous study [33] where it was observed that different SiC ratios in the reaction
gas produced rough smooth and irregular pyramid-like grain surfaces This further
affects the growth morphology and cohesion stress between grains For example the
smooth grain surface favours the parallel grain growth The weak grain boundary
cohesion could be the micro crack initiation zone while the strong grain boundary
could transfer the stress to stress concentration zone Here the role of grain
morphology is studied later in terms of stress concentration zone under indentation
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
122
433 Microstructural analysis of fracture behaviour under the indenter
SiC coating under nano-indentation on the polished external surface at a maximum
indentation load of 160 mN It can be seen that the median crack propagation root
deflected slightly and changed from intergranular to transgranular fracture as shown
in Fig 44(a) It is worth noticing that the median crack observed under
nano-indentation was not found under indentation because the indentation cracking
mode depends on the condition of the indenter tip [34] Higher magnification images
(Fig 44(b)) show that a large number of micro cracks were produced at the
elasticplastic interface
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
123
Both intergranular and transgranular cracks were observed near the median crack
initiation zone These cracks are under a tensile stress dominated by Mode I cracks as
the elastic-plastic stress field gives the highest tensile stress around this interface
according to a previous report (see Ref [35]) Moreover micro-cracks were observed
surrounding the median crack and also at the median crack tip as shown in Fig 44(c)
and Fig 44(d) respectively Figure 44(c) illustrates that the micro-cracks are along
the grain boundaries while the micro-cracks around the crack tip were found to both
pass through the grains and along grain boundaries (Fig 44(d))
Non-stoichiometric SiC coatings (S2 and S3) show quite different crack morphologies
under the indenter from that in the stoichiometric SiC (S1) coating as shown in Fig
310 in chapter 3 It can be seen that the propagation root of median cracks in S3 SiC
and S2 SiC coatings were affected by the microstructures as in Fig 310(a) and (c) in
chapter 3 Moreover a lateral crack was found in the S2 SiC coating The irregular
median crack propagation route in non-stoichiometric SiC coatings seems to be
related to the laminar structure
Fig 45 Cross-sectional SEM image of the S1 SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
Figure 45 shows the cross section of S1 SiC coating and the laminar structure (as
indicated by the dashed lines) is perpendicular to the grain growth direction It was
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
124
discussed in chapter 3 that the laminar structure is due to either nano-pores or a high
concentration of stacking faults and it is much less evident in the stoichiometric SiC
coating as compared to the coatings with impurities [22] In the S3 SiC coating (Fig
310(b) in chapter 3) a larger amount of micro cracks either intergranular or
transgranular were found under the indenter than in the S1 and S2 SiC coatings
The fracture mechanism of materials is influenced by their microstructure and the
fracture toughness could be enhanced by changing it For example ceramics
containing micro-cracks during fabrication could be associated with good fracture
behaviour but low strength and hardness since the micro-cracks usually serve as the
failure origins A better solution is to fabricate materials with microstructures that can
form stress induced micro-cracks under an external force [36] In FBCVD SiC a
number of micro cracks were observed under the indenter (Fig 44(b) Fig 310(b)
and (d) in chapter 3) from where the main cracks initiated and propagated away from
this zone According to a previous study although the tip of the main crack leaves the
micro-cracked zone under the indenter the wake region can provide stress shielding
against some further crack extension [37]
Thus the micro-cracks under the indentation (Fig 44(b) Fig 310(a) and (c) in
chapter 3) seem to be a mechanism for the toughening behaviour of FBCVD SiC by
dissipating the fracture energy for brittle fracture Micro-cracks were also found near
the main crack tip and surrounding the main crack for example in the stoichiometric
SiC coating (Fig 44(c) and (d)) This further confirms the toughening behaviour
through micro-cracking In CVD SiC which has a slightly lower fracture toughness
(around 33 MPa m12
) only a few micro-cracks were observed under the indentation
[38] which could be caused by indentation-induced slip bands As a result the
micro-cracks formed under the indentation near the main crack seem to be the reason
for the high VIF fracture toughness in SiC coatings when a high hardness is obtained
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
125
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a) S2
SiC (b) S3 SiC
Stress concentration zones are known to facilitate the nucleation of micro-cracks so a
large amount of micro-faults (eg pores) and weak grain boundaries (inducing the
micro-cracks under an external stress) could increase the VIF fracture toughness A
higher VIF fracture toughness in the extra-C SiC than in stoichiometric SiC coatings
may be due to the presence of the nano-pores (as shown in Fig 35(b) in chapter 3)
The S3 SiC has an even higher VIF fracture toughness than the S2 SiC coating and
this may correspond to a larger number of micro-cracks under the indentation We
assume this difference is due to their varied grain boundary morphologies as shown
in Fig 46 For example we observed different length of cracks on the cross section
(Fig 43) with cracks parallel to the grain growth direction shorter than cracks
perpendicular to the grain growth direction This is because along grain growth
direction itrsquos more likely to produce micro-cracks along the grain boundary As we see
in Fig 46 grains interact with each other in extra-C SiC (Fig 46(a)) forming branch
grains while in S3 SiC grains grow parallel (Fig 46(b)) According to a previous
study it is easier for parallel grains to form a transgranular fracture when the grain
boundaries are along the loading axis [39] This can explain the larger number of
transgranular micro-cracks under the indentation in the extra-Si SiC compared to the
extra-C coatings (Fig 310(b) in chapter 3) which caused different VIF fracture
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
126
toughness This different grain morphology could be caused by the
non-stoichiometries and further work needs to be done to study how excess C or Si
affects the microstructure of the SiC
44 Conclusions
In summary micro-indentation on the polished external surface of the SiC coating in
TRISO particles has been successfully applied to measure the VIF fracture toughness
of the silicon carbide (SiC) Three different types of SiC coatings (stoichiometric SiC
SiC with excess silicon and SiC with excess carbon) produced on spherical particles
by FBCVD were analysed The VIF fracture toughness (measured on the polished
external surface) in these three coatings investigated in this study was observed to
vary between 35 and 49 MPa m12
The results have shown that the VIF fracture
toughness is influenced by the microstructure and non-stoichiometry of SiC coatings
For FBCVD SiC coatings a high VIF fracture toughness accompanied with superior
hardness was attributed to the formation of micro-cracks The difference in VIF
fracture toughness was proposed to be dominated by the laminar defects and grain
morphologies in the SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
127
45 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo and D A Petti
Handbook of SiC properties for fuel performance modeling J Nucl Mater 371
(2007) 329-77
[2] N Swaminathan P J Kamenski D Morgan and I Szlufarska Effects of grain
size and grain boundaries on defect production in nanocrystalline 3C-SiC Acta
Mater 58 (2010) 2843-53
[3] G K Miller D A Petti D J Varacalle and J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[4] D A Petti J Buongiorno J T Maki R R Hobbins and G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[5] K Bongartz E Gyarmati H Schuster and K Tauber Brittle Ring Test - Method
for Measuring Strength and Youngs Modulus on Coatings of Htr Fuel Particles J
Nucl Mater 62 (1976) 123-37
[6] K Bongartz E Gyarmati H Nickel H Schuster and W Winter Measurement of
Youngs Modulus and Fracture Stress on Htr Particle Coatings by Brittle Ring Test
J Nucl Mater 45 (1972) 261-64
[7] M W Kim J H Kim H K Lee J Y Park W J Kim and D K Kim Strength
of chemical vapor deposited silicon carbide films using an internal pressurization
test J Ceram Process Res 10 (2009) 373-77
[8] T S Byun J D Hunn J H Miller L L Snead and J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[9] X Zhao R M Langford J Tan and P Xiao Mechanical properties of SiC
coatings on spherical particles measured using the micro-beam method Scripta
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
128
Mater 59 (2008) 39-42
[10] E Lopez-Honorato P J Meadows J Tan and P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[11] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram and P Xiao Youngs modulus measurements of SiC coatings on
spherical particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[12] ACKadak RGNallinger MJDriscoll SYip DGWilson HCNo JWang
HMaclean TGalen and CWang et al Modular Pebble Bed Reactor Project
University Research Consortium Annual Report Beijing 2000
[13] J I Federer Parametric Study of Silicon-Carbide Coatings Deposited in a
Fluidized-Bed Thin Solid Films 40 (1977) 89-96
[14] G R Anstis P Chantikul B R Lawn and D B Marshall A Critical-Evaluation
of Indentation Techniques for Measuring Fracture-Toughness 1 Direct Crack
Measurements J Am CeramSoc 64 (1981) 533-38
[15] M T Laugier Palmqvist Toughness in Wc-Co Composites Viewed as a Ductile
Brittle Transition J Mater Sci Lett 6 (1987) 768-70
[16] M T Laugier Palmqvist Indentation Toughness in Wc-Co Composites J Mater
Sci Lett 6 (1987) 897-900
[17] W D Nix and R Saha Effects of the substrate on the determination of thin film
mechanical properties by nanoindentation Acta Mater 50 (2002) 23-38
[18] J Lankford and D L Davidson Crack-Initiation Threshold in Ceramic Materials
Subject to Elastic-Plastic Indentation J Mater Sci 14 (1979) 1662-68
[19] Z Li A Ghosh A S Kobayashi and R C Bradt Indentation
Fracture-Toughness of Sintered Silicon-Carbide in the Palmqvist Crack Regime J
Am CeramSoc 72 (1989) 904-11
[20] H Hatta M Zoguchi M Koyama Y Furukawa and T Sugibayashi
Micro-indentation method for evaluation of fracture toughness and thermal
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
129
residual stresses of SiC coating on carboncarbon composite Adv Compos Mater
12 (2003) 155
[21] C B Ponton and R D Rawlings Vickers Indentation Fracture-Toughness Test 1
Review of Literature and Formulation of Standardized Indentation Toughness
Equations Mater Sci Tech Ser 5 (1989) 865-72
[22] H Zhang E Lopez-Honorato A Javed X Zhao and P Xiao Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc In Press (2011)
[23] A Leonardi F Furgiuele S Syngellakis and R J K Wood Analytical
Approaches to Stress Intensity Factor Evaluation for Indentation Cracks J Am
Ceram Soc 92 (2009) 1093-97
[24] M C Osborne J C Hay L L Snead and D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[25] R D Dukino and M V Swain Comparative Measurement of Indentation
Fracture-Toughness with Berkovich and Vickers Indenters J Am CeramSoc 75
(1992) 3299-304
[26] K H Park S Kondo Y Katoh and A Kohyama Mechanical properties of
beta-SiC after Si- and dual Si plus He-ion irradiation at various temperatures
Fusion Sci Technol 44 (2003) 455-59
[27] S Nogami S Ohtsuka M B Toloczko A Hasegawa and K Abe Deformation
during surface modification of silicon carbide using rare-gas ion-beam irradiation
Pricm 4 Forth Pacific Rim International Conference on Advanced Materials and
Processing Vols I and Ii 1367-70 3028 (2001)
[28] G D Quinn and R C Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[29] J Tan Mechanical properties of SiC in TRISO fuel particle PhDThesis
University of Manchester Manchester 2010
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
130
[30] K Kaneko M Kawasaki T Nagano N Tamari and S Tsurekawa
Determination of the chemical width of grain boundaries of boron- and
carbon-doped hot-pressed beta-SiC by HAADF imaging and ELNES line-profile
Acta Mater 48 (2000) 903-10
[31] B Reznik D Gerthsen W G Zhang and K J Huttinger Microstructure of SiC
deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499-508
[32] R A Shatwell K L Dyos C Prentice Y Ward and R J Young Microstructural
analysis of silicon carbide monofilaments J Microsc-Oxford 201 (2001) 179-88
[33] M J Hernandez G Ferro T Chassagne J Dazord and Y Monteil Study of
surface defects on 3C-SiC films grown on Si(111) by CVD J Cryst Growth 253
(2003) 95-101
[34] D S Harding W C Oliver and G M Pharr Cracking during nanoindentation
and its use in the measurement of fracture toughness Thin Films Stresses and
Mechanical Properties V 356 (1995) 663-68
[35] ACFischer-Cripps Introduction to contact mechanics Springer New York
2000
[36] DJGreen An introduction to the mechanical properties of ceramics Cambridge
University Press Cambridge 1998
[37] S B Biner A Numerical-analysis of crack-growth in microcracking brittle solids
Acta Metall Mater 42 (1994) 3643-51
[38] K H Park T Hinoki and A Kohyama Influence of irradiation-induced defects
on fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[39] H Horii and S Nematnasser Brittle failure in compression - splitting faulting
and brittle-ductile transition Philos T Roy Soc A 319 (1986) 337-74
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
131
CHAPTER 5 Influence of Interfacial Roughness on Fracture
Strength of SiC Coatings
51 Introduction
During the irradiation process of TRI-Isotropic (TRISO) fuel particles the high
tensile stress could be accumulated at crack tips These tips were due to direct
penetration of the cracks formed in the PyC layer or the high stress concentration as a
result of the debonding of IPyCSiC interface [1 2] When the tensile stress inside of
the particle exceeded the critical fracture stress of the SiC coating it caused the
failure of the whole particle [3] Furthermore the fracture strength is a main
parameter used in modeling the probability of failure of fuel particles so it is
important to measure the fracture strength of SiC to determine their performance
which is determined from the maximum tensile stress
Different methods such as hemi-spherical bending [4] crush test [5 6] and inner
pressure [6] were introduced to measure the fracture strength of SiC coating in
TRISO fuel particle The fracture strength was in a range and could be characterised
by the Weibull distribution function [4-6] The common vague conclusion derived
from previous results is the significant effect of the IPyCSiC interface on the fracture
strength [4-6] The interface was also found to affect the primary failure mechanism
by determining if the load can transmit through the SiC [6] Previous analyses are
consistent with the well-known prescription that the fracture strength of ceramic
materials varies largely and it is dependent on the size and surface condition of the
specimen [7-9] Among these methods the latest modified crush test proposed by
Byun et al[510] showed a well controlled scatter of the fracture strength in a given
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
132
sample
Although the importance of the interface has been noticed the lack of an accurate and
scientific description of the interface has limited the further study about its
relationship with the fracture strength Roughness is a commonly used terminology to
describe the interface and it could be measured by atomic force microscope and
characterised by the standard deviation of the vertical features [11 12] However
roughness is not enough to describe the interface and to relate it to fracture strength
[13] Due to the importance of the statistical analysis for ceramic materials the
self-affine theory was used to characterise the complex interface numerically
according to previous studies [14-17] A self-affine interface is characterised by a
correlation length the saturation roughness and the roughness exponent [18] A
similarly straightforward approach was applied to demonstrate the importance of the
interfacial roughness on the mechanical properties [19] showing that interfaces with
big and sharp irregularity fail first
In this work the modified crush test was used to measure the fracture strength of a
SiC layer deposited at different temperatures The IPyCSiC interface was well
described by self-affine theory Therefore the effect of the IPyCSiC interface and
dimension of particles together with other possible influences such as porosity and
grain size on the fracture strength were discussed The improvement of this work is
being able to do statistical analysis on the interfacial roughness
52 Experimental details
521 Materials
In this Chapter the buffer pyrolytic carbon and dense pyrolytic carbon coatings were
deposited on the top of ZrO2 kernel (~ Φ500 μm) by fluidized bed chemical vapour
deposition Thirteen SiC coatings were deposited at different temperature flow rate
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
133
MTS concentration and added gas as shown in Table 51 The deposition conditions
were chosen according to previous studies to get different microstructures and more
deposition mechanisms of SiC coating can be found in Ref [20] For fracture strength
measurement the SiC particles were mounted with thermoplastic resin and ground to
about 55 portion of the sphere and polished using increasingly fine diamond
suspensions until frac14 μm SiC shells were released from surrounded PyC layers by
oxidizing at 700 ordmC for 8 hours and further washed in an ultrasonic bath with acetone
for 5 minutes
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Sample Temperature
(ordmC)
MTS
(vol )
Added gas concentration Flow rate
(LMin)
Radius
Thickness (~)
S1 1300 91 05vol C3H
6 600 72
S2 1300 91 01vol C3H
6 600 76
S3 1280 91 01vol C3H
6 600 83
S4 1300 91 -- 600 85
S5 1400 19 57vol Ar 778 87
S6 1500 22 82vol Ar 700 90
S7 1500 19 89vol Ar 778 101
S8 1500 22 79vol Ar 700 112
S9 1400 19 57vol Ar 777 117
S10 1300 19 57vol Ar 778 129
S11 1500 19 89vol Ar 777 151
S12 1500 22 76vol Ar 700 158
S13 1500 19 57vol Ar 778 190
The difference between sample S5 and S9 S7 and S11 is the thickness of the PyC layer MTS
methyltrichlorosilane Lmin the flow rate measured in liter per minute To produce SiC coatings with
particular microstructures and compositions different deposition conditions were chosen which were
contributed to Dr Eddie Lopez-Honorator
522 Test method and analysis
The crush test taking the contact area into consideration was used in this study [2 5
21] and the loading profile of the crush system is shown in Fig 51 When a partial
spherical shell (Radius R thickness t) was diametrically loaded by an external load F
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
134
concentrated on a small circular area (radius 0 ) the maximum membrane stress and
bending stress could be calculated by the equations developed by Roark and Young
[21] The combination of the maximum bending and membrane stress (Local fracture
strengthL
f ) in the inner side of the shell was the maximum fracture strength for
partially loaded shell (around 55 of the sphere)
The fracture strength of brittle SiC coating is best considered as a distribution rather
than a fixed number and the most widely used expression for characterisation is the
cumulative distribution functionmdashWeibull distribution function [7 22] In the current
study the distribution of local fracture strength and fracture strength for a full
spherical shell were characterised by the Weibull distribution The Weibull modulus m
is derived from the local fracture strength (Eq 14 in Chapter 2) The calculation of the
fracture strength for the full spherical shell (F
f ) is based on the size effect (scaling
factor mtRr 122
0 ))(4( R radius of the particle t thickness of SiC shell 0
radius of residual impression after loading) which is equal to the partial strength
divided by the scaling factor [5 7] More details about fracture strength calculation
are available in Ref [5]
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
According to a previous study [5] one reason for the difference of local fracture
10 ordm
t
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
135
strength in a given batch of coating is due to different sizes of residual impression
( 0 ) under which the distribution of defects could be different To reduce the
influence of the 0 the radius (R) at the edge of the residual impression was kept at
an angle of around 10ordm (as shown in Fig 51) from the loading axis by inserting
different kind of soft metal It varied slightly (the ratio of standard deviation to mean
value is around 10) in each batch of SiC
The crush test was carried out in a universal tensile machine INSTRON 5569
(INSTRON High Wycombe Bucks) with a 100 N maximum load cell For each batch
of SiC shell (except for S13) at least 30 specimens were tested at room temperature
with a crosshead speed of 0005 mms The failure load recorded by the tensile
machine was used as the fracture load The individual impression left on the soft
metal (Nickel alloy cold worked copper or brass) was marked under corresponding
load and its diameter was measured by optical microscope (times100 ZESIS Company
German)
523 Characterisation methods
A Philips XL30 FEG-SEM (Philips Eindhoven Netherlands) was used to characterise
IPyCSiC interfacial roughness grain size and porosity from the finely polished cross
section of SiC coatings Characterisation of the IPyCSiC interfacial roughness was
realized by editing the SEM images (in the magnification of times1600) with the Image J
software and extracted it as a line from the background SEM image The interfacial
roughness could be described by a series of pairs of x (distance tangential to the
interface) and y (distance normal to the interface) coordinates assuming the interface
is flat at a scale of 70 microm
Porosity was measured by controlling the threshold of SEM images (times1600 TIF) at a
gray level and adjusted to distinguish pores from grains with the Image J software
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
136
Pore fraction was defined as the ratio of the pores and the total area of the SEM image
Grain size of FBCVD SiC coatings varied in a range and in a columnar shape It was
characterised by measuring mean width and length of single crystals from SEM
images (times6400) and the grain size of the coatings is represented by the mean width
timeing the length of grains A FEG-TEM (TecnaiTM G2
F30 U-TWIN) was used to
observe the IPyCSiC interfacial roughness and TEM samples were prepared by
focused ion beam milling The linear regression method was used to analyze and
quantify the influences of parameters on the fracture strength and Weibull modulus
53 Results and discussions
531 Fracture strength and dimensional effect
Table 52 gives the summary of the measured and calculated parameters for all the
coatings It includes the diameter of impression (mean value 2 0 ) force (mean value
F) Weibull modulus (derived from local fracture strength m) local fracture strength
(L
fmean value) and fracture strength for the full spherical shell (
F
fmean value)
Table 52 Summary of measured and calculated parameters for all the coatings
Sample 2 0 μm F N L
f MPa Modulus (m) Scaling Factor
For Size Effect
F
f MPa
S 1 15239 2235 1784 7397 185 963
S 2 15043 1999 1599 7687 183 872
S 3 14898 1540 1446 7459 187 774
S 4 16052 2042 1620 8261 178 908
S 5 17018 2573 1810 7927 178 1018
S 6 16220 1885 1648 6953 193 855
S 7 14662 1691 1974 7755 190 1019
S 8 14905 1336 1717 7102 198 868
S 9 13040 1088 1825 6495 223 820
S10 16410 1215 1472 6801 204 722
S11 16165 1006 1430 6104 219 652
S12 14677 903 1512 6616 205 737
S13 11586 489 1762 4912 300 587
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
137
As given in Table 52 a significant difference (49-257 N) of the load among SiC
coatings was obtained According to a previous study [5] the variation is mainly
caused by different thicknesses (varied from 30 μm to 60 μm) of SiC coatings
because the relatively thin coating tends to reach higher strength concentration at
fracture
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
The Weibull modulus derived from the local fracture strength (as given in Fig 52) is
in the range of 49-86 (as shown in Table 52) and it falls into the category of moduli
for ceramics materials (from 5 to 30) This range of Weibull modulus is similar to the
values obtained from the brittle ring tests which also gave a similar range of the local
fracture strength [23 24] In different batches of SiC coatings it was found that the
Weibull modulus decreases linearly with the increase of the ratio of outer radius (R) to
the thickness of SiC coatings ( tR ) as shown in Fig 53 The ratio of Rt accounts
for up to 778 (2R from linear regression) of differences of the modulus This is
because the tR ratio is a critical dimension value for the strength distribution of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
138
SiC shell and it represents the relative thickness of SiC coating The higher the ratio
is the thinner the SiC coating So it corresponds to the larger inner surface area
resulting in larger scattering sizes of the critical flaws This observation is consistent
with the previous finite element modeling results showing that the Weibull modulus is
related to the sample dimension [10]
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
As given in Table 52 the scaling factor (effective area-parameter based on the local
fracture strength) between the local fracture strength and the fracture strength of the
full shell are in the range of 18-30 The results are consistent with Byun et alrsquos study
(19-31) [5] and it indicated the importance of the size effect on the fracture strength
of the full shell
The fracture strength for the full spherical shell of thirteen SiC coatings were given in
the form of Weibull plots as shown in Fig 54 The mean fracture strength for the full
spherical shell was in the range of 587-1019 MPa (as given in Table 52) which is
higher than the range of 330-650 MPa obtained by Byun et al [5] This is because the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
139
Rt ratio (above 11) in Ref [5] falls into the higher value categary in current work as
shown in Fig 53
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Because the Weibull modulus is dominated by the tR ratio (Fig 53) its influence on
fracture strength for a full spherical shell could also be from this ratio as shown in
Fig 55 It shows that the fracture strength for the full shell decreases nearly linearly
with the increase of the tR ratio which produces a difference of 6528 (2R derived
from linear curve fit which represents fair agreement) of differences In this work the
similar range of Rt ratio (above 11) corresponds to the fracture strength lower than
850 MPa (as shown in Fig 55) which reduced the difference from previous results
[5] Furthermore the fracture strength of about 1000 MPa was obtained when the Rt
was about 8 [25] and it is similar as the result given in Fig 55 This again
demonstrated the importance of the geometry on the fracture strength of SiC coating
Therefore it is important to eliminate the external influence and study the influences
of microstructures such as interfacial roughness porosity and grain size on fracture
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
140
strength which are discussed in the following parts
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
532 Observe and qualify the effect of interfacial roughness on fracture strength
According to Griffith fracture theory the fracture strength (L
f ) is a function of the
critical flaw size (C) and the fracture toughness ( ICK ) as shown in the following
equation [26]
12( )
L ICf
K Z
Yc (1)
Y is a loading geometrical parameter Z is the flaw size parameter The magnitude of
the critical flaw size could be related to the IPyCSiC interfacial irregularities
The interfacial flaw shape of SiC coatings is modeled from the surface morphology of
PyC coating during deposition process as shown in Fig 56(a) The crack was taken
as a semi-circular surface crack as given in Fig 56(b) where Y is 2 and Z is 16 (Y
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
141
Z are geometrical constants introduced in Eq (1) [26] The fracture toughness of SiC
coatings in TRISO fuel particle was taken to be 33 MPamiddotm12
according to previous
report [27] Taking the result of the local fracture strength from individual SiC coating
into Eq (1) the magnitude of the critical flaw size C could be obtained
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Figure 46 shows the redraws of the IPyCSiC interfacial roughness from SEM images
and the calculated critical flaw sizes according to Eq (1) (range and mean values) for
all specimens are given in the right columns If the fracture initiated at the IPyCSiC
interface as proposed in previous studies [4-6] the calculated critical flaw size range
of each type of SiC coating was expected to match the size range of the interfacial
irregularities
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
142
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
In Fig 57 most of the calculated critical flaw sizes according to Eq (1) are in the
same magnitude as the flaw size observed directly from the interfacial profile images
and this indicates that the dominant effect of the surface roughness on the local
fracture strength For example the direct observation of the biggest flaw size from the
profile is about 43 μm and 26 μm in sample S9 and S13 respectively and they are in
the range of the calculated defect sizes of 09-65 μm and 17-47 μm for S9 and S13
respectively However exceptions were found such as specimens S1 and S2 which
show slightly higher calculated surface flaw size than the observation from SEM
images Furthermore it is difficult to accurately characterise the difference of the
interfacial roughness by observing the converted images and give specific
information (such as shape) of single profile (shown in Fig 57) The estimation of
the shape of surface irregularities to be half-circular could also result in the error on
the critical flaw size calculation [7] To give a direct estimation about the influence of
interfacial roughness on local fracture strength the scaling behavior of IPyCSiC
interface need to be characterised by a statisticalnumerical method
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
143
533 Characterise and quantify the interfacial roughness
Self-affine theory has become a standard tool in the study of various rough interfaces
[18 28 29] Here it was the first time being proposed to describe the IPyCSiC
interfacial roughness accurately and scientifically and then was used to quantify the
relationship between interfacial roughness and local (intrinsic) fracture strength and
fracture strength of the full shell
5331 Self-affine theory introduction and experimental setup
In order to describe the IPyCSiC interfacial roughness with specific parameters an
easy way is using a height-height function [29 30]
2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)
where the x axis is along the IPyCSiC interface and ( )h x is the surface height profile
The amplitude of the roughness ( )h x is correlated with the length scale x and
lt gt denotes the spatial average over ( )h x in a planar reference surface If the
interfacial roughness of IPyCSiC were self-affine the correlation of x and
h should follow the power law relationship (Eq (2)) and it could be obtained by the
log-log plot of x and h The (for self-affine surface 0lt lt1) is the roughness
exponent and it describes the degree of surface roughness at short length scales [31]
This short length scale is shorter than correlation length ξ which is another parameter
used to describe the self-affine surface (besides the surface roughness h and
roughness exponent ) It is the average distance between the features in the surface
profiles within which the surface variations are correlated [28] Therefore the small
(close to 0) characterises extremely jagged or irregular interfaces while large
value characterise interface with smooth hills and valleys [32]
For all the samples the scaling properties of IPyCSiC interface (as shown in Fig 57)
are characterised by their one-dimensional height-height correlation function Eq (2)
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
144
The characteristic parameters of the digitalized IPyCSiC interfacial roughness are as
follows The resolution between two points along x axis is 020833 μm and x
changes by timing the resolution with integer (1 2 3hellip15) According to previous
self-affine theory study [16] the number of recorded points along the x axis was
taken in the range of 250-400 in this work corresponding to the length of 50-70 μm
for different IPyCSiC interfaces
5332 Results of self-affine theory
Figure 58 is a log-log plot showing the variation of h as a function of the distance
x for three SiC coatings The h varied as a power law of x (solid line ) when
x ltξ while remained nearly constant ˗ saturation roughness (σ0 dashed parallel
lines) for x gtξThese results indicated that these three IPyCSiC interfacial
roughness were self-affine with the roughness exponent of around 063-067 For the
rest of the samples the same scaling characterisation method was used Theξ σ0 and
are given in Table 53
Fig 58 Log-log representation of the height-height correlation function h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
ξ3 ξ12 ξ6
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
145
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Sample σ0 (μm) ζ ξ(μm) σ0ξ
S 1 02378 05903 06250 03804
S 2 04142 06950 08333 04971
S 3 06701 06673 16666 04021
S 4 06825 05244 14583 04680
S 5 05271 06308 14581 03615
S 6 08500 06343 20833 04080
S 7 04293 05162 14583 02944
S 8 07452 05107 14583 05110
S 9 05453 06099 12500 04362
S10 06953 05490 13044 05330
S11 05806 04949 10417 05574
S12 07584 06899 16666 04550
S13 05522 02971 18750 02945
The roughness exponent values for the 93 of IPyCSiC interface were in the range
of 05-07 (as shown in Table 53) This indicated the self-affine measurement is
reliable according to Schmittbuhl and Vilottersquos review [14] which showed that this
range of roughness exponents could have the minimum characterisation errors
Furthermore these roughness exponents are comparable except specimen S13 and it
was consistent with the observation of the interfacial roughness (Fig 57) in which
only specimen S13 showed the high degree of high frequency and short wavelength
irregularities (the dark pits in S13 profile) According to previous study [31] the
concentration of the roughness exponent values could be attributed to the same
original mechanism of the IPyCSiC interface which was produced by the FBCVD
under different conditions As a result the different roughness exponent value could
not describe the difference of the IPyCSiC interface
As shown in Table 53 the saturation roughness (σ0) and correlation length (ξ) are in
the range of 024-085 μm 063-208 μm respectively (Table 53) According to
previous studies [16 17 30] the σ0 and ξ couldnrsquot represent the interfacial
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
146
irregularities correlated with the critical flaw size Because the σ0 value range was
nearly one magnitude lower than the calculated critical flow size (mean value range of
2-4 μm) and the dimension of ξ was perpendicular to the calculated critical flaw size
direction Furthermore it was found that σ0 and ξ values were correlated to the sample
size (recorded points) [16] With the increase of the sample size for the same profile
both the ξ and the σ0 values increased and indicated these two parameters may not be
intrinsic properties of the samples However the roughness ratio σ0ξ is constant
which was found in both the current work and previous study [16]
As a result of above discussions the roughness ratio of σ0ξ was proposed to
characterise the interfacial roughness which could represent the sharpness of the
interfacial irregularities according to Ref [30] For example the low ξ value
corresponded to narrow surface irregularity when the σ0 and values were the same
With the increase of the σ0 value the surface irregularity became deep and narrow
which was hazard to the mechanical properties according to previous simulation work
on the fracture strength of SiC coatings [22] The above observations and analysis
results are supported by previous study [31] when length scale x gt ξ (shown in
Fig 58) the roughness ratio σ0ξ describes mainly the long-wavelength roughness
characteristics which could be statistically equal to the effect of the critical flaw size
on fracture strength
534 Quantify the influence of interface roughness on fracture strength
Figure 59 gives the influence of roughness ratio on the local fracture strength and it
contributes to nearly 50 (R2 from linear regression) of variation of the local fracture
strength It shows that the local fracture strength decrease linearly with the increase of
the roughness ratio This result approves previous findings about the importance of
the interfacial roughness [4-6] and is correlated with the Griffth fracture theory (Eq
(1)) about the importance of the shape and dimension of critical flaws Furthermore
the relation between interfacial roughness has been characterised quantitatively and a
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
147
linear relationship between roughness ratio and local fracture strength is proposed
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Except for the interfacial roughness the local fracture strength could also be affected
by the fracture toughness as shown in Eq (1) Although Vickers-indentation fracture
behavior of SiC coatings was different due to the laminar defects and grain
morphology [33] the fracture toughness of SiC was found to be insensitive to the
microstructure of materials [34] This could be attributed to the fact that
Vickers-indentation provided a static propagation of the crack while the real fracture
toughness was measured dynamically In this work the fast fracture process could
overtake the effect of microstructure on the different static fracture behaviour [5 25]
Since porosity and grain size were main microstructural variations in SiC coatings [1]
their effects on fracture strength were estimated
The characterisation and quantification of grain size and porosity were shown in Table
54 The grain size was found to have no effect on fracture strength according to
previous studies [5] which was also indicated from the regress analysis (R2 is close to
0) No influence was found by regressing the local fracture strength on pores
Therefore the dominant influence on the local fracture strength is from the roughness
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
148
ratio
Table 54 Results and variations influences on fracture strength for SiC coating
Specimen S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S10 S11 S12 S13
Grain size
(μm2)
04 06 06 08 20 20 20 28 20 08 20 28 25
Porosity
(Area )
0 0 0 0 05 04 12 09 03 0 08 21 20
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
Because the fracture strength for a full spherical shell is a function of the Weibull
modulus and local fracture strength [5] it was affected by factors such as the
dimension ratio of thickness to radius of the coating (as shown in Fig 55) the
roughness ratio (as shown in Fig 510) Figure 510 shows the influence of roughness
ratio on fracture strength of the full shell The linear relationship was found in 12
samples as indicated by the dashed line in Fig 510 and it could explain about 68
(2R from linear regression) of difference in fracture strength of the full particle The
high roughness ratio would decrease the fracture strength of the full shell linearly The
deviated point of sample S13 could be due to its largest Rt ratio (as shown in Fig
55) which may have over taken the effect of the roughness ratio (Work about the size
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
149
effect on the fracture strength has being carried out)
54 Conclusions
The fracture strength of SiC coatings deposited under different conditions were
measured by the modified crush test and analyzed by the statistical analysis (Weibull
function and Self-affine theory) The influences on fracture strength were studied
such as the IPyCSiC interfacial roughness specimen size and porosities Following
results were obtained
(1) Weibull modulus and fracture strength of the full shell were significantly affected
by the ratio of radius to thickness of SiC coating and both of them decrease
linearly with the increase of the ratio
(2) The dominant effect of the IPyCSiC interfacial roughness on intrinsic fracture
strength was found by matching the SEM images with the calculated critical flaw
size based on the Griffith fracture theory
(3) The interfacial roughness were successfully characterised by a
numericalstatistical method and the roughness ratio representing the shape of the
irregularities was proposed to be a unique parameter among different coatings
(4) The difference of the local fracture strength was dominated by the roughness ratio
and it decreased linearly with the increase of the roughness ratio It is been the
first time that the interfacial roughness was numerically related to the fracture
strength
(5) Microstructures such as grain boundaries and porosity were found to have
neglectable influence on fracture strength
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
150
55 References
[1] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[2] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the tri-isotropic-coated fuel particle J
Am Ceram Soc 90 (2007) 184-91
[3] T Nozawa L L Snead Y Katoh J H Miller E Lara-Curzio Determining the
shear properties of the PyCSiC interface for a model TRISO fuel J Nucl Mater
350 (2006) 182-94
[4] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
Fuel Particles for High-Temperature Gas-Cooled Reactors J Am Ceram Soc 56
(1973) 36-41
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[6] S G Hong T S Byun RA Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the TRI-Isotropic-coated fuel particle
J Am Ceram Soc 90 (2007) 184-91
[7] D J Green An introduction to the mechanical properties of ceramics Cambridge
solid state science series Cambridge Cambridge University press 1998
[8] R Danzer Some notes on the correlation between fracture and defect statistics
Are Weibull statistics valid for very small specimens J Eur Ceram Soc 26
(2006) 3043-49
[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
Transgranular Cleavage J Mech Phys Solids 34 (1986) 477-97
[10] J W Kim T S Byun Y Katoh Optimization of fracture strength tests for the
TRISO layers of coated fuel particles by finite element analysis 33rd international
conference on advanced ceramics and composites Daytona Beach FL2009
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
151
[11] W N W Chen X Nie A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
Ceram Soc 92 (2009) 1287-95
[12] R T Wu X Wang A Atkinson On the interfacial degradation mechanisms of
thermal barrier coating systems Effects of bond coat composition Acta Mater 58
(2010) 5578-85
[13] X Nie W N W Chen A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
Ceram Soc 92 (2009) 1287-95
[14] J Schmittbuhl J P Vilotte S Roux Reliability of Self-Affine Measurements
Phys Rev E 51 (1995) 131-47
[15] J T M De Hosson G Palasantzas Roughness effect on the measurement of
interface stress Acta Mater 48 (2000) 3641-45
[16] L Ponson H Auradou M Pessel V Lazarus J P Hulin Failure mechanisms
and surface roughness statistics of fractured Fontainebleau sandstone Phys Rev
E 76 (2007) 036108-14
[17] L Ponson H Auradou P Vie J P Hulin Low self-affine exponents of
fractured glass ceramics surfaces Phys Rev Lett 97 (2006) 125501-4
[18] F Spaepen Interfaces and stresses in thin films Acta Mater 48 (2000) 31-42
[19] W G Sloof T S Hille T J Nijdam A S J Suiker S Turteltaub Damage
growth triggered by interface irregularities in thermal barrier coatings Acta Mater
57 (2009) 2624-30
[20] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[21] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[22] G K Miller D A Petti J T Maki D L Knudson An evaluation of the effects
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
152
of SiC layer thinning on failure of TRISO-coated fuel particles J Nucl Mater
355 (2006) 150-62
[23] K Bongartz E Gyarmati H Schuster KTauber The brittle ring test A method
for measuring strength and Youngrsquos modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[24] K Minato K Fukuda K Ikawa Strength of silicon-carbide coating layers of
fuel Pparticles for high-temperature gas-cooled reactors J Nucl Sci Tech 19
(1982) 69-77
[25] J W Kim T S Byun Y T Katoh Optimization of fracture tests for the SiC
layer of coated fuel particles by finite element analysis Ceram Nucl Appl DOI
1010029780470584002 ch13 2010
[26] S Gonzalez B Ferrari R Moreno C Baudin Strength analysis of
self-supported films produced by aqueous electrophoretic deposition J Am
Ceram Soc 88 (2005) 2645-48
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] B N Dev A Roy K Bhattacharjee H P Lenka D P Mahapatra Ge growth
on self-affine fractal Si surfaces influence of surface roughness J Phys D Appl
Phys 42 (2009) 145303-10
[29] J Feder Fractals Plenum New York 1988
[30] J T M De Hosson R Van Tijum Effects of self-affine surface roughness on the
adhesion of metal-polymer interfaces J Mater Sci 40 (2005) 3503-08
[31] G Palasantzas Roughness spectrum and surface width of self-affine fractal
surfaces via the K-correlation model Phys Rev B 48 (1993) 14472-78
[32] P Meakin Fractals scaling and growth far from equilibrium Cambridge
Cambridge University Press 1998
[33] H Zhang E Loacutepez-Honorato A Javed I Shapiro and P Xiao A study of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
153
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc 95 (2012) 1086-92
[34] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany and A H
Heuer Fracture toughness of polycrystalline silicon carbide thin films Apply
Phys Lett 86 (2005) 071920-22
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
154
CHAPTER 6 Effect of Thermal Treatment on
Microstructure and Fracture Strength of SiC Coatings
61 Introduction
The mechanical properties of the as-deposited SiC coatings have been widely studied
eg Youngrsquos modulus and hardness [1-3] fracture toughness [4] and fracture strength
[5] etc However after it experiences the high temperature the composition and the
microstructure of the SiC coating may change which consequently influences the
mechanical properties It has been found that mechanical properties of SiC such as
Youngrsquos modulus and hardness are less affected when experiencing the current fuel
operation temperature (less than 1600 ordmC) [1 6] even after thermal treatment
temperatures of 1980 ordmC [7] To enhance the operational temperature of the high
temperature reactor in the future design it would be necessary to understand the
evolution of microstructure and mechanical properties of SiC coatings at even higher
temperature Some research [8-10] has been carried out to study the effect of high
temperature (more than 2000 ordmC) thermal treatment on the density and microstructure
of the fuel particle Itrsquos concluded that fuel failure and fission product release
dependent on SiC thermal stability at high temperature [9] Rooyen et al[11]
measured the annealing temperature effect on the fracture strength of SiC coatings It
is found that the fracture strength increases after thermal treatment at temperature up
to 2000 ordmC decreases in strength after thermal treatment at 2100 ordmC However no
clear explanation was given on this result
Due to the importance of the SiC on the safety of this fuel it is necessary to study the
thermal stability of SiC and characterise any change in microstructure and mechanical
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
155
properties It has been previously found that SiC deposited at 1300 ordmC with the
addition of propylene and methyltrichlorosilane as gas precursors not only have good
mechanical properties such as hardness and Youngrsquos modulus [3] fracture toughness
[4] but also have high silver and palladium diffusion resistance [12 13] Therefore in
this Chapter we thermally treated SiC coatings deposited at a range of temperature
(1300-1500 ordmC) at 2000 ordmC for 1 hour in argon atmosphere The change of fracture
strength and thermal stability of SiC coating were studied in terms of composition and
microstructural change of the coatings after thermal treatment
62 Experimental details
Four batches of SiC coatings (with nearly stoichiometry) deposited by Fluidized bed
chemical vapour deposition at different tempearure were chosen to study the thermal
treatment effect on the evolution of the microstructure and fracture strength Table 61
gives the deposition conditions of coatings studied and symbols used to describe each
sample The stoichiometry was measured by the Raman spectroscopy (Renishaw 1000
Raman microprobe system with 514 nm Argon laser) The laser beam was focused on
the surface of the cross section through a times50 objective lens
Table 61 Deposition conditions of SiC coatings
Sample Temperature
(oC)
MTS concentration
(vol)
Added gas
concentration
Stoichiometry
SiC1 1280 91 01vol C3H6 SiC
SiC2 1300 91 01vol C3H6 SiC+C
SiC3 1400 19 57vol Ar SiC
SiC4 1500 22 79vol Ar SiC+C
The inner side of the coating is stoichiometric (23 of the thickness) while outside of the coating is
SiC with excess C The microstructure characterization was done in the inner side coating while the
fracture strength measurement is related to the full coating SiC+C means that the C peak around
1300-1500 cm-1
was observed in SiC coating Chosen of deposition conditions was contributed to Dr
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
156
Eddie Lopez-Honorato
The sample preparation for fracture strengths measurement is the same as described in
Chapter 5 As introduced before thermal treatment was carried out at 2000 ordmC for 1
hour in argon protected atmosphere on SiC half shells The same fracture strength test
and equipment settings as described in Chapter 5 were used in this Chapter
In addition to Raman spectroscopy the microstructure of SiC coatings before and
after thermal treatment was also characterised using X-ray diffraction (PW 1830
Philips) with a Cu Kα1 radiation source The XRD samples were the SiC segments
(fractured SiC shells without external residual stress) Scanning electron microscopy
(Philips XL30 FEG-SEM) was used to characterise the change in morphologies of
SiC coatings Porosity was measured by setting a threshold of the SEM images
(times1600 TIF) at a gray level and adjusted to distinguish pores from grains with Image
J software Three SEM images were measured for each SiC coating Average pore size
(diameter nm) and the pore fraction (area ratio of pores to the total area as observed
by SEM) were obtained For transmission electron microscopy (TEM) the specimens
were prepared by crushing the SiC shell and dispersing the fragments on a carbon
holy film copper grid and crystal structures were characterised using an FEG-TEM
(TecnaiTM G2
F30 U-TWIN)
63 Results
631 Fracture strength of SiC coatings
Figure 61 shows the Weibull distribution of the local fracture strength ( L
f ) in SiC
coatings before and after thermal treatment at 2000 ordmC It gives a direct observation on
the decrease of the local fracture strength in coating SiC2 SiC3 and SiC4 after
thermal treatment while the local fracture strength of coating SiC1 is nearly
overlapped with the as-deposited coating The magnitude of the mean local fracture
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
157
strength (as summarised in Table 62) could represent the decrease trend of the full
batch of the coating in current study
Fig 61 Weibull plots of local fracture strength ( L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
The Weibull modulus (m) was obtained by linearly fitting the curves shown in Fig 61
It shows that the Weibull modulus decreased by 14 07 and 21 in coating SiC1 SiC3
and SiC4 respectively however it increased slightly (by 12) in SiC2 after heat
treatment As shown in Fig 61 the Weibull modulus derived from linear fitting is
affected by the deviation of few points from the linear distribution of the local fracture
strength (as shown in Fig 61) For example in sample SiC3 the slightly decrease
could be attributed to the deviation of the lowest points According to previous study
[14] the slight decrease (07) of Weibull modulus in SiC3 could be neglected since
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
158
the deviated points could be caused by different failure mechanisms involved in the
fracture process [14]
Fig 62 Weibull modulus plots of fracture strength of the full shell ( F
f ) before
(black triangle) and after (red circle) thermal treatment
Figure 62 shows the Weibull plots of fracture strength of the full shell ( F
f ) before
and after thermal treatment at 2000 degC In the same batch of coatings (the same size
effect) the fracture strength of the full shell increase with the increase of the Weibull
modulus and local fracture strength according to previous study [5] Therefore the
decrease of local fracture strength and increase of the modulus in SiC2 could explain
the slight change (decreased 25 MPa obtained from Table 62) of the fracture strength
of the full shell after thermal treatment In the other three samples the fracture
strength of the full shell decreased significantly (more than 110 MPa obtained from
Table 62) after thermal treatment due to the decrease of local fracture strength and
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
159
unchanged modulus)
Table 62 summarized the results of the fracture strength measured before and after
thermal treatment at 2000 degC including the Weibull modulus (m) derived from the
distribution of the local fracture strength ( L
f ) the mean local fracture strength and
fracture strength of the full shell ( F
f ) After thermal treatment the mean local
fracture strength of coatings decreased significantly except SiC1 coating which
retained the same level as in as-deposited coating The mean fracture strength of the
full shell was reduced after thermal treatment in a different degree but the change of
Weibull modulus is more complex which shows both decreased and increased values
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the full shell before and after thermal
treatment
Sample m (from
L
f )
as deposited 2000degC
L
f MPa
as deposited 2000degC
F
f MPa
as deposited 2000degC
SiC1 75 61 1445 1421 774 660
SiC2 77 89 1599 1395 872 847
SiC3 65 58 1824 1333 820 548
SiC4 74 53 1717 1443 858 587
As concluded from Fig 61 Fig 62 and Table 62 the fracture strength decreases
less in coatings deposited at lower temperature (about 1300 degC) than those deposited
at higher temperature (1400-1500 degC) This is consistent with previous study about
high properties of SiC coatings deposited at low temperature such as the hardness
Youngrsquos modulus and resistance to the fission products [12 13 15]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
160
632 Change in morphologies
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after (c) and (d) SiC2 before and after
(e) and (f) SiC3 before and after (g) and (h) SiC4 before and after thermal treatment
Dashed and solid arrows indicate growth direction and pores respectively
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
161
Figure 63 gives the SEM images showing the microstructure of SiC coatings before
and after thermal treatment at 2000 ordmC Before thermal treatment no pores were found
in SiC1 and SiC2 coatings (Fig 63(a) and (c)) while nano-pores were found in SiC3
coating (Fig 63(e)) and even bigger (micrometres) pores were occasionally found in
SiC4 coating (Fig 63(g)) Among four as-deposited coatings SiC4 has highest area
fraction of pores (~09) followed by SiC3 (~03) coating (Fig 63 (a) (c) (e) and
(g) summarized in Table 63)
After thermal treatment at 2000 ordmC pores with different size and area fraction were
observed in all the coatings even though as-deposited SiC1 and SiC2 were free of
pores as shown in Fig 63(b) (d) (f) and (h) The amount of pores formed in treated
SiC1 coating (area fraction of ~05 ) is lower than the other three coatings which
have similar area fraction of pores (~14 ~13 and ~15 for SiC2 SiC3 and
SiC4 respectively given in Table 63) Similar to the content of the pores the pore
size (mean size of ~50 nm) in SiC1 is smaller than in the other coatings (gt 100 nm)
Among coatings SiC2 SiC3 and SiC4 much larger pores (micro-meter sized as in
Fig 63(f) and (h)) were produced in SiC3 and SiC4 coatings after thermal treatment
compared with nano-sized pores in SiC2 Furthermore it is found that most of pores
in coatings SiC2 SiC3 and SiC4 were formed along the grain boundaries and triple
junctions as we can see from Fig 63(d) (f) and (h)
The pores are uniformly distributed through the coatings and no area free of pores or
area with highly concentrated pores is observed However there are connections of
pores (2 or 3 pores formed closely) in SiC2 SiC3 and SiC4 as indicated by solid
arrows in Fig 63(d) (f) and (h) and the diameter of the porous connection zone
(black circle in Fig 63(d) (f) and (h)) could be in the magnitude of few micrometres
The connection of pores could easily become larger pores of few micrometres
diameter under external tensile strength due to the high strength concentration [14]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
162
Fig 64 The IPyCSiC interfacial roughness of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermally treated at 2000 degC (right
in each figure) The white arrow points towards to the interface irregularities (except
for thermally treated SiC4 coating (d)) black circle represents the pores in SiC
coatings
Figure 64 gives the evolution of interfacial roughness in different coatings after
thermal treatment at 2000 ordmC to study their influence on the change of fracture
strength Compared with the as-deposited coating the changes of the interfacial
roughness in SiC1 are similar to SiC3 which show the smoother interface with
interval of irregularities were observed Fig 64(a) and (c) However different from
as-deposited coatings with defects mainly at the interface defects (pores) are also
observed through the coating after thermal treatment (as seen in Fig 61(b) (f) and
Fig 64(a) (c)) Furthermore the size of pores is in the same magnitude as their
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
163
interfacial roughness (shown in Fig 64(a) and (c))
The change of the interfacial roughness in SiC2 is more significant than SiC1 and
SiC3 since pores formed as part of the interface (indicated by arrows in Fig 64(b))
and they are larger than the pores formed in the coating (circle in Fig 64(b))
Different from others three coatings the IPyCSiC interface of SiC4 becomes
smoother (Fig 64(e)) after thermal treatment compared with as-deposited coating so
the defects (pores) within the coating are bigger than surface irregularities
633 Evolution in microstructure
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermally
treated at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and
SiC2 inset shows the peak shift of as-deposited (dash line) and after thermal
treatment (solid line) (b) is SiC4 and inset is the high angle diffraction peak after
thermal treatment showing splitting while it is a single peak in as-deposited coating
Figure 65 gives XRD results of the as-deposited and thermally treated samples
which show the presence of the β-SiC in coatings The peak presents at 2θ~335ordm is
from the crystallographic errors which could either be due to the stacking faults or
the disordered α-SiC according to previous descriptions [16 17] It is found that the
intensity ratio of the 2θ~335ordm peak to the (111) plane peak (2θ~356ordm) decreased after
thermal treatment in all the coatings The coating SiC4 also shows the split of high
angle diffraction peaks (inset of the Fig 65(b) 2θ~613ordm and 713ordm) which is
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
164
attributed to the X-ray double diffraction and this implies the high crystallites after
thermal treatment
Figure 66 is the HRTEM image of sample SiC4 after thermal treatment in which the
stacking faults and micro twins could still be seen The stacking sequence of
ABCACBACBACB was observed as shown in the dashed square zone in Fig 66
According to study about crystal structure [18] this stacking sequence is supposed to
be the micro twins compared with the rest 3C stacking sequence rather than the
6H-SiC domain Furthermore the (111) peak shifted to the high angle after thermal
treatment in all the coatings as shown in the inset of Fig 65(a) which corresponded
to the decrease of the crystal constant
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Figure 67 gives the Raman spectroscopic results of SiC coatings before and after
thermal treatment The carbon peak at 1300-1600 cm-1
was found in the as-deposited
SiC2 and SiC4 coatings According to previous studies [4 19] the intensity ratio of
I1600I796 indicated that the estimated amount of excess C was less than 05 at in
this study The peak between TO and LO peaks (around 882 cm-1
) was attributed to
the stacking faults or highly disordered stacking faults cluster [3 15 20-22]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
165
After thermal treatment the weak carbon related peaks appeared at around 1395 cm-1
and 1600 cm-1
(G band) in sample SiC1 SiC2 and SiC4 The peak around 1395 cm-1
could represent the methyl group and amorphous carbon structures and G band is due
to the stretching mode of all pairs of sp2 atoms in chains and rings [23] The arising of
the 2D peak (also called G peak 2715 cm-1
) after thermal treatment was observed in
sample SiC2 SiC3 and SiC4 which is the second order of zone-boundary phonons
[24]Considering the amount of excess carbon in SiC coatings the symmetry of the
2D peak indicates that the carbon after treatment is more likely to be graphene rather
than graphite [24] which means the concentration of excess C is low in SiC coatings
It is also found that the intensity ratio of the disordered stacking faults (around 882
cm-1
) to the TO peak decreases in all samples after thermal treatment (shown in Fig
67)
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings The lower line is before thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
166
treatment and the upper line is after thermal treatment at 2000 degC in individual
sample
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
Sample Porosity ()
As 2000degC
Stoichiometry
As 2000degC
Critical Defects
As 2000degC
SiC1 0 05 0 C clusters Inter Inter+ Pore
SiC2 0 14 C clusters Ordered C Inter Inter
SiC3 03 13 0 Ordered C Inter Inter+ Pore
SiC4 09 15 C cluster Ordered C Inter Pore
First order Raman spectroscopy (1200-1600 cm-1
) Represents the carbon structure related to the
methyl group or amorphous carbon structures (contains SP2 and SP
3) [23] Second order (2700 cm
-1)
single layer grapheme related carbon materials [24]
Represents the interface irregularities
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
Furthermore the narrowing of the TO peak was found (the inset in Fig 67 (b)) in the
Raman spectroscopy Although it could be an overlap of two peaks at around 796 cm-1
and 789 cm-1
in coatings before and after thermal treatment the peak at 789 cm-1
corresponding to the stacking sequence of ABCACBhellip [25] is more likely to be
micro-twins in current study(as shown in Fig 66) Table 63 summarized the main
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
167
morphological and microstructural change of SiC coatings before and after thermal
treatment
Particularly for sample SiC3 except for the appearance of weak 2D peak after thermal
treatment without visible first order carbon peaks in the sample SiC3 the precipitates
were also observed from both inner and outside of the shell These precipitates were
demonstrated to be the single 3C-SiC crystal by Raman spectroscopy as shown in Fig
68 Raman spectra of precipitates represents the incident direction of the laser is
perpendicular to the SiC single crystal (111) plane which the LO mode at around 970
cm-1
is forbidden when Raman spectra were obtained in a backscattering geometry
[22] (The appearance of the forbidden LO band might be due to to finite collecting
angle of the spectrometer)
64 Discussion
641 Influence of interfacial roughness and pores on fracture strength
To evaluate the critical flaw size we used the equation 1
2( )
L ICf
K Z
Yc for tensile
strength (local fracture strength) and the case for the semi-circular surface crack
(Y=125 [26]) of radius c and inside holes (Y= π12
[14]) of diameter 2a When the
fracture toughness ( ICK ) of the SiC coating was taken as 33 MPa m-12
[27] the
critical surface defect radius and the diameter of the inside pores were calculated to be
in the range of 15 ndash 78 microm obtained from all the coatings The mean critical flaw
size is in the range of 30 ndash 40 microm after thermal treatment The calculated critical
flaw sizes are in the same magnitude as the defects observed at the IPyCSiC interface
and the pores in the SiC coatings after thermal treatment (see in Fig 63 and Fig 64)
Therefore the decrease of the local fracture strength after thermal treatment could be
related to the formation of these defects in SiC coatings Accordingly the sources of
critical defects were summarized in Table 63 for coatings before and after thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
168
treatment The interfacial roughness and pores within the coating compete to be the
critical flaws Once the size of interfacial irregularities is lower than critical flaw size
and rarely distributed their effect on fracture strength could be decreased or even
excluded according to previous study [14] Therefore the pores inside the coating
with the diameter of 2a would be considered as the main failure origins [14] These
could explain the decrease of local fracture strength in coatings SiC2 SiC3 and SiC4
which have micrometer pores formed within the coatings andor at the interface while
the local fracture strength is less affected in coating SiC1 due to formation of
nanometer pores
The Weibull modulus is related to the specimen size loading method and defects
distribution [5 14] In this study the specimen size and the loading morphology could
be excluded for one kind of SiC coating so the change of the modulus is due to the
degree of the scattering of the critical flaw size under the tensile strength The
interfacial irregularities in SiC2 became narrower and deeper (about 4 microm of depth as
shown in Fig 64(c)) after thermal treatment and they are also bigger than the pores
generated within the coating So the critical flaw in SiC2 after thermal treatments is
due to the interfacial irregularities (Table 62) with less scattered size under the
loading area than as-deposited coating which increased the Weibull modulus
However the critical defects in the other coatings include pores within the coatings
(shown in Fig 64 and Table 62) For example in SiC4 the critical flaw is only from
pores within the coating after thermal treatment due to the lack of interstitial
irregularities (Fig 64(h)) This enlarged the distribution of critical flaws after thermal
treatment which leads to the decrease of the Weibull modulus in different degree The
change of the fracture strength of the full shell depends on both Weibull modulus and
local fracture strength as discussed before [5] Our result showed that the SiC coating
deposited at low temperature of 1300 ordmC produced less critical flaws and smaller
decrease of the fracture strength of the full shell (see Table 63)
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
169
642 Mechanism of microstructural change
Changes in SiC coatings after thermal treatment include the formation of pores the
decreased intensity of the 2θ~335 ordm peak (crystallographic errors) in XRD the arising
of Raman peaks around 1395 cm-1
and 2715 cm-1
According to previous studies [8
10 21 25 28 29] we propose that these changes after thermal treatment could be
attributed to phase transformation or the diffusion of defects such as vacancies and
interstitials
If the 2θ~335ordm peak is from amorphous α-SiC its intensity ratio to (111) diffraction
peak would increase after heat treatment Because the presence of α-SiC phase in
β-SiC could promote the transformation of β-SiC into α-SiC [29] Conversely the
intensity of 2θ~335ordm peak decreased after thermal treatment in this work as observed
in Fig 65 and no α-SiC phase segregation (Fig 66) was found by HRTEM after
thermal treatment Furthermore the transformation from disordered α-SiC into β-SiC
after thermal treatment is also excluded because high pressure and high temperature
are needed for this process to happen [29] Therefore it is concluded that the 2θ~335ordm
peak derived from stacking faults and they could be annihilated at current
environment according to previous studies [8 28 30]
Stacking faults were surrounded by defects such as dislocations vacancies and
interstitials [10 15 31] so the high density of stacking faults in this work
corresponded to the high amount of native defects The annihilation of stacking faults
after thermal treatment indicated the reduction of these defects and it could reduce
the lattice constant In this work the decrease of the lattice constant was found after
thermal treatment as indicated by the peak shift of (111) plane in XRD results (Fig
65) and the crystallisation (ordering) was also reflected from the decreased intensity
of the 2θ~335ordm peak (Fig 65) and Raman defect peak (around 882 cm-1
) (Fig 67)
Therefore the formation of pores is due to the annealing of defects through the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
170
diffusion of vacancies or interstitials which are common even in high-purity CVD
SiC [32] However diffusion of native defects depended on their concentration which
was constrained by different composition of SiC (deviation from stoichiometry) [31]
For example for the C-rich cubic SiC the dominant defect is the CSi antisite (Si atom
site was occupied by C atom in tetrahedral structure) [31]
According to above analysis the formation mechanism of pores could be governed by
different kinds of defects In SiC1 coating the smallest and least content of pores
formed after thermal treatment is most likely caused by the annealing of stacking
faults surrounded by the dislocations and vacancies which is consistent with previous
study about the thermal treatment effect on stoichiometric SiC [28] In SiC coating
with excess carbon the microstructure evolution could be more complex as
demonstrated by the presence of the graphene layer (Raman peak at 2700 cm-1
)
According to previous studies [31 33] this is attributed to the existence of the CSi
antisite and vacancies which form the vacancy cluster and antisite clusters after
thermal treatment at 2000 degC
The microstructure change in SiC3 coating is different from SiC1 The diffusion
mechanism in SiC3 was supposed to be involved with the interstitials since the single
SiC crystal precipitate was found out of the coating(Fig 68) This also resulted in
higher amount of the pores in SiC3 than in SiC1 after thermal treatment It is
proposed that the different diffusion mechanism found in stoichiometric SiC1 (Si and
C vacancies) and SiC3 (tetragonal interstitials) could be due to different deposition
conditions which produced different kinds of dominant native defects The larger
pores formed in SiC3 and SiC4 could be due to larger grain size than SiC1 and SiC2
(different deposition temperature) because most of pores were near to the grain
boundaries and triple junctions (as shown in Fig 63(d) (f) and (h)) The diffusion of
native defects also affects the interfacial irregularities and the diffusion mechanism in
SiC coatings is being studied in our research group
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
171
65 Conclusions
The SiC coatings deposited at temperature range of 1300-1500 degC with composition
near-to the stoichiometry were thermally treated at 2000 degC in Ar atmosphere for 1
hour to study the effect of thermal treatment on microstructure and fracture strength
The following conclusions were obtained
(1) The local (intrinsic) fracture strength decreased in a varied degree after
thermal treatment and it was due to the formation of pores along the IPyCSiC
interface and in the coatings
(2) The Weibull modulus decreased once the pores have similarbigger size
asthan interfacial irregularities and distribute uniformly within coatings while
it increased with the size of pores much smaller than interfacial irregularities
after thermal treatment
(3) After thermal treatment no phase transformation was found in SiC coatings
and the crystallographic error (2θ~335 ordm) detected by XRD was demonstrated
to be stacking faults which were annihilated during this process
(4) The formation of pores after thermal treatment was attributed to the diffusion
of intrinsic defects such as vacancies interstitials and antisites Different
content and size of pores were observed in different coatings which are
presumed to have different kinds of native defects in as-deposited coatings
produced at different conditions
(5) The vacancies are supposed to be the dominant defects in stoichiometric SiC
deposited at 1280 ordmC however in other coatings the dominant defects could
be a combination of vacancies antisites and interstitials based on Raman
results before and after thermal treatment Furthermore the diffusion of native
defects also affects interfacial roughness after thermal treatment which needs
further study
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
172
66 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook of
SiC properties for fuel performance modeling J Nucl Mater 371 (2007) 329-77
[2] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[3] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidised
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
[4] H Zhang E Loacutepez-Honorato A Javed I Shapiro P Xiao A study of the
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc (2011) DOI
101111j1551-2916201105044x
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of fracture
stress for the SiC Layer of TRISO-Coated fuel particles using a modified crush
test method Int J Appl Ceram Tech 7 (2010) 327-37
[6] G H Lohnert H Nabielek W Schenk The fuel-element of the Htr-module a
prerequisite of an inherently safe reactor Nucl Eng Des 109 (1988) 257-63
[7] I J Van Rooyen J H Neethling J Mahlangu Influence of temperature on the
micro-and nanostructures of experimental PBMR TRISO coated particles A
comparative study Proceedings of the 4th
international topical meeting on high
temperature reactor technology HTR 2008 September 28-October 1 2008
Washington DC USA HTR 2008-58189
[8] Y Kurata K Ikawa K Iwamoto The effect of heat-treatment on density and
structure of SiC J Nucl Mater 92 (1980) 351-53
[9] D T Goodin Accident condition performance of fuels for high-temperature
gas-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[10] N Shirahata K Kijima A Nakahira K Tanaka Thermal stability of stacking
faults in Beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
173
[11] J van Rooyen J H Neethling P M van Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[12] E Loacutepez-Honorato K Fu P J Meadows J Tan and P Xiao Silicon carbide
coatings resistant to attack by palladium J Am Ceram Soc 93 (2010) 4135-41
[13] E Loacutepez-Honorato H Zhang D X Yang P Xiao Silver diffusion in silicon
carbide J Am Ceram Soc 94 (2011) 3064-71
[14] D J Green An Introduction to the Mechanical Properties of Ceramics
Cambridge University Press Cambridge 1998
[15] H Zhang E Loacutepez-Honorato A Javed X Zhao J Tan P Xiao A Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc (2012) DOI101016jjeurceramsoc201112014
[16] H Tateyama H Noma Y Adachi M Komatsu Prediction of stacking faults in
βndashSilicon carbide X-Ray and NMR studies Chem Mater 9 (1997) 766- 72
[17] K R Carduner S S Shinozaki M J Okosz C R Peters T J Whalen
Characterization of β-Silicon carbide by silicon-29 solid-state NMR transmission
electron microscopy and powder X-ray diffraction J Am Ceram Soc 73 (1990)
2281-86
[18] httptfuni-kieldematwisamatdef_enkap_6advancedt6_3_2html
[19] S M Dong G Chollon C Larbrugere M Lahaye A Guette J L Brunee M
Couzi R Naslain and D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[20] M Havel D BaronL Mazerolles P Colomban Phonon confinement in SiC
nanocrystals comparison of the size determination using transmission electron
microscopy and Raman spectroscopy Appl Spet 61 (2007) 855-59
[21] V V Pujar J D Cawley Effect of stacking faults on the X-Ray diffraction
profiles of 3C-SiC powder J Am Ceram Soc 78 (1995) 774-82
[22] Y L Ward R J Young R A Shatwell Effect of excitation wavelength on the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
174
Raman scattering from optical phonons in silicon carbide monofilaments J Appl
Phys 102 (2007) 023512 -17
[23] X J Li J Hayashi C Z Li FT-Raman spectroscopic study of the evolution of
char structure during the prolysis of a victorian brown coal Fuel 85 (2006)
1700-07
[24] A C Ferrari J C Meyer V Scardaci C Casiraghi M Lazzeri F Mauri S
Piscanec D Jiang K S Novoselov S Roth A K Geim Raman spectrum of
graphene and graphene layers Phys Rev Lett 97 (2006) 187401-04
[25] S Nakashima H Harima Raman investigation of SiC polytypes Phys Stat Sol
A-Appl Res 162 (1997) 39-64
[26] GKBasal Effect of flaw shape on strength of seramics J Am Ceram Soc 59
(1976) 87-8
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] K Koumoto S Takeda CH Pai High-resolution electron microscopy
observation of stacking faults in βndashSiC J Am Ceram Soc 72 (1989) 1985-87
[29] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J Am Ceram Soc 84 (2001) 3013-16
[30] K Koumoto S Takeda C H Pai T Sato H Yanagida High-resolution electron
microscopy observations of stacking faults in β-SiC J Am Ceram Soc 72 (1989)
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[31] C Wang J Bernholc Formation energies abundances and the electronic
structure of native defects in cubic SiC Phys Rev B 38 (1998) 12752-55
[32] E Janzen N T Son B Magnusson A Ellison Intrinsic defects in high-purity
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[33] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-09
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
175
CHAPTER 7 Microstructure and Mechanical Properties of
Pyrolytic Carbon Coatings
71 Introduction
Pyrolytic carbon (PyC) coatings forming part of the TRI-Isotropic (TRISO) fuel
particle are important for the stability of this type of nuclear fuel Without appropriate
microstructure and mechanical properties of PyC coatings the stress generated inside
the particle due to internal gas pressure andor the dimensional change (anisotropic
shrinkage or creep) introduced in this layer during irradiation process could result in
the failure of the full particle [1-5] Fundamental understanding about relationship
between mechanical properties and microstructure of PyC coatings could help to
analyse the failure mechanism and model the probability of failure of TRISO fuel
particles [1 5] However their relations in PyC are complex [3 6-8] Kaae [7] found
that mechanical properties were related to the density crystal size and anisotropy but
they are not controlled by a single variable For example Youngrsquos modulus increased
with density for isotropic carbons with constant crystallite size but decreased with
increasing anisotropy for carbon with constant density and crystalline size In a
separate work [3] density had a dominant effect on the hardness and Youngrsquos
modulus in relative low density PyC coatings whereas no controlling factor was
given for high density PyC coatings
Nano-indentation is an effective way to study microstructural effects on mechanical
properties of PyC coatings because it could help with the understanding of the
deformation mechanism and measure Youngrsquos modulus and hardness spontaneously
Among studies on mechanical properties in carbon related materials under
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
176
depth-sensing indentation [3 9-15] few explanations about the nature of their
deformation mechanism have been discussed [9 10 13 15] First the hysteresis was
assumed to due to the slip of graphene layers in nano-meter grains and the energy
loss was attributed to the friction between graphene layers under compression stress
[9 10] Second the dislocation pileups were assumed to be responsible for energy
loss [13] but this idea failed to account for the reversible deformation [15] The most
recent theory suggested that the origin of the hysteresis was due to the formation of
(incipient) kink bands [15] This theory was found to be a universal explanation for
most laminar structured materials but the nature of initial kink band was not clear
[15]
During pressing process of TRISO fuel particles into fuel elements they experience a
final thermal treatment of 1 h above 1800 ordmC to drive off any residual impurities and
improve thermal conductivity of the fuel compact [16] The evolution of
microstructure of carbon related materials have been widely studied [17-20] Few
researches measured changes of mechanical properties after thermal treatment [19
20] but there is a lack of understanding about effect of microstructural evolution on
mechanical properties in PyC coatings Therefore in this Chapter together with the
microstructural properties the deformation mechanism under indentation influences
on mechanical properties and their change after thermal treatment in PyC coatings are
studied
72 Experimental details
Pyrolytic carbon (PyC) was coated on alumina particles (Φ 500 μm) by fluidised bed
chemical vapour deposition by Dr Eddie Loacutepez-Honorato and PyC coatings with
different density was chosen to study the mechanical properties Table 61 gives the
density and texture (orientation angle) of PyC coatings and more about deposition
mechanism could be found in Ref [21] The number of sample sequence Ci (i=1
2hellip11) starts from highest density to lowest density with density of 19 gcm3 as
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
177
border line to distinguish highlow density PyC which was measured by the
Archimedes method in ethanol For thermal treatment the coatings were first
grounded into fragments and then removed the alumina kernel The fragments of PyC
were then thermal treated at 1800 degC and 2000 degC for 1 hour in argon atmosphere For
further understanding of microstructural evolution during thermal treatment sample
C5 was thermal treated at 1300 1400 1500 and 1600 degC for 1 hour
Table 71 PyC coatings with different density and orientation angle
PyC
(High density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
PyC
(Low density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
C1 2122plusmn0059 58 C6 1855plusmn0050 63
C2 2087plusmn0183 37 C7 1738plusmn0013 73
C3 2047plusmn0030 60 C8 1635plusmn0008 71
C4 2029plusmn0015 43 C9 1603plusmn0024 71
C5 2000plusmn0061 43 C10 1414plusmn0002 85
C11 1400plusmn0024 81
Orientation angle was obtained from the full width of half maximum of azimuthal intensity scan of
SAED pattern for more information in Ref [22] Productions of PyC coatings measurement of
orientation and density measurement are contributed by Dr Eddie Loacutepez-Honorato et al
The selected area electron diffraction (SAED) patterns were obtained with the use of a
FEG-TEM (see Chapter 3) and orientation angle was measured by the azimuthal
intensity scans of SAED pattern (selected aperture diameter of 200 nm) Further
details about this measurement were shown in a previous study [22] Transmission
electron microscopy (TEM) samples were obtained by focus ion beam milling High
resolution TEM samples were prepared by dispersing the fragments on a carbon holey
film copper grid X-ray diffraction (see Chapter 3) was used to obtain domain sizes of
PyC coatings After correction of intrinsic instrumental effect the out of plane and
in-plane domain sizes (along c-axis and a-axis in graphite crystal structure) Lc and La
were qualitatively estimated from XRD data by applying the Scherrer equation to the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
178
(002) and (110) reflections respectively [23] In as-deposited PyC coatings the (110)
peak was too weak to estimate accurately on the La Raman spectroscopy (633 nm
Helium ion laser source) was performed by single spot measurements (spot size was
carefully controlled to be the same for each test) of around 2 μm diameter using a times50
objective lens The laser power of less than 05 mW (10) was used with the step
size of 60 seconds and twice accumulations For each sample 5 different positions
were measured The band fitting of the first order spectra was carried out with
GRAMS32 software
To reduce the influence of surface roughness on indentation test the PyC coatings
were ground with successive finer grades of SiC paper and polished down to a 1 microm
grid diamond paste The same nano-indentation as in Chapter 3 was used The
measurements were performed at fixed loading rate of 1 mNS reaching the
maximum load of 100 mN For each coating at least 25 indentations were conducted
on the sample surface to increase the reliability of the results The Olive and Pharr
method [24] was used to analyse all the data
73 Results
731 Microstructure of PyC coatings
In order to study the influences of microstructure on mechanical properties it is
necessary to know the nature of structure which makes one sample from another eg
disorders domain size crystallinity etc and their evolution after thermal treatment
7311 Raman spectroscopy
Figure 71 is a Raman spectroscopy for an as-deposited high density PyC coating (C5
200 gcm3) which exhibits two relatively broad Raman bands at around 1335 cm
-1
and 1600 cm-1
The first band corresponds to the D band which is attributed to double
resonant Raman scattering and represents the in-plane defects [21 25 26] The
second band is an overlap of broadened G (1580 cm-1
) and D (1620 cm-1
) bands due
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
179
to high disordered pyrolytic carbon [27] The G band is due to the stretching modes of
pairs of sp2 atoms in graphene planes whereas D represents the similar defects
structure as the D band [18 27] It is convenient to consider 1600 cm-1
band a single
G peak for practical purposes when comparing different samples or the overall
structural evolution of a given PyC coating [27]
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
According to previous studies [25-32] on fitting similar Raman spectra shown in Fig
71 a simple two-symmetric-line fit (D and G bands) could not fit it well Therefore
the Raman spectra of high density PyC coatings (C1-C5 gt 19 gcm3) were
deconvoluted into above peaks at about 1220 cm-1
1335 cm-1
1500 cm-1
and 1600
cm-1
( Fig 71) The band at about 1500 cm-1
(Drsquorsquo) is attributed to interstitial defects
which could act as coupling (covalent band) between two graphene layers or adjacent
overlapped domains [25 28] The I band at around 1220 cm-1
is due to C-C on hydro
aromatic rings [28] The Raman spectra mean the high degree of in-plane andor
out-of-plane disorders in high density PyC coatings represented mainly by the full
width at half maximum (FWHM) of the D band [28] and intensity ratio (the area ratio
of the 1500 cm-1
peak to the sum of four peaks shown in Fig 71) of the Drdquo bands
[25] respectively
D
I
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
180
Figure 72 is the Raman spectra of high density PyC coating C5 after thermal
treatment at temperature of 1300 1400 1600 and 1800 ordmC The FWHM of the D band
decreased significantly from about 150 cm-1
(as-deposited) to about 106 cm-1
(1400
ordmC) and then to about 40 cm-1
(1800 ordmC) Similarly the intensity ratio of the Drdquo was
reduced from about 0135 (as-deposited) to about 0110 (1400 ordmC) and then to about
0078 (1800 ordmC) Another change is the split of G and D bands after thermal treatment
at 1800 ordmC (Fig 72) The above changes indicate that disorders in high density PyC
coatings are low energy structural defects ie degree of disorder is low according to a
previous study [28]
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
181
After thermal treatment the degree of microstructural changes of low density PyC
coatings C6-C8 (164-186 gcm3) is slightly different from even lower density
coatings C9-C11 (140-160 gcm3) so they are described separately Figure 73 shows
Raman spectra of low density PyC coatings (a) C7 and (b) C10 before and after
thermal treatment at 1800 ordmC Similar to high density PyC the as-deposited coatings
C6-C8 contains four Raman bands After thermal treatment the FWHM of the D peak
in C7 decreased from about 120 cm-1
to 57 cm-1
and the intensity ratio of interstitial
defects was also reduced (from 0116 to 0042 Fig 73(b)) In coating C10 only
slightly decrease of FWHM of the D peak (from about 83 cm-1
to 57 cm-1
) was found
after thermal treatment at 1800 ordmC (Fig 73(b)) No split of the G and D bands was
observed in low density PyC coatings
With increase in density of PyC the FWHM of the D band the concentration of the
Drdquo band and the degree of their changes after thermal treatment increase considerably
which suggest that the disorder defects in PyC are different with variation of density
and thermal treatments change the degree of the disorder
7312 Domain sizes
Table 72 summarises the out-of-plane domain size (crystallite size perpendicular to
the graphene plane Lc) and in-plane domain size (crystallite size along the graphene
plane La) measured by XRD in PyC coatings before and after thermal treatment The
Lc is in the range of 1-3 nm in all the as-deposited coatings and it is slightly bigger in
high density (about 2-3 nm) coatings than low density (about 1-2 nm) coatings After
thermal treatment at 1800 ordmC the Lc increased significantly which is about 5 times
and 2-3 times larger than in as-deposited high density and low density PyC coatings
respectively It is 2-4 times larger in high density PyC than low density PyC coatings
The La in high density (about 6 nm) is larger than low density PyC coatings (3-4 nm)
after thermal treatment at 1800 ordmC Both Lc and La remained unchanged after thermal
treatment at 2000 ordmC in all PyC coatings (This is explained in section 741) The
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
182
increase of domain size indicated the ordering process in PyC coatings after thermal
treatment which may involve annealing of different kinds of disorders
Table 72 Domain size of as-deposited and thermal treated PyC coatings
Sample As deposited 1800 2000
Lc (nm) La (nm) Lc (nm) La (nm) Lc (nm) La (nm)
High density (gt19 gcm3)
C1 21 -- 112 -- 116 53
C2 21 -- 132 63 154 69
C3 22 -- 98 66 111 63
C4 24 -- 95 57 118 63
C5 20 -- 120 60 152 73
Low density (lt 19 gcm3)
C6 22 -- 50 42 56 44
C7 18 -- 38 36 50 34
C8 14 -- 31 33 27 39
C9 11 -- 27 32 31 34
C10 17 -- 24 33 27 35
C11 11 -- 27 35 27 33
7313 Evolution of crystallinity
Figure 74 is the TEM images of high density PyC (C5) before and after thermal
treatment The dark field TEM show bright areas (Fig 74(a) and (b)) that represent
graphene layers with similar orientation in the selected direction of the diffraction
pattern A decrease of the orientation angle from 43 ordm to 25 ordm is found after thermal
treatment at 1800 ordmC which is obtained from the full width at half maximum of
azimuthal intensity scan of SAED pattern (insets in Fig4(a) and (b)) A bright field
TEM image of a conical microstructure after thermal treatment (Fig 74(c) dashed
rectangle in Fig 74(b)) which shows the voids at the top of conical structures The
above observations show that thermal treatment increases anisotropy and results in the
volume shrinkage and generation of voids in high density PyC coatings
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
183
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Figure 75 is the typical HRTEM away from the top of conical growth feature (eg
OA=43 ordm
OA=25 ordm
Top
Voids
100 nm
(c)
(a) (b)
5 nm
Moireacute
fringes
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
184
white circle in Fig 74(c)) in high density PyC coatings (C1) before and after thermal
treatment at 1800 ordmC The wrinkled short graphene fringes in as deposited high
density PyC (Fig 75(a)) were replaced by distorted planes in a larger scale with a
bigger radius of curvature (white arrow in Fig 75(b)) The common number of
parallel layers (Fig 75(a) (002) plane white parallel lines) is 2-4 in as-deposited C1
which increased to about 30 (Fig 75(b) between white parallel lines) The moireacute
fringes were observed after thermal treatment (black arrow in Fig 75(b)) which
correspond to black bars in the bright field TEM (eg dashed black rectangle in Fig
74(c)) According to the generation mechanism of moireacute fringes [33] the on-going
ordering process along the c-axis is related to the increase of number of parallel layers
and evolution (decrease) of the inter plane distance of (002) planes
Figure 76 gives the bright field TEM and HRTEM images showing the
microstructure evolution in a low density PyC coating (C7) Globular growth features
with diameters of about 400 nm were observed in as-deposited C7 as shown in Fig
76(a) and the HRTEM image shows 2-3 layers of parallel planes (Fig 76(b)) In low
density PyC coatings the graphene fringes are longer and less oriented than in high
density coatings (reflected from orientation angle shown in Table 71 and Fig 13 in
Ref [21]]) After thermal treatment the short dark bars andor dots (as indicated by
the white arrows Fig 76(c)) were observed which is due to the moireacute fringes as
shown in Fig 76(d) The number of parallel layer increased up to 8-10 (Fig 76(d))
and it reflects the slight crystallinity after thermal treatment In the other low density
PyC coatings C9-C11 the TEM images are similar with the as-deposited low density
PyC coatings (as shown in Fig 14 and Fig 13(c) in Ref [21]) Furthermore the
orientation angle is almost the same in all low density PyC before and after thermal
treatment
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
185
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
732 Mechanical properties of PyC coatings
7321 Force-displacement curve
Figure 77 gives the force-displacement curve of PyC coatings with different density
under the maximum load of 60 mN and 100 mN by nano-indentation The unloading
curve did not completely retrace the loading curve but still returned to the origin This
process is called anelastic behaviour or hysteresis behaviour and the anelastic
reversible indentation processes with an enclosed loop are found in all the PyC
coatings
(a) (b)
100 nm 5 nm
5 nm
Sphere-like
particle
Tops
Moireacute fringes Sphere-like
particle
Top (d)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
186
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
The maximum indentation depth in low density PyC (C6-C11 lt 19 gcm3) is deeper
than in high density PyC coatings (C1-C5 gt 19 gcm3) under the same load and the
low density PyC also shows larger hysteresis loop area The ratio of the hysteresis
energy (area within the loading-unloading loop) to total loading energy (area under
loading curve) in high density PyC is lower than in low density PyC coatings For
example the ratios of sample C3 C9 and C11 are 0243 0270 and 0292 respectively
Furthermore the deformation behaviour of all PyC coatings showed the hysteresis
behaviour after thermal treatment up to 2000 ordmC The high density PyC after thermal
treatment at 1800 ordmC (red curve in Fig 77) shows anelasticity however the ratio of
its hysteresis energy (0249) is much higher than in as-deposited coating (0174)
According to previous studies [10 34] the low ratio obtained in high density PyC
coatings under pyramidal indenter corresponds to high elasticity while low density
exhibits high hysteresis (anelasticity high viscosity))
Under indentation the hardness is defined as the mean pressure the material will
support under load according to Oliver and Pharrrsquos study [24] This pressure is equal
to the load at maximum load divided by the contact area (according to eqs (7 10 11)
hc
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
187
in Chapter 2) However the residual depth hf is zero and no pleastic deformation is
observed after unloading The hardness obtained by Oliver and Pharr method does not
reflect the resistance of plastic deformation of material but it could represent the
degree of unelastic deformation qualitatively Therefore the mean pressure (P) value is
used which could reflect the anelastic properties of PyC coatings
7322 Youngrsquos modulus and the mean pressure
Figure 78 gives the Youngrsquos modulus (E) and the mean pressue (P) of as-deposited
PyC coatings as a function of density For low density PyC coatings (C6-C11 lt 19
gcm3) Youngrsquos modulus and the mean pressure increase almost linearly with the
density For high density PyC coatings (C1-C5 gt 19 gcm3) both Youngrsquos modulus
and the mean pressure reach plateaus which are independent of density It indicates
that mechanical properties of high PyC coatings are dominated by other factors
which are discussed in session 744
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
Table 73 shows the Youngrsquos modulus and the mean pressure of PyC coatings with
different density before and after thermal treatment at 1800 and 2000 ordmC After
thermal treatment at 1800 ordmC Youngrsquos modulus decreased by around 50 and the the
mean pressure is reduced by around 69 in high density PyC coatings (C1-C5 gt19
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
188
gcm3) whereas minor change is observed when thermal treatment temperature
further increased to 2000 ordmC Previous study [20] showed similar results about
changes of mechanical properties in high density PyC after thermal treatment at
different temperature In low density PyC coatings C6-C8 (164-186 gcm3) the
mean pressure and Youngrsquos modulus decreased by about 23 and 8 after thermal
treatment at 1800 ordmC respectively which is consistent with Rooyen et alrsquos results
[19] and further decreased by 18 and 15 by increasing thermal treatment
temperature to 2000 ordmC In low density coatings C9-C11 (140-160 gcm3) little
change in mechanical properties after thermal treatment up to 2000 ordmC was found and
it is similar as the isotropic low density PyC [20] Mechanical properties and their
change after thermal treatment in PyC coatings are different with different density
Table 73 Changes of mechanical properties of PyC coatings after thermal treatment
Sample As deposited Thermal treated at 1800 Thermal treated at 2000
P (GPa) E (GPa) P (GPa) E (GPa) P (GPa) E (GPa)
High density
C1 468plusmn025 2670plusmn119 103plusmn018 1482plusmn131 090plusmn013 1337plusmn093
C2 435plusmn048 2513plusmn117 132plusmn019 1091plusmn069 076plusmn021 1204plusmn126
C3 490plusmn036 2878plusmn117 -- -- 091plusmn026 1271plusmn125
C4 397plusmn019 2291plusmn076 171plusmn010 1313plusmn034 110plusmn010 1370plusmn051
C5 456plusmn010 2610plusmn036 132plusmn015 1177plusmn051 177plusmn025 1361plusmn101
Low density
C6 388plusmn035 2165plusmn191 296plusmn022 1912plusmn113 244plusmn023 1647plusmn088
C7 395plusmn053 2149plusmn200 292plusmn036 1934plusmn114 232plusmn033 1568plusmn182
C8 354plusmn027 1945plusmn070 292plusmn036 1904plusmn113 232plusmn063 1678plusmn240
C9 284plusmn040 1938plusmn094 226plusmn057 1677plusmn178 263plusmn042 1733plusmn151
C10 189plusmn009 1266plusmn035 213plusmn019 1363plusmn076 188plusmn023 1381plusmn087
C11 168plusmn017 1166plusmn082 178plusmn034 1284plusmn106 086plusmn014 1167plusmn151
74 Discussions
The main findings of this study can be summarised as follows 1) PyC with different
density show different full width at half maximum (FWHM) of the D band and
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
189
concentration of the Drsquorsquo band which suggests that they have different types of disorder
TEM observation shows longer graphene fringes with lower density PyC (Fig 13 in
Ref [21]) thermal treatments decrease the degree of disorder while PyC with higher
density (gt19 gcm3) shows higher degree of decrease 3) initial increase in PyC
density until 19 gcm3 lead to proportional increase in Youngrsquos modulus (E) and the
mean pressure (P) while further increase in density has no effect on E and P 4)
hysteresis occurred after nano-indentation of PyC while the degree of hysteresis is
controlled by the PyC density and heat treatments
741 Disorders and their changes after thermal treatment
High density PyC Coatings (C1-C5 gt 19 cmg3) The dominant in-plane disorders
are domain boundaries according to a previous study [21] which generates high
FWHM of the D band due to the low energetic disorientations (eg domains andor
graphene layers) [25 28] The Drsquorsquo band (interstitial defects) is due to the amorphous
carbon structure which is composed of mainly disordered sp2 atoms and a low
amount of sp3 atoms [27 28 35] Particularly the sp3 lines are out of plane defects
which could be formed in high density PyC coatings [36] Therefore it is assumed
that the microstructure in high density PyC is composed of disoriented nano-size
graphite domains connected by amorphous carbon
After thermal treatment the reductions of the out-of-plane defects and the tilt and
twist in graphite planes are observed which could contribute to the increase of Lc
(out-of-plane domain size) as shown in HRTEM image (Fig 75) It was supposed
that the equilibrium shear stress were generated by in-plane defects and out-of-plane
defects in PyC coatings [25] once the out-of-plane defects was reduced the in-plane
stress would tend to straighten the graphite planes Furthermore the decreases of
FWHM of the D band and the orientation angle (Fig 72 and 4) show the ordering
arrangement of graphite layers is due to the healing of in-plane disorientations The
unchanged domain size Lc could be a result of a combination of increased number of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
190
parallel graphene layers and decreased inter distance of (002) plane As a conclusion
the increase of domain size Lc could be due to the coalescence of domain size andor
graphene layers through reorientation and remove of interstitial defects which
usually started at temperature of about 900-1200 ordmC [17 25] No La (in-plane domain
size) value was obtained in as-deposited PyC and the overlap of the G and the Drsquo
bands indicates it is below 4 nm above which two bands split [37] After thermal
treatment at 1800 ordmC the La is about 6 nm in high density PyC coatings (Table 72
and splitting of G and Drsquo bands was shown in Fig 72) which demonstrates the
slightly increase of La It is attributed to the annihilation of low energetic in-plane
disorientations which could usually be removed at temperature above 1500 ordmC [25]
Since the high temperature above 2000 ordmC is needed to remove the rest high energetic
in-plane defects for high density PyC according to previously study [25 28] it could
explain the La remained nearly constant after thermal treatment further increased to
2000 ordmC The ordering of graphite layers is responsible for the formation of voids (Fig
74(c)) since the ordering could reduce the volume and increase the density of PyC
coatings after thermal treatment [38]
Low density PyC Coatings (C6-C11 lt 19 cmg3) The main defect is the
5-memebered rings in coatings C9-C11 by comparing the Raman spectroscopy (Fig
73(a)) with a previous study [21] In low density coatings C6-C8 (164-186 gcm3)
the degree of in-plane disorder is less than in high density coatings but higher than
coatings C9-C11 (140-160 gcm3 indicated by the FWHM of the D band) and the
out-of-plane defects are much higher than low density PyC coatings (Fig 73) After
thermal treatment the in-plane disorder is similar as in coatings C9-C11 Therefore
the dominant in-plane defects are supposed to be a combination of domain boundaries
and 5-membered rings The slightly increase of domain size Lc in low density PyC
coatings is due to the decrease of interfacial defects through reorientation of domains
However they have much lower degree of increase of Lc than high density coatings
this could be due to low anisotropy in low density PyC coatings which makes it
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
191
difficult to reorient domains and remove the weak defects [17 25] The domain size
La was assumed to be unchanged since ordering in-plane disorders took place at
temperature above 2400 ordmC in low density PyC due to presence of 5-member rings
[17] It is worth to notice that the graphene fringes do not represent the in-plane
domain size in low density PyC due to the curvature caused by 5-memebered rings
[21] Due to the exist of 5-membered rings in low density PyC coatings the
microstructure is lightly affected by thermal treatment
742 Hysteresis after indentation
The increase in density of PyC leads to decrease in hysteresis after indentation and
density of PyC also dominate types and degree of disorders During indentation of
PyC hysteresis is caused by the slip of graphene planes whereas the disorders such as
interstitial defects or 5-memebered rings are supposed to be responsible for the
reversible deformation The hysteresis was also observed in other carbon materials
such as single crystal graphite [15] polycrystalline graphite [15] glassy carbon [9
10] Similar explanations about the effect of slip of graphene layers on the hysteresis
behaviour under indentation were given and it suggests that the deformation
mechanism is related to a common structure in different carbon materials which are
graphene planes
The slip of graphene planes has been demonstrated available The shear modulus (micro)
of graphite is 23 GPa (between graphene layers) [39] Based on the relation of τth= micro
30 [39 40] the theoretical shear stress (τth) of graphite is estimated to be 0077 GPa
This shear stress is much lower than the yield stress under Berkovich indenter for
graphite (03-05 GPa) [15] Under indentation the slip of graphene planes consumes
energy but recovers to the original shape after unload Lower density PyC has longer
fringes than that in higher density PyC (Fig 13 Ref [21]) therefore the panes can
slip for a longer distance under shear stresses generated by nano-indentation
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
192
Reversible deformation is due to presence of interstitial defects or highly curved
5-memebered rings For indentation of crystallite graphite the kink band could be
generated during the initial indentation process then reviersible deformation occurs
under further indentation [15] similar as that shown in Fig 77 In our PyC coatings
disorder in the PyC plays a similar role as the kink band in the crystallite graphite
The slip direction is parallel to the graphene planes so the in-plane defects presents at
the tilt and twist of two adjacent domains could not stop and reflect the slip Only
those defects perpendicular to the slip direction can contribute to the reversible
deformation such as interstitial defects or the highly curved 5-memebered rings
(caused fibrous graphene planes as shown in Fig 13(c) Ref [21])
After heat treatment the growths of the in-plane fringes increase the degree of the
hysteresis in PyC coatings For example the straightened graphene fringes (Fig 75)
caused by reorientation and removes of interstitials facilitate the hysteresis
significantly (the ratio of hysteresis energy to total loading energy increased from
0174 to 0249 Fig 77)
743 Mechanical property of low density PyC coatings
In as deposited low density PyC (C6-C11 gt 19 gcm3) Youngrsquos modulus and the
mean pressure are dominated by the density which is consistent with previous studies
[3 7 41] because of the effect of porous structure [3 21] As discussed in session
741 the disorders in low density PyC coatings play an important part on the stability
of microstructure which could reflect changes of mechanical properties After thermal
treatment the mechanical properties remained almost unchanged in PyC coatings
C9-C11 (140-160 gcm3) and this could be explained by the insignificant change of
microstructures at the presence of 5-membered rings The slightly decrease of
mechanical properties were found in coatings C6-C8 (164-186 gcm3) which is due
to the ordering of graphene planes through reduction of interstitial defects which
could enhance hysteresis and decrease the mean pressure No voids and change of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
193
orientation was observed after thermal treatment in coatings C6-C8 so Youngrsquos
modulus is slightly affected It is concluded that the mean pressure and Youngrsquos
modulus are functions of density in as-deposited low density coatings and their
evolution after thermal treatment is controlled by disorders such as interstitials andor
5-membered rings
744 Mechanical Property of high density PyC coatings
In high density PyC coatings (C1-C5 gt 19 gcm3) Youngrsquos modulus and the mean
pressure are independent of density so they are discussed regarding to variation of
texture domain size and concentration of interstitial defects (the area ratio of the 1500
cm-1
peak to the sum of four peaks shown in Fig 71) Table 74 summarises
microstructure parameters and mechanical properties of high density PyC coatings
Mechanical properties are not controlled by domain size and orientation angle which
is converse to the previous study [41] It is found that Youngrsquos modulus and the mean
pressure in high density PyC coatings decrease with the reduction of concentration of
interstitial defects (as shown in Table 74)
Table 74 The parameters used to explain different mechanical properties of high
density PyC (C1-C5 gt 19 gcm3)
Sample Density
(gcm3)
Texture
OA (deg)
Domain
size (nm)
IinterstialAll Pressure
(GPa)
Modulus
(GPa)
C3 2047 plusmn0030 60 22 013955plusmn000374 490plusmn036 2878plusmn117
C1 2122 plusmn0059 58 21 013513plusmn000399 468plusmn025 2670plusmn119
C5 2000 plusmn0061 43 20 013456plusmn000561 456plusmn010 2610plusmn036
C2 2087 plusmn0183 37 21 013036plusmn000433 435plusmn048 2513plusmn117
C4 2029 plusmn0015 43 24 011823plusmn001628 397plusmn019 2291plusmn076
The physical meaning of the above observation can be explained by the effect of
interstitial defects on the deformation mechanism in high density PyC coatings First
the high concentration of interstitial defects could reduce the energy consumption by
the reversible slip of graphene planes (eg in Fig 77) and it corresponds to high the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
194
mean pressure in high density PyC coatings Second in-plane Youngrsquos modulus is
much higher than out-of plane Youngrsquos modulus in graphite so the bonding between
graphene planes becomes important when the orientation effect could be neglected in
high density PyC (Table 74) For example in sample C4 and C5 the high Youngrsquos
modulus was obtained in C5 which have high amount of covalent band (interstitial
defects sp2 and sp3 in Fig 71) in the direction perpendicular to graphene planes The
high concentration of interstitial defects in high density PyC could also reduce the
influences of orientation angle on the high Youngrsquos modulus This could explain the
similar Youngrsquos modulus in C1 and C5 which have different orientation angles
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
After thermal treatment at temperature range of 1300-1800 ordmC in C5 (about 200
gcm3) the effect of concentration of interstitial defects on mechanical properties was
again demonstrated as given in Table 75 The mechanical properties decrease
gradually with the increase of thermal treatment temperature until 1600 ordmC and then a
dramatic decrease at 1800 ordmC The decrease is related to the reduction of content of
interstitial defects (Table 75) Furthermore no other relationship between mechanical
properties and microstructural features such as FWHM of the D band intensity of D
band and G band in Raman spectroscopy is found in the current work Therefore the
concentration of interstitial defects is proposed to dominant mechanical properties of
high density PyC coatings This idea about effect of interstitial defects on mechanical
properties is similar as the cross-link theory [8] which suggested that the mechanical
properties is related to the length and number of links between domains Furthermore
Temperature (ordmC) IinterstialAll Pressure (GPa) Youngrsquos modulus (GPa)
0 013456plusmn 000561 456plusmn010 2610plusmn 036
1300 011882plusmn000906 430plusmn010 2519plusmn060
1400 011045plusmn000278 413plusmn010 2407plusmn070
1500 009598plusmn000034 406plusmn022 2439plusmn070
1600 009469plusmn000219 391plusmn016 2344plusmn036
1800 007756plusmn000199 132plusmn015 1177plusmn051
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
195
the significant decrease of the the mean pressure and Youngrsquos modulus after 1800 ordmC
could be due to the straightening of graphene layers and formation of voids (Fig
74(c)) respectively To conclude the mechanical properties in high density PyC
coatings before and after thermal treatment from 1300 to 1800 ordmC decrease with the
reduction of concentration of interstitial defects
74 Conclusions
Disorders in PyC coatings was characterised by Raman spectroscopy A
combination of high degree of in-plane (domain boundaries) and out-of plane
defects (interstitial defects) prevail in high density PyC while the 5-membered
rings are dominant defects in low density PyC coatings
In high density PyC coatings the significant increase of domain size Lc is
attributed to the coalescence of domainsgraphene layers through reorientation and
reduction of interstitial defects During this process the graphene planes were
straightened resulting in slightly increase of La
In low density PyC coatings the microstructure remained almost unchanged after
thermal treatment due to the presence of the 5-membered rings which need high
temperature to be reduced
The hysteresis deformation behaviour was found in all PyC coatings before and
after thermal treatment under nano-indentation The nature of hysteresis is
suggested to be Slip of graphene planes consumes energy (hysteresis loop) and
disorders (interstitial defects and highly curved 5-memebered rings in high density
and low density PyC coatings respectively) are responsible for the reversible
deformation (unloading curve back to origin)
The mean pressure and Youngrsquos modulus are functions of density in low density
PyC coatings and their changes after thermal treatment are insignificant which
are due to the almost unchanged microstructure
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
196
In high density PyC coatings the mean pressure and Youngrsquos modulus are
independent of density orientation angle and domain size but they are related to
the concentration of interstitial defects After thermal treatment the decrease of
mechanical properties is attributed to the reduction of interstitial defects leading
to the straightening of graphene planes and formation of voids
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
197
75 References
[1] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques thin solid films 469-70 (2004) 214-20
[2] D G Martin Considerations pertaining to the achievement of high burn-ups in
HTR fuel Nucl Eng Des 213 (2002) 241-58
[3] E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure and
mechanical properties of pyrolytic carbon produced by fluidized bed chemical
vapour deposition Nucl Eng Des 238 (2008) 3121-28
[4] G K Miller D A Petti A J Varacalle J T Maki Consideration of the effects
on fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[5] A C Kada R Gnallinger M J Driscoll S Yip D G Wilson H C No et al
Modular pebble bed reactor In Modular pebble bed reactor project University
research consortium annual report 2000
[6] G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
[7] J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[8] F G Emmerich C A Luengo Youngrsquos modulus of heat-treated carbons A
theory for nongraphitizing carbons Carbon 31 (1993) 333-39
[9] J S Field MVSwain The indentation characterisation of mechanical properties
of various carbon materials Glassy carbon coke and pyrolytic graphite Carbon
34 (1996) 1357-66
[10] N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[11] M V Swain J S Field Investigation of the mechanical properties of two glassy
carbon materials using pointed indetners Philos Mag A 74 (1996) 1085-96
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
198
[12] N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philos Mag A 82 (2002) 1873-81
[13] M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated carbons
J Am Ceram Soc 85 (2002) 1522-28
[14] A Richter R Ries R Smith MHenkel B Wolf Nanoindentation of diamond
graphite and fullerene films Diamond Relat Mater 9 (2000) 170-84
[15] MW Barsoum A Murugaiah S R Kalidindi T Zhen Y Gogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[16] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
treatment J Nucl Mater 374 (2008) 445-52
[17] F G Emmerich Evolution with heat treatment of crystallinity in carbons Carbon
33 (1995) 1709-15
[18] M A Pimenta G Dresselhaus M S Dresselhaus L G Cancado A Jorio R
Saito Studying disorder in graphite-based systems by Raman spectroscopy Phys
Chem Chem Phys 9 (2007) 1276-91
[19] I J Van Rooyen J H Neethling J Mahlangu Influence of Temperature on the
Micro-and Nanostructures of Experimental PBMR TRISO Coated Particles A
Comparative Study Proceedings of the 4th
international topical meeting on high
temperature reactor technology Washington DC USA HTR 2008-58189
[20] J C Bokros R J Price Deformation and fracture of pyrolytic carbons deposited
in a fluidized bed Carbon 3 (1966) 503-19
[21] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-I Effect of deposition conditions on microstructure
Carbon 47 (2009) 396-10
[22] P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
199
[23] S Bernard O Beyssac K Benzerara N Findling G Tzvetkov G E Brown Jr
XANES raman and XRD study of anthracene-based coke and saccharose-based
chars submitted to high-temperature pyrolysis Carbon 48 (2010) 2506-16
[24] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[25] J N Rouzaud A Oberlin C Beny-bassez Carbon films structure and
microstructure (optical and electron microscopy Raman spectroscopy) Thin solid
film 105 (1983) 75-96
[26] S Potgieter-Vermaak N Maledi N Wagner J H P Van Heerden R Van
Grieken J HPotgieter Raman spectroscopy for the analysis of coal a review J
Raman Spectrosc 42 (2011) 123-29
[27] A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-photon coupling doping and nonadiabatic effects Solid state commun
143 (2007) 47-57
[28] J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy electron
diffraction and few other techniques Carbon 44(2006) 1833-44
[29] G A Zickler B Smarsly NGierlinger H Peterlik O Paris A reconsideration
of the relationship between the crystallite size La of carbons determined by X-ray
diffraction and Raman spectroscopy Carbon 44 (2006) 3239-46
[30] A Cuesta P Dhamelincourt J Laureyns A Martinez-Alonso JMD Tascon
Raman microprobe studies on carbon materials Carbon 32 (1994) 1523-32
[31] A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
200
[32] S Yamauchi Y Kurimoto Raman spectroscopic study on pyrolyzed wood and
bark of Japanese cedar temperature dependence of Raman parameters J Wood
Sci 49 (2003) 235-40
[33] D B Williams C B Carter Transmission electron microscopy A textbook for
materials science Springer New York p 392-97
[34] M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[35] T Jawhari A Roid J Casado Raman spectroscopic characterization of some
commercially available carbon black materials Carbon 33 (1995) 1561-5
[36] G L Dong K J Huumlttinger Consideration of reaction mechanisms leading to
pyrolytic carbon of different textures Carbon 40 (2002) 2515-28
[37] A Jorio E H Martins Ferreira M V O Moutinho F Stavale C A Achete R
B Capaz Measuring disorder in graphene with the G and D bands Phys Status
Solidi B 247 (2010) 2980-82
[38] R Piat Y Lapusta T Boumlhlke M Guellali BReznik D Gerthsen TChen R
Oberacker M J Hoffmann Microstructure-induced thermal stresses in pyrolytic
carbon matrices at temperatures up to 2900 ordmC J Eur Ceram Soc 27 (2007)
4813-20
[39] J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[40] A H Cottrell Dislocations and plastic flow in crystals Clarendon Press Oxford
1972 p 162
[41] J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
CHAPTER 8 Conclusions and Future Works
201
CHAPTER 8 Conclusions and Future Works
This work provides both fundamental understanding and techniqual guidance on the
mechanical properties and their relationship with microstructures of SiC and PyC
coatings in TRISO fuel particles The measurement of hardness and Youngrsquos modulus
of SiC coatings could be used in the modelling work to study the peroperty of the
failure of the fuel particlues and these results have been published The measurement
of the fracture toughness of SiC in TRISO fuel particle has solved one of the
techniqual problems in field and the study contributes to the study of the fracture
behaviour of SiC coatings The fracture strength measurement has enriched the
strength data of SiC coatings before and after thermal treatment (related paper is
under revision) The characterisation of the interfacial roughness has provided a direct
method to correlate the relationship between fracture strength and interfacial
roughness The mechanical properties of PyC coatings provide foundamental
understanding about the deformation mechanism of the PyC coatings under
indentation The effect of thermal treatment on the mechanical properties has given a
preguidance about the behaviour of the PyC coatings at high temperature
81 Conclusions
(1) In SiC coatings deposited at 1300 ordmC by fluidised bed chemical vapour deposition
the Youngrsquos modulus was an exponential function of the porosity and the high
hardness was attributed to the high density of dislocations and their interactions
The initiation and propagation of micro cracks under the confined shear stress was
found to be responsible for the mechanism of plastic deformation Based on this
hardness-related plastic deformation mechanism the variation of hardness in the
three types of SiC coating was due to different grain morphologies
CHAPTER 8 Conclusions and Future Works
202
(2) The fracture beneath the Vickers indenter consists of Palmqvist cracks as
observed using SEM in above SiC coatings Based on this crack mode Vickers
indentation fracture toughness values of 351-493 MPa m12
were obtained It was
found that stress-induced micro-cracks seem to be a mechanism for the fracture
behaviour The presence of defects such as nano-pores and less constraint grain
boundaries could generate more micro cracks which dissipated energy from the
main cracks
(3) Fracture strength measured by modified crush test give less scattered values
within a given sample by distributing the load under a contact area It has been
found that Weibull modulus and fracture strength of the full shell were
significantly affected by the ratio of radius to thickness of the coating and both of
them decrease linearly with the increase of this ratio
(4) The numericalstatistical analysis was able to characterize the interfacial
roughness of different coatings and the roughness ratio representing the
irregularities was proposed to be a unique parameter for this description The
difference of the local (intrinsic) fracture strength was dominated by the
roughness ratio and it decrease linearly with the increase of the roughness ratio
The roughness ratio has the similar effect on the difference of fracture strength of
the full shell
(5) After heat treatment at 2000 degC the local fracture strength was reduced due to the
formation of pores in the coatings which could act as the enlarged critical flaw
size The Weibull modulus decreased when the pores in SiC coatings became
critical flaws while it increased once more uniformly distributed critical flaws
along the IPyCSiC interface were formed The formation of pores was mainly
related to the annihilation of stacking faults and diffusion of intrinsic defects such
as vacancies interstitials and antisites
CHAPTER 8 Conclusions and Future Works
203
(6) The hysteresis deformation mechanism was proposed to be due to the slip of
graphene planes which constraint by interstitial defects and highly curved
5-membered rings in high density and low density PyC coatings respectively
(7) The hardness and Youngrsquos modulus were related to the concentration of
interstitial defects and density in high density and low density PyC coatings
respectively Their changes in high density PyC is more significant than in low
density PyC coatings after heat treatment over 1800 ordmC due to the annihilation of
interstitial defects and reorientation of graphene layers
82 Suggestions for future work
(1) According to current study high amount of native defects were found in SiC
deposited at low temperature and it would be interesting to study their effects on
the thermal stability in a certain range of temperature such as from 1200-2000 ordmC
The study of the diffusion of native defects in SiC could also assist the study of
diffusion behaviour of fission products because these defects are more active and
they tend to reach the equilibrium during annealing process Due to different
deposition conditions the dominant species of native defects could be different in
different coatings therefore it is also important to study the deposition effect on
thermal stability of SiC coatings
(2) Itrsquos important to know how the microstructure change of SiC coatings deposited at
low temperature after irradiation because they showed robust mechanical
properties and high resistance to fission products It has been found they have high
amount of dislocations and stacking faults which accompanied by interstitials and
vacancies as reflected from the enlarged lattice constant According to this it is
supposed that after irradiation the volume change of SiC will be small because of
the pre-exist lattice defects Therefore study of the irradiation effect (at different
operational temperature) on SiC deposited at low temperature would be
promising
CHAPTER 8 Conclusions and Future Works
204
(3) Although current study has proposed to use self-affine theory to characterize the
interfacial roughness more work about their effects on fracture strength need to
be explored For example find out if the derived linear function between
roughness ratio and fracture strength in the current study could be used to explain
the differences of fracture strength in other tests To do further demonstration it is
necessary to reduce the geometrical influence and choose SiC coatings has
similar microstructure but different IPyCSiC interface These samples could be
prepared by just changing the deposition condition of IPyC while keep it same for
SiC coatings
List of Contents
4
521 Materials 132
522 Test method and analysis 133
523 Characterisation methods 135
53 Results and discussions 136
531 Fracture strength and dimensional effect 136
532 Observe and qualify the effect of interfacial roughness on fracture strength
140
533 Characterise and quantify the interfacial roughness 143
5331 Self-affine theory introduction and experimental setup 143
5332 Results of self-affine theory 144
534 Quantify the influence of interface roughness on fracture strength 146
54 Conclusions 149
55 References 150
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings 154
61 Introduction 154
62 Experimental details 155
63 Results 156
631 Fracture strength of SiC coatings 156
632 Change in morphologies 160
633 Evolution in microstructure 163
64 Discussion 167
641 Influence of interfacial roughness and pores on fracture strength 167
642 Mechanism of microstructural change 169
65 Conclusions 171
66 References 172
CHAPTER 7 Microstructure and Mechanical Properties of Pyrolytic Carbon
Coatings 175
71 Introduction 175
72 Experimental details 176
73 Results 178
731 Microstructure of PyC coatings 178
7311 Raman spectroscopy 178
7312 Domain sizes 181
List of Contents
5
7313 Evolution of crystallinity 182
732 Mechanical properties of PyC coatings 185
7321 Force-displacement curve 185
7322 Youngrsquos modulus and the mean pressure 187
74 Discussions 188
741 Disorders and their changes after thermal treatment 189
742 Hysteresis after indentation 191
743 Mechanical property of low density PyC coatings 192
744 Mechanical Property of high density PyC coatings 193
74 Conclusions 195
75 References 197
CHAPTER 8 Conclusions and Future Works 201
81 Conclusions 201
82 Suggestions for future work 203
Abstract
6
Abstract
Mechanical and Microstructural Study of Silicon carbide and Pyrolytic Carbon
Coatings in TRISO Fuel Particles
The University of Manchester
Huixing Zhang
Doctor of Philosophy in Materials Science
TRISO fuel particles have been developed as nuclear fuels used for a generation IV
nuclear reactor high temperature reactor Such particle consists of a fuel kernel
pyrolytic carbon (PyC) and silicon carbide (SiC) coatings This study has been carried
out to establish a relationship between mechanical properties and microstructures of
SiC coating and PyC coatings produced by fluidized bed chemical vapour deposition
Indentations were used to measure hardness Youngrsquos modulus and fracture behaviour
of SiC and PyC coatings Fracture strength of SiC coatings was measured by crush
test Microstructure of SiC and PyC was mainly characterised by transmission
scanning electron microscopy and Raman spectroscopy
For SiC coatings produced at 1300 ordmC Youngrsquos modulus is an exponential function of
relative density Hardness of SiC coatings is higher than the bulk SiC produced by
CVD and it is attributed to the high density of dislocations and their interactions The
deformation mechanism of SiC coatings under indentation is explained by presence of
defects such as grain boundaries and nano-pores The fracture of these coatings
beneath the Vickers indentation is the Palmqvist cracks and indentation fracture
toughness was in the range of 35-49 MPa m12
The stress-induced micro-cracks are
assumed to be the mechanism for the high indentation fracture toughness Different
hardness and fracture toughness in these SiC coatings are attributed to influences of
defects and grain morphology
Measurement of fracture strength was carried out on SiC coatings deposited at
1300-1500 ordmC Weibull modulus and fracture strength of the full shell are dominated
by the ratio of radius to thickness of coatings and decrease linearly with the increase
of this ratio The influence of SiCPyC interfacial roughness on fracture strength of
the SiC was quantified by self-affine theory The fracture strength decreases linearly
with the increase of the roughness ratio which is the long-wavelength roughness
characteristic After thermal treatment at 2000 ordmC fracture strength decreased in SiC
coatings due to the formation of pores which are results of diffusion of native defects
in as-deposited SiC coatings and the change of Weibull modulus is related to the size
and distribution of pores
For low density PyC coatings Youngrsquos modulus and the mean pressure increase with
the increase of the density however for high density PyC coatings they are
determined by interstitial defects The hysteresis deformation behaviour under
nano-indenation has been found be affected by density variation and thermal
treatment which is proposed to be due to the disorder structure in PyC coatings
Declaration
7
Declaration
No Portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Copyright Statment
8
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this thesis)
owns any copyright in it (the lsquolsquoCopyrightrsquorsquo) and she has given the University of
Manchester certain rights to use such Copyright including for administrative
purposes
ii Copies of this thesis either in full or in extracts and whether in hard or electronic
copy may be made only in accordance with the Copyright Desings and Patents Act
1988 (as amended) and regulations issued under it or where appropriate in
accordance with licensing agreements which the University has from time to time
This page must form part of any such copies made
iii The ownership of certain Copyright patens designs trade marks and other
intellectual property (the lsquolsquoIntellectual Property Rightsrsquorsquo) and any reproductions of
copyright works in the thesis for example graphs and tables (lsquolsquoReproductionsrsquorsquo)
which may be described in this thesis may not be owned by the author and may be
owned by third parties Such intellectual Properties Rights and Reproductions cannot
and must not be made available for use without the prior written permission of the
owner(s) of the relevant Intellectual Property Rights andor Reproductions
iv Further information on the conditions under which disclosure publication and
commercialization of this thesis the Copyright and any Intellectual Property andor
Reproductions described in it may take place is available in the University IP policy
(see httpwwwcampusmanchesteracukmedialibrarypoliciesintellectual-property
Pdf) in any relevant Thesis restriction declarations deposited in the University
Library The University Libraryrsquos regulations (see
httpwwwmanchesteracuklibraryaboutusregulations) and in the Universityrsquos
policy on presentation of Thesis
Acknowledgement
9
Acknowledgement
I will always be appreciative to Professor Ping Xiao for his support and guidance
during this project period and his enthusiasm for work and positive attitude towards
life inspired me I am thankful for what he shared about his own experience doing
research which impressed me and motivated me to make improvement
I would like to thank in particular Dr Eddie Loacutepez-Honorato for his patient guidance
on my experiments and valuable advices on my project His caution on preparing
delicate specimen infected me and helped me through my project He was always
there listening my ideas and discussing with me and he has set an example for being
a good researcher
I give my thanks to all the members in ceramic coating group old and new and I
treasure and appreciate this chance working with you
I would like to give my great gratitude to Dr Alan Harvey for his kind help on
transmission electron microscopy Mr Andrew Forest and Mr Kenneth Gyves on
nano- and micro-indentation Mr Andrew Zadoroshnyj on Raman spectroscopy Dr
Ali Gholinia and Dr Ferridon Azough on TEM sample preparation Dr Judith
Shackleton and Mr Gary Harrison on X-ray diffraction Mr Christopher Wilkins and
Mr Michael Faulkner on scanning electron microscopy and Mr Stuart Mouse on
tensile tests
I am grateful to my dear friends Yola David and Dean and you make my life more
colourful and interesting I would like to thank my beloved parents and brother for
your love care and support and you are great examples of hard work and kindness
My thanks also go to the ORS scheme the CSC grant and the F-BRIDGE for their
financial support during my PhD studies
List of Figures
10
List of Figures
CHAPTER 1 Introduction
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Fig 12 Behaviour of coated layers in fuel a particle [10]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
CHAPTER 2 Literature Review
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
List of Figures
11
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation[62]
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
List of Figures
12
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC coatings Measured by
Indentation
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
List of Figures
13
BF-TEM and (b) DF-TEM
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for extra-Si SiC coatings
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
Fig 45 Cross-sectional SEM image of stoichiometric SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
List of Figures
14
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a)
extra-C SiC (b) extra-Si SiC
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
Fig 58 Log-log representation of the height-height correlation function ∆h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
List of Figures
15
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC coatings
Fig 61 Weibull plots of local fracture strength (L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
Fig 62 Weibull modulus plots of fracture strength of the whole shell (F
f ) before
(black triangle) and after (red circle) thermal treatment
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after thermal treatment (c) and (d) SiC2
before and after thermal treatment (e) and (f) SiC3 before and after thermal treatment
(g) and (h) SiC4 before and after thermal treatment Dashed and solid arrows indicate
growth direction and pores respectively
Fig 64 The IPyCSiC interfacial morphology of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermal treated at 2000 degC (right in
each figure) The white arrow points towards to the interface irregularities (except for
thermal treated SiC4 coating (d)) black circle represents the pores in SiC coatings
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermal treated
at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and SiC2 inset
shows the peak shift of as-deposited (dash line) and after thermal treatment (solid
line) (b) is SiC4 and inset is the high angle diffraction peak after thermal treatment
showing splitting while it is a single peak in as-deposited coating
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
List of Figures
16
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
List of Tables
17
List of Tables
CHAPTER 2 Literature Review
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Table 23 Elastic tensors of 3C-SiC at room-temperature
Table 24 Vickers and nano-indentation hardness of polycrystalline CVD SiC
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Table 26 Summary of the hardness and Youngrsquos modulus for pyrolytic carbon
measured by different methods
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Measured by Indentation
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχv
along the radial and tangential directions
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Table 52 Summary of measured and calculated parameters for all the coatings
List of Tables
18
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Table 54 Results and variations influences on fracture strength for SiC coating
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings
Table 61 Deposition conditions of SiC coatings
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the whole shell before and after thermal
treatment
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
Table 71 PyC coatings deposition conditions and physical properties
Table 72 Domain size (XRD) of as-deposited and thermal treated PyC coatings
Table 73 Changes of mechanical properties after thermal treatment of PyC coatings
Table 74 The parameters used to explain different mechanical properties of high
density PyC
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
CHAPTER 1 Introduction
19
CHAPTER 1 Introduction
11 TRI-Isotropic (TRISO) fuel particles
A fission reaction is about that a large atomic nucleus (such as Uranium-235) is hit by
a neutron and absorbs the neutron forming a larger unstable nucleus The unstable
larger atomic nuclear breaks into two small nuclei and releases a high amount of
energy more neutrons beta and alpha particles and gamma The energy release is
much greater than for traditional fuels eg 1 g Uranium nuclear fuel releases the
same amount of energy as approximately 3 tonne of coal [1] The energy can be
transferred through the cooling system and used to boil the water to make steam to
drive a turbine and electrical generator in a nuclear power station
The high-temperature gas cooled reactor is one of the most promising candidates for
the production of nuclear energy according to its unique features For example it has
high coolant outlet temperature (850-1000 degC) which provides more efficient
electricity production due to the increased difference of the hot and cold coolant
temperatures [2] Furthermore it has the safety advantages due to the enclosure of the
fuel kernel (such as UO2 UC) within few layers of ceramic coatings Currently the
most common technique to fabricate fuels for operating the next generation
high-temperature gas cooled reactors is the TRISO fuel particles coating system [3]
The TRISO system was designed not only to retain all fission products during neutron
irradiation but also to withstand the thermo-mechanical stresses generated during
service [4]
CHAPTER 1 Introduction
20
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Figure 11 is the schematic of TRISO fuel particles embedded in a graphite matrix A
TRISO fuel particle consists of a fuel kernel and coating layers of porous pyrolytic
carbon (PyC) called buffer layer inner dense PyC (IPyC) silicon carbide (SiC) and an
outer dense PyC (OPyC) [5] and these layers were designed to have different
purposes The buffer layer absorbs metallic fission products recoils from kernel and
provides a space for fission product gases It also takes the volume change caused by
the kernel swelling without transmitting forces to outer layers The dense and
isotropic IPyC layer stops the chlorine from reacting with the kernel during deposition
of SiC and provides a firm substrate for the SiC layer Furthermore it protects the
SiC layer from most of the fission products and carbon monoxide during operation
The OPyC layer protects SiC layer during the remainder of the fabrication process
and provides structural stability to the particle during irradiation [3] The high
mechanical properties of SiC are needed to contain the high pressure generated in the
kernel and withstand the stress developed by the dimensional change of IPyC [3]
CHAPTER 1 Introduction
21
12 Failure mechanism
The radiation effects on the performance of the fuel particles such as fundamental
performance characteristics and fission product relsease mechanisms have been well
understood Different testing conditions (eg temperature up to 1300 degC and the does
of neutron) reflected the senariors encountered real applications [6-8]
During irradiation a number of potential failure mechanisms were revealed according
to several tests of coated fuel particles conducted in material test reactors and in
real-time operating HTR reactors [6-8] Chemically the corrosion of SiC by the
fission product palladium has been observed in almost all kinds of fuel compositions
and is considered as one of the key factors influencing the fuel performance However
this could be avoided by limiting the fuel temperature irradiation time or increase the
thickness of SiC layer [9] Mechanically the built up of the internal gas pressure (eg
CO) of irradiated particle and the neutron induced embrittlement of PyC coatings
could promote the failutre of the TRISO fuel particle The primary mechanisms which
may result in mechanical failure of TRISO fuel particles and lead ultimately to fission
product release depends significantly on the magnitude of the de-bonding strength
between IPyC and SiC layers [3 9]
121 Traditional pressure vessel failure mode
In this mode the failure was assumed to occur due to simple overload of the SiC layer
due to internal pressure build-up from fission gas [10] Both IPyC and OPyC layers
shrink during operation because of the irradiation exposure [11] This causes
compression stress in the SiC layer and tensile stress in the PyC layers Failure of the
SiC layer can only occur if the internal gas pressure is high enough to overcome the
compressive stress and critical stress of the SiC layer itself
CHAPTER 1 Introduction
22
Fig 12 Behaviour of coated layers in fuel a particle [10]
Figure 12 shows the basic behaviour modelled in a three layers standard model [10]
It shows that both IPyC and OPyC layers shrink and creep during irradiation but the
SiC layer exhibits only elastic deformation A portion of gas pressure is transmitted
through the IPyC layer to the SiC The pressure continually increases as irradiation of
the particle goes However if the PyC layer could remain in tension the failure by
fracture of SiC layer would be less likely to happen in this mode When the failure of
the PyC layer occurs a tensile hoop stress in the SiC layer is generated This leads to
the development of the stress concentration mode provided by the fracture of the inner
PyC layer
122 Stress concentration mode
In this mode it is been proposed that there is a point at which the fracture strength of
the IPyC would be exceeded during exposure When this occurs a radial crack will
form in the IPyC layer The crack could either penetrate through the SiC layer or
partially de-bonding the IPyCSiC interface This would lead to severe stress
concentration near the crack tip and it could reach the maximum of 440 MPa
according to previous simulation work [10] Once de-bonding goes through the whole
interface the source of stress in the SiC layer would be fission product gas build-up
CHAPTER 1 Introduction
23
and this case has similar failure mechanism of traditional pressure vessel failure mode
Although this process could decrease the probability of failure compared with the
stress concentration case the probability of failure may be higher than the traditional
failure mode Because the stress generated in the SiC layer after de-bonding would
increase [3]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
All these behaviours make it easier for the SiC layer to reach its fracture strength and
lead to the radial crack and failure of the SiC results in an instantaneous release of
elastic energy that should be sufficient to cause simultaneous failure of the
pyrocarbon layer Shown in Fig 13 is a photomicrograph illustrating the failure of a
TRISO coating According to the above discussion all the carbon layers are partially
designed to support or protect the SiC layer The SiC layer serves as the main
containment barrier for gas and metallic fission products [3] and high mechanical
properties of the SiC layer are needed However without appropriate microstructure
and mechanical properties of the PyC layer the stresses or structural changes
introduced in this layer during the irradiation process could result in the failure of the
whole particle [9 12] Furthermore mechanical properties such as the hardness (It is
CHAPTER 1 Introduction
24
the resistance to plasticpermanent deformation of materials under constant load from
a sharp object) Youngrsquos modulus (It reflects the resistance to reversible deformation
of a material) fracture toughness (It describes the ability of a material containing a
crack to resist fracture) and fracture strength (It is the maximum stress at which a
specimen fails via fracture) of SiC and PyC coatings are also important factors for the
safety design and evaluation of the TRISO coating system [10]
13 Goals of dissertation
Due to the importance of mechanical properties of SiC and PyC layers in keeping the
integrity of TRISO fuel particles and providing adequate information for modelling
the probability of failure of particles a good understanding of the elastic plastic and
fracture properties and their relation with microstructure is necessary Therefore all
the work carried out in this project is aimed at studying the relationship between
microstructure and mechanical properties of these two layers aiming to provide a
fundamental understanding about the deformation mechanism and solve the practical
issues
Due to small scale of SiC and PyC coatings two main techniques used to measure
mechanical properties are micronano-indenation and crush test Furthermore to study
the effect of microstructures on mechanical properties characterization techniques
such as transmissionscanning electron microscope and Raman spectroscopy are
widely used in the current work
In this thesis Chapter 2 reviews the recent progress in microstructural characterisation
and mechanical properties of SiC and PyC related materials which provides basic
information with regard to future study about hardness Youngrsquos modulus
deformation mechanism and fracture behaviour in these
Chapter 3 studies the influences of microstructure on hardness and Youngrsquos modulus
CHAPTER 1 Introduction
25
of SiC coatings and focuses on understanding the deformation mechanism of SiC
under nano-indentation The fracture toughness of these SiC coatings is measured by
Vickers-indentation and the importance of crack modes is discussed in Chapter 4
In Chapter 5 the fracture strength of SiC coatings in TRISO fuel particles is measured
and influence of the IPyCSiC interface on fracture strength is discussed Effect of
thermal treatment on fracture strength and microstructure of SiC coatings deposited at
different conditions are introduced in Chapter 6
Chapter 7 investigates the microstructure and mechanical properties of PyC coatings
with focus on deformation mechanism under indentation and the effect of density and
disorders on mechanical properties before and after thermal treatment
At last the main results and conclusions together with suggestions on future work are
given in Chapter 8
CHAPTER 1 Introduction
26
14 References
[1] httpnuclearinfonetNuclearpowerTheScienceOfNuclearPower
[2] J J Powers Fuel performance modelling of high burnup transuranic TRISO fuels
Disertation of Master University of California Berkeley 2009
[3] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[4] D L Hanson J J Saurwein D W McEachern A S Shoeny Development plan
for advanced high temperature coated-particle fuels Report Nopc000513
[5] httpwwwmpafrprocessphp
[6] W Burck H Nabielek A Christ H Ragos AW Mehner HTR coated particle
fuel irradiation behaviour and performance prediction Specialists meeting on
gas-cooled reactor fuel development and spent fuel treatment IWGGCR-8 1983
174-88
[7] H Nickel H Nabielek G Pott A W Mehner Long-time experience with the
development of HTR fuel elements in Germany Nucl Eng Des 217 (2002)
141-51
[8] H Nabielek W Kuhnlein W Schenk W Heit A Christ and H Ragoss
Development of advanced HTR fuel elements Nucl Eng Des 121 (1990)
199-210
[9] K G Miller D A Petti J Varacalle T Maki Consideration of the effects on
fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[10] A C Kadak R G Ballinger M JDriscoll et al Modular pebble bed reactor
project university research consortium Annual report INEELEXT-2000-01034
MIT-ANP-PR-075
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
CHAPTER 1 Introduction
27
treatment J Nucl Mater 374 (2008) 445-52
[12] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
CHAPTER 2 Literature Review
28
CHAPTER 2 Literature Review
21 Introduction
To model the probability of failure of fuel particles a number of key mechanical
properties of silicon carbide (SiC) are needed such as Youngrsquos modulus hardness
fracture toughness and fracture strength [1 2] These properties could be affected by
the microstructure of SiC coatings such as orientation porosities grain size and
defects [1-5] The small dimensions of the SiC coating limits the techniques available
to measure its mechanical properties However the development of the
nano-indentation has provided an important tool for probing the mechanical properties
of small volumes of material From the load ndash displacement data many mechanical
properties such as hardness Youngrsquos modulus and even fracture behaviour can be
determined [6] When an indentation system is used in conjunction with a focused ion
beam system and a transmission electron microscope images of deformation under
the nano-indentation can be obtained and the 3-D crack morphology can even be
reconstructed [7] Since there is a need to explain the high mechanical properties of
SiC deposited at temperature of 1300 ordmC by fluidized-bed chemical vapour deposition
[8] this combination of techniques could provide fundamental understanding of the
deformation mechanisms during indentation Another important parameter is fracture
strength and there have always been efforts to establish one method to characterise
fracture strength of SiC for example by brittle-ring test [9] whole particle crush test
[10] and modified crush test [5] Furthermore the high temperature application of SiC
and the compact of fuel pellet could affect the microstructure of SiC [2] which would
lead to the changes of mechanical properties
CHAPTER 2 Literature Review
29
The pyrolytic carbon (PyC) has been introduced by previous studies [11-14] and is
important in helping the SiC act as the main loading bearing layer The high
mechanical properties such as Youngrsquos modulus and anelasticity of PyC are necessary
to protect from damage caused by internal stresses and by external mechanical
interactions [12] However cracking and debonding between the SiC and inner PyC
layers could increase the probability of failure of TRISO fuel particles [13 14] It was
shown that without appropriate microstructure and mechanical properties of PyC the
structural or stress changes introduced in the coating during irradiation process could
result in total failure of the particle [11 13] The microstructure of PyC varied under
different deposition conditions [15] and it dominates the mechanical properties of
PyC coatings Therefore in this Chapter we review both the microstructure of SiC
and PyC including atomic structure morphology and defects and their mechanical
properties eg hardness Youngrsquos modulus deformation behaviour etc
22 Microstructure of silicon carbide
221 Atomic structure
The basic structural unit in SiC is a covalently bonded tetrahedron a carbon atom is at
the centre of four silicon atoms (C-Si4) and vice versa (Si-C4) The length of each
bond and the local atomic environment are nearly identical while the stacking
sequence of the tetrahedral bonded Si-C bilayers could be different The different
stacking sequences give SiC more than 250 polytypes [16] of which the 3C 4H 6H
and 15R are the most common The leading number of polytypes shows the repetition
of the SindashC pair and the letter C H and R represents the cubic hexagonal and
rhombohedral crystals respectively The 3C is the only cubic polytype in which the
stacking sequence of the planar unit of Si and C in tetrahedral coordination is depicted
as ABCABC in the lt111gt direction The cubic SiC crystal is called β-SiC and all
the other polytypes are α-SiC The crystal structures of 3C- 4H- 6H- and 15R-SiC
are schematically illustrated in Fig 21(a) [17] and corresponding XRD images were
CHAPTER 2 Literature Review
30
shown in Fig 21(b) [18]
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Although the transformation of SiC polytypes is primarily dependent on temperature
it could be affected by purity of the pre-existing phase pressure andor stacking faults
[19-22] The cubic form of SiC (β -SiC) is believed to be more stable than the
hexagonal structure (α-SiC eg 6H-SiC) below 2100 ordmC [19] However the polytype
of 2H-SiC which has the simplest stacking sequence is rarely observed at higher
temperature Krishna et al [20] reported that single crystals of 2H-SiC can be easily
transformed to 3C-SiC on annealing in argon at temperatures above 1400 ordmC It was
CHAPTER 2 Literature Review
31
found that the pre-existence of α-SiC (except 2H-SiC) could promote β-SiC
transformation to α-SiC while the transformation from α-SiC (6H-SiC) back to β-SiC
(3C-SiC) needs high temperature and pressure [21]
It has also been shown that the phase transformation could be closely related to
pre-existing defects such as stacking faults and their distribution [18] of which the
concentration is high even in single crystal SiC [22] Furthermore due to their low
formation energy the other intrinsic defects such as vacancies interstitials and
antisites were found to be common in SiC [23] These defects could affect mechanical
properties of SiC [8] so it is important to review their structure and properties
222 Defects in SiC
2221 Stacking faults and dislocations
A stacking fault is a disordered part of the ordered sequence in fcc crystal and the
most common stacking faults in cubic SiC are intrinsic and extrinsic stacking faults
(ISF and ESF) [24] For ISF the resulting stacking sequence is ABCACABC
if a double layer B is removed (condensation of vacancies) as for instance shown in
Fig 22[24] The ESF could be thought of as adding a double layer to the stacking
sequence (condensation of interstitials) resulting stacking sequence of
ABCACBCABChellip
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
CHAPTER 2 Literature Review
32
Another interpretation of the stacking faults is related to a twist of the three equivalent
bonds between two bilayers by 180deg [24] There may be an intrinsic shear stress
which could promote the glide of partial dislocations and thereby result in a faulted
crystal containing an error in stacking sequence so itrsquos reasonable to interpret
stacking faults in this way [25] Compared with dislocations and vacancies no bonds
are broken by stacking faults leading to a small energy difference between faulty and
perfect structures [26]
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
[27] [28] [24] [29] [30] [31] [32]
ESF (mJ m-1
) -15 -- -28 -6 -61 -154 -323
ISF (mJ m-1
) 12 34 -34 14 138 111 -71
Table 21 lists the formation energy of stacking faults in SiC and it shows that
extrinsic stacking faults have much lower formation energy than intrinsic stacking
faults in fact the values become negative The negative formation energy of stacking
faults in 3C-SiC means they can be formed very easily even more easily than perfect
3C-SiC As a result the stacking faults in 3C-SiC are spontaneously formed and most
likely in the form of extrinsic faults in the lt111gt direction Furthermore due to the
low energy of formation the length of a stacking fault can only be limited by the size
of the crystal or the presence of other defects that act as obstacles [33]
CHAPTER 2 Literature Review
33
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
The morphology of stacking faults in SiC observed by TEM is given in Fig 23 It
shows that the stacking faults could form a small domain (around 1 nm thick in Fig
23(a)) with different distances between small domains When a large concentration of
stacking faults exists in SiC it has been claimed that a conversion of cubic SiC to
hexagonal SiC on the nano-scale could happen by twinning [35] Furthermore the
stacking sequence of the faulted 3C-SiC was previously treated as random mixing of
α-type unit structures such as 6H and 4H in the 3C structure [36] Therefore it is
important to identify the properties and the microstructure of stacking faults of SiC
layers in TRISO fuel particles because the presence of α-SiC could result in reduction
of strength under irradiation which was due to enhanced possibility of anisotropic
swelling of α-SiC under irradiation compared to β-SiC [37]
(a) (b)
(c)
CHAPTER 2 Literature Review
34
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Figure 24 gives the XRD images of SiC in TRISO fuel particle deposited by fluidized
bed chemical vapour deposition showing the extra peak at 2θ~335ordm a high
background intensity at the peak at 2θ~353ordm and the broadening of the 3C peaks [8]
This is different from the perfect atomic structure of 3C-SiC as shown in Fig 21(b)
According to a previous simulation study [18] this kind of XRD diffraction pattern
could be caused by the existence of a high density of stacking faults and twins in the
regular cubic sequences It was demonstrated that it was unlikely to be due to the
presence of 2H-SiC or other polytypes [18] and two possible explanations were given
First two types of crystalline 3C-SiC with different populations of faults and twins
and second one type of crystal having clusters of faulted regions In SiC single
crystals although the concentration of stacking faults and twins is high the density of
dislocations is low (102-10
5cm
2) compared with metallic materials [22]
Figure 25 shows schematic images of the dislocations in face centred cubic (fcc)
crystals (β-SiC) The perfect dislocation is the (111) lt110gt system with burgers
vector of b=a2[110] (0308 nm) in SiC as shown in Fig 25(a) The perfect
dislocation could be easily dissociated into two partial dislocations of a6[121] and a6
CHAPTER 2 Literature Review
35
[21-1] as shown in Fig5 (a) and (b) because this reduces the total energy As a result
of this split a stacking fault must also be produced between the two partial
dislocations [38] Figure 25 (c) and (d) are lt110gt projections showing the Shockley
and Frank partial dislocations and their formation all related to the formation of
stacking faults
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
(a)
(b)
(c) (d)
CHAPTER 2 Literature Review
36
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
By comparing with previous studies [39-41] it is found that the relationship between
dislocation and stacking faults is complex The stacking faults have influences on the
mechanical properties for example enhancing the mobility of dislocations [39]
Different roles of stacking faults in II-VI heterostructures and devices have been
observed and results indicate that the stacking faults serve as the sources of misfit
dislocations [40] It is necessary to study the propagation of stacking faults or the
formation of stacking faults under stress and their influence on the properties of SiC
For example generation of stacking faults is shown to have occurred during the
fracture process together with the corresponding partial dislocation Furthermore
Agarwal et al [41] observed the growth of stacking faults from certain basal plane
dislocation within the base layer of the SiC
2222 Non-stoichiometric and point defects
Another common class of defects in SiC are non-stoichiometric (excess silicon or
carbon) and point defects [23 41 42] The purity of SiC may have effect on the
crystal structure strength corrosion resistance thermal conductivity diffusion
coefficient and other coating properties depending on its amount [43] The purity
could also affect defects in SiC eg if the stoichiometry deviates (even less than 1)
the concentrations of point defects in cubic SiC were found to be elevated [23]
Although the effect of point defects on general behaviour of nuclear fuel during
application process is not clear but their effect on microstructure evolution during
thermal treatment could be significant [44]
Silicon in SiC Stoichiometric 3C-SiC has generally been obtained at temperatures
between 1500 and 1600 [45] with carbon and silicon codeposited above and below
this temperature range By adding propylene as another carbon source the deposition
temperature of stoichiometric SiC could be reduced to about 1300 [8] The extra-Si
CHAPTER 2 Literature Review
37
SiC is less commonly investigated compared with the extra-C SiC because it has
been found that during the irradiation process the extra-Si plays a negative role in
material properties due to its low melting point [1] It has been found that the effect of
excess-Si on the Youngrsquos modulus and hardness it is more likely depending on its
amount and location [8 46]
Raman spectroscopy is an effective way to identify free Si both in amorphous and
crystalline phases eg it detected excess-Si when the XRD result showed the SiC was
stoichiometric [8] If the extra-Si is high (could be detected by XRD) TEM could be
used to detect its location and characterise the Si lattice contrast For example TEM
was carried out using both high resolution [35 47] and dark field imaging modes [48]
The HRTEM images in Fig 26 show the 3C-SiC crystallite with Si inclusions in
which nano-crystalline 3C-SiC and Si are separated by a weakly crystallized
interphase
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
(a)
(b) (c)
β-SiC
β-SiC
β-SiC
β-SiC
Si
Si
025 nm
025 nm
025 nm
0 312 nm
0312 nm
CHAPTER 2 Literature Review
38
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
Figure 27 shows bright-field and dark-field images of extra-Si SiC It shows the
crystalline Si as bright points in the dark background located at the grain boundaries
[48] The above observations were carried out in SiC with more than 1 at excess Si
(by comparing the intensity of Si Raman peak) as such observations are difficult
when the amount of excess Si is low Since the Youngrsquos modulus in SiC with low
amount of excess Si was comparable to that of stoichiometric SiC[8 46] it may have
unique properties that are worth further exploitation
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Carbon in SiC Excess C can also be identified by Raman spectroscopy but it is more
difficult to quantify its content and observe where this extra carbon exists due to its
small atomic number A comparative method was used to measure the content of
excess carbon by combining Raman spectroscopy auger electron spectroscopy
electron probe microanalysisand X-ray photoelectron spectroscopy [49] Once the
carbon concentration was measured (by above methods) the ratio of free excess to
SiC peak intensity (I796I1600) of Raman spectroscopy could be obtained as shown in
Fig 28 and the excess carbon concentration in the nearly stoichiometric SiC could
(a) (b)
CHAPTER 2 Literature Review
39
be estimated [49]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
There are few reports regarding the location of excess C in SiC The research carried
out by KKaneko et al [50] in carbon-doped hot pressed szlig-SiC showed that grain
boundaries were found to be free of any second phase by HRTEM although excess C
is found to form the second graphite phase Mykhaylyk and Gadzira revealed that
extra-C atoms are located as planar defects [51] The C atoms in the β-SiC structure
were supposed to arrange either as diamond-like carbon interlayers or as
non-correlated point defects after sintering of the as-synthesized powder at high
pressures and high temperature Since it showed that the presence of excess C atoms
in SiC crystal structure changes the local atomic environment [52] they may exist
within the SiC crystal and be correlated with other defects
The above discussion about the excess Si and C indicates that their influences on
properties of SiC depend on their content and that they could be discussed together
with the other point defects when their amount is low (less than 1 at ) [23]
Point defects in SiC SiC has eight kinds of point defects which keep the tetrahedral
symmetry of the perfect SiC crystal [23] They are carbon vacancies (Vc) silicon
vacancies (VSi ) carbon antisites (CSi) silicon antisite (Sic) a tetrahedral interstitial
silicon atom surrounded by four Si atoms (SiTSi) a tetrahedral interstitial silicon atom
CHAPTER 2 Literature Review
40
surrounded by four C atoms (SiTC) a tetrahedral interstitial carbon atom surrounded
by four Si atoms (CTSi) and a tetrahedral interstitial carbon atom surrounded by four
C atoms (CTC) [23] The formation energies for these defects are listed in Table 22
Due to their low formation energies the individual antisites and vacancies
particularly CSi were expected to appear even in as-deposited coatings [53 54]
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Vc VSi Sic CSi SiTSi SiTC CTSi CTC
Ef (eV) 59 68 73 11 150 147 86 110
The importance of point defects for different applications of SiC was studied and
these properties were studied in the relation to the properties of the point defects
including their formation annealing and interaction with each other [53] According
to Raulsrsquos study [54] the actual results of diffusion of CSi are more likely to be the
formation of CSi clusters which could be promoted by the diffusion of vacancies For
the coexistence of self-interstitials and vacancies (eg in irradiated material) it has
been found that the annealing temperature for VSi and Vc by recombination in β-SiC
were about 500 ordmC and 750 ordmC respectively [55] For as-deposited β-SiC without
interstitials the annealing process was only dominated by the out-diffusion of
vacancies the disappearances of VSi and Vc were found at temperature of 1400 ordmC and
1600 ordmC respectively [54] It is also been found that the migration of silicon vacancies
is easier than carbon vacancies due to its lower migration energy barrier Furthermore
in the case of excess carbon inside SiC the carbon clusters may form in SiC after
annealing and the size of the cluster depends on the content of interstitial carbon [56]
The general atomic-scale microstructure of SiC was reviewed above which showed
high degree of defects such as stacking faults dislocations vacancies and antisites
CHAPTER 2 Literature Review
41
The kind and concentration of these defects could affect the mechanical properties
such as hardness Youngrsquos modulus and fracture behaviour of SiC Since variation of
mechanical properties could also be due to other microstructural factors such as grain
size and density the relationship between microstructure and mechanical properties
are further reviewed in the following session
23 Properties of silicon carbide
231 Youngrsquos modulus
Youngrsquos modulus is physically related to the atomic spacing atomic bond strength
and bond density It is accepted that high-purity SiC material eg CVD SiC exhibits
the highest elastic modulus and that a porous microstructure with a high
concentration of impurities could decrease the elastic modulus [1 57] In contrast
neither grain size nor polytype was recognized as having a significant effect on the
elastic modulus of SiC in coated fuel [1 58]
Table 23 Elastic tensors of 3C-SiC at room-temperature
C11 (GPa) C12 (GPa) C44 (GPa) Z Ref
3C-SiC a 3523 1404 2329 18196 [59]
3C-SiC b 511 128 191 10026 [1]
3C-SiC c 390 142 256 -- [60]
3C-SiC a 420 126 287 19503 [61]
a Theoretical calculations
b Sonic resonance measurement
c Raman Spectroscopy
According to the definition of Youngrsquos modulus an important factor which could
affect its value for SiC material is the texture which is the degree of anisotropy (lack
of randomness with regard to the orientation) of SiC crystals The Youngrsquos modulus is
different by a combining of elastic tensors for deformation of the crystal in different
CHAPTER 2 Literature Review
42
orientation The elastic tensors or the stiffness tensors reflect the linear stress-strain
relation of a material There are 81 elastic tensors because the stresses and strains
have 9 components each However due to the symmetries of the SiC the tensors were
reduced to 3 unknown values They could be measured by sonic resonant method [1]
and Raman spectroscopy [60] based on vibrational theory of the crystal lattice They
are defined for SiC in Table 23 and will cause the variation of Youngrsquos modulus for
anisotropic materials The elastic tensors for 3C-SiC identified by previous theoretical
and experimental results [59-61] are substantially different from the current updates
of sonic resonance data The difference could be caused by the difference of the size
of SiC mateirals which could introduce the influences of defects such as grain
boundaries and stacking faults It was proposed to be more reasonable estimation for
SiC in TRISO fuel particle [1]
A measurement of the anisotropy in β-SiC (faced centre cubic crystals) is the ratio of
the two shear moduli [3] 100 shear modulus and 110 shear modulus μ0 and μ1
respectively which is
0 44
1 11 12
2CZ
C C
(1)
the parameter Z is known as the Zener ratio or elastic anisotropy factor (given for
different elastic tensor Table 23) When Zgt1 the Youngrsquos modulus is minimum
along lt100gt and a maximum along lt111gt and the representational surfaces for
Youngrsquos modulus in cubic crystals is shown in Fig 29 For the case when Z=1 the
cubic crystal would also be isotropic and the representation surface would be
spherical
CHAPTER 2 Literature Review
43
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
If the samples were random polycrystals which means samples are isotropic the
theoretical Youngrsquos modulus can be unambiguously given by [3]
3
[1 ( 3 )]E
B
(2)
While bulk modulus and shear modulus are
11 122
3
C CB
(3)
1
0 1
1 0
52( 6 )
(4)
where 0 44C 1 11 12( ) 2C C and
01
0 0
3( 2 )
5 (3 4 )
B
B
(5)
The theoretical value can be gained when the elastic constants are known Using the
Eqs (2-5) the theoretical Youngrsquos modulus E was calculated to be 496 GPa for
isotropic SiC materials when the elastic tensor obtained by Lambrecht et al was used
The calculated value is close to the Youngrsquos modulus measured by nano-indentation
(about 527 GPa) of isotropic bulk CVD SiC [62] But this value is higher than the
Youngrsquos modulus measured by nano-indentation of SiC in TRISO fuel particle which
is about 450 GPa [8 46]
By using the elastic tensors measured by sonic resonance in Snead et alrsquos study [1]
CHAPTER 2 Literature Review
44
the calculated Z (10026) is very close to 1 and it means the Youngrsquos modulus in
TRISO coated fuel particle may show no orientation effect According to Eqs (2-5)
the calculated Youngrsquos modulus is about 459 GPa under the elastic tensors given in
Ref [1] This value is close to the Youngrsquos modulus measured by nano-indentation in
TRISO fuel particle regardless of the orientation effect [1 8 46] Therefore for
TRISO fuel particle the recommended elastic tensors measured by sonic resonances
were supposed to be appreciable due to the scale and the microstructure similarities of
SiC materials [1]
Another significant factor which affects the Youngrsquos modulus is the density The
elastic modulus E at room temperature can be empirically expressed in an exponential
function of porosity pV as [63]
0 exp( )pE E CV (6)
where 0E is the elastic modulus and C is a constant of 357 for a pore-free bulk CVD
SiC pV is the ratio of the relative density difference to the theoretical density of SiC
(322 gcm3)
The relationship between density and Youngrsquos modulus of different kinds of SiC
materials measured by different methods were summarised in a previous study [1] as
shown in Fig 210 It has been found that the standard deviation of elastic modulus of
SiC is about plusmn 10 when the density is higher than 99 and increased to plusmn 15 for
porosity higher than 1
CHAPTER 2 Literature Review
45
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
232 Hardness
In a brittle material indentation hardness is defined as the mean pressure the material
will support under load and it is a complex property which could involve crack
initiation and propagation and the development of new surfaces during the
indentation process [1] Furthermore the value of hardness measured by indentation
also depends on external factors Due to the difference in dimensions of materials
such as the bulk small scale and thin film materials indentation on the nano- micro-
and even macro-scale have been used to measure the hardness [64] The hardness of
β-SiC related material has mainly been investigated by Vickers and nano-indentation
techniques (introduced in the later part of this session according to Ref [65]) as
summarized in Table 24 Reviews have found that the nano-hardness is generally
higher than Vickers hardness [1] which was attributed to the indentation size effect
Although few hardness values of β-SiC are available to be compared (given in Table
24) it shows the difference of hardness within a given sample Regardless of external
influences on the measurement of hardness generally it can be affected by grain size
or grain morphology [46] density composition and defects [1 8 66] To identify the
CHAPTER 2 Literature Review
46
controlling factor for hardness it is necessary to understand the deformation
mechanism of SiC under indentation
Table 24 Vickers and nano-indentation hardness of β-SiC related materials
Deformation mechanism Research into the deformation mechanism of SiC have
shown the availability of dislocation related plasticity [70] phase transformation
(cubic phase to amorphous) [71 72] fracture mechanisms [73] and also the
combination of any two or three [62 73]
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
First the dislocation related plastic deformation was found in single crystal 6H-SiC
[70] and the propagation morphology of dislocations was observed after indentation
as shown in Fig 211 This observation confirmes that the dislocation slip is a
Materials Vickers hardness (GPa) Nano-hardness (GPa) Ref
Single β-SiC (001) 28 -- [67]
CVD β-SiC 207-32 325-406 [466668]
FBCVD β-SiC -- 36-42 [8]
Sintered β-SiC 211-239 -- [69]
500 nm
CHAPTER 2 Literature Review
47
mechanism of plastic deformation from nucleation of a few dislocation loops (at or
near the theoretical strength) to extensive dislocation plasticity
Furthermore the dislocation related plastic deformation in polycrystalline CVD β-SiC
(with micro meters grain size) was first observed by Zhao et al [62] It was found that
the initiation of the plastic deformation was reflected by the burst (pop-in) of the
force-displacement curve which is similar as the initiation of plastic deformation in
metallic materials as shown in Fig 212(a)
According to the Hertzian contact theory [74] the burst was attributed to initiation of
the dislocation glide by comparing the shear stress generated under the indentation at
that load with the theoretical shear stress in β-SiC [62] During the whole indentation
process it was shown that shear slip is the predominant deformation mechanism and
that cracks were associated with the shear faults Figure 212(b) is one of the TEM
images showing the microstructure under indentation and it shows the dislocation
induced shear bands at one side of indent [62] which depend on the orientation of
grains
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation [62]
Second following the observations of phase transformation under indentation in
silicon [75] and the formation of SiC amorphous phase during high speed machining
(a) (b)
CHAPTER 2 Literature Review
48
process [71] the investigation of phase transformation under indentation was carried
out in SiC [7274] It has been demonstrated thermodynamically that the direct
amorphization is less likely to happen under nano-indentation [76] The
amorphization observed in single crystal SiC was attributed to the formation
propagation and accumulation of dislocations which formed the disordered phase at
the maximum stress region under a punch indentation [71] In SiC with nanometers
grain size the molecular dynamic study indicated thedominated deformation under
nano-indenation is a crossover of the indentation-induced crystallization to
disordering leading to amorphization [72] as shown in Fig 213
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Further studies demonstrated that the phase transformation from β-SiC to α-SiC is not
possible under nano-indentation because a pressure of nearly 100 GPa is needed [76]
even when assisted by high dislocation density shear stress and temperature This
simulation work concluded that the primary response of β-SiC to nano-indentation is
dislocation nucleation and propagation which has been confirmed by experimental
observations [62]
Third the plastic deformation of β-SiC under indentation was divided into two parts
CHAPTER 2 Literature Review
49
which are primary dislocation initiation and propagation and the formation of micro
cracks [73] The former contributes to 13 of plastic deformation under indentation
while the later provides 23 of total deformation The hardness related plastic
deformation could be explained well by this mechanism which included above two
process as discussed in previous studies [1 46 62] Moreover considering the effect
of micro cracks the deformation mechanism under indentation could be related to
other factors which could contribute to the formation of micro cracks such as
porosity grain boundaries and stacking faults in SiC [3]
Youngrsquos modulus and hardness of coatings in TRISO fuel particle can be measured by
nanoindentation due to the limitation of small dimension A typical
load-displacement curve and the deformation pattern under nanoindentation of an
elastic-plastic sample during and after indentation are shown in Fig 214 in which the
hc is contact indentation depth and hs is the displacement of the surface at the perimeter
of the contact [65] The peak load and displacement are Pmax and hmax respectively
and the diameter of the contact circle is 2a During unloading process the elastic
displacements are recovered and when the indenter is fully withdrawn the final depth
of the residual hardness impression is hf [65]
Nanoindentation hardness is the ratio of the load to the projected contact area of the
indentation The mean pressure that the material can support under indentation is
defined as the hardness From the loadndashdisplacement curve as in Fig 214(a) hardness
can be gain when the load is at the maximum value
A
PH max (7)
where A is the projected contact area
CHAPTER 2 Literature Review
50
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
The elastic modulus of the indented sample can be inferred from the initial unloading
contact stiffness S=dPdh ie the slope of the initial portion of the unloading curve A
geometry-independent relation involving contact stiffness contact area and elastic
modulus can be derived as follows
2A
S E
(8)
where szlig is a constant that depends on the geometry of the indenter (szlig=1034 for a
Berkovich indenter) [65] and Er is the reduced elastic modulus which accounts for the
fact that elastic deformation occurs in both the sample and the indenter Er is given by
CHAPTER 2 Literature Review
51
22 11 1 i
r i
vv
E E E
(9)
where E and υ are the elastic modulus and Poissonrsquos ratio for the sample respectively
and Ei and υi are the same quantities for the indenter For diamond Ei=1141 GPa and
υi=007[65]
For an indenter with a known geometry the projected contact area is a function of the
contact depth The area function for a perfect Berkovich indenter is given
by 2245 cA h Indenters used in practical nanoindentation testing are not ideally sharp
Therefore tip geometry calibration or area function calibration is needed A series of
indentations is made on fused quartz at depths of interest A plot of A versus hc can be
curve fit according to the following functional form
11 12 1 1282 4
1 2 3 8245 c c c c cA h C h C h C h C h (10)
where C1 through C8 are constants In some cases only the first three constants were
considered
The contact depth can be estimated from the load-displacement data using
maxmaxc
Ph h
S (11)
Where ε is a constant that depends on the indenter geometry (ε=075 for a Berkovich
indenter)
It is worth noting that high Youngrsquos modulus and hardness does not gurantee the
suitability of ceramic material to an engineering application because of the
importance of other mechanical properties such as fracture toughness and fracture
strength
CHAPTER 2 Literature Review
52
233 Fracture toughness
The definition of fracture toughness from Munz and Fett is [77] if a component or a
test specimen with a crack is loaded the stress intensity K1 increases with increasing
load until unstable crack propagation occurs at a critical value of K1 This critical
value is the fracture toughness (KIC) Therefore the measurement of fracture
toughness should be made on sample with a pre-crack however due to the small size
of SiC coating methods could be used are limited Although the most recently
developed micro-beam bending test could measure the fracture toughness of SiC in
TRISO fuel particles [78] this process is costly and time consuming because it
involves the preparation of micro-beams and notched cantilevers by focused ion beam
milling which limites the application of this technique
Indentation is now one of the most commonly used techniques to evaluate the fracture
toughness of ceramics and coating systems because it is easy to perform does not
need special samples and causes only negligible surface damage However some
researchers have declared that the indentation method is not suitable for the
measurement of fracture toughness [79 80] They concluded that the indentation
method does appear to represent some form of a complex crack arrest phenomenon
but that this occurrs in the presence of a multiple-crack path and a highly complex
residual stress field
Despite of these considerations the indentation method is an effective way to
compare the fracture behaviour of materials [80] particularly for small size specimens
and it provides information about the crack initiation and propagation Figure 215 is
the most typical characterization of the crack system generated by Vickers indentation
[81] This crack system is termed as median-radial cracking and consists of
approximately semi-circular cracks
CHAPTER 2 Literature Review
53
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
The mode of crack initiation and propagation under an indenter proposed by Chiang
et al explains many of the features observed in indentation crack patterns and is the
most recent advance [82] It was found that radial cracks are the first to initiate
trigged by a combination of the highly tensile surface stress field and the availability
of surface flaws [74 82] These cracks grow on unloading and can either propagate
into the plastic zone (half penny cracks) or terminate in the elastic zone (Palmqvist
cracks) [83] depending on the microstructure of the material
For different types of crack modes such as half-penny and Palmqvist cracks different
equations were developed based on theoretical analysis of stress field and empirically
calibrations to calculate the fracture toughness under indentation For example in the
half penny crack model the Vickers indentation fracture toughness was most
frequently determined using the relationship proposed by Anstis et al [84] This
equation was first inferred based on isotropic materials and it is suitable for general
application to well-developed cracks [84]
1 2
3 2( )IC
E PK
H c (12)
Where P is the indentation load c is the radial crack length from indentation centre to
crack tip E and H are the Youngrsquos Modulus and hardness of the materialand χ
denoted as the geometrical constant which is independent of the materials The Eq
CHAPTER 2 Literature Review
54
(12) was developed on the basis of half penny cracking in homogeneous brittle
materials under high load for example in glasses [84]
The above information shows that it is possible to compare fracture toughness under
indentation in SiC coatings with different microstructures The fracture toughness of
SiC could depend on a large number of factors such as grain size porosity micro
cracks and inclusions which could dissipate the fracture energy from the main crack
[3] According to a previous review [1] fracture toughness of SiC peaks at the grain
size range of 1-5 microm So fracture toughness of SiC in TRISO fuel particle is likely to
be influenced by the grain size due to the similar range of grain size Although micro
cracks and pores could improve fracture toughness they would decrease the strength
[3] which is detrimental for the safe design of fuel particles Over several decades
studies have worked to improve the fracture toughness by introducing a
heterogeneous microstructure such as weak grain boundary phases [85] In the
heterogeneous phase toughening mechanism the cracks could initiate in or be
reflected into weak defects and thereby dissipate the fracture energy for the main
crack propagation Furthermore the distribution of grain boundary character (the
crystallagraphic type and frequency of grain boundaries) and morphology could
influence the fracture toughness [85 86] Different grain boundary orientations and
their frequency were found to affect the fracture toughness by controlling the
intergranular fracture of materials [86] Different grain morphologies such as
elongated grains could increase the fracture toughness by crack bridging or by
generating micro cracks along grain boundaries or triple junctions [85] No
heterogeneous phase is supposed to exist in SiC in TRISO fuel particles so the
fracture toughness is most likely to be affected by grain morphologies or as-deposited
defects
According to the Griffth fracture theory once the size of the critical flaw is the same
the fracture toughness is propotional to the fracture strength which is another
CHAPTER 2 Literature Review
55
parameter used in modelling of the probability of the failure of fuel particle
234 Fracture strength
For brittle materials the fracture strength is best considered as a distribution rather
than a fixed value as the flaws (such as surface cracks pores and inclusions) from
which fracture initiates vary in size and type (result in different frature strength value)
between nominally identical samples [3] The Weibull approach is a commonly used
empirical method to characterise the strength of a brittle material It assumes a simple
power-law stress function (eg in Eqs (18-20)) for the survival of the elements
which is integrated over the body volumesurface area (as shown in Eqs (19) and
(21)) In many cases this function gives results in the form of Weibull modulus (m in
Eq (19)) and characterstic strength which describe the width and magnitude of the
strength distribution [3] The Weibull modulus is the slope of Log-Log distribution
function of the survival of elements and strength (Eq (19)) For engineering
application the high Weibull modulus represents the small variation of the fracture
strengthes for a given material
Higher Weibull modulus reflects lower variability of the strength and it is typically in
the range of 5-20 [3] The commonly used strength test methods for bulk ceramics are
uniaxial tension three- and four-point bending However the small dimensions of
TRISO fuel particles make it difficult to measure the strength by those conventional
methods As a consequence some specific methods were developed in the last few
decades such as O-ring test [87 88] C-ring test [88] hemisphere bending [10]
internal pressurization [89] and crush test [5 89 90] The schematic of easily
repetitive fracture strength test geometries are given in Fig 216 and the obtained
fracture strength by different methods was shown in Table 25
CHAPTER 2 Literature Review
56
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Methods L
f (MPa) Weibull Modulus F
f (MPa) Ref
O-ring compression 596-1412 41-66 -- 87
O-ring compression 1050-1890 48-94 -- 88
C-ring Compression 980-2200 40-90 -- 88
Semi-spherical bend 720-1350 70-80 340-620 10
Inner pressurization -- 43-62 222-448 89
Crush test -- 58-75 356-427 89
Crush test 770-1324 40-73 330-647 5
Crush test 1484-1721 135-183 1045-1091 90
L
f Local fracture strength F
f Fracture strength of the full particle
The local fracture strength is in the range of 596-2200 MPa and the fracture strength
of the whole particle varies from 222 MPa to 1091 MPa Such significant variation is
tought to be caused by the differences in specimen size and loading mode which were
related to the nature of the Weibull distribution [1 3] It has been demonstrated that
specimens with larger volumesurface area (under the same loading mode) have lower
strength because there is an increased probability that a larger flaw exists in a larger
body Similarly when there is no volume difference the loading mode which stresses
larger area has lower local fracture strength [3] These discussions show the
importance of regulating the fracture strength test method and producing specimens
with regular shape and size
CHAPTER 2 Literature Review
57
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
The modified crush test developed by Byun et al [5] is recommended for the fracture
strength measurement of SiC in TRISO fuel particles because it considered the effect
of contacting area between SiC shell and plunger which reduced the variation and
uncertainty of the stress distribution under tensile stress
Modified crush test When a partial spherical shell is diametrically loaded by an
external load F concentrated on a small circular contact area of radius 0 the
maximum membrane stress and bending stress are given by [91]
2
1 2
1membrane
FC
t
(13)
CHAPTER 2 Literature Review
58
2 2
1bending
FC
t
(14)
where ν is the Poisson ratio t is the thickness of shell and C1 and C2 were defined as
2
1 0115004022050 C (15)
)27031exp(204412 C (16)
2 2 2 1 4
0[12(1 ) ( )]r R t (17)
max membrane bending (18)
where max (L
f ) is the fracture strength for locally loaded specimens R is the outer
diameter of shell t is the thickness of the SiC shell The distribution of local fracture
strength is analysed by the Weibull distribution function which presents the
cumulative probability of failure P as [5]
mL
f
E
m
s
F
fSdAP
00
exp1exp1
(19)
where L
f m 0 and ES are the local fracture strength the Weibull modulus the
characteristic sterngth and the size effect factor respectively The size effect factor is
dAS
m
s L
f
F
f
E
Byun et al [5] used the probability estimator as follows
1
N
iPi (20)
where iP is the probability of failure for the i th-ranked strength and N is the
CHAPTER 2 Literature Review
59
sample size The increased probability that the full SiC shell has more critical flaws
compared with the stress-weighted surface is corrected by the size effect and the
fracture strength of the full shell (F
f ) is given
L
f
m
L
f
m
F
E
L
EF
ftR
r
S
S
1
2
2
0
1
)(4
(21)
After adjusting the size effect the fracture strength of the full particl of different SiC
coatings could be compared In a previou study [87] the difference of the fracture
strength was attributed to the microstructural variations which were determined by
deposition conditions [87] More detailed analysis [510] showed that the variation of
fracture strength was due to factors such as porosity roughness of the IPyCSiC
interface and grain size For example Evans et al [10] observed that the surface
roughness influenced the failure of the particle withstrength improved by reducing
the inner surface roughness According to above discussion the variation of Weibull
modulus could be attributed to the different test methods flaw distribution and sample
size [3 5]
Micostructure and mechanical properties of as-deposited SiC are reviewed above
which may change after high temperature treatment and the degree of evolution could
be different due to variational deposition conditions of SiC coatings As summarized
in a previous study [92] one of the critical properties for SiC layers in TRISO fuel
particle is that the microstructure remains unchanged after thermal treatment at 2000
ordmC for 1 hour in an inert atmosphere as determined by electron microscopy and X-ray
diffraction
235 Effect of thermal treatment on SiC
The SiC with perfect crystal structure tends to have good high temperature thermal
stability however due to the concentration and type of imperfections generated
CHAPTER 2 Literature Review
60
during deposoition process its thermal stability could be affected Defects such as
stacking faults vacancies and interstitials in as-deposited SiC coatings affect the
microstructural change after thermal treatment [93-96] For example the phase
transformation from β- to α-SiC generally happened at temperatures above 2100 ordmC
[19] but it could take place at lower temperature (gt 1700 ordmC) in special cases (eg
CVD β-SiC deposited on Si substrate with high amount of stacking faults) [93]
During high temperature thermal treatment (about 2000 ordmC) of CVD β-SiC one
significant microstructural change would be the annihilation of stacking faults [94
95] A thermodynamics study [94] has shown that the mechanism of reduction of the
stacking faults was due to the diffusion of Si or C atoms and it also demonstrated that
the migration energy of Si atoms was smaller than C atoms Considering the
abundance of intrinsic defects (section 222) there has been little investigation of
their effects on microstructure change of β-SiC after thermal treatment Furthermore
the effects of high temperature thermal treatment on mechanical properties such as
the hardness Youngrsquos modulus [97] and strength [98] have been carried out Their
results showed that mechanical properties showed little change when the treatment
temperature was lower than 2000 ordmC while there was decrease in the strength after
thermal treatment at 2100 ordmC
24 Microstructure and properties of pyrolytic carbon
In this part the microstructure of carbon related material is reviewed first which is
followed by the measurement of Youngrsquos modulus and hardness Furthermore to
know the controlling factor on mechanical properties of PyC coatings different
deformation mechanisms under indentation are introduced A brief review about effect
of thermal treatment on properties of PyC coatings is given
CHAPTER 2 Literature Review
61
241 Microstructure of pyrolytic carbon
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
The graphite structure consists of graphene sheets having localized in-plane σ (sp2)
hybrids bonds and delocalized out of plane π (pz) orbital bonds connecting graphene
sheets The out-of-plane bond is a van der Waals interaction which is much weaker
than sp2 and sp
3 hybrids Pyrolytic carbon is a material with some covalent bonding
between its graphene layers as a result of imperfections (defects) in its structure [99]
Figure 217 gives schematics and TEM images showing different microstructures of
PyC with different densities The growth features are polyhedral or conical shape in
high density pyrolytic carbon (Fig 217 (ab)) but are globular in low density
pyrolytic carbon (Fig 217(cd)) [15] It shows that the microstructure of pyrolytic
carbon consists of growth features between 200 nm- 1000 nm in size (Fig 217 (b)
and (d)) [15] Pores were formed at the boundaries or triple junctions between growth
(a) (b)
(c) (d)
CHAPTER 2 Literature Review
62
features
According to previous studies [15101] individual growth features contain crystallites
(domains) as shown schematically in Fig 218(a) They are composed of a series of
curved graphene layers randomly rotated with respect to each other along the c-axis
[101] The dimensions of the crystal were described by La (diameter of crystal along
the χ direction) and Lc (height of the crystal perpendicular to χy plane) as shown in
Fig 218(a) Regarding the definition of the PyC there are defects within the growth
features together with crystallites A local atomic structure of less ordered graphene
layers is shown in Fig 218(b) which could reflect the plane defects in graphene
layers [102]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
A high density of defects such as dislocation loops and kink bands were observed in
ball milled graphite by HRTEM as shown in Fig 219(a) The distorted
microstructure of graphite was also inferred from the striped diffraction points in
selected area electron diffraction image (Fig 219(b)) [103] since the diffraction
pattern gives information on orientation of crystal planes Compared with ball milled
graphite the HRTEM image of pyrolytic carbon has higher amount of defects as
shown in Fig 19(c) which is reflected from the highly distorted lattice planes and low
texture The selected area electron diffraction image of pyrolytic carbon (Fig 219(d)
with eperture diameter of 200 nm) showed arc shaped diffraction patterns [15 104]
The arc represents the overlap of diffraction patterns from different graphite domains
CHAPTER 2 Literature Review
63
with different orientations and this indicats that the microstructure is more distorted
eg smaller domain size and increased random orientation of domains In heavily
disordered PyC it is not possible to observe the individual dislocations or other
defects which is thought to be due to the numerous defects such as tilt boundaries
which obscure individual defects as described in Ref [105]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
Raman spectroscopy is one of the most effective techniques to characterise the defects
in carbon materials and has previously been used to characterise the microstructure of
PyC [15 106] These spectra can identify even quantify the microstructure such as
crystallite boundaries and size disorders (5-memebered rings) and chemical bonding
type Figure 220 shows the evolution of the Raman spectra with the change of the
CHAPTER 2 Literature Review
64
in-plane defect types The carbon spectra of Fig 220(a-c) showed increased and
broadened D signal and the main in-plane defects observed in these structures were
supposed to be domain boundaries [15] In Fig 220(d-e) the D signal became shaper
which was attributed to the formation of five-member rings [15]
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
The high density of disorders such as in-plane domain boundaries makes the Raman
bands become broder and overlapped with each other as shown in Fig 220(c) which
inferred the structure of turbostratic or high density PyC [10 15] According to
previous studies [106 107] the broadened Raman bonds could be deconvoluted into a
number of peaks which correspond to different types of disordered structure in
carbon materials Figure 221 is an example of a first order Raman spectra fitted with
Lorentzian and Gaussian functions and it includs I (~1170 cm-1
) D (~1330 cm-1
) Drdquo
(~1500 cm-1
) G (~1580 cm-1
) and Drsquo(~1618 cm-1
) bands [106] The Drdquo peak was
CHAPTER 2 Literature Review
65
attributed to amorphous carbon with a certain amount of sp3 carbon [106108] which
could reflect the interstitial defects coupling to the graphene layers or adjacent
domains [109]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
242 Mechanical properties of pyrolytic carbon
The different deformation mechanism of carbon materials compared to ceramic
materials results in distinct force-displacement curves which show the complete
recovery of the unloading curve [110 111] Therefore we describe the mechanical
properties of PyC coatings and deformation mechanism of carbon materials
2421 Youngrsquos modulus and hardness
Due to the importance of PyC in the nuclear industry mechanical properties were
measured by three-point bending [102 112] and nano-indentation [113-115] Table
26 gives the Youngrsquos modulus and hardness of PyC measured by different methods
In three-point bending tests the mechanical properties were functions of density
orientation angle and domain size No individual factor could clearly explain the
variation in Youngrsquos modulus strength or fracture toughness [112116] In previous
nano-indentation tests the low density PyC was found to have low hardness and
Youngrsquos modulus [114] whereas the influence on mechanical properties was
CHAPTER 2 Literature Review
66
uncertain which could be due to lack of investigation about the deformation
mechanisms
Table 26 Summary of the hardness and Youngrsquos modulus for PyC measured by
different methods
Methods Density range
(gcm3)
Youngrsquos modulus
(GPa)
Hardness
(GPa)
Ref
3-point-bending 150-212 310-427 -- 112
137-206 165-281 -- 116
Nano-indentation 185-190 255 + 2 -- 114
165-203 235-270 30-44 115
155-187 70-150 05-18 115
135-212 125-346 15-48 113
Youngrsquos modulus was changed from PSI to GPa
Figure 222 is a schematic of the typical force-displacement curve of different kinds
of materials under indentation [65110111] The curve of carbon materials shows a
completely recovery and no net displacement after unloading as shown in Fig
222(a) In carbon materials the force-displacement curve formed a closed loop and
this phenomenon was called anelastic deformation behaviour [14 117] This was
related to the internal friction of materials but there is controversy regarding the
sources of the internal friction [14105111] Since the force-displacement curve gives
information about the energy change during indentation the deformation behaviour of
carbon material can be analysed by the energy method
The energy distribution under indentation is shown in Fig 222 which includs the
hysteresis energy (Uh) and unloading energy (Uunloading) and the total energy (loading
energy Uloading) is the sum of the above two energies [110] As shown in Fig 222 the
ratio of the hysteresis energy to total loading energy could be different for different
microstructure of carbon materials [118] The ratio could be used to estimate the
CHAPTER 2 Literature Review
67
flexibility of elasticityductility [110119] For example a low ratio corresponds to
higher elasticity whist a high ratio meants higher ductility
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
The different force-displacement curve of carbon materials was compared with the
irreversible deformation behaviour of materials with linear elasticity such as SiC as
shown in Fig 214(a) [65] In linear elastic deformation the final displacement of hf
was left after complete unloading and the unloading curve nearly followed the linear
relationship Furthermore the area between the loading and unloading curves
represents the energy consumed by the plastic deformation which could be due to the
movement of dislocations and formation of micro cracks [1 62]
2422 Deformation mechanism
Reversible slip and sliding friction theory In this theory the complete recovery of
strain was due to the reversible slip of graphene planes and the energy loss was
attributed to the friction during the slip which was caused by a compressive stress on
the graphene layers [110111] The theory was obtained by considering an arbitrary
grain located at some position in a radially declining hydrostatic stress field below a
spherical indenter as shown in Fig 223 [110111] The force was resolved into
CHAPTER 2 Literature Review
68
compressive stress perpendicular to and shear stress parallel to the slip plane By
using the equation proposed by Kelly [120] the shear component (τ τ0 shear stress
with and without friction respectively) may be expressed as τ= τ0 +μσ where μ is a
friction coefficient and σ is normal stress component To initiate slip between
graphene layers the shear stress needs to exceed some critical value Therefore the
inter-layer slip with friction was supposed to be the mechanism of anelastic
deformation The authors [110111] also concluded that the hysteresis during
unloading appeared to be a natural result of friction between the graphene layers but
additional mechanisms were supposed to be operating in the different forms of
graphitic materials Furthermore the study did not give a clear explanation about how
the reversibility of the basal plane slip was realized
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Dislocation pileup theory This idea was derived from isotropic carbon after thermal
treatment at the temperature range of 880-2600 ordmC by using micro indentation [121]
The authors attributed the unique unloadingreloading behaviour of the
well-graphitized carbons to the slip of dislocation networks on graphitic basal planes
which is partially or fully reversible It is supposed that the dislocations could pile up
at grain boundaries as in metals The stress at grain boundaries due to dislocation pile
ups could reverse the dislocation movement during indentation unloading but it did
CHAPTER 2 Literature Review
69
not explain why deformation behaviour of PyC is unlike that of metals This is also
the reason that other researches [105] doubt this theory because it fails to explain the
nature of the reversible behaviour [121]
Kink band theory It was suggested that the origin of the loops obtained in single
polycrystalline and porous carbons is the formation of incipient kink band and kink
bands [105] The kink band model was proposed by Frank and Stroh [122] as
shown in Fig 224 which showed pairs of dislocations of opposite sign nucleate and
grow at the tip of a thin elliptical kink (not clear about the nature) The stability of
kink bands depended on a shear stress [122]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
In this theory since the dislocations were confined to the basal plane the hysteresis
process was attributed to the reversible movement of the dislocation along a long
distance The same mechanism was used to explain the deformation behaviour of the
bulk polycrystalline graphite The microstructural change under indentation should
first be related to the kink band initiation and then further microstructure change
could be reflected in the accumulation of other chemical bonds which could resist
dislocation glide
CHAPTER 2 Literature Review
70
2423 Effect of thermal treatment on properties of PyC
The effect of thermal treatment on the microstructure of carbon materials has been
widely studied [112 123 124] The change of the microstructure of carbon materials
during thermal treatment mainly involves the growth of the domain size (in-plane
crystal size along a axis) La and (along c axis crystal size) Lc with the increase of
temperature For different kinds of carbon materials these evolutions started at
different temperatures For example the crystal growth in-plane happened at 400-600
ordmC for graphitisable carbon and could continue up to high temperature the
coalescence of crystallites along the c-axis started above 1000-1200 ordmC the
coalescence of crystallites along ab direction occurred at temperature above 1400 ordmC
[124] For carbons with strong cross-linking (non-graphitisable) the coalescence of
domains usually happened at temperatures higher than 2400 ordmC [124] Although the
increase in anisotropy and density during processing of coated particle fuel was
reported by Hunn et al [11] no change in texture was identified on PyC due to the
post deposition of SiC shown in Lopeacutez-Honorato et alrsquos study [125] Furthermore no
significant change of mechanical properties was obtained after thermal treatment at
temperatures in the range 1000-1980 ordmC in PyC coatings with density of about 19
gcm3 [97] however a decrease of Youngrsquos modulus was observed in high density
(above 2 gcm3) PyC coatings [125] It was assumed that certain microstructures of
PyC would be less affected by thermal treatment
25 Summary
The microstructure and mechanical properties of SiC and PyC were reviewed in this
Chapter and the information obtained is summarized below
(1) It is common for SiC to have defects such as stacking fautls and dislocations
non-stoichiometry and point defects due to their low formation energy
particularly in SiC deposited by chemical vapour deposition
CHAPTER 2 Literature Review
71
(2) Defects interact with each other Stacking faults could be the result of gliding
of partial dislocations Vacancies promoted diffusion of antisites forming
antisite clusters
(3) The Youngrsquos modulus of SiC coatings in TRISO fuel particle is affected
mainly by texture and porosity
(4) Hardness related plastic deformation in single and polycrystalline (nano-meter
or micro-meter grain size) SiC is related to dislocation propagation fracture
of crystallites or phase transformation
(5) A combination of indentation together with electron microscopy is an
effective way to study the fracture behaviour of SiC coatings in TRISO fuel
particle
(6) Fracture strength of SiC coating in TRISO fuel particle varies significantly in
different measurements and the modified crush test is recommended The
interface roughness and porosity are found to be main factors controlling
fracture strength of SiC coatings
(7) The typical change of microstructure after thermal treatment in SiC is the
annihilation of stacking faults through the diffusion of vacancies
(8) The disorder in PyC coatings could be significant such as domain boundaries
and 5-membered rings Raman spectroscopy together with transmission
electron microscopy are important techniques to characterize these disorders
(9) Carbon related materials show hysteretic deformation behaviour under
indentation Different deformation mechanisms are proposed which all relate
to the slip of graphene layers
CHAPTER 2 Literature Review
72
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329-77
[2] DT Goodin Accident condition performance of fuels for high-temperature gas
-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[3] D J Green An Introduction to the mechanical properties of ceramics 1st ed
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[4] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
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[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
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[6] X Li B Bhushan A review of nanoindentation continuous stiffness
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[7] A Grabulov U Ziese HW Zandbergen TEMSEM investigation of
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[8] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
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[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
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[10] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
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56 (1973) 36-41
CHAPTER 2 Literature Review
73
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
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[12] D G Martin Considerations pertaining to the achievement of high burn-ups in
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[14] G K Miller D A Petti J T Maki Consideration of the effects of partial
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CHAPTER 2 Literature Review
74
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[26] P T B Shaffer A review of the structure of silicon carbide Acta Crystal Sec B
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[35] B Reznik DGerthsen W Zhang K J Huumlttinger Microstructure of SiC
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[42] N W Mueggenburg H M Jaeger S R Nagel Stress transmission through
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[44] A Gali N T Son E Janzeacuten Electrical characterization of metastable carbon
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[46] J Tan Mechanical properties of SiC in TRISO fuel particle PhD Thesis
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[47] Z R Huang B Liang DL Jiang S H Tan Preparation of nanocrystal SiC
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[48] R A Shatwell K L Dyos C P Rentice Y Ward R J Young
Microstructural analysis of silicon carbide monofilaments J Microscopy 201
(2001) 179-88
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[49] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
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[50] K Kaneko M Kawasaki T Nagano et al Determination of the chemical width
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imaging and ELNES line-profile Acta Materialia 48 (2000) 903-10
[51] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[52] O O Mykhaylyk YZ Khimyak JP Attfield Phase Segregation in Silicon
Carbide-Carbon Solid Solutions from XRD and NMR Studies Chem Mater 14
(2002) 1348-35
[53] E Janzeacuten N T Son N Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[54] E Rauls Th Frauenheim A Gali PDeaacutek Theoretical study of vacancy
diffusion and vacancy-assisted clustering of antisites in SiC Phys Rev B 68
(2003) 155208-09
[55] N T Son P N Hai E Janzeacuten Carbon vacancy-related defect in 4H and 6H SiC
Phys Rev B 63 (2001) 201201-04
[56] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-10
[57] J M Grow R A Levy Micromechanical characterization of chemically vapor
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[58] T D Guldn H Nickel Coated particle fuels Nucl Technol 35 (1977) 206-35
[59] KB Tolpygo Optical elastic and piezoelectric properties of ionic and valence
crystals with ZnS type lattice Sov Phys Solid State 2 (1961) 2367
[60] D W Feldman J H Parker Jr J W Choyke L Patrick Phonon dispersion
curves by Raman scattering in SiC polytypes 3C 4H 6H 15R and 21R Phys
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CHAPTER 2 Literature Review
77
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[62] X Zhao R M Langford I P Shapiro P Xiao Onset plastic deformation and
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[63] R W Rice Mechanical properties of ceramics and composites 1st ed New
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[64] O Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
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[65]W C Oliver GMPharr An improved technique for determining hardness and
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[66] MC Osborne JC Hay LL Snead Mechanical- and physical-property changes
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[67] D M Teter Computational alchemy the search for new superhard materials
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[68] S Nagappa M Zupan CA Zorman Mechanical characterization of
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[69] M J Slavin G D Quinn Mechanical property evaluation at elevated
temperature of sintered β-silicon carbide Inter J High Tech Ceram 2 (1986)
47-63
[70] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
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[71] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
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Rev B 71 (2005) 174113-23
[72] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
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[73] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
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[74] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
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[75] I Zarudi J Zou L C Zhang Microstructures of phases in indented silicon A
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[76] M Mishra I Szlufarska Possibility of high-pressure transformation during
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[77] D Munz T Fett Ceramics Mechcanical properties failure properties failure
behavior and materials selection Springer Verlag NewYork 1999 p 20
[78] X Zhao RM Langford J Tan P Xiao Mechanical properties of SiC coatings
on spherical particles measured using the micro-beam method Scripta Mater 59
(2008) 39ndash42
[79] G D Quinn RC Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[80] R Morrell Fracture toughness testing for advanced technical ceramics
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[81] R E Cook G M Pharr Direct observation and analysis of indentation cracking
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[82] S S Chiang D B Marshall AG Evans The response of solids to elasticplastic
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[83] M T Laugier Palmqvist toughness in Wc-Co composites viewed as a ductile
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[84] G R Anstis P Chantikul B R Lawn D B Marshall A critical-evaluation of
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[85] X F Zhang Q Yang L C D Jonghe Microstructure development in
hot-pressed silicon carbide effects of aluminium boron and carbon additives
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[86] T Watanabe The impact of grain boundary character distribution on fracture in
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[87] S J Xu J G Zhou B Yang B Z Zhang Effect of deposition temperature on
the properties of pyrolytic SiC 224 (1995) 12-16
[88] K Bongartz E Gyarmati H Schuster K Tauber Brittle ring test ndash method for
measuring strength and Youngs modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[89] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the Tri-Isotropic-Coated fuel particle
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[90] J W Kim TSByun YKatoh Optimization of fracture strength tests for the SiC
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[91] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[92] SDKurbakov TAMireev Deposition of high-density silicon carbide coatings
by fluidized-bed pyrolysis of chlorinated silane derivatives Solid Fuel Chem 43
(2009) 113-23
[93] M Hundhausen R Puumlsche J Roumlhrl L Ley Characterization of defects in
silicon carbide by Raman spectroscopy Phys Stat Sol 245 (2008) 1356-68
[94] N Shirahata K Kijima A Nakahira and K Tanaka Thermal stability of
stacking faults in beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
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[95] W S Seo C H Pai K Koumoto H Yanagida Microstructure development and
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443-47
[96] Z G Cambaz G N Yushin Y Gogotsi K L Vyshnyakova L N
Pereselentseva Formation of carbide-derived carbon on beta-silicon carbide
whiskers J Am Ceram Soc 89 (2006) 509-14
[97] I J V Rooyen J H Neethling J Mahlangu Influence of temperature on the
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temperature reactor technology HTR 2008 September 28-October 1 2008
Washington DC USA HTR 2008-58189
[98] I J v Rooyen J H Neethling P M v Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[99] httpenwikipediaorgwikiPyrolytic_carbon
[100]J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
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[101]Z Q Li C J Lu Z P Xia Y Zhou Z Luo X-ray diffraction patterns of
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[102]W P Hoffman W C Hurley P M Liu T W Owens The surface topography
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[103]J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[104]P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
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81
[105]M W Barsoum A Murugaiah S R Kalidindi T Zhen YGogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[106]J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
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electron diffraction and few other techniques Carbon 44 (2006) 1833-44
[107]A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
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[108]A C Ferrari Raman spectroscopy of graphene and graphite Disorder
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[109]J N Rouzaud A Oberlin Carbon films Structure and microtexture (optical and
electron microscopy Raman spectroscopy) Thin Solid Films 105 (1983) 75-96
[110]N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[111]N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philosophical Magazine A 82 (2002) 1873-81
[112]J C Bokros R J Price Deformation and fracture of pyrolytic carbons
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[113]E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure
and mechanical properties of pyrolytic carbon produced by fluidized bed
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[114]C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by
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[115]G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
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[116]J L Kaae Relations between the structure and the mechanical properties of
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[117]L M Brown In H Libelt R Talreja Fatigue and creep of composites
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[118]M Skai The Meyer hardness A measure for plasticity J Mater Res 14 (1999)
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[119]M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics ndash adding
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[120]B T Kelly The physics of graphite Applied Science Publications London
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[121]M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated
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[122]F C Frank A N Stroh On the theory of kinking Proc Phys Soc 65 (1952)
811-21
[123]R F Franklin Royal Society London A London 1951 209 196
[124]F G Emmerich Evolution with heat treatment of crystallinity in carbons
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[125]E Loacutepez-Honorato P J Meadows R A Shatwell P Xiao Characterization
of the anisotropy of pyrolytic carbon by Raman spectroscopy Carbon 48 (2010)
881-90
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
83
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC
Coatings Measured by Indentation
31 Introduction
The silicon carbide (SiC) coating is the most important component for structural
integrity of Tri-isotropic (TRISO) fuel particles as it sustains most of the internal
pressure produced by the fission gases produced in the kernel [1-3] Youngrsquos modulus
and hardness are mechanical properties used in modeling to estimate the failure
probability of TRISO fuel particles [4] The values at room temperature are used due
to the fact that the Youngrsquos modulus slightly decreased at elevated temperature in SiC
material and the higher value could be kept until the temperature reached 2000 degC [1]
It was also found that SiC material with higher hardness at room temperature
maintains higher hardness values at temperatures up to 1600 degC [1] To achieve a
reliable fuel design a better understanding of the mechanical properties of the SiC
layer at room temperature needs to be established
It is difficult to use traditional methods to measure hardness and Youngrsquos modulus
due to the small dimension of the TRISO fuel particles (~1 mm) Nano-indentation
has made it possible to measure the hardness and Youngrsquos modulus accurately [5 6]
for a coating of such a small dimension Furthermore this method also offers the
ability to study the deformation behaviour under the indentation [7-12] as the
indentation stress field is of a localized character
Loacutepez-Honorato et alrsquos [5] study of SiC deposited at 1300 degC by fluidized bed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
84
chemical vapour deposition (FBCVD) showed that the SiC coatings produced under
those conditions had high hardness (gt 42 GPa) and Youngrsquos modulus (~455 GPa)
They found that even samples with the composition of SiC+C or SiC+Si showed high
mechanical properties It was shown that the coatings had sub-micrometer (lt1 μm
diameter) grain size but due to the complex microstructure the mechanism controlling
the hardness and Youngrsquos modulus was unknown Researchers [10 11 13-16] have
made efforts to study the deformation mechanism under indentation in SiC single
crystals and polycrystals (with a grain size lt 100 nm or grain size gt 1μm) Szlufarska
et al [15] suggested a crossover mechanism from indentation-induced crystallization
to deformation-dominated amorphization in nano-crystalline SiC
From the work reported [11 16 17] it is clear that dislocation initiation and
propagation is the primary response for the plastic deformation under an indentation
in single crystal and polycrystalline (gt 1μm) SiC Further it has also been found
while studying the microstructure [11 16 17] that defects such as stacking faults and
dislocations were present in these polycrystalline (gt 1 μm) SiC materials
(nano-indentation hardness less than 36 GPa) However the amount of defects were
lower compared to the low temperature (ie 1300 o
C vs 1500 o
C) FBCVD SiC [5]
The discrepancies in the microstructure and mechanical properties still demand
further explanation on the deformation mechanism of low temperature FBCVD SiC
This chapter focus on the fundamental study on the mechanical properties of SiC we
have investigated the Youngrsquos modulus and hardness of three sub-micrometer FBCVD
SiC coatings using the indentation method The microstructure and mechanical
properties are explained on the basis of defects observed with a transmission electron
microscope (TEM) The deformation behaviour underneath a nano-indentation is
discussed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
85
32 Experimental details
Silicon carbide (SiC) coatings were produced on top of highly-dense pyrolytic carbon
coatings using fluidized-bed chemical vapour deposition (FBCVD) method The SiC
coatings with varied stoichiometry and deposited at low temperature of 1300 oC by
Loacutepez-Honorato et alrsquos [5] were chosen and studied in this Chapter Table 1 gives the
deposition conditions of these coatings which were found and demonstrated to give
superberb mechanical properties in prevous studies [5] Figure 31(a) and (b) show the
polished cross-section (x-y plane) and (b) polished external surface section (x-z plane)
of TRISO fuel particles (defining the directions used in the later part of this Chapter)
Densities were measured by the Archimedes method in ethanol (density is the mean
value of three tests the weight of SiC shells is 01-03 g) Composition was measured
by Raman spectroscopy (Renishaw 1000 Raman system with a 514 nm argon laser
source) with a single spot measurements of around 1 microm diameter through an times50
objective lens as shown in Fig 31 (c) Two peaks at around 794 and 970 cm-1
are for
SiC and the asymmetric peaks around 200-500 cm-1
and 1500 cm-1
are acoustic SiC
and second order SiC respectively (S1 coating) [5] Carbon peaks are around 1360
and 1600 cm-1
(S2 coating) and the peak at 520 cm-1
represents silicon (S3 coating)
[5] It was estimated that the excess C amount is less than 1 at in S2 by measuring
the intensity ratios of I1600I794 and compared to previous study [18] where Raman
spectroscopy and elemental analysis (EPMA AES and XPS) were used
The phase and composition were also analysed using X-ray diffraction (XRD PW
1830 Philips Eindhoven The Netherlands) with Cu Kα1 radiation Figure 31(d)
shows the XRD spectra of the three types of SiC coatings All three coatings exhibit
the β-SiC phase A very small shoulder peak around 2θ=345deg was also obtained from
the coatings which indicated the presence of stacking faults No evidence of a Si or C
peak was found in the XRD result This was probably due to the fact that the
additional levels of Si and C were very small (le 1at ) and it would be difficult to
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
86
identify these traces using XRD [5 19]
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
Codes H2MTCS (volvol) Additives Temperature Density (gcm3)
S1 (SiC) 10 01vol Propylene 1300 o
C 3173 + 0029
S2 (SiC+C) 10 10 vol Propylene 1300 o
C 3135 + 0034
S3 (SiC+Si) 10 -- 1300 o
C 3188 + 0002
SiC+C or SiC+Si means that nearly stoichiometric SiC with low excess C or Si less than 1 at
Productions of samples are contributed by Dr Eddie Loacutepez-Honorato
SiC coated fuel particles were hot mounted in copper-loaded conductive resin To
reduce the influence of the surface roughness the FBCVD SiC coatings were first
ground down to obtain a flat surface where the nano-indentation could be carried out
The flat surface was further polished using increasingly finer diamond suspensions
until frac14 μm and finally polished using a 003 μm colloidal silica suspension The
thickness of the coating after final polishing was estimated to be around 60 μm A
final surface roughness of lt 5 nm was detected by atomic force microscopy (AFM)
Youngrsquos modulus and hardness were measured using a nano-indenterTM
XP (MTS
System Corp USA) and a micro-indenter (CSM Instruments Switzerland)
Nano-indentation was made using a Berkovich indenter calibrated with a standard
silica specimen Before the measurement the initial contact of the indenter with the
specimen surface was checked and the compliance of the loading column was
corrected Arrays of indentations were performed on each specimen with an interval
of 20 times the indentation depth between each indentation The penetration depth for
the measurement of Youngrsquos modulus and hardness was 500 nm All data were
analysed using the Oliver and Pharr method [7] Micro-indentation was made using a
Vickers indenter at a maximum load of 3 N and the interval between each indentation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
87
was also kept to 20 times the indentation depth of ~26 μm
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
(c)
(d)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
88
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Moreover a high purity (gt999995) and fully dense polycrystalline 3C-SiC bulk
(diameter 3 cm thickness 15 cm) sample fabricated by static CVD (Rohm amp Haas
Ltd UK) was used as a reference sample in order to confirm the accurate mechanical
property measurements for FBCVD SiC coatings The Raman spectroscopy of bulk
CVD SiC was the inset in Fig 31(b) and no excess C or Si was found in it
To observe the grain morphology more clearly the finely polished (no scratch could
be seen under optical microscopes times50) cross-section (Fig 1(a)) of the coatings were
chemically etched using Murakamirsquos solution (10 g sodium hydroxide and 10 g
potassium ferricyanide in 100 ml of boiling water) The surface morphology of
coatings was characterized using scanning electron microscopy (Field emission gun
Philips XL30 FEG-SEM) A transmission electron microscope TEM (FEG-TEM
Tecnai TM
G2 F30 U-TWIN 300KV) was used to study the microstructure of the
coating layer before and after indentation For cross-sectional analysis of indentations
TEM samples were made from thin plates which are parallel to one edge and through
the center of Berkovich indentation using a focused ion beam (FIB FEI Nova 600
Dual Beam system) milling For high resolution TEM (HRTEM) the samples were
prepared using an ion beam milling method
33 Results
331 Hardness and Youngrsquos modulus
Figure 32 shows the typicl load-displacement curve of SiC coatings and the hardness
(H) and Youngrsquos modulus (E) as a function of composition of the three types of
coatings The load-displacment curve (Fig 32(a)) shows a smooth character of the
deformation process during nanoindentation There is multiple mini lsquopop-inrsquo events
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
89
reflected on the hardness curve which started at the beginning from the low
indentation load These mini lsquopop-inrsquo can not provide enough consumption of the
internal stresses induced by indenter as it was needed for the initiation and
propagation of dislocations so no well-pronounced lsquopop-inrsquo effect was observed from
the load-displacement curve
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Measurements were made on the x-z plane of SiC coatings (Fig 31(b)) and static
bulk CVD SiC for both micro- and nano-indentation to give reliable comparison with
previous studies [20-23] In the reference material the nano-hardness (36 GPa) and
Youngrsquos modulus (496 GPa) of bulk CVD SiC are nearly the same as in a previous
(c) (b)
(a)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
90
study [20] namely 36 GPa and 503 GPa respectively From Fig 32(b) it can be seen
that S1 has a higher hardness compared with S2 and S3 Further the values of
hardness obtained by nano-indentation (Fig 32(b)) are higher than by
micro-indentation for all samples
For low temperature FBCVD coatings the nano-hardness varies in the range 39 GPa
to 44 GPa whereas the micro-hardness varies between 36 GPa - 42 GPa These values
are at least 8 higher than the bulk static CVD SiC which has a nano-hardness ~36
GPa and a micro-hardness ~32 GPa (see Fig 32(b)) Moreover the low temperature
FBCVD SiC coatings have higher hardness as compared to a previous study of CVD
SiC for which the hardness values varied in the range of 25-39 GPa as measured by
nano-indentation under the similar experimental conditions [20-23]
In FBCVD SiC coatings Youngrsquos modulus of all three coatings is lower than the bulk
CVD SiC (see Fig 32(c)) which is an average Youngrsquos modulus (438 GPa) of
polycrystalline CVD SiC reported by Roy et al[24] The difference in hardness and
Youngrsquos modulus data could not be simply explained by the existence of C or Si due
to their low concentration (lt 1 at ) and location in the coatings which has been
addressed in detail in previous study [25] Therefore the difference of hardness and
modulus could be related to other microstructure such as pores which could vary
from atomic scale to micrometres which is discussed in the following session
Both nano- and micro-hardness results (Fig 32(b)) are higher than the available data
for polycrystalline CVD SiC [20-23] as discussed above and the correct measurement
of SiC coatings with small dimensions was ensured by comparing with the bulk CVD
SiC As mentioned the hardness and Youngrsquos modulus measured by
micro-indentation are slightly lower than the values measured by nano-indentation
because cracks were formed under micro-indentation due to the higher indentation
load
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
91
332 Microstructure of low temperature FBCVD SiC
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Figure 33 shows SEM images of the three etched FBCVD SiC coatings In all three
coatings the width and length of columnar grains were found to be approximately 200
nm and 1-2 μm respectively These are found to be much smaller than the SiC coating
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
92
produced at a temperature of 1500 degC which had width ~1μm and length ~4-5 μm
[17] They are also smaller than the SiC showing dislocation movement under the
indentation deformation zone which was produced at temperature of 1500-1600 degC
by FBCVD and 1500 degC by static CVD with grain size of 1-5 μm and 5-10 μm
respectively [11 16]
Although the grain size is in a similar range for three coatings (as mentioned above)
due to different deposition conditions the grain morphologies of three coatings vary
First a less laminar structure was observed in the S1 coating (see Fig 33 (a)) as
compared to the coatings with excess C or Si (Fig 33 (c) and (e)) Fig 33 (b) shows
the existence of triple junctions (dashed circle) that could resist the movement of
grain boundaries and dislocation slip [12] Pores were also observed along the laminar
structure after etching In the S2 coating it has a large amount of a laminar structure
running through a single grain (laminar structure parallel to growh direction) as
illustrated in Fig3 (d) The information of grain morphology in S2 was mostly a
laminar structure perpendicular to the growth direction after etching (Fig 33(d))
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
To get more information about the grains morphology in S2 coating a TEM image
05 μm
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
93
was taken and shown in Fig 34 Figure 34 shows that grains in S2 coating interact
(branch-like grain growth pattern on the lower-left part of Fig 34) with each other
which is similar as in sample S1 (Fig 33(b)) and grains form branch like structures
In the S3 coating (as can be seen in Fig 33 (f)) a parallel growth of grains with less
interaction among grains was observed
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
According to a previous study [25] about definition of grain boundary the grain
boundary in the S3 coating is smooth while in the S1 and S2 coating the grain
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
94
boundaries are rough which could result in branch-like grain growth pattern It could
be attributed to the different CSi ratio in reaction gas which produce SiC with
different morphologies on the (111) crystal plane which may have three different
morphologies rough smooth and pyramidal defect [26] Grains with differently
finished surfaces could lead to different grain growth morphologies because of
different surface energy For example in rough grain boundaries of S1 and S2
coatings branch like crystals were found as in Fig 33(b) and Fig 34
Figure 35 shows bright field TEM images of the S1 coating S2 and S3 coatings The
columnar grains were observed to grow perpendicular to the coating surface which
was consistent with the SEM results Further nano porous layers normal to the
coating growth direction are observed in the S2 coating (see Fig5 (b)) The formation
of porosity in thin films could be due to differences in diffusion of growth species the
incident molecule direction and deposition of secondary phases such as excess Si or C
[27]
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
BF-TEM and (b) DF-TEM
At low deposition temperatures the probability of a precursor reaching the edge of the
nucleus is considerably lower compared with that of arriving on the top due to a low
surface diffusion As these nuclei grow the areas immediately around them will suffer
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
95
from a shadowing effect blocking the arrival of new molecules and the formation of
new nuclei Since the diffusivity of atoms is low and no new nuclei are formed in
those regions gaps will be formed among grains A wrinkled like defect layer was
seen in the S3 coating (Fig 35 (c)) which could be attributed to the interruption of
the SiC crystallization growth during the deposition process such as crystal lattice
misorientation as seen in Fig 36
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
No obvious laminar defect was observed in the S1 coating by TEM this could be due
5 nm
(a) (b)
5 nm
5 nm
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
96
to less interruption during deposition process According to above observation it was
proposed that the laminar structure observed in SEM images indicates some
instability during the fabrication process resulting in the deposition of the nano- and
micro-pores and misorientation This was attributed the variations in circulation and
deposition occurring close to the nozzle or at the hot zone [5]
Stacking faults were observed for all three types of samples as shown in Fig 35 with
a higher density than for the SiC deposited at a temperature of 1500 C [11 16 17]
These stacking faults could cause an intrinsic residual stress due to the coexistence of
the partial dislocations This was supported by the high resolution TEM images
(shown in Fig 37) exhibiting wave pattern fringes and they could only be observed
in one direction which is determined by the intrinsic stress
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Since the dislocation mobility under nano-indentation deformation has not been fully
understood in hard ceramic materials therefore it is significant to study this
behaviour in FBCVD SiC coatings with a sub-micrometer grain size However it is
difficult to observe the dislocations under the two-beam or weak beam dark field
2 nm
(a)
(111)
[110]
(111)
Sessile
dislocations
(b)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
97
conditions due to the high density of defects In the present study the reversed fast
Fourier transform (FFT) images of the corresponding high resolution TEM images
was used to obtain information about the dislocations This method has been used in
many cases for dislocation observations [28]
Figure 38(a) shows a high resolution TEM image of a S1 coating which was taken as
a representative image to compare the atomic structure of all three coatings Figure
38(b) is the reverse FFT image using the marked inset diffraction pattern of Fig
37(a) in which sessile and glide dislocations can be observed The dislocation
density was calculated from the total number of glide dislocations divided by the area
in the image [29 30] From the analysis of images shown in Fig 38 the dislocation
density in S1 coatings was found to be 1013
cm2 The same magnitude of dislocations
density was found in the S2 and S3 coatings as shown in Fig 37 (three HRTEM
images were analysed for each coating)
333 Deformation behaviour under the indentation
The deformation zone under the indentation was investigated through the images of
FIB milled TEM samples in order to study the deformation mechanism of the low
temperature FBCVD SiC coatings Figure 39 shows the bright field TEM images
showing the mechanical behaviour of a S1 coating under nano-indentation on the x-z
plane (Fig 31(b)) at a maximum indentation depth of 500 nm
Figure 39(a) is an overview of the deformation area under an indentation A median
crack has formed just underneath the surface and has a direction aligned with the
indenter tip impression A higher magnification image around the elastic and plastic
interface is shown in Fig 39(b) It can be seen that a large amount of inter-granular
and trans-granular micro cracks were produced around the median crack initiation
zone This is substantially different from the dislocation-related plastic deformation
behaviour [10 11 16 31] which usually has a severe plastically deformed region
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
98
with few or no cracks Moreover the micro cracks were also observed in the C and D
zones under the indentation
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Figure 39(c) shows that micro cracks that are formed along the grain boundaries
which tend to follow the shear band direction with the formation of a few
trans-granular cracks In Fig 39(d) it can be seen that shear band micro cracks were
formed in one single grain (see inset in the left bottom corner of Fig 39(d)) This
single grain has a large amount of defects which are supposed to be the as-deposited
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
99
defects as shown in Fig 35(a) Shear band cracks were also observed just underneath
the indenter tip (right top inset in Fig 39(d)) As a result a shear band dominated
deformation zone can be seen in Fig 39(c d) under the indentation in a S1 coating
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
The S2 and S3 coatings only show a micro crack pattern which is different from S1
coating Figure 310 gives the TEM images of the S2 and S3 coatings showing the
mechanical reaction underneath the indentation It can be seen from Fig 310(a) and
Fig 310(c) that the median cracks are not always produced under the indentation for
S2 and S3 coatings However some irregular cracks in S3 coatings and lateral cracks
in S2 were produced In particular in the S3 coating (Fig 310(b)) more micro cracks
either intragrain or transgrain were found than in the S1 and S2 coatings This is due
to the fact that the most micro cracks propagate along the grain boundaries in S1 and
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
100
S2 coatings (Fig 39(b) and Fig 310(d)) A careful analysis of the TEM images
shows that only micro cracks were found under the indentation and no
dislocation-induced shear band was observed This is different from previous studies
on the deformation behaviour of polycrystalline SiC [11 16 31] For example in bulk
polycrystalline CVD SiC [11] it was found that it has more dislocation slip bands
rather than micro cracks either in grains or along grain boundaries even though the
indentation load is higher than the load used in the FBCVD SiC based materials The
possible reason of this discrepancy is discussed later Moreover no amorphous phase
and α-SiC phase was formed under the indentation observed by diffraction and bright
field TEM images which is consistent with the work of Mishra and Szlufarska [32]
34 Discussion
High hardness and Youngrsquos modulus were obtained in the sub-micrometer grain size
coatings produced at a low temperature by FBCVD In the S1 coatings the
nano-hardness is ~22 higher while the micro-hardness is ~31 higher compared to
a commercial CVD SiC The higher hardness was also obtained in S2 and S3 coatings
All the coatings retained a higher Youngrsquos modulus than those SiC materials having
high hardness in previous study (equal or higher than 40 GPa nano-hardness) [33]
making these coatings unique among polycrystalline phase brittle ceramic material
Under nano-indentation only micro cracks were found in the deformation zone The
results seem to be consistent with the conventional view of the failure mechanism of
brittle ceramics at room temperature [34] The lack of dislocation and the high Peierls
force are reasons for fracture to occur in brittle materials However
dislocation-related plastic deformation routinely occurred in hardness testing because
the indentation stress field offers conditions of stress conductive to plastic
deformation [11 13 16 34] Molecular dynamic simulations even demonstrate that
13 of the hardness-related deformation is from dislocation-related plastic deformation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
101
while 23 comes from fracture in SiC [31] It is rare to see a deformation zone
dominated by micro cracks in polycrystalline SiC such as in FBCVD SiC coatings
(Fig9 and Fig10 and see for example Ref [11 16 31]) With the above questions
we first estimated the factors controlling Youngrsquos modulus in FBCVD SiC coatings
followed by a study of the mechanism of superior hardness and deformation under an
indentation which influence the hardness in the three coatings
341 Influence of porosity on Youngrsquos modulus
Youngrsquos modulus presents a material constant for uniaxial tensile deformation which
is physically related to the atomic spacing inter atomic bond strength and bond
density In a low temperature FBCVD SiC coating it was shown from XRD
measurements that a shoulder peak was observed in addition to the β-SiC (111)
diffraction peak which corresponded to a crystal plane spacing of ~0266 nm (Fig
31(c)) Moreover we found that the XRD peak shifted to a lower diffraction angle
compared with the bulk CVD SiC According to the XRD pattern in Fig 31(c) the
crystal lattice constants of about 04366 04368 and 04368 nm for S1 S2 and S3
coatings were obtained respectively However the crystal lattice constant for bulk
CVD SiC is ~04359 nm (XRD pattern obtained by the same condition was shown in
Ref 25)
Further crystal orientation impurities and porosity may affect the Youngrsquos modulus
As the Youngrsquos modulus on the x-z plane (Fig 31(b)) was similar to the value
obtained along the cross-section (Fig 31(a)) [5 25] which meant that the orientation
has no effect on Youngrsquos modulus Moreover as discussed before the effect of C or Si
in S2 was found to have no effect on the difference of hardness and Youngrsquos modulus
Excluding these two factors (orientation and impurities) the effect of porosity on
variation of the elastic properties in three coatings was investigated The presence of
nano-pores in S2 coating as in Fig 35(b) results in a lower density Although no
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
102
pores were directly observed by TEM in the S1 and S3 coatings their density is lower
than the theoretical density of SiC Thus the elastic modulus E at room temperature
can be expressed in an exponential function of porosity pV [35] as
0 exp( )pE E CV (1)
where 0E = 496 GPa is the elastic modulus and C = 357 is a constant for a pore-free
bulk CVD SiC pV is the ratio of the relative density difference to the theoretical
density of SiC (322 gcm3)
The calculated Youngrsquos modulus for S1 S2 and S3 coatings is 465 plusmn 15 446 plusmn 17 and
473 plusmn 1 GPa respectively which follows a trend similar to the experimental data
presented in Fig 32 It was concluded that the different Youngrsquos modulus in the three
low temperature FBCVD SiC coatings is attributed to porosity although the
experimental Youngrsquos modulus data of FBCVD SiC coatings is slightly lower than the
values calculated using the Eq(1) The difference between calculated and measured
value of FBCVD SiC coatings is due to the fact that the 0E from pore-free bulk
CVD SiC instead of pore-free FBCVD SiC coatings (not available) FBCVD SiC
coatings have larger crystal lattice constant (~0437 nm) than bulk CVD SiC (~04359
nm) as discussed above Since the expanded lattice constant leads to a decrease of the
Youngrsquos modulus according to a previous study [20] the 0E of pore-free FBCVD SiC
coating is expected to be lower than bulk CVD SiC
342 Mechanism for High hardness
From previous studies [10 11 16 31] dislocation nucleation and glide is the primary
response of SiC under nano-indentation Formation of shear bands due to dislocations
has also been reported [11] which were found under the plastic deformation zone
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
103
when indentations were made on a particular grain in polycrystalline SiC and at the
grain boundaries Moreover dislocation nucleation is also correlated with the discrete
pop-ins observed in the force-displacement curve [32] No pop-ins was found due to
the presence of a large amount of dislocations in the present study Dislocation
mobility can be estimated similar to the case of a metallic material having intrinsic
dislocations Mishra and Szlufarska [32] worked on the dislocation mobility in
3C-SiC using large-scale molecular dynamics simulations The results indicated that
dislocation mobility decreased by dislocation interaction as its density reached a
saturation value This is similar to the work hardening effect in a metallic material [34]
We estimated the stress ( ) needed for dislocation to move using Taylorrsquos work
hardening equation [34] given by
1 2
0 Gb (2)
where 0 is the shear stress for a dislocation to move without any obstacle and the
value of 0 taken was 75 GPa [13] is a numerical constant depending on the
locking strength of a nod The value of taken was 8 [36] b is Burgers vector
where b = 0178 nm for a Shockley partial dislocation in SiC initiated and gliding on a
close packed (111) plane and is the density of glide dislocations G is the shear
modulus which can be written as
2(1 )
EG
(3)
where is the Poissonrsquos ratio and E is the Youngrsquos modulus The dislocation density
was ~03times1012
cm2 The calculated shear stress according to Eq (2) was ~52 GPa and
this value is much higher than the theoretical shear stress which is in the range of
295-4312 GPa obtained from previous reports [37-39] The theoretical shear stress is
the maximum stress provided for the dislocation nucleation and propagation in SiC
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
104
crystals Therefore the dislocation-related yield behaviour could not occur under the
plastic deformation zone in sub-micrometer FBCVD SiC coatings
The superior hardness value in FBCVD SiC coatings is attributed to the immobility of
the dislocations In the case of the SiC-C solid solution [40] the occurrence of a high
density of dislocations causes a strain-hardening effect Furthermore given that
dislocations could be motivated by the shear stress a phase transformation from a
crystalline phase to an amorphous could occur [32] However no amorphous phase
was observed under the nano-indentation (Fig 37 and 8) nor was dislocation
movement band observed in this study This suggests that the dislocation-related
phase transformation did not occur under the indentation
343 Deformation mechanism under nano-indentation
The hardness-related plastic deformation which occurs due to the nucleation and
propagation of micro cracks in FBCVD SiC coatings can be explained as follows
(i) The onset of plastic deformation under the indentation occurs as the maximum
shear stress approaches the yield stress [41] According to 15H Y (Y is the yield
stress H is the hardness) the yield stress in FBCVD SiC coatings is around 26 GPa
The yield stress is lower than the stress needed for the movement of dislocations and
the theoretical shear stress [37-39] This indicates that the hardness-related plastic
deformation first occurred by the nucleation of defect-induced cracks which
propagated to the indented surface (see inset (top right) in Fig 39(d)) The
deformation impression was accommodated by the densification of defects such as
the pores dislocation pile ups and grain boundaries as in Fig 33(b)
(ii) The shear stress was used to promote the movement of dislocations under the
indentation and form slip bands in previous studies [10 11 42] The highest amount
of micro cracks were observed in FBCVD SiC coatings contrary to plastic
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
105
deformation under the indentation found in previous studies [10 11 42] The micro
cracks formed in the hardness-related plastic deformation zone is the Mode-II crack)
[43] as shown in Fig 39(c) and (d) Unlike Mode-I which is dominated by the tensile
stress a Mode-II crack is the consequence of a confined shear stress [34] At the
interface of the elasticplastic deformation branch-like micro cracks were observed
as in Fig 39(b) The above discussions distinguish the hardness-related plastic
deformation mechanism in FBCVD from previous studies on ceramics which showed
dislocations are the main deformation mechanism underneath the indentation [31 44]
A unique hardness-related plastic deformation mechanism was used to explain the
difference in hardness of all three types of FBCVD SiC coatings According to Qian
et al [45] the hardness could reach an asymptotic value with the saturation of the
micro cracks growth population In three FBCVD SiC coatings studied here different
amounts of micro cracks were found (Fig 39(b) and Fig 310(b d)) and micro cracks
nucleated at stress concentration zones such as the grain boundaries or defects within
the grains Thus the difference in hardness was attributed to the grain morphologies
as shown in Fig 33 which gives different degree of resistance to the initiation and
propagation of micro cracks In the S1 coating triple junctions hamper grain
boundary shear by forming interlocks [12] which could resist and deflect the initiation
and propagation of micro cracks In the S2 coating elongated grains interact with the
surrounding small grains which could also provide interlocks (Fig 33(d) and Fig
34) The slightly lower hardness of the S2 coating as compared to the S1 coating is
due to the nano pores as seen in Fig 35(b) A lack of triple junctions and grain
interactions could be the reason for the lower hardness in the S3 coating as it has a
parallel crystalline morphology which has less constraint towards the initiation and
propagation of cracks
35 Conclusions
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
106
The microstructure and mechanical properties of three types of FBCVD SiC coatings
(SiC SiC+C and SiC+Si) were studied FBCVD SiC coatings with a sub-micrometer
grain size were deposited on simulated TRISO fuel particles by FBCVD at a low
temperature (1300 oC) The mechanical properties were studied using micro and
nano-indention The microstructures were studied using SEM and TEM It was
found that the Youngrsquos modulus of all three coatings differ which was attributed due
to the presence of nano-pores The high hardness of FBCVD SiC coatings was due to
the large amount of defects particularly the high density of dislocations It is found
that the interactions between dislocations reduced their mobility and make
dislocation-related plastic deformation unavailable We suggest that the work
hardening effect is the reason for the high hardness in the sub-micrometer grain size
FBCVD SiC coatings A hardness related-deformation mechanism was attributed to
the initiation and propagation of micro cracks The nano-indentation indent volume is
most likely be accommodated by the densification of defects such as the pores As a
result the hardness difference in FBCVD SiC coatings is due to the different grain
morphologies producing different amounts of micro cracks
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
107
36 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[2] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[3] D A Petti J Buongiorno J T Maki R R Hobbins G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[4] A C Kadak R Gnallinger M J Driscoll S Yip D G Wilson H C No J
Wang H Maclean T Galen C Wang J Lebenhaft T Zhai D A Petti W K
Terry H D Gougar A M Ougouag C H Oh R L Morre G K Miller J T
Maki G R Smolik D J Varacalle Modular pebble bed reactor Modular pebble
bed reactor project University research consortium annual report Beijing 2000
[5] E Lopez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[6] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram P Xiao Youngs modulus measurements of SiC coatings on spherical
particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[7] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[8] C H Chien S R Jian C T Wang J Y Juang J C Huang Y S Lai
Cross-sectional transmission electron microscopy observations on the Berkovich
indentation-induced deformation microstructures in GaN thin films J Phys D
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
108
Appl Phys 40 (2007) 3985-90
[9] T C Tan C A Merrill J B Orton A K Cheetham Anisotropic mechanical
properties of polymorphic hybrid inorganic-organic framework materials with
different dimensionalities Acta Mater 57 (2009) 3481-96
[10] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
related isostructural materials to nanoindentation Slip vs densification Mater
Res Soc Symp P 522 (1998) 113-18
[11] X Zhao X R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of 3C-SiC upon indentation at room temperature J Am
Ceram Soc 94 (2011) 3509-14
[12] D Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
mechanism of plastic deformation in macro- micro- and nanoindentation
processes J Phys D Appl Phys 41 (2008) 074016-24
[13] H P Chen R K Kalia A Nakano P Vashishta I Szlufarska
Multimillion-atom nanoindentation simulation of crystalline silicon carbide
Orientation dependence and anisotropic pileup J Appl Phys 102 (2007)
063514-22
[14] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[15] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[16] G Chollon J M Vallerot D Helary S Jouannigot Structural and textural
changes of CVD-SiC to indentation high temperature creep and irradiation J Eu
Ceram Soc 27 (2007) 1503-11
[17] D Heacutelary X Bourrat ODugne G Maveyraud M Peacuterez O Guillermier
Microstructures of silicon carbide and pyrocarbon coatings for fuel particles for
high temperature reactors 2nd international topical meeting on high temperature
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
109
reactor technology Beijing China 2004
[18] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[19] T Fukuzaki K Tanaka K Nishimoto Y Mur K Nishio and R Tamura
Magnetic property and microstructure of Nd-Fe-B-M (M=Si C) bulk
pnanocomposite magnets prepared by spark plasma sintering method - art no
012015 J Phys Conf Ser 106 (2008) 12015-124
[20] M C Osborne J C Hay L L Snead D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[21] K H Park S Kondo Y Katoh A Kohyama Mechanical properties of beta-SiC
after Si- and dual Si plus He-ion irradiation at various temperatures Fusion Sci
Technol 44 (2003) 455-59
[22] S Nagappa M Zupan C A Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
Mater 59 (2008) 995-98
[23] C Bellan J Dhers Evaluation of young modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[24] S Roy C Zorman M Mehregany R Deanna C Deeb The mechanical
properties of polycrystalline 3C-SiC films grown on polysilicon substrates by
atmospheric pressure chemical-vapor deposition J Appl Phys 99 (2006)
044108-20
[25] J Tan Mechanical properties of SiC in TRISO fuel particle Thesis University of
Manchester 2010
[26] M J Hernandez G Ferro T Chassagne J Dazord Y Monteil Study of surface
defects on 3C-SiC films grown on Si (111) by CVD J Cryst Growth 253 (2003)
95-101
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
110
[27] E S Machlin Materials science in microelectronics I The relationships between
thin film processing and structure 2nd
ed Oxford Elsevier Science 2005
p206-47
[28] A Nakamura T Yamamoto Y Ikuhara Direct observation of basal dislocation
in sapphire by HRTEM Acta Mater 50 (2002) 101-08
[29] H Y Shin S K Kwon Y I Chang M J Cho K H Park Reducing
dislocation density in GaN films using a cone-shaped patterned sapphire substrate
J Cryst Growth 311 (2009) 4167-70
[30] W D Callister Materials science and engineering An introduction 7th ed
Australia John Wiley amp Sons Australia Limited 2006 p191-99
[31] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
materials with a density functional theory J Appl Phys 104 (2008) 053508-16
[32] M Mishra I Szlufarska Possibility of high-pressure transformation during
nanoindentation of SiC Acta Mater 57 (2009) 6156-65
[33] A R Beaber L J Qi J Hafiz P H Mcmurry J V R Heberlein W W
Gerberich S L Girshick Nanostructured SiC by chemical vapor deposition and
nanoparticle impaction Surf Coat Tech 202 (2007) 871-75
[34] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
p162-91
[35] R W Rice Mechanical properties of ceramics and composites 1st ed New
York Marcel Dekker 2000 p457-534
[36] U Messerschmidt Dislocation dynamics during plastic deformation Part 2
Ceramic Single Crystals Springer Series in Materials Science On line 2010
p264
[37] S Ogata J Li N Hirosaki Y Shibutani S Yip Ideal shear strain of metals and
ceramics Phys Rev B 70 (2004) 104104-10
[38] Y Umeno Y Kinoshita T Kitamura Ab initio DFT study of ideal shear
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
111
strength of polytypes of silicon carbide Strength Mater 40 (2008) 2-6
[39] Y Umeno M Cerny Effect of normal stress on the ideal shear strength in
covalent crystals Phys Rev B 77 (2008) 100101-04
[40] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[41] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000 p139-77
[42] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[43] A A Wereszczak K E Johanns O M Jadaan Hertzian Ring Crack Initiation
in Hot-Pressed Silicon Carbides J Am Ceram Soc 92 (2009) 1788-95
[44] S L Lloyd A Castellero F Giuliani Y Long K K Mclaughlin J M
Molina-Aldareguia N A Stelmashenko L J Vandeperre W J Clegg
Observations of nanoindents via cross-sectional transmission electron microscopy
a survey of deformation mechanisms P Roy Soc a-Math Phy 461 (2005)
2521-43
[45] J Qian L L Daemen Y Zhao Hardness and fracture toughness of moissanite
Diam Relat Mater 14 (2005) 1669-72
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
112
CHAPTER 4 Vickers Indentation Fracture Toughness of
SiC Coatings
41 Introduction
Silicon carbide (SiC) layer is considered to be the most important component for
structural integrity as during the operation of a nuclear reactor it has the ability to
sustain most of the internal pressure caused by gaseous fission products produced in
the kernel and retain most of the fission products [1-4] Previous work was focused on
the investigation of mechanical properties (Youngrsquos modulus and fracture strength) of
SiC coatings on TRISO particles using different techniques such as a ring test [5 6]
a crush test [7 8] a micro-cantilever test [9] and indentation [10 11] However few
reports exist on the measurement of the fracture toughness of SiC coatings even
though it is a property used in modeling to estimate the failure probability of TRISO
fuel particles [12] For example Kadak et al [12] used a fracture toughness value of
33 plusmn 053 MPa m12
This value was obtained from bulk SiC produced by a static
CVD method The fracture toughness value may well differ for SiC coatings produced
by fluidized bed chemical vapour deposition (FBCVD) on TRISO fuel particles [10]
Because microstructure of SiC produced by static CVD and FBCVD methods could
vary significantly For example the static CVD SiC usually has larger grain size and
high density while FBCVD SiC with large grain size is usually accompanied with
porosity [13] Different grain size range and porosity fraction can lead to variation of
fracture toughness [1 2] Therefore the fracture toughness value of bulk SiC may not
be truly representative of SiC coatings used in nuclear fuel applications To our
knowledge the only available data on the fracture toughness of a SiC layer on TRISO
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
113
fuel particle is reported by Zhao et al[9] where the fracture toughness was measured
by the micro-beam method However this method is time consuming and expensive
restricting its implementation as a standard characterization technique where
repetitive measurements are required to confirm the reproducibility of experimental
data
In this Chapter micro-indentation is used to investigate the fracture behaviour of
different SiC coatings produced (on TRISO fuel particles) by FBCVD due to its
capacity to measure the mechanical properties in a small area and produce visible
cracks [14-16] The fracture behaviour under an indenter is also studied using a
transmission electron microscope (TEM) in order to give better understanding of the
fracture mechanism The characteristics of the SiC microstructures are then correlated
with their fracture behaviour
42 Experimental details
The SiC coatings used are the same as the ones in Chapter 3 and the deposition
conditions were shown in Table 31 Chapter 3
For the micro-indentation study SiC coated fuel particles were hot mounted in
copper-loaded conductive resin (to get better SEM images) and then ground to a
cross-section (as shown in Fig 31(a)) or polished a flat external surface (as shown in
Fig 31(b)) In this Chapter the y direction is called radial direction x is called
tangential direction according to Fig 31(a) and (b) The samples were then polished
using increasingly fine diamond suspensions to 14 μm Indentation fracture
toughness measurements were performed using a Vickers diamond indenter (CSM
Instruments Switzerland) Due to the through-thickness (in the radial direction)
failure behaviour of a SiC coating in a TRISO fuel particle under tensile stresses
generated from gases due to nuclear reactions similar tensile stresses could be
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
114
generated from indentation of polished external surface of TRISO particles which
could generate cracks along the radial direction (y direction in Fig 31(b)) of the
TRISO particles as well The indentations were carried out under a maximum load of
3 N (corresponding to a maximum indentation depth of ~26 μm) To avoid PyC
influence the thickness of SiC coatings (in the section as shown in Fig 31(b)) were
kept to ~60 μm after polishing which is more than 20 times the indentation depth
In this case the elastic zone has not expanded to the substrate according to the
criterion that indentation depth is less than 10 of coating thickness [17] For each
sample six indents were made on the polished external surface of SiC perpendicular
to the radial direction with a separation of 70 μm between each indent
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference [25]
The calculation of the VIF fracture toughness must account for the crack profile under
the indenter whether the cracks are of the Palmqvist mode or half-penny mode which
are illustrated in Fig 41 The halfpenny crack system is formed by the joining of
radial cracks as shown in Fig 41(a) while the Palmqvist crack system is always
shallow as shown in Fig 41(b)
To observe the crack impression under the indenter on the polished external surface
an indentation (as in Fig 42(a)) with a final indentation depth of 26 μm was
sequentially polished with 6 μm diamond suspensions The surface was polished until
the plastic deformation zone was exposed together with the radial cracks (as shown in
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
115
Fig 42(b) Afterwards polishing continued until the removal of the plastic
deformation zone (as shown in Fig 42(c)) The surface showed no cross-over
cracking present as illustrated in Fig 41(a) and this confirms the presence of the
Palmqvist mode cracks on the polished external surface of SiC coatings under the
Vickers indenter The three polished samples showed the same crack propagation
mode and this is consistent with previous reports [18 19] where a Palmqvist crack
system has been observed in SiC at low loads (lt 10 N)
The Palmqvist crack mode allows the VIF fracture toughness to be calculated using
the equation proposed by Laugier [15 16] given as
1 2 23
3 2( ) ( )IC v
a E PK
l H c
(1)
In Eq (1) the geometrical constant v is a calibrated value using the already known
fracture toughness due to the variation in use of the Vickers hardness or the
nano-hardness [14 16 20 21] The 2a and l are the lengthes of diagonal and radial
crack length of Vickers indentation (as shown later in Fig 43) respectively c=a+l
the E and H are Youngrsquos modulus and hardness measured by nano-indentation P is
the load of Vickers indentation Therefore this geometrical constant was calibrated
before it was used to calculate the VIF fracture toughness of SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
116
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
117
The only already known fracture toughness was measured on the cross-section of
extra-Si SiC coatings using a micro-beam bending method [9] so the calibration of
v was carried out on the cross section (as in Fig 31(a)) of the same coating
According to Eq(1) the hardness (H ) and Youngrsquos modulus (E) are nano-hardness
and Youngrsquos modulus as measured in a previous study [22] P is the load a is the
impression half diagonal l is the crack length and c is the half diagonal crack length
(see later in Fig 43) To get the load and dimensional values of indentations a total
of 8 indentations at different loads (3 35 and 4 N) were applied on the cross-section
of the extra-Si SiC coating
The crack lengths were measured using a scanning electron microscope (Philips XL30
FEG-SEM) FEG-TEM (Tecnai TM
G2 F30 U-TWIN 300KV) which was used to
study the fracture behaviour under the indenter For the TEM study the cross
sectional specimens for the indents were prepared using focused ion beam milling
(FIB FEI Nova 600 Dual Beam system) Note that due to the large deformation zone
(gt10 μm diameter) and radial crack length (gt15 μm) observed from micro-indent
impression it was not possible to produce a sufficiently large TEM sample by the FIB
technique This limitation restricted us to study the fracture behaviour under a sharper
indenter (Berkovich) with lower load
43 Results and discussion
431 VIF fracture toughness study
Figure 43 is the crack morphology observed in S3 (SiC + Si) coating cross-section It
shows that the fracture resistance is different in the tangential and radial directions of
the cross-section which is consistent with the previous measurements along these
directions measured by the micro beam method [9] Different crack lengths along the
tangential and radial directions observed from 8 indentations are illustrated in Table
41 Correspondingly fracture toughness values of 347 MPa m12
and 672 MPa m12
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
118
taken from Ref [9] were used as the standard values for the tangential and radial
directions of the SiC coating respectively According to Eq (1) taking into account
observed and measured parameters (KIC a c l H and E) the geometric constant
value v was calculated in each indentation for each direction (Table 41)
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for S3 SiC coatings
Table 41 illustrates the indentation parameters and the calibrated geometrical
constant v for the Palmqvist crack mode According to the results shown in Table
41 the calibrated mean value of v is 002008plusmn000273 and this value is within
the range of the geometrical constant value (0014-0023) from previous theoretical
studies [14 23] By using nano-indentation hardness and Youngrsquos modulus v was
taken as 002 for the calculation of the VIF fracture toughness in SiC layers in this
study which is the upper limit of 0016plusmn0004 used for previous studies of bulk
CVD SiC using the HE from micro-indentation [14 24-27]
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
119
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχ
v along the radial and tangential directions
Load Radial direction
Tangential direction
a (μm) c (μm) l (μm) χv a (μm) c (μm) l (μm) χv
3 N 6650 13125 6475 0020368 6685 18285 11600 0023088
6900 13090 6190 0019473 6995 15470 8475 0015013
6675 11895 5220 0015749 6120 16615 10495 0019880
6695 13130 6435 0020249 6555 15935 9380 0017057
6790 12610 5820 0017997 6425 18275 11850 0023783
35 N 7195 14970 7775 0022404 7235 20790 13555 0024930
6670 14080 7410 0020721 6715 18160 11445 0019412
4 N 7770 15855 8085 0020967 7390 20240 12850 0020187
χv 002008 plusmn 000273
Note The geometrical constantsχv presented in Table 41 were calculated using Eq(1) The fracture
toughness along the radial (672 MPa m12
) and tangential directions (347 MPa m12
) were taken from
Ref 9
Although the Vickers indentation method for fracture toughness measurement has
been discredited as a mean to obtain true fracture toughness [28] and always gives a
lower fracture toughness value than that obtained using the standard methods (such as
single edge V-norched bending)[1] the values obtained can be compared with each
other This is particular important for small samples and thin coatings since Vickers
indentation provides a method to quantify fracture behaviour when it is not feasible to
obtain true fracture toughness However to get reasonable comparison of Vickers
indentation fracture toughness in SiC coatings the following conditions should be
met
(1) SiC materials produced four regular radial cracks along the corners of the
Vickers indenter For indentation at the polished external surface of SiC
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
120
coatings deposited by FBCVD similar fracture resistance along different
orientation at the surface should be obtained
(2) The calibration of the geometrical constant should be made v was obtained
as 002 based on previous experimental results (see above)
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
Sample Grain size range (μm) Vickers toughness (MPa m12
)
S1 (SiC) 02-2 351plusmn042
S2 (SiC + C) 02-2 403plusmn043
S3 (SiC + Si) 02-2 493plusmn016
Table 42 presents the measured VIF fracture toughness on the polished external
surface using equation (1) for the SiC coatings in which the deposition conditions and
grain size were given It can be seen that the SiC coating with excess Si (S3) has
highest indentation fracture toughness followed by SiC with excess carbon (S2) and
stoichiometric SiC coatings (S1)
Vickers indentation fracture toughness values obtained in this study are slightly higher
than that of commercial CVD β-SiC which has been reported to vary from 24 to 33
MPa m12
measured by the same method [24 26 27] The VIF fracture toughness of
49 MPa m12
for extra-Si SiC measured on a polished external surface is between
347 and 672 MPa m12
when measured on a cross section by micro-beam method [9]
This is consistent with the observation of radial crack length differences ndash the crack
length on the polished external surface is between those in the tangential and radial
direction on the cross-section It is suggested that Vickers indentation is an effective
method for the characterization of fracture behaviour of FBCVD SiC coatings
Moreover the high hardness and Youngrsquos modulus of these three coatings [22] do not
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
121
cause a decrease in fracture toughness which is explained in the later part of this
paper
432 Influence of non-stoichiometries on the VIF fracture toughness
The VIF fracture toughness in S2 SiC coating is ~14 higher than the value for S1
SiC coatings and this can not be attributed to heterogeneous toughening due to the
excess carbon being at the grain boundaries Due to the low content of excess C it is
difficult to identify such an excess at the grain boundaries [29] Previous work
reported in Ref[30] showed that there was no presence of carbon at the grain
boundaries for a concentration up to 1 wt excess C In our case a similar situation
was found in S3 SiC coating where excess Si has not been found along the grain
boundaries Previous studies had [31 32] shown that excess Si in SiC was observed in
grains or near the grain boundaries by TEM only when the amount of excess Si is
high enough (such that it could be detected by XRD or a much higher Raman
spectroscopic intensity)Thus it is assumed that the excess Si could not be considered
as giving heterogeneous toughening which caused a ~43 higher VIF fracture
toughness in the S3 SiC than the S1 SiC coatings As a result the small amount of
excess carbon or silicon in SiC coatings does not seem to have influence on the VIF
fracture toughness through serving as the heterogeneous phase along the grain
boundary
The excess Si or C could be related to different grain morphologies according to
previous study [33] where it was observed that different SiC ratios in the reaction
gas produced rough smooth and irregular pyramid-like grain surfaces This further
affects the growth morphology and cohesion stress between grains For example the
smooth grain surface favours the parallel grain growth The weak grain boundary
cohesion could be the micro crack initiation zone while the strong grain boundary
could transfer the stress to stress concentration zone Here the role of grain
morphology is studied later in terms of stress concentration zone under indentation
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
122
433 Microstructural analysis of fracture behaviour under the indenter
SiC coating under nano-indentation on the polished external surface at a maximum
indentation load of 160 mN It can be seen that the median crack propagation root
deflected slightly and changed from intergranular to transgranular fracture as shown
in Fig 44(a) It is worth noticing that the median crack observed under
nano-indentation was not found under indentation because the indentation cracking
mode depends on the condition of the indenter tip [34] Higher magnification images
(Fig 44(b)) show that a large number of micro cracks were produced at the
elasticplastic interface
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
123
Both intergranular and transgranular cracks were observed near the median crack
initiation zone These cracks are under a tensile stress dominated by Mode I cracks as
the elastic-plastic stress field gives the highest tensile stress around this interface
according to a previous report (see Ref [35]) Moreover micro-cracks were observed
surrounding the median crack and also at the median crack tip as shown in Fig 44(c)
and Fig 44(d) respectively Figure 44(c) illustrates that the micro-cracks are along
the grain boundaries while the micro-cracks around the crack tip were found to both
pass through the grains and along grain boundaries (Fig 44(d))
Non-stoichiometric SiC coatings (S2 and S3) show quite different crack morphologies
under the indenter from that in the stoichiometric SiC (S1) coating as shown in Fig
310 in chapter 3 It can be seen that the propagation root of median cracks in S3 SiC
and S2 SiC coatings were affected by the microstructures as in Fig 310(a) and (c) in
chapter 3 Moreover a lateral crack was found in the S2 SiC coating The irregular
median crack propagation route in non-stoichiometric SiC coatings seems to be
related to the laminar structure
Fig 45 Cross-sectional SEM image of the S1 SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
Figure 45 shows the cross section of S1 SiC coating and the laminar structure (as
indicated by the dashed lines) is perpendicular to the grain growth direction It was
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
124
discussed in chapter 3 that the laminar structure is due to either nano-pores or a high
concentration of stacking faults and it is much less evident in the stoichiometric SiC
coating as compared to the coatings with impurities [22] In the S3 SiC coating (Fig
310(b) in chapter 3) a larger amount of micro cracks either intergranular or
transgranular were found under the indenter than in the S1 and S2 SiC coatings
The fracture mechanism of materials is influenced by their microstructure and the
fracture toughness could be enhanced by changing it For example ceramics
containing micro-cracks during fabrication could be associated with good fracture
behaviour but low strength and hardness since the micro-cracks usually serve as the
failure origins A better solution is to fabricate materials with microstructures that can
form stress induced micro-cracks under an external force [36] In FBCVD SiC a
number of micro cracks were observed under the indenter (Fig 44(b) Fig 310(b)
and (d) in chapter 3) from where the main cracks initiated and propagated away from
this zone According to a previous study although the tip of the main crack leaves the
micro-cracked zone under the indenter the wake region can provide stress shielding
against some further crack extension [37]
Thus the micro-cracks under the indentation (Fig 44(b) Fig 310(a) and (c) in
chapter 3) seem to be a mechanism for the toughening behaviour of FBCVD SiC by
dissipating the fracture energy for brittle fracture Micro-cracks were also found near
the main crack tip and surrounding the main crack for example in the stoichiometric
SiC coating (Fig 44(c) and (d)) This further confirms the toughening behaviour
through micro-cracking In CVD SiC which has a slightly lower fracture toughness
(around 33 MPa m12
) only a few micro-cracks were observed under the indentation
[38] which could be caused by indentation-induced slip bands As a result the
micro-cracks formed under the indentation near the main crack seem to be the reason
for the high VIF fracture toughness in SiC coatings when a high hardness is obtained
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
125
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a) S2
SiC (b) S3 SiC
Stress concentration zones are known to facilitate the nucleation of micro-cracks so a
large amount of micro-faults (eg pores) and weak grain boundaries (inducing the
micro-cracks under an external stress) could increase the VIF fracture toughness A
higher VIF fracture toughness in the extra-C SiC than in stoichiometric SiC coatings
may be due to the presence of the nano-pores (as shown in Fig 35(b) in chapter 3)
The S3 SiC has an even higher VIF fracture toughness than the S2 SiC coating and
this may correspond to a larger number of micro-cracks under the indentation We
assume this difference is due to their varied grain boundary morphologies as shown
in Fig 46 For example we observed different length of cracks on the cross section
(Fig 43) with cracks parallel to the grain growth direction shorter than cracks
perpendicular to the grain growth direction This is because along grain growth
direction itrsquos more likely to produce micro-cracks along the grain boundary As we see
in Fig 46 grains interact with each other in extra-C SiC (Fig 46(a)) forming branch
grains while in S3 SiC grains grow parallel (Fig 46(b)) According to a previous
study it is easier for parallel grains to form a transgranular fracture when the grain
boundaries are along the loading axis [39] This can explain the larger number of
transgranular micro-cracks under the indentation in the extra-Si SiC compared to the
extra-C coatings (Fig 310(b) in chapter 3) which caused different VIF fracture
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
126
toughness This different grain morphology could be caused by the
non-stoichiometries and further work needs to be done to study how excess C or Si
affects the microstructure of the SiC
44 Conclusions
In summary micro-indentation on the polished external surface of the SiC coating in
TRISO particles has been successfully applied to measure the VIF fracture toughness
of the silicon carbide (SiC) Three different types of SiC coatings (stoichiometric SiC
SiC with excess silicon and SiC with excess carbon) produced on spherical particles
by FBCVD were analysed The VIF fracture toughness (measured on the polished
external surface) in these three coatings investigated in this study was observed to
vary between 35 and 49 MPa m12
The results have shown that the VIF fracture
toughness is influenced by the microstructure and non-stoichiometry of SiC coatings
For FBCVD SiC coatings a high VIF fracture toughness accompanied with superior
hardness was attributed to the formation of micro-cracks The difference in VIF
fracture toughness was proposed to be dominated by the laminar defects and grain
morphologies in the SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
127
45 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo and D A Petti
Handbook of SiC properties for fuel performance modeling J Nucl Mater 371
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[2] N Swaminathan P J Kamenski D Morgan and I Szlufarska Effects of grain
size and grain boundaries on defect production in nanocrystalline 3C-SiC Acta
Mater 58 (2010) 2843-53
[3] G K Miller D A Petti D J Varacalle and J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[4] D A Petti J Buongiorno J T Maki R R Hobbins and G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[5] K Bongartz E Gyarmati H Schuster and K Tauber Brittle Ring Test - Method
for Measuring Strength and Youngs Modulus on Coatings of Htr Fuel Particles J
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[6] K Bongartz E Gyarmati H Nickel H Schuster and W Winter Measurement of
Youngs Modulus and Fracture Stress on Htr Particle Coatings by Brittle Ring Test
J Nucl Mater 45 (1972) 261-64
[7] M W Kim J H Kim H K Lee J Y Park W J Kim and D K Kim Strength
of chemical vapor deposited silicon carbide films using an internal pressurization
test J Ceram Process Res 10 (2009) 373-77
[8] T S Byun J D Hunn J H Miller L L Snead and J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[9] X Zhao R M Langford J Tan and P Xiao Mechanical properties of SiC
coatings on spherical particles measured using the micro-beam method Scripta
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
128
Mater 59 (2008) 39-42
[10] E Lopez-Honorato P J Meadows J Tan and P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[11] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram and P Xiao Youngs modulus measurements of SiC coatings on
spherical particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[12] ACKadak RGNallinger MJDriscoll SYip DGWilson HCNo JWang
HMaclean TGalen and CWang et al Modular Pebble Bed Reactor Project
University Research Consortium Annual Report Beijing 2000
[13] J I Federer Parametric Study of Silicon-Carbide Coatings Deposited in a
Fluidized-Bed Thin Solid Films 40 (1977) 89-96
[14] G R Anstis P Chantikul B R Lawn and D B Marshall A Critical-Evaluation
of Indentation Techniques for Measuring Fracture-Toughness 1 Direct Crack
Measurements J Am CeramSoc 64 (1981) 533-38
[15] M T Laugier Palmqvist Toughness in Wc-Co Composites Viewed as a Ductile
Brittle Transition J Mater Sci Lett 6 (1987) 768-70
[16] M T Laugier Palmqvist Indentation Toughness in Wc-Co Composites J Mater
Sci Lett 6 (1987) 897-900
[17] W D Nix and R Saha Effects of the substrate on the determination of thin film
mechanical properties by nanoindentation Acta Mater 50 (2002) 23-38
[18] J Lankford and D L Davidson Crack-Initiation Threshold in Ceramic Materials
Subject to Elastic-Plastic Indentation J Mater Sci 14 (1979) 1662-68
[19] Z Li A Ghosh A S Kobayashi and R C Bradt Indentation
Fracture-Toughness of Sintered Silicon-Carbide in the Palmqvist Crack Regime J
Am CeramSoc 72 (1989) 904-11
[20] H Hatta M Zoguchi M Koyama Y Furukawa and T Sugibayashi
Micro-indentation method for evaluation of fracture toughness and thermal
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
129
residual stresses of SiC coating on carboncarbon composite Adv Compos Mater
12 (2003) 155
[21] C B Ponton and R D Rawlings Vickers Indentation Fracture-Toughness Test 1
Review of Literature and Formulation of Standardized Indentation Toughness
Equations Mater Sci Tech Ser 5 (1989) 865-72
[22] H Zhang E Lopez-Honorato A Javed X Zhao and P Xiao Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc In Press (2011)
[23] A Leonardi F Furgiuele S Syngellakis and R J K Wood Analytical
Approaches to Stress Intensity Factor Evaluation for Indentation Cracks J Am
Ceram Soc 92 (2009) 1093-97
[24] M C Osborne J C Hay L L Snead and D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[25] R D Dukino and M V Swain Comparative Measurement of Indentation
Fracture-Toughness with Berkovich and Vickers Indenters J Am CeramSoc 75
(1992) 3299-304
[26] K H Park S Kondo Y Katoh and A Kohyama Mechanical properties of
beta-SiC after Si- and dual Si plus He-ion irradiation at various temperatures
Fusion Sci Technol 44 (2003) 455-59
[27] S Nogami S Ohtsuka M B Toloczko A Hasegawa and K Abe Deformation
during surface modification of silicon carbide using rare-gas ion-beam irradiation
Pricm 4 Forth Pacific Rim International Conference on Advanced Materials and
Processing Vols I and Ii 1367-70 3028 (2001)
[28] G D Quinn and R C Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[29] J Tan Mechanical properties of SiC in TRISO fuel particle PhDThesis
University of Manchester Manchester 2010
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
130
[30] K Kaneko M Kawasaki T Nagano N Tamari and S Tsurekawa
Determination of the chemical width of grain boundaries of boron- and
carbon-doped hot-pressed beta-SiC by HAADF imaging and ELNES line-profile
Acta Mater 48 (2000) 903-10
[31] B Reznik D Gerthsen W G Zhang and K J Huttinger Microstructure of SiC
deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499-508
[32] R A Shatwell K L Dyos C Prentice Y Ward and R J Young Microstructural
analysis of silicon carbide monofilaments J Microsc-Oxford 201 (2001) 179-88
[33] M J Hernandez G Ferro T Chassagne J Dazord and Y Monteil Study of
surface defects on 3C-SiC films grown on Si(111) by CVD J Cryst Growth 253
(2003) 95-101
[34] D S Harding W C Oliver and G M Pharr Cracking during nanoindentation
and its use in the measurement of fracture toughness Thin Films Stresses and
Mechanical Properties V 356 (1995) 663-68
[35] ACFischer-Cripps Introduction to contact mechanics Springer New York
2000
[36] DJGreen An introduction to the mechanical properties of ceramics Cambridge
University Press Cambridge 1998
[37] S B Biner A Numerical-analysis of crack-growth in microcracking brittle solids
Acta Metall Mater 42 (1994) 3643-51
[38] K H Park T Hinoki and A Kohyama Influence of irradiation-induced defects
on fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[39] H Horii and S Nematnasser Brittle failure in compression - splitting faulting
and brittle-ductile transition Philos T Roy Soc A 319 (1986) 337-74
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
131
CHAPTER 5 Influence of Interfacial Roughness on Fracture
Strength of SiC Coatings
51 Introduction
During the irradiation process of TRI-Isotropic (TRISO) fuel particles the high
tensile stress could be accumulated at crack tips These tips were due to direct
penetration of the cracks formed in the PyC layer or the high stress concentration as a
result of the debonding of IPyCSiC interface [1 2] When the tensile stress inside of
the particle exceeded the critical fracture stress of the SiC coating it caused the
failure of the whole particle [3] Furthermore the fracture strength is a main
parameter used in modeling the probability of failure of fuel particles so it is
important to measure the fracture strength of SiC to determine their performance
which is determined from the maximum tensile stress
Different methods such as hemi-spherical bending [4] crush test [5 6] and inner
pressure [6] were introduced to measure the fracture strength of SiC coating in
TRISO fuel particle The fracture strength was in a range and could be characterised
by the Weibull distribution function [4-6] The common vague conclusion derived
from previous results is the significant effect of the IPyCSiC interface on the fracture
strength [4-6] The interface was also found to affect the primary failure mechanism
by determining if the load can transmit through the SiC [6] Previous analyses are
consistent with the well-known prescription that the fracture strength of ceramic
materials varies largely and it is dependent on the size and surface condition of the
specimen [7-9] Among these methods the latest modified crush test proposed by
Byun et al[510] showed a well controlled scatter of the fracture strength in a given
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
132
sample
Although the importance of the interface has been noticed the lack of an accurate and
scientific description of the interface has limited the further study about its
relationship with the fracture strength Roughness is a commonly used terminology to
describe the interface and it could be measured by atomic force microscope and
characterised by the standard deviation of the vertical features [11 12] However
roughness is not enough to describe the interface and to relate it to fracture strength
[13] Due to the importance of the statistical analysis for ceramic materials the
self-affine theory was used to characterise the complex interface numerically
according to previous studies [14-17] A self-affine interface is characterised by a
correlation length the saturation roughness and the roughness exponent [18] A
similarly straightforward approach was applied to demonstrate the importance of the
interfacial roughness on the mechanical properties [19] showing that interfaces with
big and sharp irregularity fail first
In this work the modified crush test was used to measure the fracture strength of a
SiC layer deposited at different temperatures The IPyCSiC interface was well
described by self-affine theory Therefore the effect of the IPyCSiC interface and
dimension of particles together with other possible influences such as porosity and
grain size on the fracture strength were discussed The improvement of this work is
being able to do statistical analysis on the interfacial roughness
52 Experimental details
521 Materials
In this Chapter the buffer pyrolytic carbon and dense pyrolytic carbon coatings were
deposited on the top of ZrO2 kernel (~ Φ500 μm) by fluidized bed chemical vapour
deposition Thirteen SiC coatings were deposited at different temperature flow rate
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
133
MTS concentration and added gas as shown in Table 51 The deposition conditions
were chosen according to previous studies to get different microstructures and more
deposition mechanisms of SiC coating can be found in Ref [20] For fracture strength
measurement the SiC particles were mounted with thermoplastic resin and ground to
about 55 portion of the sphere and polished using increasingly fine diamond
suspensions until frac14 μm SiC shells were released from surrounded PyC layers by
oxidizing at 700 ordmC for 8 hours and further washed in an ultrasonic bath with acetone
for 5 minutes
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Sample Temperature
(ordmC)
MTS
(vol )
Added gas concentration Flow rate
(LMin)
Radius
Thickness (~)
S1 1300 91 05vol C3H
6 600 72
S2 1300 91 01vol C3H
6 600 76
S3 1280 91 01vol C3H
6 600 83
S4 1300 91 -- 600 85
S5 1400 19 57vol Ar 778 87
S6 1500 22 82vol Ar 700 90
S7 1500 19 89vol Ar 778 101
S8 1500 22 79vol Ar 700 112
S9 1400 19 57vol Ar 777 117
S10 1300 19 57vol Ar 778 129
S11 1500 19 89vol Ar 777 151
S12 1500 22 76vol Ar 700 158
S13 1500 19 57vol Ar 778 190
The difference between sample S5 and S9 S7 and S11 is the thickness of the PyC layer MTS
methyltrichlorosilane Lmin the flow rate measured in liter per minute To produce SiC coatings with
particular microstructures and compositions different deposition conditions were chosen which were
contributed to Dr Eddie Lopez-Honorator
522 Test method and analysis
The crush test taking the contact area into consideration was used in this study [2 5
21] and the loading profile of the crush system is shown in Fig 51 When a partial
spherical shell (Radius R thickness t) was diametrically loaded by an external load F
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
134
concentrated on a small circular area (radius 0 ) the maximum membrane stress and
bending stress could be calculated by the equations developed by Roark and Young
[21] The combination of the maximum bending and membrane stress (Local fracture
strengthL
f ) in the inner side of the shell was the maximum fracture strength for
partially loaded shell (around 55 of the sphere)
The fracture strength of brittle SiC coating is best considered as a distribution rather
than a fixed number and the most widely used expression for characterisation is the
cumulative distribution functionmdashWeibull distribution function [7 22] In the current
study the distribution of local fracture strength and fracture strength for a full
spherical shell were characterised by the Weibull distribution The Weibull modulus m
is derived from the local fracture strength (Eq 14 in Chapter 2) The calculation of the
fracture strength for the full spherical shell (F
f ) is based on the size effect (scaling
factor mtRr 122
0 ))(4( R radius of the particle t thickness of SiC shell 0
radius of residual impression after loading) which is equal to the partial strength
divided by the scaling factor [5 7] More details about fracture strength calculation
are available in Ref [5]
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
According to a previous study [5] one reason for the difference of local fracture
10 ordm
t
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
135
strength in a given batch of coating is due to different sizes of residual impression
( 0 ) under which the distribution of defects could be different To reduce the
influence of the 0 the radius (R) at the edge of the residual impression was kept at
an angle of around 10ordm (as shown in Fig 51) from the loading axis by inserting
different kind of soft metal It varied slightly (the ratio of standard deviation to mean
value is around 10) in each batch of SiC
The crush test was carried out in a universal tensile machine INSTRON 5569
(INSTRON High Wycombe Bucks) with a 100 N maximum load cell For each batch
of SiC shell (except for S13) at least 30 specimens were tested at room temperature
with a crosshead speed of 0005 mms The failure load recorded by the tensile
machine was used as the fracture load The individual impression left on the soft
metal (Nickel alloy cold worked copper or brass) was marked under corresponding
load and its diameter was measured by optical microscope (times100 ZESIS Company
German)
523 Characterisation methods
A Philips XL30 FEG-SEM (Philips Eindhoven Netherlands) was used to characterise
IPyCSiC interfacial roughness grain size and porosity from the finely polished cross
section of SiC coatings Characterisation of the IPyCSiC interfacial roughness was
realized by editing the SEM images (in the magnification of times1600) with the Image J
software and extracted it as a line from the background SEM image The interfacial
roughness could be described by a series of pairs of x (distance tangential to the
interface) and y (distance normal to the interface) coordinates assuming the interface
is flat at a scale of 70 microm
Porosity was measured by controlling the threshold of SEM images (times1600 TIF) at a
gray level and adjusted to distinguish pores from grains with the Image J software
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
136
Pore fraction was defined as the ratio of the pores and the total area of the SEM image
Grain size of FBCVD SiC coatings varied in a range and in a columnar shape It was
characterised by measuring mean width and length of single crystals from SEM
images (times6400) and the grain size of the coatings is represented by the mean width
timeing the length of grains A FEG-TEM (TecnaiTM G2
F30 U-TWIN) was used to
observe the IPyCSiC interfacial roughness and TEM samples were prepared by
focused ion beam milling The linear regression method was used to analyze and
quantify the influences of parameters on the fracture strength and Weibull modulus
53 Results and discussions
531 Fracture strength and dimensional effect
Table 52 gives the summary of the measured and calculated parameters for all the
coatings It includes the diameter of impression (mean value 2 0 ) force (mean value
F) Weibull modulus (derived from local fracture strength m) local fracture strength
(L
fmean value) and fracture strength for the full spherical shell (
F
fmean value)
Table 52 Summary of measured and calculated parameters for all the coatings
Sample 2 0 μm F N L
f MPa Modulus (m) Scaling Factor
For Size Effect
F
f MPa
S 1 15239 2235 1784 7397 185 963
S 2 15043 1999 1599 7687 183 872
S 3 14898 1540 1446 7459 187 774
S 4 16052 2042 1620 8261 178 908
S 5 17018 2573 1810 7927 178 1018
S 6 16220 1885 1648 6953 193 855
S 7 14662 1691 1974 7755 190 1019
S 8 14905 1336 1717 7102 198 868
S 9 13040 1088 1825 6495 223 820
S10 16410 1215 1472 6801 204 722
S11 16165 1006 1430 6104 219 652
S12 14677 903 1512 6616 205 737
S13 11586 489 1762 4912 300 587
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
137
As given in Table 52 a significant difference (49-257 N) of the load among SiC
coatings was obtained According to a previous study [5] the variation is mainly
caused by different thicknesses (varied from 30 μm to 60 μm) of SiC coatings
because the relatively thin coating tends to reach higher strength concentration at
fracture
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
The Weibull modulus derived from the local fracture strength (as given in Fig 52) is
in the range of 49-86 (as shown in Table 52) and it falls into the category of moduli
for ceramics materials (from 5 to 30) This range of Weibull modulus is similar to the
values obtained from the brittle ring tests which also gave a similar range of the local
fracture strength [23 24] In different batches of SiC coatings it was found that the
Weibull modulus decreases linearly with the increase of the ratio of outer radius (R) to
the thickness of SiC coatings ( tR ) as shown in Fig 53 The ratio of Rt accounts
for up to 778 (2R from linear regression) of differences of the modulus This is
because the tR ratio is a critical dimension value for the strength distribution of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
138
SiC shell and it represents the relative thickness of SiC coating The higher the ratio
is the thinner the SiC coating So it corresponds to the larger inner surface area
resulting in larger scattering sizes of the critical flaws This observation is consistent
with the previous finite element modeling results showing that the Weibull modulus is
related to the sample dimension [10]
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
As given in Table 52 the scaling factor (effective area-parameter based on the local
fracture strength) between the local fracture strength and the fracture strength of the
full shell are in the range of 18-30 The results are consistent with Byun et alrsquos study
(19-31) [5] and it indicated the importance of the size effect on the fracture strength
of the full shell
The fracture strength for the full spherical shell of thirteen SiC coatings were given in
the form of Weibull plots as shown in Fig 54 The mean fracture strength for the full
spherical shell was in the range of 587-1019 MPa (as given in Table 52) which is
higher than the range of 330-650 MPa obtained by Byun et al [5] This is because the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
139
Rt ratio (above 11) in Ref [5] falls into the higher value categary in current work as
shown in Fig 53
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Because the Weibull modulus is dominated by the tR ratio (Fig 53) its influence on
fracture strength for a full spherical shell could also be from this ratio as shown in
Fig 55 It shows that the fracture strength for the full shell decreases nearly linearly
with the increase of the tR ratio which produces a difference of 6528 (2R derived
from linear curve fit which represents fair agreement) of differences In this work the
similar range of Rt ratio (above 11) corresponds to the fracture strength lower than
850 MPa (as shown in Fig 55) which reduced the difference from previous results
[5] Furthermore the fracture strength of about 1000 MPa was obtained when the Rt
was about 8 [25] and it is similar as the result given in Fig 55 This again
demonstrated the importance of the geometry on the fracture strength of SiC coating
Therefore it is important to eliminate the external influence and study the influences
of microstructures such as interfacial roughness porosity and grain size on fracture
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
140
strength which are discussed in the following parts
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
532 Observe and qualify the effect of interfacial roughness on fracture strength
According to Griffith fracture theory the fracture strength (L
f ) is a function of the
critical flaw size (C) and the fracture toughness ( ICK ) as shown in the following
equation [26]
12( )
L ICf
K Z
Yc (1)
Y is a loading geometrical parameter Z is the flaw size parameter The magnitude of
the critical flaw size could be related to the IPyCSiC interfacial irregularities
The interfacial flaw shape of SiC coatings is modeled from the surface morphology of
PyC coating during deposition process as shown in Fig 56(a) The crack was taken
as a semi-circular surface crack as given in Fig 56(b) where Y is 2 and Z is 16 (Y
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
141
Z are geometrical constants introduced in Eq (1) [26] The fracture toughness of SiC
coatings in TRISO fuel particle was taken to be 33 MPamiddotm12
according to previous
report [27] Taking the result of the local fracture strength from individual SiC coating
into Eq (1) the magnitude of the critical flaw size C could be obtained
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Figure 46 shows the redraws of the IPyCSiC interfacial roughness from SEM images
and the calculated critical flaw sizes according to Eq (1) (range and mean values) for
all specimens are given in the right columns If the fracture initiated at the IPyCSiC
interface as proposed in previous studies [4-6] the calculated critical flaw size range
of each type of SiC coating was expected to match the size range of the interfacial
irregularities
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
142
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
In Fig 57 most of the calculated critical flaw sizes according to Eq (1) are in the
same magnitude as the flaw size observed directly from the interfacial profile images
and this indicates that the dominant effect of the surface roughness on the local
fracture strength For example the direct observation of the biggest flaw size from the
profile is about 43 μm and 26 μm in sample S9 and S13 respectively and they are in
the range of the calculated defect sizes of 09-65 μm and 17-47 μm for S9 and S13
respectively However exceptions were found such as specimens S1 and S2 which
show slightly higher calculated surface flaw size than the observation from SEM
images Furthermore it is difficult to accurately characterise the difference of the
interfacial roughness by observing the converted images and give specific
information (such as shape) of single profile (shown in Fig 57) The estimation of
the shape of surface irregularities to be half-circular could also result in the error on
the critical flaw size calculation [7] To give a direct estimation about the influence of
interfacial roughness on local fracture strength the scaling behavior of IPyCSiC
interface need to be characterised by a statisticalnumerical method
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
143
533 Characterise and quantify the interfacial roughness
Self-affine theory has become a standard tool in the study of various rough interfaces
[18 28 29] Here it was the first time being proposed to describe the IPyCSiC
interfacial roughness accurately and scientifically and then was used to quantify the
relationship between interfacial roughness and local (intrinsic) fracture strength and
fracture strength of the full shell
5331 Self-affine theory introduction and experimental setup
In order to describe the IPyCSiC interfacial roughness with specific parameters an
easy way is using a height-height function [29 30]
2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)
where the x axis is along the IPyCSiC interface and ( )h x is the surface height profile
The amplitude of the roughness ( )h x is correlated with the length scale x and
lt gt denotes the spatial average over ( )h x in a planar reference surface If the
interfacial roughness of IPyCSiC were self-affine the correlation of x and
h should follow the power law relationship (Eq (2)) and it could be obtained by the
log-log plot of x and h The (for self-affine surface 0lt lt1) is the roughness
exponent and it describes the degree of surface roughness at short length scales [31]
This short length scale is shorter than correlation length ξ which is another parameter
used to describe the self-affine surface (besides the surface roughness h and
roughness exponent ) It is the average distance between the features in the surface
profiles within which the surface variations are correlated [28] Therefore the small
(close to 0) characterises extremely jagged or irregular interfaces while large
value characterise interface with smooth hills and valleys [32]
For all the samples the scaling properties of IPyCSiC interface (as shown in Fig 57)
are characterised by their one-dimensional height-height correlation function Eq (2)
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
144
The characteristic parameters of the digitalized IPyCSiC interfacial roughness are as
follows The resolution between two points along x axis is 020833 μm and x
changes by timing the resolution with integer (1 2 3hellip15) According to previous
self-affine theory study [16] the number of recorded points along the x axis was
taken in the range of 250-400 in this work corresponding to the length of 50-70 μm
for different IPyCSiC interfaces
5332 Results of self-affine theory
Figure 58 is a log-log plot showing the variation of h as a function of the distance
x for three SiC coatings The h varied as a power law of x (solid line ) when
x ltξ while remained nearly constant ˗ saturation roughness (σ0 dashed parallel
lines) for x gtξThese results indicated that these three IPyCSiC interfacial
roughness were self-affine with the roughness exponent of around 063-067 For the
rest of the samples the same scaling characterisation method was used Theξ σ0 and
are given in Table 53
Fig 58 Log-log representation of the height-height correlation function h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
ξ3 ξ12 ξ6
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
145
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Sample σ0 (μm) ζ ξ(μm) σ0ξ
S 1 02378 05903 06250 03804
S 2 04142 06950 08333 04971
S 3 06701 06673 16666 04021
S 4 06825 05244 14583 04680
S 5 05271 06308 14581 03615
S 6 08500 06343 20833 04080
S 7 04293 05162 14583 02944
S 8 07452 05107 14583 05110
S 9 05453 06099 12500 04362
S10 06953 05490 13044 05330
S11 05806 04949 10417 05574
S12 07584 06899 16666 04550
S13 05522 02971 18750 02945
The roughness exponent values for the 93 of IPyCSiC interface were in the range
of 05-07 (as shown in Table 53) This indicated the self-affine measurement is
reliable according to Schmittbuhl and Vilottersquos review [14] which showed that this
range of roughness exponents could have the minimum characterisation errors
Furthermore these roughness exponents are comparable except specimen S13 and it
was consistent with the observation of the interfacial roughness (Fig 57) in which
only specimen S13 showed the high degree of high frequency and short wavelength
irregularities (the dark pits in S13 profile) According to previous study [31] the
concentration of the roughness exponent values could be attributed to the same
original mechanism of the IPyCSiC interface which was produced by the FBCVD
under different conditions As a result the different roughness exponent value could
not describe the difference of the IPyCSiC interface
As shown in Table 53 the saturation roughness (σ0) and correlation length (ξ) are in
the range of 024-085 μm 063-208 μm respectively (Table 53) According to
previous studies [16 17 30] the σ0 and ξ couldnrsquot represent the interfacial
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
146
irregularities correlated with the critical flaw size Because the σ0 value range was
nearly one magnitude lower than the calculated critical flow size (mean value range of
2-4 μm) and the dimension of ξ was perpendicular to the calculated critical flaw size
direction Furthermore it was found that σ0 and ξ values were correlated to the sample
size (recorded points) [16] With the increase of the sample size for the same profile
both the ξ and the σ0 values increased and indicated these two parameters may not be
intrinsic properties of the samples However the roughness ratio σ0ξ is constant
which was found in both the current work and previous study [16]
As a result of above discussions the roughness ratio of σ0ξ was proposed to
characterise the interfacial roughness which could represent the sharpness of the
interfacial irregularities according to Ref [30] For example the low ξ value
corresponded to narrow surface irregularity when the σ0 and values were the same
With the increase of the σ0 value the surface irregularity became deep and narrow
which was hazard to the mechanical properties according to previous simulation work
on the fracture strength of SiC coatings [22] The above observations and analysis
results are supported by previous study [31] when length scale x gt ξ (shown in
Fig 58) the roughness ratio σ0ξ describes mainly the long-wavelength roughness
characteristics which could be statistically equal to the effect of the critical flaw size
on fracture strength
534 Quantify the influence of interface roughness on fracture strength
Figure 59 gives the influence of roughness ratio on the local fracture strength and it
contributes to nearly 50 (R2 from linear regression) of variation of the local fracture
strength It shows that the local fracture strength decrease linearly with the increase of
the roughness ratio This result approves previous findings about the importance of
the interfacial roughness [4-6] and is correlated with the Griffth fracture theory (Eq
(1)) about the importance of the shape and dimension of critical flaws Furthermore
the relation between interfacial roughness has been characterised quantitatively and a
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
147
linear relationship between roughness ratio and local fracture strength is proposed
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Except for the interfacial roughness the local fracture strength could also be affected
by the fracture toughness as shown in Eq (1) Although Vickers-indentation fracture
behavior of SiC coatings was different due to the laminar defects and grain
morphology [33] the fracture toughness of SiC was found to be insensitive to the
microstructure of materials [34] This could be attributed to the fact that
Vickers-indentation provided a static propagation of the crack while the real fracture
toughness was measured dynamically In this work the fast fracture process could
overtake the effect of microstructure on the different static fracture behaviour [5 25]
Since porosity and grain size were main microstructural variations in SiC coatings [1]
their effects on fracture strength were estimated
The characterisation and quantification of grain size and porosity were shown in Table
54 The grain size was found to have no effect on fracture strength according to
previous studies [5] which was also indicated from the regress analysis (R2 is close to
0) No influence was found by regressing the local fracture strength on pores
Therefore the dominant influence on the local fracture strength is from the roughness
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
148
ratio
Table 54 Results and variations influences on fracture strength for SiC coating
Specimen S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S10 S11 S12 S13
Grain size
(μm2)
04 06 06 08 20 20 20 28 20 08 20 28 25
Porosity
(Area )
0 0 0 0 05 04 12 09 03 0 08 21 20
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
Because the fracture strength for a full spherical shell is a function of the Weibull
modulus and local fracture strength [5] it was affected by factors such as the
dimension ratio of thickness to radius of the coating (as shown in Fig 55) the
roughness ratio (as shown in Fig 510) Figure 510 shows the influence of roughness
ratio on fracture strength of the full shell The linear relationship was found in 12
samples as indicated by the dashed line in Fig 510 and it could explain about 68
(2R from linear regression) of difference in fracture strength of the full particle The
high roughness ratio would decrease the fracture strength of the full shell linearly The
deviated point of sample S13 could be due to its largest Rt ratio (as shown in Fig
55) which may have over taken the effect of the roughness ratio (Work about the size
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
149
effect on the fracture strength has being carried out)
54 Conclusions
The fracture strength of SiC coatings deposited under different conditions were
measured by the modified crush test and analyzed by the statistical analysis (Weibull
function and Self-affine theory) The influences on fracture strength were studied
such as the IPyCSiC interfacial roughness specimen size and porosities Following
results were obtained
(1) Weibull modulus and fracture strength of the full shell were significantly affected
by the ratio of radius to thickness of SiC coating and both of them decrease
linearly with the increase of the ratio
(2) The dominant effect of the IPyCSiC interfacial roughness on intrinsic fracture
strength was found by matching the SEM images with the calculated critical flaw
size based on the Griffith fracture theory
(3) The interfacial roughness were successfully characterised by a
numericalstatistical method and the roughness ratio representing the shape of the
irregularities was proposed to be a unique parameter among different coatings
(4) The difference of the local fracture strength was dominated by the roughness ratio
and it decreased linearly with the increase of the roughness ratio It is been the
first time that the interfacial roughness was numerically related to the fracture
strength
(5) Microstructures such as grain boundaries and porosity were found to have
neglectable influence on fracture strength
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
150
55 References
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[2] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the tri-isotropic-coated fuel particle J
Am Ceram Soc 90 (2007) 184-91
[3] T Nozawa L L Snead Y Katoh J H Miller E Lara-Curzio Determining the
shear properties of the PyCSiC interface for a model TRISO fuel J Nucl Mater
350 (2006) 182-94
[4] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
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[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
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Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[6] S G Hong T S Byun RA Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the TRI-Isotropic-coated fuel particle
J Am Ceram Soc 90 (2007) 184-91
[7] D J Green An introduction to the mechanical properties of ceramics Cambridge
solid state science series Cambridge Cambridge University press 1998
[8] R Danzer Some notes on the correlation between fracture and defect statistics
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[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
Transgranular Cleavage J Mech Phys Solids 34 (1986) 477-97
[10] J W Kim T S Byun Y Katoh Optimization of fracture strength tests for the
TRISO layers of coated fuel particles by finite element analysis 33rd international
conference on advanced ceramics and composites Daytona Beach FL2009
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
151
[11] W N W Chen X Nie A A Wereszczak D W Templeton Effect of Loading
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[12] R T Wu X Wang A Atkinson On the interfacial degradation mechanisms of
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[13] X Nie W N W Chen A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
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[14] J Schmittbuhl J P Vilotte S Roux Reliability of Self-Affine Measurements
Phys Rev E 51 (1995) 131-47
[15] J T M De Hosson G Palasantzas Roughness effect on the measurement of
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[16] L Ponson H Auradou M Pessel V Lazarus J P Hulin Failure mechanisms
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[17] L Ponson H Auradou P Vie J P Hulin Low self-affine exponents of
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[18] F Spaepen Interfaces and stresses in thin films Acta Mater 48 (2000) 31-42
[19] W G Sloof T S Hille T J Nijdam A S J Suiker S Turteltaub Damage
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[20] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
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[21] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[22] G K Miller D A Petti J T Maki D L Knudson An evaluation of the effects
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
152
of SiC layer thinning on failure of TRISO-coated fuel particles J Nucl Mater
355 (2006) 150-62
[23] K Bongartz E Gyarmati H Schuster KTauber The brittle ring test A method
for measuring strength and Youngrsquos modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[24] K Minato K Fukuda K Ikawa Strength of silicon-carbide coating layers of
fuel Pparticles for high-temperature gas-cooled reactors J Nucl Sci Tech 19
(1982) 69-77
[25] J W Kim T S Byun Y T Katoh Optimization of fracture tests for the SiC
layer of coated fuel particles by finite element analysis Ceram Nucl Appl DOI
1010029780470584002 ch13 2010
[26] S Gonzalez B Ferrari R Moreno C Baudin Strength analysis of
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[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] B N Dev A Roy K Bhattacharjee H P Lenka D P Mahapatra Ge growth
on self-affine fractal Si surfaces influence of surface roughness J Phys D Appl
Phys 42 (2009) 145303-10
[29] J Feder Fractals Plenum New York 1988
[30] J T M De Hosson R Van Tijum Effects of self-affine surface roughness on the
adhesion of metal-polymer interfaces J Mater Sci 40 (2005) 3503-08
[31] G Palasantzas Roughness spectrum and surface width of self-affine fractal
surfaces via the K-correlation model Phys Rev B 48 (1993) 14472-78
[32] P Meakin Fractals scaling and growth far from equilibrium Cambridge
Cambridge University Press 1998
[33] H Zhang E Loacutepez-Honorato A Javed I Shapiro and P Xiao A study of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
153
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc 95 (2012) 1086-92
[34] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany and A H
Heuer Fracture toughness of polycrystalline silicon carbide thin films Apply
Phys Lett 86 (2005) 071920-22
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
154
CHAPTER 6 Effect of Thermal Treatment on
Microstructure and Fracture Strength of SiC Coatings
61 Introduction
The mechanical properties of the as-deposited SiC coatings have been widely studied
eg Youngrsquos modulus and hardness [1-3] fracture toughness [4] and fracture strength
[5] etc However after it experiences the high temperature the composition and the
microstructure of the SiC coating may change which consequently influences the
mechanical properties It has been found that mechanical properties of SiC such as
Youngrsquos modulus and hardness are less affected when experiencing the current fuel
operation temperature (less than 1600 ordmC) [1 6] even after thermal treatment
temperatures of 1980 ordmC [7] To enhance the operational temperature of the high
temperature reactor in the future design it would be necessary to understand the
evolution of microstructure and mechanical properties of SiC coatings at even higher
temperature Some research [8-10] has been carried out to study the effect of high
temperature (more than 2000 ordmC) thermal treatment on the density and microstructure
of the fuel particle Itrsquos concluded that fuel failure and fission product release
dependent on SiC thermal stability at high temperature [9] Rooyen et al[11]
measured the annealing temperature effect on the fracture strength of SiC coatings It
is found that the fracture strength increases after thermal treatment at temperature up
to 2000 ordmC decreases in strength after thermal treatment at 2100 ordmC However no
clear explanation was given on this result
Due to the importance of the SiC on the safety of this fuel it is necessary to study the
thermal stability of SiC and characterise any change in microstructure and mechanical
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
155
properties It has been previously found that SiC deposited at 1300 ordmC with the
addition of propylene and methyltrichlorosilane as gas precursors not only have good
mechanical properties such as hardness and Youngrsquos modulus [3] fracture toughness
[4] but also have high silver and palladium diffusion resistance [12 13] Therefore in
this Chapter we thermally treated SiC coatings deposited at a range of temperature
(1300-1500 ordmC) at 2000 ordmC for 1 hour in argon atmosphere The change of fracture
strength and thermal stability of SiC coating were studied in terms of composition and
microstructural change of the coatings after thermal treatment
62 Experimental details
Four batches of SiC coatings (with nearly stoichiometry) deposited by Fluidized bed
chemical vapour deposition at different tempearure were chosen to study the thermal
treatment effect on the evolution of the microstructure and fracture strength Table 61
gives the deposition conditions of coatings studied and symbols used to describe each
sample The stoichiometry was measured by the Raman spectroscopy (Renishaw 1000
Raman microprobe system with 514 nm Argon laser) The laser beam was focused on
the surface of the cross section through a times50 objective lens
Table 61 Deposition conditions of SiC coatings
Sample Temperature
(oC)
MTS concentration
(vol)
Added gas
concentration
Stoichiometry
SiC1 1280 91 01vol C3H6 SiC
SiC2 1300 91 01vol C3H6 SiC+C
SiC3 1400 19 57vol Ar SiC
SiC4 1500 22 79vol Ar SiC+C
The inner side of the coating is stoichiometric (23 of the thickness) while outside of the coating is
SiC with excess C The microstructure characterization was done in the inner side coating while the
fracture strength measurement is related to the full coating SiC+C means that the C peak around
1300-1500 cm-1
was observed in SiC coating Chosen of deposition conditions was contributed to Dr
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
156
Eddie Lopez-Honorato
The sample preparation for fracture strengths measurement is the same as described in
Chapter 5 As introduced before thermal treatment was carried out at 2000 ordmC for 1
hour in argon protected atmosphere on SiC half shells The same fracture strength test
and equipment settings as described in Chapter 5 were used in this Chapter
In addition to Raman spectroscopy the microstructure of SiC coatings before and
after thermal treatment was also characterised using X-ray diffraction (PW 1830
Philips) with a Cu Kα1 radiation source The XRD samples were the SiC segments
(fractured SiC shells without external residual stress) Scanning electron microscopy
(Philips XL30 FEG-SEM) was used to characterise the change in morphologies of
SiC coatings Porosity was measured by setting a threshold of the SEM images
(times1600 TIF) at a gray level and adjusted to distinguish pores from grains with Image
J software Three SEM images were measured for each SiC coating Average pore size
(diameter nm) and the pore fraction (area ratio of pores to the total area as observed
by SEM) were obtained For transmission electron microscopy (TEM) the specimens
were prepared by crushing the SiC shell and dispersing the fragments on a carbon
holy film copper grid and crystal structures were characterised using an FEG-TEM
(TecnaiTM G2
F30 U-TWIN)
63 Results
631 Fracture strength of SiC coatings
Figure 61 shows the Weibull distribution of the local fracture strength ( L
f ) in SiC
coatings before and after thermal treatment at 2000 ordmC It gives a direct observation on
the decrease of the local fracture strength in coating SiC2 SiC3 and SiC4 after
thermal treatment while the local fracture strength of coating SiC1 is nearly
overlapped with the as-deposited coating The magnitude of the mean local fracture
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
157
strength (as summarised in Table 62) could represent the decrease trend of the full
batch of the coating in current study
Fig 61 Weibull plots of local fracture strength ( L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
The Weibull modulus (m) was obtained by linearly fitting the curves shown in Fig 61
It shows that the Weibull modulus decreased by 14 07 and 21 in coating SiC1 SiC3
and SiC4 respectively however it increased slightly (by 12) in SiC2 after heat
treatment As shown in Fig 61 the Weibull modulus derived from linear fitting is
affected by the deviation of few points from the linear distribution of the local fracture
strength (as shown in Fig 61) For example in sample SiC3 the slightly decrease
could be attributed to the deviation of the lowest points According to previous study
[14] the slight decrease (07) of Weibull modulus in SiC3 could be neglected since
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
158
the deviated points could be caused by different failure mechanisms involved in the
fracture process [14]
Fig 62 Weibull modulus plots of fracture strength of the full shell ( F
f ) before
(black triangle) and after (red circle) thermal treatment
Figure 62 shows the Weibull plots of fracture strength of the full shell ( F
f ) before
and after thermal treatment at 2000 degC In the same batch of coatings (the same size
effect) the fracture strength of the full shell increase with the increase of the Weibull
modulus and local fracture strength according to previous study [5] Therefore the
decrease of local fracture strength and increase of the modulus in SiC2 could explain
the slight change (decreased 25 MPa obtained from Table 62) of the fracture strength
of the full shell after thermal treatment In the other three samples the fracture
strength of the full shell decreased significantly (more than 110 MPa obtained from
Table 62) after thermal treatment due to the decrease of local fracture strength and
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
159
unchanged modulus)
Table 62 summarized the results of the fracture strength measured before and after
thermal treatment at 2000 degC including the Weibull modulus (m) derived from the
distribution of the local fracture strength ( L
f ) the mean local fracture strength and
fracture strength of the full shell ( F
f ) After thermal treatment the mean local
fracture strength of coatings decreased significantly except SiC1 coating which
retained the same level as in as-deposited coating The mean fracture strength of the
full shell was reduced after thermal treatment in a different degree but the change of
Weibull modulus is more complex which shows both decreased and increased values
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the full shell before and after thermal
treatment
Sample m (from
L
f )
as deposited 2000degC
L
f MPa
as deposited 2000degC
F
f MPa
as deposited 2000degC
SiC1 75 61 1445 1421 774 660
SiC2 77 89 1599 1395 872 847
SiC3 65 58 1824 1333 820 548
SiC4 74 53 1717 1443 858 587
As concluded from Fig 61 Fig 62 and Table 62 the fracture strength decreases
less in coatings deposited at lower temperature (about 1300 degC) than those deposited
at higher temperature (1400-1500 degC) This is consistent with previous study about
high properties of SiC coatings deposited at low temperature such as the hardness
Youngrsquos modulus and resistance to the fission products [12 13 15]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
160
632 Change in morphologies
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after (c) and (d) SiC2 before and after
(e) and (f) SiC3 before and after (g) and (h) SiC4 before and after thermal treatment
Dashed and solid arrows indicate growth direction and pores respectively
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
161
Figure 63 gives the SEM images showing the microstructure of SiC coatings before
and after thermal treatment at 2000 ordmC Before thermal treatment no pores were found
in SiC1 and SiC2 coatings (Fig 63(a) and (c)) while nano-pores were found in SiC3
coating (Fig 63(e)) and even bigger (micrometres) pores were occasionally found in
SiC4 coating (Fig 63(g)) Among four as-deposited coatings SiC4 has highest area
fraction of pores (~09) followed by SiC3 (~03) coating (Fig 63 (a) (c) (e) and
(g) summarized in Table 63)
After thermal treatment at 2000 ordmC pores with different size and area fraction were
observed in all the coatings even though as-deposited SiC1 and SiC2 were free of
pores as shown in Fig 63(b) (d) (f) and (h) The amount of pores formed in treated
SiC1 coating (area fraction of ~05 ) is lower than the other three coatings which
have similar area fraction of pores (~14 ~13 and ~15 for SiC2 SiC3 and
SiC4 respectively given in Table 63) Similar to the content of the pores the pore
size (mean size of ~50 nm) in SiC1 is smaller than in the other coatings (gt 100 nm)
Among coatings SiC2 SiC3 and SiC4 much larger pores (micro-meter sized as in
Fig 63(f) and (h)) were produced in SiC3 and SiC4 coatings after thermal treatment
compared with nano-sized pores in SiC2 Furthermore it is found that most of pores
in coatings SiC2 SiC3 and SiC4 were formed along the grain boundaries and triple
junctions as we can see from Fig 63(d) (f) and (h)
The pores are uniformly distributed through the coatings and no area free of pores or
area with highly concentrated pores is observed However there are connections of
pores (2 or 3 pores formed closely) in SiC2 SiC3 and SiC4 as indicated by solid
arrows in Fig 63(d) (f) and (h) and the diameter of the porous connection zone
(black circle in Fig 63(d) (f) and (h)) could be in the magnitude of few micrometres
The connection of pores could easily become larger pores of few micrometres
diameter under external tensile strength due to the high strength concentration [14]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
162
Fig 64 The IPyCSiC interfacial roughness of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermally treated at 2000 degC (right
in each figure) The white arrow points towards to the interface irregularities (except
for thermally treated SiC4 coating (d)) black circle represents the pores in SiC
coatings
Figure 64 gives the evolution of interfacial roughness in different coatings after
thermal treatment at 2000 ordmC to study their influence on the change of fracture
strength Compared with the as-deposited coating the changes of the interfacial
roughness in SiC1 are similar to SiC3 which show the smoother interface with
interval of irregularities were observed Fig 64(a) and (c) However different from
as-deposited coatings with defects mainly at the interface defects (pores) are also
observed through the coating after thermal treatment (as seen in Fig 61(b) (f) and
Fig 64(a) (c)) Furthermore the size of pores is in the same magnitude as their
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
163
interfacial roughness (shown in Fig 64(a) and (c))
The change of the interfacial roughness in SiC2 is more significant than SiC1 and
SiC3 since pores formed as part of the interface (indicated by arrows in Fig 64(b))
and they are larger than the pores formed in the coating (circle in Fig 64(b))
Different from others three coatings the IPyCSiC interface of SiC4 becomes
smoother (Fig 64(e)) after thermal treatment compared with as-deposited coating so
the defects (pores) within the coating are bigger than surface irregularities
633 Evolution in microstructure
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermally
treated at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and
SiC2 inset shows the peak shift of as-deposited (dash line) and after thermal
treatment (solid line) (b) is SiC4 and inset is the high angle diffraction peak after
thermal treatment showing splitting while it is a single peak in as-deposited coating
Figure 65 gives XRD results of the as-deposited and thermally treated samples
which show the presence of the β-SiC in coatings The peak presents at 2θ~335ordm is
from the crystallographic errors which could either be due to the stacking faults or
the disordered α-SiC according to previous descriptions [16 17] It is found that the
intensity ratio of the 2θ~335ordm peak to the (111) plane peak (2θ~356ordm) decreased after
thermal treatment in all the coatings The coating SiC4 also shows the split of high
angle diffraction peaks (inset of the Fig 65(b) 2θ~613ordm and 713ordm) which is
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
164
attributed to the X-ray double diffraction and this implies the high crystallites after
thermal treatment
Figure 66 is the HRTEM image of sample SiC4 after thermal treatment in which the
stacking faults and micro twins could still be seen The stacking sequence of
ABCACBACBACB was observed as shown in the dashed square zone in Fig 66
According to study about crystal structure [18] this stacking sequence is supposed to
be the micro twins compared with the rest 3C stacking sequence rather than the
6H-SiC domain Furthermore the (111) peak shifted to the high angle after thermal
treatment in all the coatings as shown in the inset of Fig 65(a) which corresponded
to the decrease of the crystal constant
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Figure 67 gives the Raman spectroscopic results of SiC coatings before and after
thermal treatment The carbon peak at 1300-1600 cm-1
was found in the as-deposited
SiC2 and SiC4 coatings According to previous studies [4 19] the intensity ratio of
I1600I796 indicated that the estimated amount of excess C was less than 05 at in
this study The peak between TO and LO peaks (around 882 cm-1
) was attributed to
the stacking faults or highly disordered stacking faults cluster [3 15 20-22]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
165
After thermal treatment the weak carbon related peaks appeared at around 1395 cm-1
and 1600 cm-1
(G band) in sample SiC1 SiC2 and SiC4 The peak around 1395 cm-1
could represent the methyl group and amorphous carbon structures and G band is due
to the stretching mode of all pairs of sp2 atoms in chains and rings [23] The arising of
the 2D peak (also called G peak 2715 cm-1
) after thermal treatment was observed in
sample SiC2 SiC3 and SiC4 which is the second order of zone-boundary phonons
[24]Considering the amount of excess carbon in SiC coatings the symmetry of the
2D peak indicates that the carbon after treatment is more likely to be graphene rather
than graphite [24] which means the concentration of excess C is low in SiC coatings
It is also found that the intensity ratio of the disordered stacking faults (around 882
cm-1
) to the TO peak decreases in all samples after thermal treatment (shown in Fig
67)
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings The lower line is before thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
166
treatment and the upper line is after thermal treatment at 2000 degC in individual
sample
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
Sample Porosity ()
As 2000degC
Stoichiometry
As 2000degC
Critical Defects
As 2000degC
SiC1 0 05 0 C clusters Inter Inter+ Pore
SiC2 0 14 C clusters Ordered C Inter Inter
SiC3 03 13 0 Ordered C Inter Inter+ Pore
SiC4 09 15 C cluster Ordered C Inter Pore
First order Raman spectroscopy (1200-1600 cm-1
) Represents the carbon structure related to the
methyl group or amorphous carbon structures (contains SP2 and SP
3) [23] Second order (2700 cm
-1)
single layer grapheme related carbon materials [24]
Represents the interface irregularities
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
Furthermore the narrowing of the TO peak was found (the inset in Fig 67 (b)) in the
Raman spectroscopy Although it could be an overlap of two peaks at around 796 cm-1
and 789 cm-1
in coatings before and after thermal treatment the peak at 789 cm-1
corresponding to the stacking sequence of ABCACBhellip [25] is more likely to be
micro-twins in current study(as shown in Fig 66) Table 63 summarized the main
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
167
morphological and microstructural change of SiC coatings before and after thermal
treatment
Particularly for sample SiC3 except for the appearance of weak 2D peak after thermal
treatment without visible first order carbon peaks in the sample SiC3 the precipitates
were also observed from both inner and outside of the shell These precipitates were
demonstrated to be the single 3C-SiC crystal by Raman spectroscopy as shown in Fig
68 Raman spectra of precipitates represents the incident direction of the laser is
perpendicular to the SiC single crystal (111) plane which the LO mode at around 970
cm-1
is forbidden when Raman spectra were obtained in a backscattering geometry
[22] (The appearance of the forbidden LO band might be due to to finite collecting
angle of the spectrometer)
64 Discussion
641 Influence of interfacial roughness and pores on fracture strength
To evaluate the critical flaw size we used the equation 1
2( )
L ICf
K Z
Yc for tensile
strength (local fracture strength) and the case for the semi-circular surface crack
(Y=125 [26]) of radius c and inside holes (Y= π12
[14]) of diameter 2a When the
fracture toughness ( ICK ) of the SiC coating was taken as 33 MPa m-12
[27] the
critical surface defect radius and the diameter of the inside pores were calculated to be
in the range of 15 ndash 78 microm obtained from all the coatings The mean critical flaw
size is in the range of 30 ndash 40 microm after thermal treatment The calculated critical
flaw sizes are in the same magnitude as the defects observed at the IPyCSiC interface
and the pores in the SiC coatings after thermal treatment (see in Fig 63 and Fig 64)
Therefore the decrease of the local fracture strength after thermal treatment could be
related to the formation of these defects in SiC coatings Accordingly the sources of
critical defects were summarized in Table 63 for coatings before and after thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
168
treatment The interfacial roughness and pores within the coating compete to be the
critical flaws Once the size of interfacial irregularities is lower than critical flaw size
and rarely distributed their effect on fracture strength could be decreased or even
excluded according to previous study [14] Therefore the pores inside the coating
with the diameter of 2a would be considered as the main failure origins [14] These
could explain the decrease of local fracture strength in coatings SiC2 SiC3 and SiC4
which have micrometer pores formed within the coatings andor at the interface while
the local fracture strength is less affected in coating SiC1 due to formation of
nanometer pores
The Weibull modulus is related to the specimen size loading method and defects
distribution [5 14] In this study the specimen size and the loading morphology could
be excluded for one kind of SiC coating so the change of the modulus is due to the
degree of the scattering of the critical flaw size under the tensile strength The
interfacial irregularities in SiC2 became narrower and deeper (about 4 microm of depth as
shown in Fig 64(c)) after thermal treatment and they are also bigger than the pores
generated within the coating So the critical flaw in SiC2 after thermal treatments is
due to the interfacial irregularities (Table 62) with less scattered size under the
loading area than as-deposited coating which increased the Weibull modulus
However the critical defects in the other coatings include pores within the coatings
(shown in Fig 64 and Table 62) For example in SiC4 the critical flaw is only from
pores within the coating after thermal treatment due to the lack of interstitial
irregularities (Fig 64(h)) This enlarged the distribution of critical flaws after thermal
treatment which leads to the decrease of the Weibull modulus in different degree The
change of the fracture strength of the full shell depends on both Weibull modulus and
local fracture strength as discussed before [5] Our result showed that the SiC coating
deposited at low temperature of 1300 ordmC produced less critical flaws and smaller
decrease of the fracture strength of the full shell (see Table 63)
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
169
642 Mechanism of microstructural change
Changes in SiC coatings after thermal treatment include the formation of pores the
decreased intensity of the 2θ~335 ordm peak (crystallographic errors) in XRD the arising
of Raman peaks around 1395 cm-1
and 2715 cm-1
According to previous studies [8
10 21 25 28 29] we propose that these changes after thermal treatment could be
attributed to phase transformation or the diffusion of defects such as vacancies and
interstitials
If the 2θ~335ordm peak is from amorphous α-SiC its intensity ratio to (111) diffraction
peak would increase after heat treatment Because the presence of α-SiC phase in
β-SiC could promote the transformation of β-SiC into α-SiC [29] Conversely the
intensity of 2θ~335ordm peak decreased after thermal treatment in this work as observed
in Fig 65 and no α-SiC phase segregation (Fig 66) was found by HRTEM after
thermal treatment Furthermore the transformation from disordered α-SiC into β-SiC
after thermal treatment is also excluded because high pressure and high temperature
are needed for this process to happen [29] Therefore it is concluded that the 2θ~335ordm
peak derived from stacking faults and they could be annihilated at current
environment according to previous studies [8 28 30]
Stacking faults were surrounded by defects such as dislocations vacancies and
interstitials [10 15 31] so the high density of stacking faults in this work
corresponded to the high amount of native defects The annihilation of stacking faults
after thermal treatment indicated the reduction of these defects and it could reduce
the lattice constant In this work the decrease of the lattice constant was found after
thermal treatment as indicated by the peak shift of (111) plane in XRD results (Fig
65) and the crystallisation (ordering) was also reflected from the decreased intensity
of the 2θ~335ordm peak (Fig 65) and Raman defect peak (around 882 cm-1
) (Fig 67)
Therefore the formation of pores is due to the annealing of defects through the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
170
diffusion of vacancies or interstitials which are common even in high-purity CVD
SiC [32] However diffusion of native defects depended on their concentration which
was constrained by different composition of SiC (deviation from stoichiometry) [31]
For example for the C-rich cubic SiC the dominant defect is the CSi antisite (Si atom
site was occupied by C atom in tetrahedral structure) [31]
According to above analysis the formation mechanism of pores could be governed by
different kinds of defects In SiC1 coating the smallest and least content of pores
formed after thermal treatment is most likely caused by the annealing of stacking
faults surrounded by the dislocations and vacancies which is consistent with previous
study about the thermal treatment effect on stoichiometric SiC [28] In SiC coating
with excess carbon the microstructure evolution could be more complex as
demonstrated by the presence of the graphene layer (Raman peak at 2700 cm-1
)
According to previous studies [31 33] this is attributed to the existence of the CSi
antisite and vacancies which form the vacancy cluster and antisite clusters after
thermal treatment at 2000 degC
The microstructure change in SiC3 coating is different from SiC1 The diffusion
mechanism in SiC3 was supposed to be involved with the interstitials since the single
SiC crystal precipitate was found out of the coating(Fig 68) This also resulted in
higher amount of the pores in SiC3 than in SiC1 after thermal treatment It is
proposed that the different diffusion mechanism found in stoichiometric SiC1 (Si and
C vacancies) and SiC3 (tetragonal interstitials) could be due to different deposition
conditions which produced different kinds of dominant native defects The larger
pores formed in SiC3 and SiC4 could be due to larger grain size than SiC1 and SiC2
(different deposition temperature) because most of pores were near to the grain
boundaries and triple junctions (as shown in Fig 63(d) (f) and (h)) The diffusion of
native defects also affects the interfacial irregularities and the diffusion mechanism in
SiC coatings is being studied in our research group
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
171
65 Conclusions
The SiC coatings deposited at temperature range of 1300-1500 degC with composition
near-to the stoichiometry were thermally treated at 2000 degC in Ar atmosphere for 1
hour to study the effect of thermal treatment on microstructure and fracture strength
The following conclusions were obtained
(1) The local (intrinsic) fracture strength decreased in a varied degree after
thermal treatment and it was due to the formation of pores along the IPyCSiC
interface and in the coatings
(2) The Weibull modulus decreased once the pores have similarbigger size
asthan interfacial irregularities and distribute uniformly within coatings while
it increased with the size of pores much smaller than interfacial irregularities
after thermal treatment
(3) After thermal treatment no phase transformation was found in SiC coatings
and the crystallographic error (2θ~335 ordm) detected by XRD was demonstrated
to be stacking faults which were annihilated during this process
(4) The formation of pores after thermal treatment was attributed to the diffusion
of intrinsic defects such as vacancies interstitials and antisites Different
content and size of pores were observed in different coatings which are
presumed to have different kinds of native defects in as-deposited coatings
produced at different conditions
(5) The vacancies are supposed to be the dominant defects in stoichiometric SiC
deposited at 1280 ordmC however in other coatings the dominant defects could
be a combination of vacancies antisites and interstitials based on Raman
results before and after thermal treatment Furthermore the diffusion of native
defects also affects interfacial roughness after thermal treatment which needs
further study
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
172
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1700-07
[24] A C Ferrari J C Meyer V Scardaci C Casiraghi M Lazzeri F Mauri S
Piscanec D Jiang K S Novoselov S Roth A K Geim Raman spectrum of
graphene and graphene layers Phys Rev Lett 97 (2006) 187401-04
[25] S Nakashima H Harima Raman investigation of SiC polytypes Phys Stat Sol
A-Appl Res 162 (1997) 39-64
[26] GKBasal Effect of flaw shape on strength of seramics J Am Ceram Soc 59
(1976) 87-8
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] K Koumoto S Takeda CH Pai High-resolution electron microscopy
observation of stacking faults in βndashSiC J Am Ceram Soc 72 (1989) 1985-87
[29] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J Am Ceram Soc 84 (2001) 3013-16
[30] K Koumoto S Takeda C H Pai T Sato H Yanagida High-resolution electron
microscopy observations of stacking faults in β-SiC J Am Ceram Soc 72 (1989)
1985-87
[31] C Wang J Bernholc Formation energies abundances and the electronic
structure of native defects in cubic SiC Phys Rev B 38 (1998) 12752-55
[32] E Janzen N T Son B Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[33] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-09
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
175
CHAPTER 7 Microstructure and Mechanical Properties of
Pyrolytic Carbon Coatings
71 Introduction
Pyrolytic carbon (PyC) coatings forming part of the TRI-Isotropic (TRISO) fuel
particle are important for the stability of this type of nuclear fuel Without appropriate
microstructure and mechanical properties of PyC coatings the stress generated inside
the particle due to internal gas pressure andor the dimensional change (anisotropic
shrinkage or creep) introduced in this layer during irradiation process could result in
the failure of the full particle [1-5] Fundamental understanding about relationship
between mechanical properties and microstructure of PyC coatings could help to
analyse the failure mechanism and model the probability of failure of TRISO fuel
particles [1 5] However their relations in PyC are complex [3 6-8] Kaae [7] found
that mechanical properties were related to the density crystal size and anisotropy but
they are not controlled by a single variable For example Youngrsquos modulus increased
with density for isotropic carbons with constant crystallite size but decreased with
increasing anisotropy for carbon with constant density and crystalline size In a
separate work [3] density had a dominant effect on the hardness and Youngrsquos
modulus in relative low density PyC coatings whereas no controlling factor was
given for high density PyC coatings
Nano-indentation is an effective way to study microstructural effects on mechanical
properties of PyC coatings because it could help with the understanding of the
deformation mechanism and measure Youngrsquos modulus and hardness spontaneously
Among studies on mechanical properties in carbon related materials under
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
176
depth-sensing indentation [3 9-15] few explanations about the nature of their
deformation mechanism have been discussed [9 10 13 15] First the hysteresis was
assumed to due to the slip of graphene layers in nano-meter grains and the energy
loss was attributed to the friction between graphene layers under compression stress
[9 10] Second the dislocation pileups were assumed to be responsible for energy
loss [13] but this idea failed to account for the reversible deformation [15] The most
recent theory suggested that the origin of the hysteresis was due to the formation of
(incipient) kink bands [15] This theory was found to be a universal explanation for
most laminar structured materials but the nature of initial kink band was not clear
[15]
During pressing process of TRISO fuel particles into fuel elements they experience a
final thermal treatment of 1 h above 1800 ordmC to drive off any residual impurities and
improve thermal conductivity of the fuel compact [16] The evolution of
microstructure of carbon related materials have been widely studied [17-20] Few
researches measured changes of mechanical properties after thermal treatment [19
20] but there is a lack of understanding about effect of microstructural evolution on
mechanical properties in PyC coatings Therefore in this Chapter together with the
microstructural properties the deformation mechanism under indentation influences
on mechanical properties and their change after thermal treatment in PyC coatings are
studied
72 Experimental details
Pyrolytic carbon (PyC) was coated on alumina particles (Φ 500 μm) by fluidised bed
chemical vapour deposition by Dr Eddie Loacutepez-Honorato and PyC coatings with
different density was chosen to study the mechanical properties Table 61 gives the
density and texture (orientation angle) of PyC coatings and more about deposition
mechanism could be found in Ref [21] The number of sample sequence Ci (i=1
2hellip11) starts from highest density to lowest density with density of 19 gcm3 as
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
177
border line to distinguish highlow density PyC which was measured by the
Archimedes method in ethanol For thermal treatment the coatings were first
grounded into fragments and then removed the alumina kernel The fragments of PyC
were then thermal treated at 1800 degC and 2000 degC for 1 hour in argon atmosphere For
further understanding of microstructural evolution during thermal treatment sample
C5 was thermal treated at 1300 1400 1500 and 1600 degC for 1 hour
Table 71 PyC coatings with different density and orientation angle
PyC
(High density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
PyC
(Low density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
C1 2122plusmn0059 58 C6 1855plusmn0050 63
C2 2087plusmn0183 37 C7 1738plusmn0013 73
C3 2047plusmn0030 60 C8 1635plusmn0008 71
C4 2029plusmn0015 43 C9 1603plusmn0024 71
C5 2000plusmn0061 43 C10 1414plusmn0002 85
C11 1400plusmn0024 81
Orientation angle was obtained from the full width of half maximum of azimuthal intensity scan of
SAED pattern for more information in Ref [22] Productions of PyC coatings measurement of
orientation and density measurement are contributed by Dr Eddie Loacutepez-Honorato et al
The selected area electron diffraction (SAED) patterns were obtained with the use of a
FEG-TEM (see Chapter 3) and orientation angle was measured by the azimuthal
intensity scans of SAED pattern (selected aperture diameter of 200 nm) Further
details about this measurement were shown in a previous study [22] Transmission
electron microscopy (TEM) samples were obtained by focus ion beam milling High
resolution TEM samples were prepared by dispersing the fragments on a carbon holey
film copper grid X-ray diffraction (see Chapter 3) was used to obtain domain sizes of
PyC coatings After correction of intrinsic instrumental effect the out of plane and
in-plane domain sizes (along c-axis and a-axis in graphite crystal structure) Lc and La
were qualitatively estimated from XRD data by applying the Scherrer equation to the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
178
(002) and (110) reflections respectively [23] In as-deposited PyC coatings the (110)
peak was too weak to estimate accurately on the La Raman spectroscopy (633 nm
Helium ion laser source) was performed by single spot measurements (spot size was
carefully controlled to be the same for each test) of around 2 μm diameter using a times50
objective lens The laser power of less than 05 mW (10) was used with the step
size of 60 seconds and twice accumulations For each sample 5 different positions
were measured The band fitting of the first order spectra was carried out with
GRAMS32 software
To reduce the influence of surface roughness on indentation test the PyC coatings
were ground with successive finer grades of SiC paper and polished down to a 1 microm
grid diamond paste The same nano-indentation as in Chapter 3 was used The
measurements were performed at fixed loading rate of 1 mNS reaching the
maximum load of 100 mN For each coating at least 25 indentations were conducted
on the sample surface to increase the reliability of the results The Olive and Pharr
method [24] was used to analyse all the data
73 Results
731 Microstructure of PyC coatings
In order to study the influences of microstructure on mechanical properties it is
necessary to know the nature of structure which makes one sample from another eg
disorders domain size crystallinity etc and their evolution after thermal treatment
7311 Raman spectroscopy
Figure 71 is a Raman spectroscopy for an as-deposited high density PyC coating (C5
200 gcm3) which exhibits two relatively broad Raman bands at around 1335 cm
-1
and 1600 cm-1
The first band corresponds to the D band which is attributed to double
resonant Raman scattering and represents the in-plane defects [21 25 26] The
second band is an overlap of broadened G (1580 cm-1
) and D (1620 cm-1
) bands due
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
179
to high disordered pyrolytic carbon [27] The G band is due to the stretching modes of
pairs of sp2 atoms in graphene planes whereas D represents the similar defects
structure as the D band [18 27] It is convenient to consider 1600 cm-1
band a single
G peak for practical purposes when comparing different samples or the overall
structural evolution of a given PyC coating [27]
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
According to previous studies [25-32] on fitting similar Raman spectra shown in Fig
71 a simple two-symmetric-line fit (D and G bands) could not fit it well Therefore
the Raman spectra of high density PyC coatings (C1-C5 gt 19 gcm3) were
deconvoluted into above peaks at about 1220 cm-1
1335 cm-1
1500 cm-1
and 1600
cm-1
( Fig 71) The band at about 1500 cm-1
(Drsquorsquo) is attributed to interstitial defects
which could act as coupling (covalent band) between two graphene layers or adjacent
overlapped domains [25 28] The I band at around 1220 cm-1
is due to C-C on hydro
aromatic rings [28] The Raman spectra mean the high degree of in-plane andor
out-of-plane disorders in high density PyC coatings represented mainly by the full
width at half maximum (FWHM) of the D band [28] and intensity ratio (the area ratio
of the 1500 cm-1
peak to the sum of four peaks shown in Fig 71) of the Drdquo bands
[25] respectively
D
I
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
180
Figure 72 is the Raman spectra of high density PyC coating C5 after thermal
treatment at temperature of 1300 1400 1600 and 1800 ordmC The FWHM of the D band
decreased significantly from about 150 cm-1
(as-deposited) to about 106 cm-1
(1400
ordmC) and then to about 40 cm-1
(1800 ordmC) Similarly the intensity ratio of the Drdquo was
reduced from about 0135 (as-deposited) to about 0110 (1400 ordmC) and then to about
0078 (1800 ordmC) Another change is the split of G and D bands after thermal treatment
at 1800 ordmC (Fig 72) The above changes indicate that disorders in high density PyC
coatings are low energy structural defects ie degree of disorder is low according to a
previous study [28]
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
181
After thermal treatment the degree of microstructural changes of low density PyC
coatings C6-C8 (164-186 gcm3) is slightly different from even lower density
coatings C9-C11 (140-160 gcm3) so they are described separately Figure 73 shows
Raman spectra of low density PyC coatings (a) C7 and (b) C10 before and after
thermal treatment at 1800 ordmC Similar to high density PyC the as-deposited coatings
C6-C8 contains four Raman bands After thermal treatment the FWHM of the D peak
in C7 decreased from about 120 cm-1
to 57 cm-1
and the intensity ratio of interstitial
defects was also reduced (from 0116 to 0042 Fig 73(b)) In coating C10 only
slightly decrease of FWHM of the D peak (from about 83 cm-1
to 57 cm-1
) was found
after thermal treatment at 1800 ordmC (Fig 73(b)) No split of the G and D bands was
observed in low density PyC coatings
With increase in density of PyC the FWHM of the D band the concentration of the
Drdquo band and the degree of their changes after thermal treatment increase considerably
which suggest that the disorder defects in PyC are different with variation of density
and thermal treatments change the degree of the disorder
7312 Domain sizes
Table 72 summarises the out-of-plane domain size (crystallite size perpendicular to
the graphene plane Lc) and in-plane domain size (crystallite size along the graphene
plane La) measured by XRD in PyC coatings before and after thermal treatment The
Lc is in the range of 1-3 nm in all the as-deposited coatings and it is slightly bigger in
high density (about 2-3 nm) coatings than low density (about 1-2 nm) coatings After
thermal treatment at 1800 ordmC the Lc increased significantly which is about 5 times
and 2-3 times larger than in as-deposited high density and low density PyC coatings
respectively It is 2-4 times larger in high density PyC than low density PyC coatings
The La in high density (about 6 nm) is larger than low density PyC coatings (3-4 nm)
after thermal treatment at 1800 ordmC Both Lc and La remained unchanged after thermal
treatment at 2000 ordmC in all PyC coatings (This is explained in section 741) The
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
182
increase of domain size indicated the ordering process in PyC coatings after thermal
treatment which may involve annealing of different kinds of disorders
Table 72 Domain size of as-deposited and thermal treated PyC coatings
Sample As deposited 1800 2000
Lc (nm) La (nm) Lc (nm) La (nm) Lc (nm) La (nm)
High density (gt19 gcm3)
C1 21 -- 112 -- 116 53
C2 21 -- 132 63 154 69
C3 22 -- 98 66 111 63
C4 24 -- 95 57 118 63
C5 20 -- 120 60 152 73
Low density (lt 19 gcm3)
C6 22 -- 50 42 56 44
C7 18 -- 38 36 50 34
C8 14 -- 31 33 27 39
C9 11 -- 27 32 31 34
C10 17 -- 24 33 27 35
C11 11 -- 27 35 27 33
7313 Evolution of crystallinity
Figure 74 is the TEM images of high density PyC (C5) before and after thermal
treatment The dark field TEM show bright areas (Fig 74(a) and (b)) that represent
graphene layers with similar orientation in the selected direction of the diffraction
pattern A decrease of the orientation angle from 43 ordm to 25 ordm is found after thermal
treatment at 1800 ordmC which is obtained from the full width at half maximum of
azimuthal intensity scan of SAED pattern (insets in Fig4(a) and (b)) A bright field
TEM image of a conical microstructure after thermal treatment (Fig 74(c) dashed
rectangle in Fig 74(b)) which shows the voids at the top of conical structures The
above observations show that thermal treatment increases anisotropy and results in the
volume shrinkage and generation of voids in high density PyC coatings
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
183
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Figure 75 is the typical HRTEM away from the top of conical growth feature (eg
OA=43 ordm
OA=25 ordm
Top
Voids
100 nm
(c)
(a) (b)
5 nm
Moireacute
fringes
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
184
white circle in Fig 74(c)) in high density PyC coatings (C1) before and after thermal
treatment at 1800 ordmC The wrinkled short graphene fringes in as deposited high
density PyC (Fig 75(a)) were replaced by distorted planes in a larger scale with a
bigger radius of curvature (white arrow in Fig 75(b)) The common number of
parallel layers (Fig 75(a) (002) plane white parallel lines) is 2-4 in as-deposited C1
which increased to about 30 (Fig 75(b) between white parallel lines) The moireacute
fringes were observed after thermal treatment (black arrow in Fig 75(b)) which
correspond to black bars in the bright field TEM (eg dashed black rectangle in Fig
74(c)) According to the generation mechanism of moireacute fringes [33] the on-going
ordering process along the c-axis is related to the increase of number of parallel layers
and evolution (decrease) of the inter plane distance of (002) planes
Figure 76 gives the bright field TEM and HRTEM images showing the
microstructure evolution in a low density PyC coating (C7) Globular growth features
with diameters of about 400 nm were observed in as-deposited C7 as shown in Fig
76(a) and the HRTEM image shows 2-3 layers of parallel planes (Fig 76(b)) In low
density PyC coatings the graphene fringes are longer and less oriented than in high
density coatings (reflected from orientation angle shown in Table 71 and Fig 13 in
Ref [21]]) After thermal treatment the short dark bars andor dots (as indicated by
the white arrows Fig 76(c)) were observed which is due to the moireacute fringes as
shown in Fig 76(d) The number of parallel layer increased up to 8-10 (Fig 76(d))
and it reflects the slight crystallinity after thermal treatment In the other low density
PyC coatings C9-C11 the TEM images are similar with the as-deposited low density
PyC coatings (as shown in Fig 14 and Fig 13(c) in Ref [21]) Furthermore the
orientation angle is almost the same in all low density PyC before and after thermal
treatment
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
185
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
732 Mechanical properties of PyC coatings
7321 Force-displacement curve
Figure 77 gives the force-displacement curve of PyC coatings with different density
under the maximum load of 60 mN and 100 mN by nano-indentation The unloading
curve did not completely retrace the loading curve but still returned to the origin This
process is called anelastic behaviour or hysteresis behaviour and the anelastic
reversible indentation processes with an enclosed loop are found in all the PyC
coatings
(a) (b)
100 nm 5 nm
5 nm
Sphere-like
particle
Tops
Moireacute fringes Sphere-like
particle
Top (d)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
186
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
The maximum indentation depth in low density PyC (C6-C11 lt 19 gcm3) is deeper
than in high density PyC coatings (C1-C5 gt 19 gcm3) under the same load and the
low density PyC also shows larger hysteresis loop area The ratio of the hysteresis
energy (area within the loading-unloading loop) to total loading energy (area under
loading curve) in high density PyC is lower than in low density PyC coatings For
example the ratios of sample C3 C9 and C11 are 0243 0270 and 0292 respectively
Furthermore the deformation behaviour of all PyC coatings showed the hysteresis
behaviour after thermal treatment up to 2000 ordmC The high density PyC after thermal
treatment at 1800 ordmC (red curve in Fig 77) shows anelasticity however the ratio of
its hysteresis energy (0249) is much higher than in as-deposited coating (0174)
According to previous studies [10 34] the low ratio obtained in high density PyC
coatings under pyramidal indenter corresponds to high elasticity while low density
exhibits high hysteresis (anelasticity high viscosity))
Under indentation the hardness is defined as the mean pressure the material will
support under load according to Oliver and Pharrrsquos study [24] This pressure is equal
to the load at maximum load divided by the contact area (according to eqs (7 10 11)
hc
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
187
in Chapter 2) However the residual depth hf is zero and no pleastic deformation is
observed after unloading The hardness obtained by Oliver and Pharr method does not
reflect the resistance of plastic deformation of material but it could represent the
degree of unelastic deformation qualitatively Therefore the mean pressure (P) value is
used which could reflect the anelastic properties of PyC coatings
7322 Youngrsquos modulus and the mean pressure
Figure 78 gives the Youngrsquos modulus (E) and the mean pressue (P) of as-deposited
PyC coatings as a function of density For low density PyC coatings (C6-C11 lt 19
gcm3) Youngrsquos modulus and the mean pressure increase almost linearly with the
density For high density PyC coatings (C1-C5 gt 19 gcm3) both Youngrsquos modulus
and the mean pressure reach plateaus which are independent of density It indicates
that mechanical properties of high PyC coatings are dominated by other factors
which are discussed in session 744
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
Table 73 shows the Youngrsquos modulus and the mean pressure of PyC coatings with
different density before and after thermal treatment at 1800 and 2000 ordmC After
thermal treatment at 1800 ordmC Youngrsquos modulus decreased by around 50 and the the
mean pressure is reduced by around 69 in high density PyC coatings (C1-C5 gt19
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
188
gcm3) whereas minor change is observed when thermal treatment temperature
further increased to 2000 ordmC Previous study [20] showed similar results about
changes of mechanical properties in high density PyC after thermal treatment at
different temperature In low density PyC coatings C6-C8 (164-186 gcm3) the
mean pressure and Youngrsquos modulus decreased by about 23 and 8 after thermal
treatment at 1800 ordmC respectively which is consistent with Rooyen et alrsquos results
[19] and further decreased by 18 and 15 by increasing thermal treatment
temperature to 2000 ordmC In low density coatings C9-C11 (140-160 gcm3) little
change in mechanical properties after thermal treatment up to 2000 ordmC was found and
it is similar as the isotropic low density PyC [20] Mechanical properties and their
change after thermal treatment in PyC coatings are different with different density
Table 73 Changes of mechanical properties of PyC coatings after thermal treatment
Sample As deposited Thermal treated at 1800 Thermal treated at 2000
P (GPa) E (GPa) P (GPa) E (GPa) P (GPa) E (GPa)
High density
C1 468plusmn025 2670plusmn119 103plusmn018 1482plusmn131 090plusmn013 1337plusmn093
C2 435plusmn048 2513plusmn117 132plusmn019 1091plusmn069 076plusmn021 1204plusmn126
C3 490plusmn036 2878plusmn117 -- -- 091plusmn026 1271plusmn125
C4 397plusmn019 2291plusmn076 171plusmn010 1313plusmn034 110plusmn010 1370plusmn051
C5 456plusmn010 2610plusmn036 132plusmn015 1177plusmn051 177plusmn025 1361plusmn101
Low density
C6 388plusmn035 2165plusmn191 296plusmn022 1912plusmn113 244plusmn023 1647plusmn088
C7 395plusmn053 2149plusmn200 292plusmn036 1934plusmn114 232plusmn033 1568plusmn182
C8 354plusmn027 1945plusmn070 292plusmn036 1904plusmn113 232plusmn063 1678plusmn240
C9 284plusmn040 1938plusmn094 226plusmn057 1677plusmn178 263plusmn042 1733plusmn151
C10 189plusmn009 1266plusmn035 213plusmn019 1363plusmn076 188plusmn023 1381plusmn087
C11 168plusmn017 1166plusmn082 178plusmn034 1284plusmn106 086plusmn014 1167plusmn151
74 Discussions
The main findings of this study can be summarised as follows 1) PyC with different
density show different full width at half maximum (FWHM) of the D band and
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
189
concentration of the Drsquorsquo band which suggests that they have different types of disorder
TEM observation shows longer graphene fringes with lower density PyC (Fig 13 in
Ref [21]) thermal treatments decrease the degree of disorder while PyC with higher
density (gt19 gcm3) shows higher degree of decrease 3) initial increase in PyC
density until 19 gcm3 lead to proportional increase in Youngrsquos modulus (E) and the
mean pressure (P) while further increase in density has no effect on E and P 4)
hysteresis occurred after nano-indentation of PyC while the degree of hysteresis is
controlled by the PyC density and heat treatments
741 Disorders and their changes after thermal treatment
High density PyC Coatings (C1-C5 gt 19 cmg3) The dominant in-plane disorders
are domain boundaries according to a previous study [21] which generates high
FWHM of the D band due to the low energetic disorientations (eg domains andor
graphene layers) [25 28] The Drsquorsquo band (interstitial defects) is due to the amorphous
carbon structure which is composed of mainly disordered sp2 atoms and a low
amount of sp3 atoms [27 28 35] Particularly the sp3 lines are out of plane defects
which could be formed in high density PyC coatings [36] Therefore it is assumed
that the microstructure in high density PyC is composed of disoriented nano-size
graphite domains connected by amorphous carbon
After thermal treatment the reductions of the out-of-plane defects and the tilt and
twist in graphite planes are observed which could contribute to the increase of Lc
(out-of-plane domain size) as shown in HRTEM image (Fig 75) It was supposed
that the equilibrium shear stress were generated by in-plane defects and out-of-plane
defects in PyC coatings [25] once the out-of-plane defects was reduced the in-plane
stress would tend to straighten the graphite planes Furthermore the decreases of
FWHM of the D band and the orientation angle (Fig 72 and 4) show the ordering
arrangement of graphite layers is due to the healing of in-plane disorientations The
unchanged domain size Lc could be a result of a combination of increased number of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
190
parallel graphene layers and decreased inter distance of (002) plane As a conclusion
the increase of domain size Lc could be due to the coalescence of domain size andor
graphene layers through reorientation and remove of interstitial defects which
usually started at temperature of about 900-1200 ordmC [17 25] No La (in-plane domain
size) value was obtained in as-deposited PyC and the overlap of the G and the Drsquo
bands indicates it is below 4 nm above which two bands split [37] After thermal
treatment at 1800 ordmC the La is about 6 nm in high density PyC coatings (Table 72
and splitting of G and Drsquo bands was shown in Fig 72) which demonstrates the
slightly increase of La It is attributed to the annihilation of low energetic in-plane
disorientations which could usually be removed at temperature above 1500 ordmC [25]
Since the high temperature above 2000 ordmC is needed to remove the rest high energetic
in-plane defects for high density PyC according to previously study [25 28] it could
explain the La remained nearly constant after thermal treatment further increased to
2000 ordmC The ordering of graphite layers is responsible for the formation of voids (Fig
74(c)) since the ordering could reduce the volume and increase the density of PyC
coatings after thermal treatment [38]
Low density PyC Coatings (C6-C11 lt 19 cmg3) The main defect is the
5-memebered rings in coatings C9-C11 by comparing the Raman spectroscopy (Fig
73(a)) with a previous study [21] In low density coatings C6-C8 (164-186 gcm3)
the degree of in-plane disorder is less than in high density coatings but higher than
coatings C9-C11 (140-160 gcm3 indicated by the FWHM of the D band) and the
out-of-plane defects are much higher than low density PyC coatings (Fig 73) After
thermal treatment the in-plane disorder is similar as in coatings C9-C11 Therefore
the dominant in-plane defects are supposed to be a combination of domain boundaries
and 5-membered rings The slightly increase of domain size Lc in low density PyC
coatings is due to the decrease of interfacial defects through reorientation of domains
However they have much lower degree of increase of Lc than high density coatings
this could be due to low anisotropy in low density PyC coatings which makes it
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
191
difficult to reorient domains and remove the weak defects [17 25] The domain size
La was assumed to be unchanged since ordering in-plane disorders took place at
temperature above 2400 ordmC in low density PyC due to presence of 5-member rings
[17] It is worth to notice that the graphene fringes do not represent the in-plane
domain size in low density PyC due to the curvature caused by 5-memebered rings
[21] Due to the exist of 5-membered rings in low density PyC coatings the
microstructure is lightly affected by thermal treatment
742 Hysteresis after indentation
The increase in density of PyC leads to decrease in hysteresis after indentation and
density of PyC also dominate types and degree of disorders During indentation of
PyC hysteresis is caused by the slip of graphene planes whereas the disorders such as
interstitial defects or 5-memebered rings are supposed to be responsible for the
reversible deformation The hysteresis was also observed in other carbon materials
such as single crystal graphite [15] polycrystalline graphite [15] glassy carbon [9
10] Similar explanations about the effect of slip of graphene layers on the hysteresis
behaviour under indentation were given and it suggests that the deformation
mechanism is related to a common structure in different carbon materials which are
graphene planes
The slip of graphene planes has been demonstrated available The shear modulus (micro)
of graphite is 23 GPa (between graphene layers) [39] Based on the relation of τth= micro
30 [39 40] the theoretical shear stress (τth) of graphite is estimated to be 0077 GPa
This shear stress is much lower than the yield stress under Berkovich indenter for
graphite (03-05 GPa) [15] Under indentation the slip of graphene planes consumes
energy but recovers to the original shape after unload Lower density PyC has longer
fringes than that in higher density PyC (Fig 13 Ref [21]) therefore the panes can
slip for a longer distance under shear stresses generated by nano-indentation
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
192
Reversible deformation is due to presence of interstitial defects or highly curved
5-memebered rings For indentation of crystallite graphite the kink band could be
generated during the initial indentation process then reviersible deformation occurs
under further indentation [15] similar as that shown in Fig 77 In our PyC coatings
disorder in the PyC plays a similar role as the kink band in the crystallite graphite
The slip direction is parallel to the graphene planes so the in-plane defects presents at
the tilt and twist of two adjacent domains could not stop and reflect the slip Only
those defects perpendicular to the slip direction can contribute to the reversible
deformation such as interstitial defects or the highly curved 5-memebered rings
(caused fibrous graphene planes as shown in Fig 13(c) Ref [21])
After heat treatment the growths of the in-plane fringes increase the degree of the
hysteresis in PyC coatings For example the straightened graphene fringes (Fig 75)
caused by reorientation and removes of interstitials facilitate the hysteresis
significantly (the ratio of hysteresis energy to total loading energy increased from
0174 to 0249 Fig 77)
743 Mechanical property of low density PyC coatings
In as deposited low density PyC (C6-C11 gt 19 gcm3) Youngrsquos modulus and the
mean pressure are dominated by the density which is consistent with previous studies
[3 7 41] because of the effect of porous structure [3 21] As discussed in session
741 the disorders in low density PyC coatings play an important part on the stability
of microstructure which could reflect changes of mechanical properties After thermal
treatment the mechanical properties remained almost unchanged in PyC coatings
C9-C11 (140-160 gcm3) and this could be explained by the insignificant change of
microstructures at the presence of 5-membered rings The slightly decrease of
mechanical properties were found in coatings C6-C8 (164-186 gcm3) which is due
to the ordering of graphene planes through reduction of interstitial defects which
could enhance hysteresis and decrease the mean pressure No voids and change of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
193
orientation was observed after thermal treatment in coatings C6-C8 so Youngrsquos
modulus is slightly affected It is concluded that the mean pressure and Youngrsquos
modulus are functions of density in as-deposited low density coatings and their
evolution after thermal treatment is controlled by disorders such as interstitials andor
5-membered rings
744 Mechanical Property of high density PyC coatings
In high density PyC coatings (C1-C5 gt 19 gcm3) Youngrsquos modulus and the mean
pressure are independent of density so they are discussed regarding to variation of
texture domain size and concentration of interstitial defects (the area ratio of the 1500
cm-1
peak to the sum of four peaks shown in Fig 71) Table 74 summarises
microstructure parameters and mechanical properties of high density PyC coatings
Mechanical properties are not controlled by domain size and orientation angle which
is converse to the previous study [41] It is found that Youngrsquos modulus and the mean
pressure in high density PyC coatings decrease with the reduction of concentration of
interstitial defects (as shown in Table 74)
Table 74 The parameters used to explain different mechanical properties of high
density PyC (C1-C5 gt 19 gcm3)
Sample Density
(gcm3)
Texture
OA (deg)
Domain
size (nm)
IinterstialAll Pressure
(GPa)
Modulus
(GPa)
C3 2047 plusmn0030 60 22 013955plusmn000374 490plusmn036 2878plusmn117
C1 2122 plusmn0059 58 21 013513plusmn000399 468plusmn025 2670plusmn119
C5 2000 plusmn0061 43 20 013456plusmn000561 456plusmn010 2610plusmn036
C2 2087 plusmn0183 37 21 013036plusmn000433 435plusmn048 2513plusmn117
C4 2029 plusmn0015 43 24 011823plusmn001628 397plusmn019 2291plusmn076
The physical meaning of the above observation can be explained by the effect of
interstitial defects on the deformation mechanism in high density PyC coatings First
the high concentration of interstitial defects could reduce the energy consumption by
the reversible slip of graphene planes (eg in Fig 77) and it corresponds to high the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
194
mean pressure in high density PyC coatings Second in-plane Youngrsquos modulus is
much higher than out-of plane Youngrsquos modulus in graphite so the bonding between
graphene planes becomes important when the orientation effect could be neglected in
high density PyC (Table 74) For example in sample C4 and C5 the high Youngrsquos
modulus was obtained in C5 which have high amount of covalent band (interstitial
defects sp2 and sp3 in Fig 71) in the direction perpendicular to graphene planes The
high concentration of interstitial defects in high density PyC could also reduce the
influences of orientation angle on the high Youngrsquos modulus This could explain the
similar Youngrsquos modulus in C1 and C5 which have different orientation angles
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
After thermal treatment at temperature range of 1300-1800 ordmC in C5 (about 200
gcm3) the effect of concentration of interstitial defects on mechanical properties was
again demonstrated as given in Table 75 The mechanical properties decrease
gradually with the increase of thermal treatment temperature until 1600 ordmC and then a
dramatic decrease at 1800 ordmC The decrease is related to the reduction of content of
interstitial defects (Table 75) Furthermore no other relationship between mechanical
properties and microstructural features such as FWHM of the D band intensity of D
band and G band in Raman spectroscopy is found in the current work Therefore the
concentration of interstitial defects is proposed to dominant mechanical properties of
high density PyC coatings This idea about effect of interstitial defects on mechanical
properties is similar as the cross-link theory [8] which suggested that the mechanical
properties is related to the length and number of links between domains Furthermore
Temperature (ordmC) IinterstialAll Pressure (GPa) Youngrsquos modulus (GPa)
0 013456plusmn 000561 456plusmn010 2610plusmn 036
1300 011882plusmn000906 430plusmn010 2519plusmn060
1400 011045plusmn000278 413plusmn010 2407plusmn070
1500 009598plusmn000034 406plusmn022 2439plusmn070
1600 009469plusmn000219 391plusmn016 2344plusmn036
1800 007756plusmn000199 132plusmn015 1177plusmn051
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
195
the significant decrease of the the mean pressure and Youngrsquos modulus after 1800 ordmC
could be due to the straightening of graphene layers and formation of voids (Fig
74(c)) respectively To conclude the mechanical properties in high density PyC
coatings before and after thermal treatment from 1300 to 1800 ordmC decrease with the
reduction of concentration of interstitial defects
74 Conclusions
Disorders in PyC coatings was characterised by Raman spectroscopy A
combination of high degree of in-plane (domain boundaries) and out-of plane
defects (interstitial defects) prevail in high density PyC while the 5-membered
rings are dominant defects in low density PyC coatings
In high density PyC coatings the significant increase of domain size Lc is
attributed to the coalescence of domainsgraphene layers through reorientation and
reduction of interstitial defects During this process the graphene planes were
straightened resulting in slightly increase of La
In low density PyC coatings the microstructure remained almost unchanged after
thermal treatment due to the presence of the 5-membered rings which need high
temperature to be reduced
The hysteresis deformation behaviour was found in all PyC coatings before and
after thermal treatment under nano-indentation The nature of hysteresis is
suggested to be Slip of graphene planes consumes energy (hysteresis loop) and
disorders (interstitial defects and highly curved 5-memebered rings in high density
and low density PyC coatings respectively) are responsible for the reversible
deformation (unloading curve back to origin)
The mean pressure and Youngrsquos modulus are functions of density in low density
PyC coatings and their changes after thermal treatment are insignificant which
are due to the almost unchanged microstructure
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
196
In high density PyC coatings the mean pressure and Youngrsquos modulus are
independent of density orientation angle and domain size but they are related to
the concentration of interstitial defects After thermal treatment the decrease of
mechanical properties is attributed to the reduction of interstitial defects leading
to the straightening of graphene planes and formation of voids
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
197
75 References
[1] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques thin solid films 469-70 (2004) 214-20
[2] D G Martin Considerations pertaining to the achievement of high burn-ups in
HTR fuel Nucl Eng Des 213 (2002) 241-58
[3] E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure and
mechanical properties of pyrolytic carbon produced by fluidized bed chemical
vapour deposition Nucl Eng Des 238 (2008) 3121-28
[4] G K Miller D A Petti A J Varacalle J T Maki Consideration of the effects
on fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[5] A C Kada R Gnallinger M J Driscoll S Yip D G Wilson H C No et al
Modular pebble bed reactor In Modular pebble bed reactor project University
research consortium annual report 2000
[6] G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
[7] J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[8] F G Emmerich C A Luengo Youngrsquos modulus of heat-treated carbons A
theory for nongraphitizing carbons Carbon 31 (1993) 333-39
[9] J S Field MVSwain The indentation characterisation of mechanical properties
of various carbon materials Glassy carbon coke and pyrolytic graphite Carbon
34 (1996) 1357-66
[10] N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[11] M V Swain J S Field Investigation of the mechanical properties of two glassy
carbon materials using pointed indetners Philos Mag A 74 (1996) 1085-96
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
198
[12] N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philos Mag A 82 (2002) 1873-81
[13] M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated carbons
J Am Ceram Soc 85 (2002) 1522-28
[14] A Richter R Ries R Smith MHenkel B Wolf Nanoindentation of diamond
graphite and fullerene films Diamond Relat Mater 9 (2000) 170-84
[15] MW Barsoum A Murugaiah S R Kalidindi T Zhen Y Gogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[16] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
treatment J Nucl Mater 374 (2008) 445-52
[17] F G Emmerich Evolution with heat treatment of crystallinity in carbons Carbon
33 (1995) 1709-15
[18] M A Pimenta G Dresselhaus M S Dresselhaus L G Cancado A Jorio R
Saito Studying disorder in graphite-based systems by Raman spectroscopy Phys
Chem Chem Phys 9 (2007) 1276-91
[19] I J Van Rooyen J H Neethling J Mahlangu Influence of Temperature on the
Micro-and Nanostructures of Experimental PBMR TRISO Coated Particles A
Comparative Study Proceedings of the 4th
international topical meeting on high
temperature reactor technology Washington DC USA HTR 2008-58189
[20] J C Bokros R J Price Deformation and fracture of pyrolytic carbons deposited
in a fluidized bed Carbon 3 (1966) 503-19
[21] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-I Effect of deposition conditions on microstructure
Carbon 47 (2009) 396-10
[22] P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
199
[23] S Bernard O Beyssac K Benzerara N Findling G Tzvetkov G E Brown Jr
XANES raman and XRD study of anthracene-based coke and saccharose-based
chars submitted to high-temperature pyrolysis Carbon 48 (2010) 2506-16
[24] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[25] J N Rouzaud A Oberlin C Beny-bassez Carbon films structure and
microstructure (optical and electron microscopy Raman spectroscopy) Thin solid
film 105 (1983) 75-96
[26] S Potgieter-Vermaak N Maledi N Wagner J H P Van Heerden R Van
Grieken J HPotgieter Raman spectroscopy for the analysis of coal a review J
Raman Spectrosc 42 (2011) 123-29
[27] A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-photon coupling doping and nonadiabatic effects Solid state commun
143 (2007) 47-57
[28] J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy electron
diffraction and few other techniques Carbon 44(2006) 1833-44
[29] G A Zickler B Smarsly NGierlinger H Peterlik O Paris A reconsideration
of the relationship between the crystallite size La of carbons determined by X-ray
diffraction and Raman spectroscopy Carbon 44 (2006) 3239-46
[30] A Cuesta P Dhamelincourt J Laureyns A Martinez-Alonso JMD Tascon
Raman microprobe studies on carbon materials Carbon 32 (1994) 1523-32
[31] A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
200
[32] S Yamauchi Y Kurimoto Raman spectroscopic study on pyrolyzed wood and
bark of Japanese cedar temperature dependence of Raman parameters J Wood
Sci 49 (2003) 235-40
[33] D B Williams C B Carter Transmission electron microscopy A textbook for
materials science Springer New York p 392-97
[34] M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[35] T Jawhari A Roid J Casado Raman spectroscopic characterization of some
commercially available carbon black materials Carbon 33 (1995) 1561-5
[36] G L Dong K J Huumlttinger Consideration of reaction mechanisms leading to
pyrolytic carbon of different textures Carbon 40 (2002) 2515-28
[37] A Jorio E H Martins Ferreira M V O Moutinho F Stavale C A Achete R
B Capaz Measuring disorder in graphene with the G and D bands Phys Status
Solidi B 247 (2010) 2980-82
[38] R Piat Y Lapusta T Boumlhlke M Guellali BReznik D Gerthsen TChen R
Oberacker M J Hoffmann Microstructure-induced thermal stresses in pyrolytic
carbon matrices at temperatures up to 2900 ordmC J Eur Ceram Soc 27 (2007)
4813-20
[39] J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[40] A H Cottrell Dislocations and plastic flow in crystals Clarendon Press Oxford
1972 p 162
[41] J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
CHAPTER 8 Conclusions and Future Works
201
CHAPTER 8 Conclusions and Future Works
This work provides both fundamental understanding and techniqual guidance on the
mechanical properties and their relationship with microstructures of SiC and PyC
coatings in TRISO fuel particles The measurement of hardness and Youngrsquos modulus
of SiC coatings could be used in the modelling work to study the peroperty of the
failure of the fuel particlues and these results have been published The measurement
of the fracture toughness of SiC in TRISO fuel particle has solved one of the
techniqual problems in field and the study contributes to the study of the fracture
behaviour of SiC coatings The fracture strength measurement has enriched the
strength data of SiC coatings before and after thermal treatment (related paper is
under revision) The characterisation of the interfacial roughness has provided a direct
method to correlate the relationship between fracture strength and interfacial
roughness The mechanical properties of PyC coatings provide foundamental
understanding about the deformation mechanism of the PyC coatings under
indentation The effect of thermal treatment on the mechanical properties has given a
preguidance about the behaviour of the PyC coatings at high temperature
81 Conclusions
(1) In SiC coatings deposited at 1300 ordmC by fluidised bed chemical vapour deposition
the Youngrsquos modulus was an exponential function of the porosity and the high
hardness was attributed to the high density of dislocations and their interactions
The initiation and propagation of micro cracks under the confined shear stress was
found to be responsible for the mechanism of plastic deformation Based on this
hardness-related plastic deformation mechanism the variation of hardness in the
three types of SiC coating was due to different grain morphologies
CHAPTER 8 Conclusions and Future Works
202
(2) The fracture beneath the Vickers indenter consists of Palmqvist cracks as
observed using SEM in above SiC coatings Based on this crack mode Vickers
indentation fracture toughness values of 351-493 MPa m12
were obtained It was
found that stress-induced micro-cracks seem to be a mechanism for the fracture
behaviour The presence of defects such as nano-pores and less constraint grain
boundaries could generate more micro cracks which dissipated energy from the
main cracks
(3) Fracture strength measured by modified crush test give less scattered values
within a given sample by distributing the load under a contact area It has been
found that Weibull modulus and fracture strength of the full shell were
significantly affected by the ratio of radius to thickness of the coating and both of
them decrease linearly with the increase of this ratio
(4) The numericalstatistical analysis was able to characterize the interfacial
roughness of different coatings and the roughness ratio representing the
irregularities was proposed to be a unique parameter for this description The
difference of the local (intrinsic) fracture strength was dominated by the
roughness ratio and it decrease linearly with the increase of the roughness ratio
The roughness ratio has the similar effect on the difference of fracture strength of
the full shell
(5) After heat treatment at 2000 degC the local fracture strength was reduced due to the
formation of pores in the coatings which could act as the enlarged critical flaw
size The Weibull modulus decreased when the pores in SiC coatings became
critical flaws while it increased once more uniformly distributed critical flaws
along the IPyCSiC interface were formed The formation of pores was mainly
related to the annihilation of stacking faults and diffusion of intrinsic defects such
as vacancies interstitials and antisites
CHAPTER 8 Conclusions and Future Works
203
(6) The hysteresis deformation mechanism was proposed to be due to the slip of
graphene planes which constraint by interstitial defects and highly curved
5-membered rings in high density and low density PyC coatings respectively
(7) The hardness and Youngrsquos modulus were related to the concentration of
interstitial defects and density in high density and low density PyC coatings
respectively Their changes in high density PyC is more significant than in low
density PyC coatings after heat treatment over 1800 ordmC due to the annihilation of
interstitial defects and reorientation of graphene layers
82 Suggestions for future work
(1) According to current study high amount of native defects were found in SiC
deposited at low temperature and it would be interesting to study their effects on
the thermal stability in a certain range of temperature such as from 1200-2000 ordmC
The study of the diffusion of native defects in SiC could also assist the study of
diffusion behaviour of fission products because these defects are more active and
they tend to reach the equilibrium during annealing process Due to different
deposition conditions the dominant species of native defects could be different in
different coatings therefore it is also important to study the deposition effect on
thermal stability of SiC coatings
(2) Itrsquos important to know how the microstructure change of SiC coatings deposited at
low temperature after irradiation because they showed robust mechanical
properties and high resistance to fission products It has been found they have high
amount of dislocations and stacking faults which accompanied by interstitials and
vacancies as reflected from the enlarged lattice constant According to this it is
supposed that after irradiation the volume change of SiC will be small because of
the pre-exist lattice defects Therefore study of the irradiation effect (at different
operational temperature) on SiC deposited at low temperature would be
promising
CHAPTER 8 Conclusions and Future Works
204
(3) Although current study has proposed to use self-affine theory to characterize the
interfacial roughness more work about their effects on fracture strength need to
be explored For example find out if the derived linear function between
roughness ratio and fracture strength in the current study could be used to explain
the differences of fracture strength in other tests To do further demonstration it is
necessary to reduce the geometrical influence and choose SiC coatings has
similar microstructure but different IPyCSiC interface These samples could be
prepared by just changing the deposition condition of IPyC while keep it same for
SiC coatings
List of Contents
5
7313 Evolution of crystallinity 182
732 Mechanical properties of PyC coatings 185
7321 Force-displacement curve 185
7322 Youngrsquos modulus and the mean pressure 187
74 Discussions 188
741 Disorders and their changes after thermal treatment 189
742 Hysteresis after indentation 191
743 Mechanical property of low density PyC coatings 192
744 Mechanical Property of high density PyC coatings 193
74 Conclusions 195
75 References 197
CHAPTER 8 Conclusions and Future Works 201
81 Conclusions 201
82 Suggestions for future work 203
Abstract
6
Abstract
Mechanical and Microstructural Study of Silicon carbide and Pyrolytic Carbon
Coatings in TRISO Fuel Particles
The University of Manchester
Huixing Zhang
Doctor of Philosophy in Materials Science
TRISO fuel particles have been developed as nuclear fuels used for a generation IV
nuclear reactor high temperature reactor Such particle consists of a fuel kernel
pyrolytic carbon (PyC) and silicon carbide (SiC) coatings This study has been carried
out to establish a relationship between mechanical properties and microstructures of
SiC coating and PyC coatings produced by fluidized bed chemical vapour deposition
Indentations were used to measure hardness Youngrsquos modulus and fracture behaviour
of SiC and PyC coatings Fracture strength of SiC coatings was measured by crush
test Microstructure of SiC and PyC was mainly characterised by transmission
scanning electron microscopy and Raman spectroscopy
For SiC coatings produced at 1300 ordmC Youngrsquos modulus is an exponential function of
relative density Hardness of SiC coatings is higher than the bulk SiC produced by
CVD and it is attributed to the high density of dislocations and their interactions The
deformation mechanism of SiC coatings under indentation is explained by presence of
defects such as grain boundaries and nano-pores The fracture of these coatings
beneath the Vickers indentation is the Palmqvist cracks and indentation fracture
toughness was in the range of 35-49 MPa m12
The stress-induced micro-cracks are
assumed to be the mechanism for the high indentation fracture toughness Different
hardness and fracture toughness in these SiC coatings are attributed to influences of
defects and grain morphology
Measurement of fracture strength was carried out on SiC coatings deposited at
1300-1500 ordmC Weibull modulus and fracture strength of the full shell are dominated
by the ratio of radius to thickness of coatings and decrease linearly with the increase
of this ratio The influence of SiCPyC interfacial roughness on fracture strength of
the SiC was quantified by self-affine theory The fracture strength decreases linearly
with the increase of the roughness ratio which is the long-wavelength roughness
characteristic After thermal treatment at 2000 ordmC fracture strength decreased in SiC
coatings due to the formation of pores which are results of diffusion of native defects
in as-deposited SiC coatings and the change of Weibull modulus is related to the size
and distribution of pores
For low density PyC coatings Youngrsquos modulus and the mean pressure increase with
the increase of the density however for high density PyC coatings they are
determined by interstitial defects The hysteresis deformation behaviour under
nano-indenation has been found be affected by density variation and thermal
treatment which is proposed to be due to the disorder structure in PyC coatings
Declaration
7
Declaration
No Portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Copyright Statment
8
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this thesis)
owns any copyright in it (the lsquolsquoCopyrightrsquorsquo) and she has given the University of
Manchester certain rights to use such Copyright including for administrative
purposes
ii Copies of this thesis either in full or in extracts and whether in hard or electronic
copy may be made only in accordance with the Copyright Desings and Patents Act
1988 (as amended) and regulations issued under it or where appropriate in
accordance with licensing agreements which the University has from time to time
This page must form part of any such copies made
iii The ownership of certain Copyright patens designs trade marks and other
intellectual property (the lsquolsquoIntellectual Property Rightsrsquorsquo) and any reproductions of
copyright works in the thesis for example graphs and tables (lsquolsquoReproductionsrsquorsquo)
which may be described in this thesis may not be owned by the author and may be
owned by third parties Such intellectual Properties Rights and Reproductions cannot
and must not be made available for use without the prior written permission of the
owner(s) of the relevant Intellectual Property Rights andor Reproductions
iv Further information on the conditions under which disclosure publication and
commercialization of this thesis the Copyright and any Intellectual Property andor
Reproductions described in it may take place is available in the University IP policy
(see httpwwwcampusmanchesteracukmedialibrarypoliciesintellectual-property
Pdf) in any relevant Thesis restriction declarations deposited in the University
Library The University Libraryrsquos regulations (see
httpwwwmanchesteracuklibraryaboutusregulations) and in the Universityrsquos
policy on presentation of Thesis
Acknowledgement
9
Acknowledgement
I will always be appreciative to Professor Ping Xiao for his support and guidance
during this project period and his enthusiasm for work and positive attitude towards
life inspired me I am thankful for what he shared about his own experience doing
research which impressed me and motivated me to make improvement
I would like to thank in particular Dr Eddie Loacutepez-Honorato for his patient guidance
on my experiments and valuable advices on my project His caution on preparing
delicate specimen infected me and helped me through my project He was always
there listening my ideas and discussing with me and he has set an example for being
a good researcher
I give my thanks to all the members in ceramic coating group old and new and I
treasure and appreciate this chance working with you
I would like to give my great gratitude to Dr Alan Harvey for his kind help on
transmission electron microscopy Mr Andrew Forest and Mr Kenneth Gyves on
nano- and micro-indentation Mr Andrew Zadoroshnyj on Raman spectroscopy Dr
Ali Gholinia and Dr Ferridon Azough on TEM sample preparation Dr Judith
Shackleton and Mr Gary Harrison on X-ray diffraction Mr Christopher Wilkins and
Mr Michael Faulkner on scanning electron microscopy and Mr Stuart Mouse on
tensile tests
I am grateful to my dear friends Yola David and Dean and you make my life more
colourful and interesting I would like to thank my beloved parents and brother for
your love care and support and you are great examples of hard work and kindness
My thanks also go to the ORS scheme the CSC grant and the F-BRIDGE for their
financial support during my PhD studies
List of Figures
10
List of Figures
CHAPTER 1 Introduction
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Fig 12 Behaviour of coated layers in fuel a particle [10]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
CHAPTER 2 Literature Review
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
List of Figures
11
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation[62]
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
List of Figures
12
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC coatings Measured by
Indentation
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
List of Figures
13
BF-TEM and (b) DF-TEM
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for extra-Si SiC coatings
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
Fig 45 Cross-sectional SEM image of stoichiometric SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
List of Figures
14
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a)
extra-C SiC (b) extra-Si SiC
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
Fig 58 Log-log representation of the height-height correlation function ∆h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
List of Figures
15
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC coatings
Fig 61 Weibull plots of local fracture strength (L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
Fig 62 Weibull modulus plots of fracture strength of the whole shell (F
f ) before
(black triangle) and after (red circle) thermal treatment
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after thermal treatment (c) and (d) SiC2
before and after thermal treatment (e) and (f) SiC3 before and after thermal treatment
(g) and (h) SiC4 before and after thermal treatment Dashed and solid arrows indicate
growth direction and pores respectively
Fig 64 The IPyCSiC interfacial morphology of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermal treated at 2000 degC (right in
each figure) The white arrow points towards to the interface irregularities (except for
thermal treated SiC4 coating (d)) black circle represents the pores in SiC coatings
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermal treated
at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and SiC2 inset
shows the peak shift of as-deposited (dash line) and after thermal treatment (solid
line) (b) is SiC4 and inset is the high angle diffraction peak after thermal treatment
showing splitting while it is a single peak in as-deposited coating
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
List of Figures
16
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
List of Tables
17
List of Tables
CHAPTER 2 Literature Review
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Table 23 Elastic tensors of 3C-SiC at room-temperature
Table 24 Vickers and nano-indentation hardness of polycrystalline CVD SiC
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Table 26 Summary of the hardness and Youngrsquos modulus for pyrolytic carbon
measured by different methods
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Measured by Indentation
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχv
along the radial and tangential directions
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Table 52 Summary of measured and calculated parameters for all the coatings
List of Tables
18
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Table 54 Results and variations influences on fracture strength for SiC coating
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings
Table 61 Deposition conditions of SiC coatings
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the whole shell before and after thermal
treatment
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
Table 71 PyC coatings deposition conditions and physical properties
Table 72 Domain size (XRD) of as-deposited and thermal treated PyC coatings
Table 73 Changes of mechanical properties after thermal treatment of PyC coatings
Table 74 The parameters used to explain different mechanical properties of high
density PyC
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
CHAPTER 1 Introduction
19
CHAPTER 1 Introduction
11 TRI-Isotropic (TRISO) fuel particles
A fission reaction is about that a large atomic nucleus (such as Uranium-235) is hit by
a neutron and absorbs the neutron forming a larger unstable nucleus The unstable
larger atomic nuclear breaks into two small nuclei and releases a high amount of
energy more neutrons beta and alpha particles and gamma The energy release is
much greater than for traditional fuels eg 1 g Uranium nuclear fuel releases the
same amount of energy as approximately 3 tonne of coal [1] The energy can be
transferred through the cooling system and used to boil the water to make steam to
drive a turbine and electrical generator in a nuclear power station
The high-temperature gas cooled reactor is one of the most promising candidates for
the production of nuclear energy according to its unique features For example it has
high coolant outlet temperature (850-1000 degC) which provides more efficient
electricity production due to the increased difference of the hot and cold coolant
temperatures [2] Furthermore it has the safety advantages due to the enclosure of the
fuel kernel (such as UO2 UC) within few layers of ceramic coatings Currently the
most common technique to fabricate fuels for operating the next generation
high-temperature gas cooled reactors is the TRISO fuel particles coating system [3]
The TRISO system was designed not only to retain all fission products during neutron
irradiation but also to withstand the thermo-mechanical stresses generated during
service [4]
CHAPTER 1 Introduction
20
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Figure 11 is the schematic of TRISO fuel particles embedded in a graphite matrix A
TRISO fuel particle consists of a fuel kernel and coating layers of porous pyrolytic
carbon (PyC) called buffer layer inner dense PyC (IPyC) silicon carbide (SiC) and an
outer dense PyC (OPyC) [5] and these layers were designed to have different
purposes The buffer layer absorbs metallic fission products recoils from kernel and
provides a space for fission product gases It also takes the volume change caused by
the kernel swelling without transmitting forces to outer layers The dense and
isotropic IPyC layer stops the chlorine from reacting with the kernel during deposition
of SiC and provides a firm substrate for the SiC layer Furthermore it protects the
SiC layer from most of the fission products and carbon monoxide during operation
The OPyC layer protects SiC layer during the remainder of the fabrication process
and provides structural stability to the particle during irradiation [3] The high
mechanical properties of SiC are needed to contain the high pressure generated in the
kernel and withstand the stress developed by the dimensional change of IPyC [3]
CHAPTER 1 Introduction
21
12 Failure mechanism
The radiation effects on the performance of the fuel particles such as fundamental
performance characteristics and fission product relsease mechanisms have been well
understood Different testing conditions (eg temperature up to 1300 degC and the does
of neutron) reflected the senariors encountered real applications [6-8]
During irradiation a number of potential failure mechanisms were revealed according
to several tests of coated fuel particles conducted in material test reactors and in
real-time operating HTR reactors [6-8] Chemically the corrosion of SiC by the
fission product palladium has been observed in almost all kinds of fuel compositions
and is considered as one of the key factors influencing the fuel performance However
this could be avoided by limiting the fuel temperature irradiation time or increase the
thickness of SiC layer [9] Mechanically the built up of the internal gas pressure (eg
CO) of irradiated particle and the neutron induced embrittlement of PyC coatings
could promote the failutre of the TRISO fuel particle The primary mechanisms which
may result in mechanical failure of TRISO fuel particles and lead ultimately to fission
product release depends significantly on the magnitude of the de-bonding strength
between IPyC and SiC layers [3 9]
121 Traditional pressure vessel failure mode
In this mode the failure was assumed to occur due to simple overload of the SiC layer
due to internal pressure build-up from fission gas [10] Both IPyC and OPyC layers
shrink during operation because of the irradiation exposure [11] This causes
compression stress in the SiC layer and tensile stress in the PyC layers Failure of the
SiC layer can only occur if the internal gas pressure is high enough to overcome the
compressive stress and critical stress of the SiC layer itself
CHAPTER 1 Introduction
22
Fig 12 Behaviour of coated layers in fuel a particle [10]
Figure 12 shows the basic behaviour modelled in a three layers standard model [10]
It shows that both IPyC and OPyC layers shrink and creep during irradiation but the
SiC layer exhibits only elastic deformation A portion of gas pressure is transmitted
through the IPyC layer to the SiC The pressure continually increases as irradiation of
the particle goes However if the PyC layer could remain in tension the failure by
fracture of SiC layer would be less likely to happen in this mode When the failure of
the PyC layer occurs a tensile hoop stress in the SiC layer is generated This leads to
the development of the stress concentration mode provided by the fracture of the inner
PyC layer
122 Stress concentration mode
In this mode it is been proposed that there is a point at which the fracture strength of
the IPyC would be exceeded during exposure When this occurs a radial crack will
form in the IPyC layer The crack could either penetrate through the SiC layer or
partially de-bonding the IPyCSiC interface This would lead to severe stress
concentration near the crack tip and it could reach the maximum of 440 MPa
according to previous simulation work [10] Once de-bonding goes through the whole
interface the source of stress in the SiC layer would be fission product gas build-up
CHAPTER 1 Introduction
23
and this case has similar failure mechanism of traditional pressure vessel failure mode
Although this process could decrease the probability of failure compared with the
stress concentration case the probability of failure may be higher than the traditional
failure mode Because the stress generated in the SiC layer after de-bonding would
increase [3]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
All these behaviours make it easier for the SiC layer to reach its fracture strength and
lead to the radial crack and failure of the SiC results in an instantaneous release of
elastic energy that should be sufficient to cause simultaneous failure of the
pyrocarbon layer Shown in Fig 13 is a photomicrograph illustrating the failure of a
TRISO coating According to the above discussion all the carbon layers are partially
designed to support or protect the SiC layer The SiC layer serves as the main
containment barrier for gas and metallic fission products [3] and high mechanical
properties of the SiC layer are needed However without appropriate microstructure
and mechanical properties of the PyC layer the stresses or structural changes
introduced in this layer during the irradiation process could result in the failure of the
whole particle [9 12] Furthermore mechanical properties such as the hardness (It is
CHAPTER 1 Introduction
24
the resistance to plasticpermanent deformation of materials under constant load from
a sharp object) Youngrsquos modulus (It reflects the resistance to reversible deformation
of a material) fracture toughness (It describes the ability of a material containing a
crack to resist fracture) and fracture strength (It is the maximum stress at which a
specimen fails via fracture) of SiC and PyC coatings are also important factors for the
safety design and evaluation of the TRISO coating system [10]
13 Goals of dissertation
Due to the importance of mechanical properties of SiC and PyC layers in keeping the
integrity of TRISO fuel particles and providing adequate information for modelling
the probability of failure of particles a good understanding of the elastic plastic and
fracture properties and their relation with microstructure is necessary Therefore all
the work carried out in this project is aimed at studying the relationship between
microstructure and mechanical properties of these two layers aiming to provide a
fundamental understanding about the deformation mechanism and solve the practical
issues
Due to small scale of SiC and PyC coatings two main techniques used to measure
mechanical properties are micronano-indenation and crush test Furthermore to study
the effect of microstructures on mechanical properties characterization techniques
such as transmissionscanning electron microscope and Raman spectroscopy are
widely used in the current work
In this thesis Chapter 2 reviews the recent progress in microstructural characterisation
and mechanical properties of SiC and PyC related materials which provides basic
information with regard to future study about hardness Youngrsquos modulus
deformation mechanism and fracture behaviour in these
Chapter 3 studies the influences of microstructure on hardness and Youngrsquos modulus
CHAPTER 1 Introduction
25
of SiC coatings and focuses on understanding the deformation mechanism of SiC
under nano-indentation The fracture toughness of these SiC coatings is measured by
Vickers-indentation and the importance of crack modes is discussed in Chapter 4
In Chapter 5 the fracture strength of SiC coatings in TRISO fuel particles is measured
and influence of the IPyCSiC interface on fracture strength is discussed Effect of
thermal treatment on fracture strength and microstructure of SiC coatings deposited at
different conditions are introduced in Chapter 6
Chapter 7 investigates the microstructure and mechanical properties of PyC coatings
with focus on deformation mechanism under indentation and the effect of density and
disorders on mechanical properties before and after thermal treatment
At last the main results and conclusions together with suggestions on future work are
given in Chapter 8
CHAPTER 1 Introduction
26
14 References
[1] httpnuclearinfonetNuclearpowerTheScienceOfNuclearPower
[2] J J Powers Fuel performance modelling of high burnup transuranic TRISO fuels
Disertation of Master University of California Berkeley 2009
[3] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[4] D L Hanson J J Saurwein D W McEachern A S Shoeny Development plan
for advanced high temperature coated-particle fuels Report Nopc000513
[5] httpwwwmpafrprocessphp
[6] W Burck H Nabielek A Christ H Ragos AW Mehner HTR coated particle
fuel irradiation behaviour and performance prediction Specialists meeting on
gas-cooled reactor fuel development and spent fuel treatment IWGGCR-8 1983
174-88
[7] H Nickel H Nabielek G Pott A W Mehner Long-time experience with the
development of HTR fuel elements in Germany Nucl Eng Des 217 (2002)
141-51
[8] H Nabielek W Kuhnlein W Schenk W Heit A Christ and H Ragoss
Development of advanced HTR fuel elements Nucl Eng Des 121 (1990)
199-210
[9] K G Miller D A Petti J Varacalle T Maki Consideration of the effects on
fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[10] A C Kadak R G Ballinger M JDriscoll et al Modular pebble bed reactor
project university research consortium Annual report INEELEXT-2000-01034
MIT-ANP-PR-075
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
CHAPTER 1 Introduction
27
treatment J Nucl Mater 374 (2008) 445-52
[12] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
CHAPTER 2 Literature Review
28
CHAPTER 2 Literature Review
21 Introduction
To model the probability of failure of fuel particles a number of key mechanical
properties of silicon carbide (SiC) are needed such as Youngrsquos modulus hardness
fracture toughness and fracture strength [1 2] These properties could be affected by
the microstructure of SiC coatings such as orientation porosities grain size and
defects [1-5] The small dimensions of the SiC coating limits the techniques available
to measure its mechanical properties However the development of the
nano-indentation has provided an important tool for probing the mechanical properties
of small volumes of material From the load ndash displacement data many mechanical
properties such as hardness Youngrsquos modulus and even fracture behaviour can be
determined [6] When an indentation system is used in conjunction with a focused ion
beam system and a transmission electron microscope images of deformation under
the nano-indentation can be obtained and the 3-D crack morphology can even be
reconstructed [7] Since there is a need to explain the high mechanical properties of
SiC deposited at temperature of 1300 ordmC by fluidized-bed chemical vapour deposition
[8] this combination of techniques could provide fundamental understanding of the
deformation mechanisms during indentation Another important parameter is fracture
strength and there have always been efforts to establish one method to characterise
fracture strength of SiC for example by brittle-ring test [9] whole particle crush test
[10] and modified crush test [5] Furthermore the high temperature application of SiC
and the compact of fuel pellet could affect the microstructure of SiC [2] which would
lead to the changes of mechanical properties
CHAPTER 2 Literature Review
29
The pyrolytic carbon (PyC) has been introduced by previous studies [11-14] and is
important in helping the SiC act as the main loading bearing layer The high
mechanical properties such as Youngrsquos modulus and anelasticity of PyC are necessary
to protect from damage caused by internal stresses and by external mechanical
interactions [12] However cracking and debonding between the SiC and inner PyC
layers could increase the probability of failure of TRISO fuel particles [13 14] It was
shown that without appropriate microstructure and mechanical properties of PyC the
structural or stress changes introduced in the coating during irradiation process could
result in total failure of the particle [11 13] The microstructure of PyC varied under
different deposition conditions [15] and it dominates the mechanical properties of
PyC coatings Therefore in this Chapter we review both the microstructure of SiC
and PyC including atomic structure morphology and defects and their mechanical
properties eg hardness Youngrsquos modulus deformation behaviour etc
22 Microstructure of silicon carbide
221 Atomic structure
The basic structural unit in SiC is a covalently bonded tetrahedron a carbon atom is at
the centre of four silicon atoms (C-Si4) and vice versa (Si-C4) The length of each
bond and the local atomic environment are nearly identical while the stacking
sequence of the tetrahedral bonded Si-C bilayers could be different The different
stacking sequences give SiC more than 250 polytypes [16] of which the 3C 4H 6H
and 15R are the most common The leading number of polytypes shows the repetition
of the SindashC pair and the letter C H and R represents the cubic hexagonal and
rhombohedral crystals respectively The 3C is the only cubic polytype in which the
stacking sequence of the planar unit of Si and C in tetrahedral coordination is depicted
as ABCABC in the lt111gt direction The cubic SiC crystal is called β-SiC and all
the other polytypes are α-SiC The crystal structures of 3C- 4H- 6H- and 15R-SiC
are schematically illustrated in Fig 21(a) [17] and corresponding XRD images were
CHAPTER 2 Literature Review
30
shown in Fig 21(b) [18]
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Although the transformation of SiC polytypes is primarily dependent on temperature
it could be affected by purity of the pre-existing phase pressure andor stacking faults
[19-22] The cubic form of SiC (β -SiC) is believed to be more stable than the
hexagonal structure (α-SiC eg 6H-SiC) below 2100 ordmC [19] However the polytype
of 2H-SiC which has the simplest stacking sequence is rarely observed at higher
temperature Krishna et al [20] reported that single crystals of 2H-SiC can be easily
transformed to 3C-SiC on annealing in argon at temperatures above 1400 ordmC It was
CHAPTER 2 Literature Review
31
found that the pre-existence of α-SiC (except 2H-SiC) could promote β-SiC
transformation to α-SiC while the transformation from α-SiC (6H-SiC) back to β-SiC
(3C-SiC) needs high temperature and pressure [21]
It has also been shown that the phase transformation could be closely related to
pre-existing defects such as stacking faults and their distribution [18] of which the
concentration is high even in single crystal SiC [22] Furthermore due to their low
formation energy the other intrinsic defects such as vacancies interstitials and
antisites were found to be common in SiC [23] These defects could affect mechanical
properties of SiC [8] so it is important to review their structure and properties
222 Defects in SiC
2221 Stacking faults and dislocations
A stacking fault is a disordered part of the ordered sequence in fcc crystal and the
most common stacking faults in cubic SiC are intrinsic and extrinsic stacking faults
(ISF and ESF) [24] For ISF the resulting stacking sequence is ABCACABC
if a double layer B is removed (condensation of vacancies) as for instance shown in
Fig 22[24] The ESF could be thought of as adding a double layer to the stacking
sequence (condensation of interstitials) resulting stacking sequence of
ABCACBCABChellip
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
CHAPTER 2 Literature Review
32
Another interpretation of the stacking faults is related to a twist of the three equivalent
bonds between two bilayers by 180deg [24] There may be an intrinsic shear stress
which could promote the glide of partial dislocations and thereby result in a faulted
crystal containing an error in stacking sequence so itrsquos reasonable to interpret
stacking faults in this way [25] Compared with dislocations and vacancies no bonds
are broken by stacking faults leading to a small energy difference between faulty and
perfect structures [26]
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
[27] [28] [24] [29] [30] [31] [32]
ESF (mJ m-1
) -15 -- -28 -6 -61 -154 -323
ISF (mJ m-1
) 12 34 -34 14 138 111 -71
Table 21 lists the formation energy of stacking faults in SiC and it shows that
extrinsic stacking faults have much lower formation energy than intrinsic stacking
faults in fact the values become negative The negative formation energy of stacking
faults in 3C-SiC means they can be formed very easily even more easily than perfect
3C-SiC As a result the stacking faults in 3C-SiC are spontaneously formed and most
likely in the form of extrinsic faults in the lt111gt direction Furthermore due to the
low energy of formation the length of a stacking fault can only be limited by the size
of the crystal or the presence of other defects that act as obstacles [33]
CHAPTER 2 Literature Review
33
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
The morphology of stacking faults in SiC observed by TEM is given in Fig 23 It
shows that the stacking faults could form a small domain (around 1 nm thick in Fig
23(a)) with different distances between small domains When a large concentration of
stacking faults exists in SiC it has been claimed that a conversion of cubic SiC to
hexagonal SiC on the nano-scale could happen by twinning [35] Furthermore the
stacking sequence of the faulted 3C-SiC was previously treated as random mixing of
α-type unit structures such as 6H and 4H in the 3C structure [36] Therefore it is
important to identify the properties and the microstructure of stacking faults of SiC
layers in TRISO fuel particles because the presence of α-SiC could result in reduction
of strength under irradiation which was due to enhanced possibility of anisotropic
swelling of α-SiC under irradiation compared to β-SiC [37]
(a) (b)
(c)
CHAPTER 2 Literature Review
34
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Figure 24 gives the XRD images of SiC in TRISO fuel particle deposited by fluidized
bed chemical vapour deposition showing the extra peak at 2θ~335ordm a high
background intensity at the peak at 2θ~353ordm and the broadening of the 3C peaks [8]
This is different from the perfect atomic structure of 3C-SiC as shown in Fig 21(b)
According to a previous simulation study [18] this kind of XRD diffraction pattern
could be caused by the existence of a high density of stacking faults and twins in the
regular cubic sequences It was demonstrated that it was unlikely to be due to the
presence of 2H-SiC or other polytypes [18] and two possible explanations were given
First two types of crystalline 3C-SiC with different populations of faults and twins
and second one type of crystal having clusters of faulted regions In SiC single
crystals although the concentration of stacking faults and twins is high the density of
dislocations is low (102-10
5cm
2) compared with metallic materials [22]
Figure 25 shows schematic images of the dislocations in face centred cubic (fcc)
crystals (β-SiC) The perfect dislocation is the (111) lt110gt system with burgers
vector of b=a2[110] (0308 nm) in SiC as shown in Fig 25(a) The perfect
dislocation could be easily dissociated into two partial dislocations of a6[121] and a6
CHAPTER 2 Literature Review
35
[21-1] as shown in Fig5 (a) and (b) because this reduces the total energy As a result
of this split a stacking fault must also be produced between the two partial
dislocations [38] Figure 25 (c) and (d) are lt110gt projections showing the Shockley
and Frank partial dislocations and their formation all related to the formation of
stacking faults
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
(a)
(b)
(c) (d)
CHAPTER 2 Literature Review
36
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
By comparing with previous studies [39-41] it is found that the relationship between
dislocation and stacking faults is complex The stacking faults have influences on the
mechanical properties for example enhancing the mobility of dislocations [39]
Different roles of stacking faults in II-VI heterostructures and devices have been
observed and results indicate that the stacking faults serve as the sources of misfit
dislocations [40] It is necessary to study the propagation of stacking faults or the
formation of stacking faults under stress and their influence on the properties of SiC
For example generation of stacking faults is shown to have occurred during the
fracture process together with the corresponding partial dislocation Furthermore
Agarwal et al [41] observed the growth of stacking faults from certain basal plane
dislocation within the base layer of the SiC
2222 Non-stoichiometric and point defects
Another common class of defects in SiC are non-stoichiometric (excess silicon or
carbon) and point defects [23 41 42] The purity of SiC may have effect on the
crystal structure strength corrosion resistance thermal conductivity diffusion
coefficient and other coating properties depending on its amount [43] The purity
could also affect defects in SiC eg if the stoichiometry deviates (even less than 1)
the concentrations of point defects in cubic SiC were found to be elevated [23]
Although the effect of point defects on general behaviour of nuclear fuel during
application process is not clear but their effect on microstructure evolution during
thermal treatment could be significant [44]
Silicon in SiC Stoichiometric 3C-SiC has generally been obtained at temperatures
between 1500 and 1600 [45] with carbon and silicon codeposited above and below
this temperature range By adding propylene as another carbon source the deposition
temperature of stoichiometric SiC could be reduced to about 1300 [8] The extra-Si
CHAPTER 2 Literature Review
37
SiC is less commonly investigated compared with the extra-C SiC because it has
been found that during the irradiation process the extra-Si plays a negative role in
material properties due to its low melting point [1] It has been found that the effect of
excess-Si on the Youngrsquos modulus and hardness it is more likely depending on its
amount and location [8 46]
Raman spectroscopy is an effective way to identify free Si both in amorphous and
crystalline phases eg it detected excess-Si when the XRD result showed the SiC was
stoichiometric [8] If the extra-Si is high (could be detected by XRD) TEM could be
used to detect its location and characterise the Si lattice contrast For example TEM
was carried out using both high resolution [35 47] and dark field imaging modes [48]
The HRTEM images in Fig 26 show the 3C-SiC crystallite with Si inclusions in
which nano-crystalline 3C-SiC and Si are separated by a weakly crystallized
interphase
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
(a)
(b) (c)
β-SiC
β-SiC
β-SiC
β-SiC
Si
Si
025 nm
025 nm
025 nm
0 312 nm
0312 nm
CHAPTER 2 Literature Review
38
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
Figure 27 shows bright-field and dark-field images of extra-Si SiC It shows the
crystalline Si as bright points in the dark background located at the grain boundaries
[48] The above observations were carried out in SiC with more than 1 at excess Si
(by comparing the intensity of Si Raman peak) as such observations are difficult
when the amount of excess Si is low Since the Youngrsquos modulus in SiC with low
amount of excess Si was comparable to that of stoichiometric SiC[8 46] it may have
unique properties that are worth further exploitation
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Carbon in SiC Excess C can also be identified by Raman spectroscopy but it is more
difficult to quantify its content and observe where this extra carbon exists due to its
small atomic number A comparative method was used to measure the content of
excess carbon by combining Raman spectroscopy auger electron spectroscopy
electron probe microanalysisand X-ray photoelectron spectroscopy [49] Once the
carbon concentration was measured (by above methods) the ratio of free excess to
SiC peak intensity (I796I1600) of Raman spectroscopy could be obtained as shown in
Fig 28 and the excess carbon concentration in the nearly stoichiometric SiC could
(a) (b)
CHAPTER 2 Literature Review
39
be estimated [49]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
There are few reports regarding the location of excess C in SiC The research carried
out by KKaneko et al [50] in carbon-doped hot pressed szlig-SiC showed that grain
boundaries were found to be free of any second phase by HRTEM although excess C
is found to form the second graphite phase Mykhaylyk and Gadzira revealed that
extra-C atoms are located as planar defects [51] The C atoms in the β-SiC structure
were supposed to arrange either as diamond-like carbon interlayers or as
non-correlated point defects after sintering of the as-synthesized powder at high
pressures and high temperature Since it showed that the presence of excess C atoms
in SiC crystal structure changes the local atomic environment [52] they may exist
within the SiC crystal and be correlated with other defects
The above discussion about the excess Si and C indicates that their influences on
properties of SiC depend on their content and that they could be discussed together
with the other point defects when their amount is low (less than 1 at ) [23]
Point defects in SiC SiC has eight kinds of point defects which keep the tetrahedral
symmetry of the perfect SiC crystal [23] They are carbon vacancies (Vc) silicon
vacancies (VSi ) carbon antisites (CSi) silicon antisite (Sic) a tetrahedral interstitial
silicon atom surrounded by four Si atoms (SiTSi) a tetrahedral interstitial silicon atom
CHAPTER 2 Literature Review
40
surrounded by four C atoms (SiTC) a tetrahedral interstitial carbon atom surrounded
by four Si atoms (CTSi) and a tetrahedral interstitial carbon atom surrounded by four
C atoms (CTC) [23] The formation energies for these defects are listed in Table 22
Due to their low formation energies the individual antisites and vacancies
particularly CSi were expected to appear even in as-deposited coatings [53 54]
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Vc VSi Sic CSi SiTSi SiTC CTSi CTC
Ef (eV) 59 68 73 11 150 147 86 110
The importance of point defects for different applications of SiC was studied and
these properties were studied in the relation to the properties of the point defects
including their formation annealing and interaction with each other [53] According
to Raulsrsquos study [54] the actual results of diffusion of CSi are more likely to be the
formation of CSi clusters which could be promoted by the diffusion of vacancies For
the coexistence of self-interstitials and vacancies (eg in irradiated material) it has
been found that the annealing temperature for VSi and Vc by recombination in β-SiC
were about 500 ordmC and 750 ordmC respectively [55] For as-deposited β-SiC without
interstitials the annealing process was only dominated by the out-diffusion of
vacancies the disappearances of VSi and Vc were found at temperature of 1400 ordmC and
1600 ordmC respectively [54] It is also been found that the migration of silicon vacancies
is easier than carbon vacancies due to its lower migration energy barrier Furthermore
in the case of excess carbon inside SiC the carbon clusters may form in SiC after
annealing and the size of the cluster depends on the content of interstitial carbon [56]
The general atomic-scale microstructure of SiC was reviewed above which showed
high degree of defects such as stacking faults dislocations vacancies and antisites
CHAPTER 2 Literature Review
41
The kind and concentration of these defects could affect the mechanical properties
such as hardness Youngrsquos modulus and fracture behaviour of SiC Since variation of
mechanical properties could also be due to other microstructural factors such as grain
size and density the relationship between microstructure and mechanical properties
are further reviewed in the following session
23 Properties of silicon carbide
231 Youngrsquos modulus
Youngrsquos modulus is physically related to the atomic spacing atomic bond strength
and bond density It is accepted that high-purity SiC material eg CVD SiC exhibits
the highest elastic modulus and that a porous microstructure with a high
concentration of impurities could decrease the elastic modulus [1 57] In contrast
neither grain size nor polytype was recognized as having a significant effect on the
elastic modulus of SiC in coated fuel [1 58]
Table 23 Elastic tensors of 3C-SiC at room-temperature
C11 (GPa) C12 (GPa) C44 (GPa) Z Ref
3C-SiC a 3523 1404 2329 18196 [59]
3C-SiC b 511 128 191 10026 [1]
3C-SiC c 390 142 256 -- [60]
3C-SiC a 420 126 287 19503 [61]
a Theoretical calculations
b Sonic resonance measurement
c Raman Spectroscopy
According to the definition of Youngrsquos modulus an important factor which could
affect its value for SiC material is the texture which is the degree of anisotropy (lack
of randomness with regard to the orientation) of SiC crystals The Youngrsquos modulus is
different by a combining of elastic tensors for deformation of the crystal in different
CHAPTER 2 Literature Review
42
orientation The elastic tensors or the stiffness tensors reflect the linear stress-strain
relation of a material There are 81 elastic tensors because the stresses and strains
have 9 components each However due to the symmetries of the SiC the tensors were
reduced to 3 unknown values They could be measured by sonic resonant method [1]
and Raman spectroscopy [60] based on vibrational theory of the crystal lattice They
are defined for SiC in Table 23 and will cause the variation of Youngrsquos modulus for
anisotropic materials The elastic tensors for 3C-SiC identified by previous theoretical
and experimental results [59-61] are substantially different from the current updates
of sonic resonance data The difference could be caused by the difference of the size
of SiC mateirals which could introduce the influences of defects such as grain
boundaries and stacking faults It was proposed to be more reasonable estimation for
SiC in TRISO fuel particle [1]
A measurement of the anisotropy in β-SiC (faced centre cubic crystals) is the ratio of
the two shear moduli [3] 100 shear modulus and 110 shear modulus μ0 and μ1
respectively which is
0 44
1 11 12
2CZ
C C
(1)
the parameter Z is known as the Zener ratio or elastic anisotropy factor (given for
different elastic tensor Table 23) When Zgt1 the Youngrsquos modulus is minimum
along lt100gt and a maximum along lt111gt and the representational surfaces for
Youngrsquos modulus in cubic crystals is shown in Fig 29 For the case when Z=1 the
cubic crystal would also be isotropic and the representation surface would be
spherical
CHAPTER 2 Literature Review
43
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
If the samples were random polycrystals which means samples are isotropic the
theoretical Youngrsquos modulus can be unambiguously given by [3]
3
[1 ( 3 )]E
B
(2)
While bulk modulus and shear modulus are
11 122
3
C CB
(3)
1
0 1
1 0
52( 6 )
(4)
where 0 44C 1 11 12( ) 2C C and
01
0 0
3( 2 )
5 (3 4 )
B
B
(5)
The theoretical value can be gained when the elastic constants are known Using the
Eqs (2-5) the theoretical Youngrsquos modulus E was calculated to be 496 GPa for
isotropic SiC materials when the elastic tensor obtained by Lambrecht et al was used
The calculated value is close to the Youngrsquos modulus measured by nano-indentation
(about 527 GPa) of isotropic bulk CVD SiC [62] But this value is higher than the
Youngrsquos modulus measured by nano-indentation of SiC in TRISO fuel particle which
is about 450 GPa [8 46]
By using the elastic tensors measured by sonic resonance in Snead et alrsquos study [1]
CHAPTER 2 Literature Review
44
the calculated Z (10026) is very close to 1 and it means the Youngrsquos modulus in
TRISO coated fuel particle may show no orientation effect According to Eqs (2-5)
the calculated Youngrsquos modulus is about 459 GPa under the elastic tensors given in
Ref [1] This value is close to the Youngrsquos modulus measured by nano-indentation in
TRISO fuel particle regardless of the orientation effect [1 8 46] Therefore for
TRISO fuel particle the recommended elastic tensors measured by sonic resonances
were supposed to be appreciable due to the scale and the microstructure similarities of
SiC materials [1]
Another significant factor which affects the Youngrsquos modulus is the density The
elastic modulus E at room temperature can be empirically expressed in an exponential
function of porosity pV as [63]
0 exp( )pE E CV (6)
where 0E is the elastic modulus and C is a constant of 357 for a pore-free bulk CVD
SiC pV is the ratio of the relative density difference to the theoretical density of SiC
(322 gcm3)
The relationship between density and Youngrsquos modulus of different kinds of SiC
materials measured by different methods were summarised in a previous study [1] as
shown in Fig 210 It has been found that the standard deviation of elastic modulus of
SiC is about plusmn 10 when the density is higher than 99 and increased to plusmn 15 for
porosity higher than 1
CHAPTER 2 Literature Review
45
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
232 Hardness
In a brittle material indentation hardness is defined as the mean pressure the material
will support under load and it is a complex property which could involve crack
initiation and propagation and the development of new surfaces during the
indentation process [1] Furthermore the value of hardness measured by indentation
also depends on external factors Due to the difference in dimensions of materials
such as the bulk small scale and thin film materials indentation on the nano- micro-
and even macro-scale have been used to measure the hardness [64] The hardness of
β-SiC related material has mainly been investigated by Vickers and nano-indentation
techniques (introduced in the later part of this session according to Ref [65]) as
summarized in Table 24 Reviews have found that the nano-hardness is generally
higher than Vickers hardness [1] which was attributed to the indentation size effect
Although few hardness values of β-SiC are available to be compared (given in Table
24) it shows the difference of hardness within a given sample Regardless of external
influences on the measurement of hardness generally it can be affected by grain size
or grain morphology [46] density composition and defects [1 8 66] To identify the
CHAPTER 2 Literature Review
46
controlling factor for hardness it is necessary to understand the deformation
mechanism of SiC under indentation
Table 24 Vickers and nano-indentation hardness of β-SiC related materials
Deformation mechanism Research into the deformation mechanism of SiC have
shown the availability of dislocation related plasticity [70] phase transformation
(cubic phase to amorphous) [71 72] fracture mechanisms [73] and also the
combination of any two or three [62 73]
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
First the dislocation related plastic deformation was found in single crystal 6H-SiC
[70] and the propagation morphology of dislocations was observed after indentation
as shown in Fig 211 This observation confirmes that the dislocation slip is a
Materials Vickers hardness (GPa) Nano-hardness (GPa) Ref
Single β-SiC (001) 28 -- [67]
CVD β-SiC 207-32 325-406 [466668]
FBCVD β-SiC -- 36-42 [8]
Sintered β-SiC 211-239 -- [69]
500 nm
CHAPTER 2 Literature Review
47
mechanism of plastic deformation from nucleation of a few dislocation loops (at or
near the theoretical strength) to extensive dislocation plasticity
Furthermore the dislocation related plastic deformation in polycrystalline CVD β-SiC
(with micro meters grain size) was first observed by Zhao et al [62] It was found that
the initiation of the plastic deformation was reflected by the burst (pop-in) of the
force-displacement curve which is similar as the initiation of plastic deformation in
metallic materials as shown in Fig 212(a)
According to the Hertzian contact theory [74] the burst was attributed to initiation of
the dislocation glide by comparing the shear stress generated under the indentation at
that load with the theoretical shear stress in β-SiC [62] During the whole indentation
process it was shown that shear slip is the predominant deformation mechanism and
that cracks were associated with the shear faults Figure 212(b) is one of the TEM
images showing the microstructure under indentation and it shows the dislocation
induced shear bands at one side of indent [62] which depend on the orientation of
grains
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation [62]
Second following the observations of phase transformation under indentation in
silicon [75] and the formation of SiC amorphous phase during high speed machining
(a) (b)
CHAPTER 2 Literature Review
48
process [71] the investigation of phase transformation under indentation was carried
out in SiC [7274] It has been demonstrated thermodynamically that the direct
amorphization is less likely to happen under nano-indentation [76] The
amorphization observed in single crystal SiC was attributed to the formation
propagation and accumulation of dislocations which formed the disordered phase at
the maximum stress region under a punch indentation [71] In SiC with nanometers
grain size the molecular dynamic study indicated thedominated deformation under
nano-indenation is a crossover of the indentation-induced crystallization to
disordering leading to amorphization [72] as shown in Fig 213
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Further studies demonstrated that the phase transformation from β-SiC to α-SiC is not
possible under nano-indentation because a pressure of nearly 100 GPa is needed [76]
even when assisted by high dislocation density shear stress and temperature This
simulation work concluded that the primary response of β-SiC to nano-indentation is
dislocation nucleation and propagation which has been confirmed by experimental
observations [62]
Third the plastic deformation of β-SiC under indentation was divided into two parts
CHAPTER 2 Literature Review
49
which are primary dislocation initiation and propagation and the formation of micro
cracks [73] The former contributes to 13 of plastic deformation under indentation
while the later provides 23 of total deformation The hardness related plastic
deformation could be explained well by this mechanism which included above two
process as discussed in previous studies [1 46 62] Moreover considering the effect
of micro cracks the deformation mechanism under indentation could be related to
other factors which could contribute to the formation of micro cracks such as
porosity grain boundaries and stacking faults in SiC [3]
Youngrsquos modulus and hardness of coatings in TRISO fuel particle can be measured by
nanoindentation due to the limitation of small dimension A typical
load-displacement curve and the deformation pattern under nanoindentation of an
elastic-plastic sample during and after indentation are shown in Fig 214 in which the
hc is contact indentation depth and hs is the displacement of the surface at the perimeter
of the contact [65] The peak load and displacement are Pmax and hmax respectively
and the diameter of the contact circle is 2a During unloading process the elastic
displacements are recovered and when the indenter is fully withdrawn the final depth
of the residual hardness impression is hf [65]
Nanoindentation hardness is the ratio of the load to the projected contact area of the
indentation The mean pressure that the material can support under indentation is
defined as the hardness From the loadndashdisplacement curve as in Fig 214(a) hardness
can be gain when the load is at the maximum value
A
PH max (7)
where A is the projected contact area
CHAPTER 2 Literature Review
50
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
The elastic modulus of the indented sample can be inferred from the initial unloading
contact stiffness S=dPdh ie the slope of the initial portion of the unloading curve A
geometry-independent relation involving contact stiffness contact area and elastic
modulus can be derived as follows
2A
S E
(8)
where szlig is a constant that depends on the geometry of the indenter (szlig=1034 for a
Berkovich indenter) [65] and Er is the reduced elastic modulus which accounts for the
fact that elastic deformation occurs in both the sample and the indenter Er is given by
CHAPTER 2 Literature Review
51
22 11 1 i
r i
vv
E E E
(9)
where E and υ are the elastic modulus and Poissonrsquos ratio for the sample respectively
and Ei and υi are the same quantities for the indenter For diamond Ei=1141 GPa and
υi=007[65]
For an indenter with a known geometry the projected contact area is a function of the
contact depth The area function for a perfect Berkovich indenter is given
by 2245 cA h Indenters used in practical nanoindentation testing are not ideally sharp
Therefore tip geometry calibration or area function calibration is needed A series of
indentations is made on fused quartz at depths of interest A plot of A versus hc can be
curve fit according to the following functional form
11 12 1 1282 4
1 2 3 8245 c c c c cA h C h C h C h C h (10)
where C1 through C8 are constants In some cases only the first three constants were
considered
The contact depth can be estimated from the load-displacement data using
maxmaxc
Ph h
S (11)
Where ε is a constant that depends on the indenter geometry (ε=075 for a Berkovich
indenter)
It is worth noting that high Youngrsquos modulus and hardness does not gurantee the
suitability of ceramic material to an engineering application because of the
importance of other mechanical properties such as fracture toughness and fracture
strength
CHAPTER 2 Literature Review
52
233 Fracture toughness
The definition of fracture toughness from Munz and Fett is [77] if a component or a
test specimen with a crack is loaded the stress intensity K1 increases with increasing
load until unstable crack propagation occurs at a critical value of K1 This critical
value is the fracture toughness (KIC) Therefore the measurement of fracture
toughness should be made on sample with a pre-crack however due to the small size
of SiC coating methods could be used are limited Although the most recently
developed micro-beam bending test could measure the fracture toughness of SiC in
TRISO fuel particles [78] this process is costly and time consuming because it
involves the preparation of micro-beams and notched cantilevers by focused ion beam
milling which limites the application of this technique
Indentation is now one of the most commonly used techniques to evaluate the fracture
toughness of ceramics and coating systems because it is easy to perform does not
need special samples and causes only negligible surface damage However some
researchers have declared that the indentation method is not suitable for the
measurement of fracture toughness [79 80] They concluded that the indentation
method does appear to represent some form of a complex crack arrest phenomenon
but that this occurrs in the presence of a multiple-crack path and a highly complex
residual stress field
Despite of these considerations the indentation method is an effective way to
compare the fracture behaviour of materials [80] particularly for small size specimens
and it provides information about the crack initiation and propagation Figure 215 is
the most typical characterization of the crack system generated by Vickers indentation
[81] This crack system is termed as median-radial cracking and consists of
approximately semi-circular cracks
CHAPTER 2 Literature Review
53
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
The mode of crack initiation and propagation under an indenter proposed by Chiang
et al explains many of the features observed in indentation crack patterns and is the
most recent advance [82] It was found that radial cracks are the first to initiate
trigged by a combination of the highly tensile surface stress field and the availability
of surface flaws [74 82] These cracks grow on unloading and can either propagate
into the plastic zone (half penny cracks) or terminate in the elastic zone (Palmqvist
cracks) [83] depending on the microstructure of the material
For different types of crack modes such as half-penny and Palmqvist cracks different
equations were developed based on theoretical analysis of stress field and empirically
calibrations to calculate the fracture toughness under indentation For example in the
half penny crack model the Vickers indentation fracture toughness was most
frequently determined using the relationship proposed by Anstis et al [84] This
equation was first inferred based on isotropic materials and it is suitable for general
application to well-developed cracks [84]
1 2
3 2( )IC
E PK
H c (12)
Where P is the indentation load c is the radial crack length from indentation centre to
crack tip E and H are the Youngrsquos Modulus and hardness of the materialand χ
denoted as the geometrical constant which is independent of the materials The Eq
CHAPTER 2 Literature Review
54
(12) was developed on the basis of half penny cracking in homogeneous brittle
materials under high load for example in glasses [84]
The above information shows that it is possible to compare fracture toughness under
indentation in SiC coatings with different microstructures The fracture toughness of
SiC could depend on a large number of factors such as grain size porosity micro
cracks and inclusions which could dissipate the fracture energy from the main crack
[3] According to a previous review [1] fracture toughness of SiC peaks at the grain
size range of 1-5 microm So fracture toughness of SiC in TRISO fuel particle is likely to
be influenced by the grain size due to the similar range of grain size Although micro
cracks and pores could improve fracture toughness they would decrease the strength
[3] which is detrimental for the safe design of fuel particles Over several decades
studies have worked to improve the fracture toughness by introducing a
heterogeneous microstructure such as weak grain boundary phases [85] In the
heterogeneous phase toughening mechanism the cracks could initiate in or be
reflected into weak defects and thereby dissipate the fracture energy for the main
crack propagation Furthermore the distribution of grain boundary character (the
crystallagraphic type and frequency of grain boundaries) and morphology could
influence the fracture toughness [85 86] Different grain boundary orientations and
their frequency were found to affect the fracture toughness by controlling the
intergranular fracture of materials [86] Different grain morphologies such as
elongated grains could increase the fracture toughness by crack bridging or by
generating micro cracks along grain boundaries or triple junctions [85] No
heterogeneous phase is supposed to exist in SiC in TRISO fuel particles so the
fracture toughness is most likely to be affected by grain morphologies or as-deposited
defects
According to the Griffth fracture theory once the size of the critical flaw is the same
the fracture toughness is propotional to the fracture strength which is another
CHAPTER 2 Literature Review
55
parameter used in modelling of the probability of the failure of fuel particle
234 Fracture strength
For brittle materials the fracture strength is best considered as a distribution rather
than a fixed value as the flaws (such as surface cracks pores and inclusions) from
which fracture initiates vary in size and type (result in different frature strength value)
between nominally identical samples [3] The Weibull approach is a commonly used
empirical method to characterise the strength of a brittle material It assumes a simple
power-law stress function (eg in Eqs (18-20)) for the survival of the elements
which is integrated over the body volumesurface area (as shown in Eqs (19) and
(21)) In many cases this function gives results in the form of Weibull modulus (m in
Eq (19)) and characterstic strength which describe the width and magnitude of the
strength distribution [3] The Weibull modulus is the slope of Log-Log distribution
function of the survival of elements and strength (Eq (19)) For engineering
application the high Weibull modulus represents the small variation of the fracture
strengthes for a given material
Higher Weibull modulus reflects lower variability of the strength and it is typically in
the range of 5-20 [3] The commonly used strength test methods for bulk ceramics are
uniaxial tension three- and four-point bending However the small dimensions of
TRISO fuel particles make it difficult to measure the strength by those conventional
methods As a consequence some specific methods were developed in the last few
decades such as O-ring test [87 88] C-ring test [88] hemisphere bending [10]
internal pressurization [89] and crush test [5 89 90] The schematic of easily
repetitive fracture strength test geometries are given in Fig 216 and the obtained
fracture strength by different methods was shown in Table 25
CHAPTER 2 Literature Review
56
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Methods L
f (MPa) Weibull Modulus F
f (MPa) Ref
O-ring compression 596-1412 41-66 -- 87
O-ring compression 1050-1890 48-94 -- 88
C-ring Compression 980-2200 40-90 -- 88
Semi-spherical bend 720-1350 70-80 340-620 10
Inner pressurization -- 43-62 222-448 89
Crush test -- 58-75 356-427 89
Crush test 770-1324 40-73 330-647 5
Crush test 1484-1721 135-183 1045-1091 90
L
f Local fracture strength F
f Fracture strength of the full particle
The local fracture strength is in the range of 596-2200 MPa and the fracture strength
of the whole particle varies from 222 MPa to 1091 MPa Such significant variation is
tought to be caused by the differences in specimen size and loading mode which were
related to the nature of the Weibull distribution [1 3] It has been demonstrated that
specimens with larger volumesurface area (under the same loading mode) have lower
strength because there is an increased probability that a larger flaw exists in a larger
body Similarly when there is no volume difference the loading mode which stresses
larger area has lower local fracture strength [3] These discussions show the
importance of regulating the fracture strength test method and producing specimens
with regular shape and size
CHAPTER 2 Literature Review
57
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
The modified crush test developed by Byun et al [5] is recommended for the fracture
strength measurement of SiC in TRISO fuel particles because it considered the effect
of contacting area between SiC shell and plunger which reduced the variation and
uncertainty of the stress distribution under tensile stress
Modified crush test When a partial spherical shell is diametrically loaded by an
external load F concentrated on a small circular contact area of radius 0 the
maximum membrane stress and bending stress are given by [91]
2
1 2
1membrane
FC
t
(13)
CHAPTER 2 Literature Review
58
2 2
1bending
FC
t
(14)
where ν is the Poisson ratio t is the thickness of shell and C1 and C2 were defined as
2
1 0115004022050 C (15)
)27031exp(204412 C (16)
2 2 2 1 4
0[12(1 ) ( )]r R t (17)
max membrane bending (18)
where max (L
f ) is the fracture strength for locally loaded specimens R is the outer
diameter of shell t is the thickness of the SiC shell The distribution of local fracture
strength is analysed by the Weibull distribution function which presents the
cumulative probability of failure P as [5]
mL
f
E
m
s
F
fSdAP
00
exp1exp1
(19)
where L
f m 0 and ES are the local fracture strength the Weibull modulus the
characteristic sterngth and the size effect factor respectively The size effect factor is
dAS
m
s L
f
F
f
E
Byun et al [5] used the probability estimator as follows
1
N
iPi (20)
where iP is the probability of failure for the i th-ranked strength and N is the
CHAPTER 2 Literature Review
59
sample size The increased probability that the full SiC shell has more critical flaws
compared with the stress-weighted surface is corrected by the size effect and the
fracture strength of the full shell (F
f ) is given
L
f
m
L
f
m
F
E
L
EF
ftR
r
S
S
1
2
2
0
1
)(4
(21)
After adjusting the size effect the fracture strength of the full particl of different SiC
coatings could be compared In a previou study [87] the difference of the fracture
strength was attributed to the microstructural variations which were determined by
deposition conditions [87] More detailed analysis [510] showed that the variation of
fracture strength was due to factors such as porosity roughness of the IPyCSiC
interface and grain size For example Evans et al [10] observed that the surface
roughness influenced the failure of the particle withstrength improved by reducing
the inner surface roughness According to above discussion the variation of Weibull
modulus could be attributed to the different test methods flaw distribution and sample
size [3 5]
Micostructure and mechanical properties of as-deposited SiC are reviewed above
which may change after high temperature treatment and the degree of evolution could
be different due to variational deposition conditions of SiC coatings As summarized
in a previous study [92] one of the critical properties for SiC layers in TRISO fuel
particle is that the microstructure remains unchanged after thermal treatment at 2000
ordmC for 1 hour in an inert atmosphere as determined by electron microscopy and X-ray
diffraction
235 Effect of thermal treatment on SiC
The SiC with perfect crystal structure tends to have good high temperature thermal
stability however due to the concentration and type of imperfections generated
CHAPTER 2 Literature Review
60
during deposoition process its thermal stability could be affected Defects such as
stacking faults vacancies and interstitials in as-deposited SiC coatings affect the
microstructural change after thermal treatment [93-96] For example the phase
transformation from β- to α-SiC generally happened at temperatures above 2100 ordmC
[19] but it could take place at lower temperature (gt 1700 ordmC) in special cases (eg
CVD β-SiC deposited on Si substrate with high amount of stacking faults) [93]
During high temperature thermal treatment (about 2000 ordmC) of CVD β-SiC one
significant microstructural change would be the annihilation of stacking faults [94
95] A thermodynamics study [94] has shown that the mechanism of reduction of the
stacking faults was due to the diffusion of Si or C atoms and it also demonstrated that
the migration energy of Si atoms was smaller than C atoms Considering the
abundance of intrinsic defects (section 222) there has been little investigation of
their effects on microstructure change of β-SiC after thermal treatment Furthermore
the effects of high temperature thermal treatment on mechanical properties such as
the hardness Youngrsquos modulus [97] and strength [98] have been carried out Their
results showed that mechanical properties showed little change when the treatment
temperature was lower than 2000 ordmC while there was decrease in the strength after
thermal treatment at 2100 ordmC
24 Microstructure and properties of pyrolytic carbon
In this part the microstructure of carbon related material is reviewed first which is
followed by the measurement of Youngrsquos modulus and hardness Furthermore to
know the controlling factor on mechanical properties of PyC coatings different
deformation mechanisms under indentation are introduced A brief review about effect
of thermal treatment on properties of PyC coatings is given
CHAPTER 2 Literature Review
61
241 Microstructure of pyrolytic carbon
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
The graphite structure consists of graphene sheets having localized in-plane σ (sp2)
hybrids bonds and delocalized out of plane π (pz) orbital bonds connecting graphene
sheets The out-of-plane bond is a van der Waals interaction which is much weaker
than sp2 and sp
3 hybrids Pyrolytic carbon is a material with some covalent bonding
between its graphene layers as a result of imperfections (defects) in its structure [99]
Figure 217 gives schematics and TEM images showing different microstructures of
PyC with different densities The growth features are polyhedral or conical shape in
high density pyrolytic carbon (Fig 217 (ab)) but are globular in low density
pyrolytic carbon (Fig 217(cd)) [15] It shows that the microstructure of pyrolytic
carbon consists of growth features between 200 nm- 1000 nm in size (Fig 217 (b)
and (d)) [15] Pores were formed at the boundaries or triple junctions between growth
(a) (b)
(c) (d)
CHAPTER 2 Literature Review
62
features
According to previous studies [15101] individual growth features contain crystallites
(domains) as shown schematically in Fig 218(a) They are composed of a series of
curved graphene layers randomly rotated with respect to each other along the c-axis
[101] The dimensions of the crystal were described by La (diameter of crystal along
the χ direction) and Lc (height of the crystal perpendicular to χy plane) as shown in
Fig 218(a) Regarding the definition of the PyC there are defects within the growth
features together with crystallites A local atomic structure of less ordered graphene
layers is shown in Fig 218(b) which could reflect the plane defects in graphene
layers [102]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
A high density of defects such as dislocation loops and kink bands were observed in
ball milled graphite by HRTEM as shown in Fig 219(a) The distorted
microstructure of graphite was also inferred from the striped diffraction points in
selected area electron diffraction image (Fig 219(b)) [103] since the diffraction
pattern gives information on orientation of crystal planes Compared with ball milled
graphite the HRTEM image of pyrolytic carbon has higher amount of defects as
shown in Fig 19(c) which is reflected from the highly distorted lattice planes and low
texture The selected area electron diffraction image of pyrolytic carbon (Fig 219(d)
with eperture diameter of 200 nm) showed arc shaped diffraction patterns [15 104]
The arc represents the overlap of diffraction patterns from different graphite domains
CHAPTER 2 Literature Review
63
with different orientations and this indicats that the microstructure is more distorted
eg smaller domain size and increased random orientation of domains In heavily
disordered PyC it is not possible to observe the individual dislocations or other
defects which is thought to be due to the numerous defects such as tilt boundaries
which obscure individual defects as described in Ref [105]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
Raman spectroscopy is one of the most effective techniques to characterise the defects
in carbon materials and has previously been used to characterise the microstructure of
PyC [15 106] These spectra can identify even quantify the microstructure such as
crystallite boundaries and size disorders (5-memebered rings) and chemical bonding
type Figure 220 shows the evolution of the Raman spectra with the change of the
CHAPTER 2 Literature Review
64
in-plane defect types The carbon spectra of Fig 220(a-c) showed increased and
broadened D signal and the main in-plane defects observed in these structures were
supposed to be domain boundaries [15] In Fig 220(d-e) the D signal became shaper
which was attributed to the formation of five-member rings [15]
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
The high density of disorders such as in-plane domain boundaries makes the Raman
bands become broder and overlapped with each other as shown in Fig 220(c) which
inferred the structure of turbostratic or high density PyC [10 15] According to
previous studies [106 107] the broadened Raman bonds could be deconvoluted into a
number of peaks which correspond to different types of disordered structure in
carbon materials Figure 221 is an example of a first order Raman spectra fitted with
Lorentzian and Gaussian functions and it includs I (~1170 cm-1
) D (~1330 cm-1
) Drdquo
(~1500 cm-1
) G (~1580 cm-1
) and Drsquo(~1618 cm-1
) bands [106] The Drdquo peak was
CHAPTER 2 Literature Review
65
attributed to amorphous carbon with a certain amount of sp3 carbon [106108] which
could reflect the interstitial defects coupling to the graphene layers or adjacent
domains [109]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
242 Mechanical properties of pyrolytic carbon
The different deformation mechanism of carbon materials compared to ceramic
materials results in distinct force-displacement curves which show the complete
recovery of the unloading curve [110 111] Therefore we describe the mechanical
properties of PyC coatings and deformation mechanism of carbon materials
2421 Youngrsquos modulus and hardness
Due to the importance of PyC in the nuclear industry mechanical properties were
measured by three-point bending [102 112] and nano-indentation [113-115] Table
26 gives the Youngrsquos modulus and hardness of PyC measured by different methods
In three-point bending tests the mechanical properties were functions of density
orientation angle and domain size No individual factor could clearly explain the
variation in Youngrsquos modulus strength or fracture toughness [112116] In previous
nano-indentation tests the low density PyC was found to have low hardness and
Youngrsquos modulus [114] whereas the influence on mechanical properties was
CHAPTER 2 Literature Review
66
uncertain which could be due to lack of investigation about the deformation
mechanisms
Table 26 Summary of the hardness and Youngrsquos modulus for PyC measured by
different methods
Methods Density range
(gcm3)
Youngrsquos modulus
(GPa)
Hardness
(GPa)
Ref
3-point-bending 150-212 310-427 -- 112
137-206 165-281 -- 116
Nano-indentation 185-190 255 + 2 -- 114
165-203 235-270 30-44 115
155-187 70-150 05-18 115
135-212 125-346 15-48 113
Youngrsquos modulus was changed from PSI to GPa
Figure 222 is a schematic of the typical force-displacement curve of different kinds
of materials under indentation [65110111] The curve of carbon materials shows a
completely recovery and no net displacement after unloading as shown in Fig
222(a) In carbon materials the force-displacement curve formed a closed loop and
this phenomenon was called anelastic deformation behaviour [14 117] This was
related to the internal friction of materials but there is controversy regarding the
sources of the internal friction [14105111] Since the force-displacement curve gives
information about the energy change during indentation the deformation behaviour of
carbon material can be analysed by the energy method
The energy distribution under indentation is shown in Fig 222 which includs the
hysteresis energy (Uh) and unloading energy (Uunloading) and the total energy (loading
energy Uloading) is the sum of the above two energies [110] As shown in Fig 222 the
ratio of the hysteresis energy to total loading energy could be different for different
microstructure of carbon materials [118] The ratio could be used to estimate the
CHAPTER 2 Literature Review
67
flexibility of elasticityductility [110119] For example a low ratio corresponds to
higher elasticity whist a high ratio meants higher ductility
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
The different force-displacement curve of carbon materials was compared with the
irreversible deformation behaviour of materials with linear elasticity such as SiC as
shown in Fig 214(a) [65] In linear elastic deformation the final displacement of hf
was left after complete unloading and the unloading curve nearly followed the linear
relationship Furthermore the area between the loading and unloading curves
represents the energy consumed by the plastic deformation which could be due to the
movement of dislocations and formation of micro cracks [1 62]
2422 Deformation mechanism
Reversible slip and sliding friction theory In this theory the complete recovery of
strain was due to the reversible slip of graphene planes and the energy loss was
attributed to the friction during the slip which was caused by a compressive stress on
the graphene layers [110111] The theory was obtained by considering an arbitrary
grain located at some position in a radially declining hydrostatic stress field below a
spherical indenter as shown in Fig 223 [110111] The force was resolved into
CHAPTER 2 Literature Review
68
compressive stress perpendicular to and shear stress parallel to the slip plane By
using the equation proposed by Kelly [120] the shear component (τ τ0 shear stress
with and without friction respectively) may be expressed as τ= τ0 +μσ where μ is a
friction coefficient and σ is normal stress component To initiate slip between
graphene layers the shear stress needs to exceed some critical value Therefore the
inter-layer slip with friction was supposed to be the mechanism of anelastic
deformation The authors [110111] also concluded that the hysteresis during
unloading appeared to be a natural result of friction between the graphene layers but
additional mechanisms were supposed to be operating in the different forms of
graphitic materials Furthermore the study did not give a clear explanation about how
the reversibility of the basal plane slip was realized
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Dislocation pileup theory This idea was derived from isotropic carbon after thermal
treatment at the temperature range of 880-2600 ordmC by using micro indentation [121]
The authors attributed the unique unloadingreloading behaviour of the
well-graphitized carbons to the slip of dislocation networks on graphitic basal planes
which is partially or fully reversible It is supposed that the dislocations could pile up
at grain boundaries as in metals The stress at grain boundaries due to dislocation pile
ups could reverse the dislocation movement during indentation unloading but it did
CHAPTER 2 Literature Review
69
not explain why deformation behaviour of PyC is unlike that of metals This is also
the reason that other researches [105] doubt this theory because it fails to explain the
nature of the reversible behaviour [121]
Kink band theory It was suggested that the origin of the loops obtained in single
polycrystalline and porous carbons is the formation of incipient kink band and kink
bands [105] The kink band model was proposed by Frank and Stroh [122] as
shown in Fig 224 which showed pairs of dislocations of opposite sign nucleate and
grow at the tip of a thin elliptical kink (not clear about the nature) The stability of
kink bands depended on a shear stress [122]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
In this theory since the dislocations were confined to the basal plane the hysteresis
process was attributed to the reversible movement of the dislocation along a long
distance The same mechanism was used to explain the deformation behaviour of the
bulk polycrystalline graphite The microstructural change under indentation should
first be related to the kink band initiation and then further microstructure change
could be reflected in the accumulation of other chemical bonds which could resist
dislocation glide
CHAPTER 2 Literature Review
70
2423 Effect of thermal treatment on properties of PyC
The effect of thermal treatment on the microstructure of carbon materials has been
widely studied [112 123 124] The change of the microstructure of carbon materials
during thermal treatment mainly involves the growth of the domain size (in-plane
crystal size along a axis) La and (along c axis crystal size) Lc with the increase of
temperature For different kinds of carbon materials these evolutions started at
different temperatures For example the crystal growth in-plane happened at 400-600
ordmC for graphitisable carbon and could continue up to high temperature the
coalescence of crystallites along the c-axis started above 1000-1200 ordmC the
coalescence of crystallites along ab direction occurred at temperature above 1400 ordmC
[124] For carbons with strong cross-linking (non-graphitisable) the coalescence of
domains usually happened at temperatures higher than 2400 ordmC [124] Although the
increase in anisotropy and density during processing of coated particle fuel was
reported by Hunn et al [11] no change in texture was identified on PyC due to the
post deposition of SiC shown in Lopeacutez-Honorato et alrsquos study [125] Furthermore no
significant change of mechanical properties was obtained after thermal treatment at
temperatures in the range 1000-1980 ordmC in PyC coatings with density of about 19
gcm3 [97] however a decrease of Youngrsquos modulus was observed in high density
(above 2 gcm3) PyC coatings [125] It was assumed that certain microstructures of
PyC would be less affected by thermal treatment
25 Summary
The microstructure and mechanical properties of SiC and PyC were reviewed in this
Chapter and the information obtained is summarized below
(1) It is common for SiC to have defects such as stacking fautls and dislocations
non-stoichiometry and point defects due to their low formation energy
particularly in SiC deposited by chemical vapour deposition
CHAPTER 2 Literature Review
71
(2) Defects interact with each other Stacking faults could be the result of gliding
of partial dislocations Vacancies promoted diffusion of antisites forming
antisite clusters
(3) The Youngrsquos modulus of SiC coatings in TRISO fuel particle is affected
mainly by texture and porosity
(4) Hardness related plastic deformation in single and polycrystalline (nano-meter
or micro-meter grain size) SiC is related to dislocation propagation fracture
of crystallites or phase transformation
(5) A combination of indentation together with electron microscopy is an
effective way to study the fracture behaviour of SiC coatings in TRISO fuel
particle
(6) Fracture strength of SiC coating in TRISO fuel particle varies significantly in
different measurements and the modified crush test is recommended The
interface roughness and porosity are found to be main factors controlling
fracture strength of SiC coatings
(7) The typical change of microstructure after thermal treatment in SiC is the
annihilation of stacking faults through the diffusion of vacancies
(8) The disorder in PyC coatings could be significant such as domain boundaries
and 5-membered rings Raman spectroscopy together with transmission
electron microscopy are important techniques to characterize these disorders
(9) Carbon related materials show hysteretic deformation behaviour under
indentation Different deformation mechanisms are proposed which all relate
to the slip of graphene layers
CHAPTER 2 Literature Review
72
26 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modeling J Nucl Mater 371 (2007)
329-77
[2] DT Goodin Accident condition performance of fuels for high-temperature gas
-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[3] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
[4] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[6] X Li B Bhushan A review of nanoindentation continuous stiffness
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[7] A Grabulov U Ziese HW Zandbergen TEMSEM investigation of
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fatigue and 3-D crack reconstruction by focused ion beam Scripta Matterialia 57
(2007) 635-38
[8] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
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[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
Transgranular Cleavage J Mech Phys Solids 34 (1986) 477-97
[10] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
Fuel Particles for High-Temperature Gas-Cooled Reactors J Am Ceram Soc
56 (1973) 36-41
CHAPTER 2 Literature Review
73
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
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Nucl Mater 374 (2008) 445-52
[12] D G Martin Considerations pertaining to the achievement of high burn-ups in
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[13] G K Miller D A Petti D J Varacalle J T Maki Consideration of the effects
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Nucl Mater 295 (2001) 205-12
[14] G K Miller D A Petti J T Maki Consideration of the effects of partial
debonding of the IPyC and particle asphericity on TRISO-coated fuel behaviour
J Nucl Mater 334 (2004) 79-89
[15] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
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microstructure Carbon 47 (2009) 396-410
[16] R Cheung Silicon carbide microelectromechnical systems for harsh
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[17] M Iwami Silicon carbide fundamentals Nuclear instruments and methods in
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[18] V V Pujar J D Cawley Effect of stacking faults on the X-ray diffraction
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[19] W F Knippenberg Growth phenomena in silicon carbide Philips Res Report
18 (1963) 161-274
[20] P Krishna RC Marshall CE Ryan The discovery of a 2H-3C solid state
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[21] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J AmCeramSoc 84 (2001) 3013-16
[22] R Stevens Defects in silicon carbide J Mater Sci 7 (1972) 517-21
CHAPTER 2 Literature Review
74
[23] C Wang J Bernholc Formation energies abundances and the electronic
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[24] P Kaumlckell JFurthmuumlller FBechstedt Stacking faults in group-IV crystals an ab
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[25] U Lindefelt H Iwata S Oumlberg P R Briddon Stacking faults in 3C- 4H and
6H-SiC polytypes investigated by an ab initio supercell method Phys Rev B 67
(2003) 155204-15
[26] P T B Shaffer A review of the structure of silicon carbide Acta Crystal Sec B
25 (1969) 477-88
[27] P J H Denteneer W v Haeringen Stacking-fault energies in semiconductors
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[28] X G Ning H Q Ye Experimental determination of the intrinsic stackingfault
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[29] P J H Denteneer W v Haeringen Ground-state properties of wurtzite silicon
carbide Solid State Commun 65 (1988) 115-19
[30] P J H Denteneer Stacking-fault energies in silicon diamond and silicon
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[31] K Karch G Wellenhofer P Pavone U Roumlssler D Strauch Proceedings of the
22nd international conference on the physics of semiconductors 1995 p 401
[32] C Cheng V Heine and R J Needs Atomic relaxation in silicon carbide
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[33] M Marinova A Mantzari E K Polychroniadis Some recent results on the
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[34] VV Pujar JD Cawley Computer simulations of diffraction effects due to
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(2001) 2645-51
[35] B Reznik DGerthsen W Zhang K J Huumlttinger Microstructure of SiC
deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499ndash508
CHAPTER 2 Literature Review
75
[36] T Mitani S Nakashima H Okumura et al Raman Scattering Analyses of
Stacking Faults in 3C-SiC Crystals Mater Sci Forum 527-29 (2006) 343-46
[37] G Newsome LL Snead T Hinoki et al Evaluation of neutron irradiated
silicon carbide and silicon carbide composites J Nucl Mater 371 (2007) 76-89
[38] httpwwwtfuni-kieldematwisamatdef_enkap_5backboner5_4_2html
[39] P Pirouz J W Yang Polytypic transformations in SiC the role of TEM
Ultramicroscopy 51 (1993)189-214
[40] S Guha J M DePuydt J Qiu Role of stacking faults as misfit dislocation
sources and nonradioactive recombination centres in II-VI heterostructures and
devices Appl Phys Lett 63 (1993) 3023-25
[41] AK Agarwal SKrishnaswami JRichmond et al Influence of basal plane
dislocation induced stacking faults on the current gain in SiC BJTs Mater Sci
Forum 527-29 (2006) 1409-12
[42] N W Mueggenburg H M Jaeger S R Nagel Stress transmission through
three-dimensional ordered granular arrays Phys Rev E 66 (2002) 031304
[43] S Somiya Y Inomata Silicon carbide ceramics-2 ceramic research and
development in Japan p1-18
[44] A Gali N T Son E Janzeacuten Electrical characterization of metastable carbon
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[45] C Chu Y Luand M Hon Growth characteristics of β-SiC by chemical vapour
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[53] E Janzeacuten N T Son N Magnusson A Ellison Intrinsic defects in high-purity
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[67] D M Teter Computational alchemy the search for new superhard materials
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[78] X Zhao RM Langford J Tan P Xiao Mechanical properties of SiC coatings
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[79] G D Quinn RC Bradt On the Vickers indentation fracture toughness test J
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[89] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
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[92] SDKurbakov TAMireev Deposition of high-density silicon carbide coatings
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[96] Z G Cambaz G N Yushin Y Gogotsi K L Vyshnyakova L N
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[97] I J V Rooyen J H Neethling J Mahlangu Influence of temperature on the
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[98] I J v Rooyen J H Neethling P M v Rooyen The influence of annealing
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136-46
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[100]J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
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[101]Z Q Li C J Lu Z P Xia Y Zhou Z Luo X-ray diffraction patterns of
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[102]W P Hoffman W C Hurley P M Liu T W Owens The surface topography
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[103]J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
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[105]M W Barsoum A Murugaiah S R Kalidindi T Zhen YGogotsi Kink bands
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[106]J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
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[107]A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
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[108]A C Ferrari Raman spectroscopy of graphene and graphite Disorder
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[109]J N Rouzaud A Oberlin Carbon films Structure and microtexture (optical and
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[110]N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
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[111]N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
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[112]J C Bokros R J Price Deformation and fracture of pyrolytic carbons
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[113]E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure
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[115]G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
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[117]L M Brown In H Libelt R Talreja Fatigue and creep of composites
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[118]M Skai The Meyer hardness A measure for plasticity J Mater Res 14 (1999)
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[119]M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics ndash adding
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[121]M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated
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[122]F C Frank A N Stroh On the theory of kinking Proc Phys Soc 65 (1952)
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[123]R F Franklin Royal Society London A London 1951 209 196
[124]F G Emmerich Evolution with heat treatment of crystallinity in carbons
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[125]E Loacutepez-Honorato P J Meadows R A Shatwell P Xiao Characterization
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881-90
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
83
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC
Coatings Measured by Indentation
31 Introduction
The silicon carbide (SiC) coating is the most important component for structural
integrity of Tri-isotropic (TRISO) fuel particles as it sustains most of the internal
pressure produced by the fission gases produced in the kernel [1-3] Youngrsquos modulus
and hardness are mechanical properties used in modeling to estimate the failure
probability of TRISO fuel particles [4] The values at room temperature are used due
to the fact that the Youngrsquos modulus slightly decreased at elevated temperature in SiC
material and the higher value could be kept until the temperature reached 2000 degC [1]
It was also found that SiC material with higher hardness at room temperature
maintains higher hardness values at temperatures up to 1600 degC [1] To achieve a
reliable fuel design a better understanding of the mechanical properties of the SiC
layer at room temperature needs to be established
It is difficult to use traditional methods to measure hardness and Youngrsquos modulus
due to the small dimension of the TRISO fuel particles (~1 mm) Nano-indentation
has made it possible to measure the hardness and Youngrsquos modulus accurately [5 6]
for a coating of such a small dimension Furthermore this method also offers the
ability to study the deformation behaviour under the indentation [7-12] as the
indentation stress field is of a localized character
Loacutepez-Honorato et alrsquos [5] study of SiC deposited at 1300 degC by fluidized bed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
84
chemical vapour deposition (FBCVD) showed that the SiC coatings produced under
those conditions had high hardness (gt 42 GPa) and Youngrsquos modulus (~455 GPa)
They found that even samples with the composition of SiC+C or SiC+Si showed high
mechanical properties It was shown that the coatings had sub-micrometer (lt1 μm
diameter) grain size but due to the complex microstructure the mechanism controlling
the hardness and Youngrsquos modulus was unknown Researchers [10 11 13-16] have
made efforts to study the deformation mechanism under indentation in SiC single
crystals and polycrystals (with a grain size lt 100 nm or grain size gt 1μm) Szlufarska
et al [15] suggested a crossover mechanism from indentation-induced crystallization
to deformation-dominated amorphization in nano-crystalline SiC
From the work reported [11 16 17] it is clear that dislocation initiation and
propagation is the primary response for the plastic deformation under an indentation
in single crystal and polycrystalline (gt 1μm) SiC Further it has also been found
while studying the microstructure [11 16 17] that defects such as stacking faults and
dislocations were present in these polycrystalline (gt 1 μm) SiC materials
(nano-indentation hardness less than 36 GPa) However the amount of defects were
lower compared to the low temperature (ie 1300 o
C vs 1500 o
C) FBCVD SiC [5]
The discrepancies in the microstructure and mechanical properties still demand
further explanation on the deformation mechanism of low temperature FBCVD SiC
This chapter focus on the fundamental study on the mechanical properties of SiC we
have investigated the Youngrsquos modulus and hardness of three sub-micrometer FBCVD
SiC coatings using the indentation method The microstructure and mechanical
properties are explained on the basis of defects observed with a transmission electron
microscope (TEM) The deformation behaviour underneath a nano-indentation is
discussed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
85
32 Experimental details
Silicon carbide (SiC) coatings were produced on top of highly-dense pyrolytic carbon
coatings using fluidized-bed chemical vapour deposition (FBCVD) method The SiC
coatings with varied stoichiometry and deposited at low temperature of 1300 oC by
Loacutepez-Honorato et alrsquos [5] were chosen and studied in this Chapter Table 1 gives the
deposition conditions of these coatings which were found and demonstrated to give
superberb mechanical properties in prevous studies [5] Figure 31(a) and (b) show the
polished cross-section (x-y plane) and (b) polished external surface section (x-z plane)
of TRISO fuel particles (defining the directions used in the later part of this Chapter)
Densities were measured by the Archimedes method in ethanol (density is the mean
value of three tests the weight of SiC shells is 01-03 g) Composition was measured
by Raman spectroscopy (Renishaw 1000 Raman system with a 514 nm argon laser
source) with a single spot measurements of around 1 microm diameter through an times50
objective lens as shown in Fig 31 (c) Two peaks at around 794 and 970 cm-1
are for
SiC and the asymmetric peaks around 200-500 cm-1
and 1500 cm-1
are acoustic SiC
and second order SiC respectively (S1 coating) [5] Carbon peaks are around 1360
and 1600 cm-1
(S2 coating) and the peak at 520 cm-1
represents silicon (S3 coating)
[5] It was estimated that the excess C amount is less than 1 at in S2 by measuring
the intensity ratios of I1600I794 and compared to previous study [18] where Raman
spectroscopy and elemental analysis (EPMA AES and XPS) were used
The phase and composition were also analysed using X-ray diffraction (XRD PW
1830 Philips Eindhoven The Netherlands) with Cu Kα1 radiation Figure 31(d)
shows the XRD spectra of the three types of SiC coatings All three coatings exhibit
the β-SiC phase A very small shoulder peak around 2θ=345deg was also obtained from
the coatings which indicated the presence of stacking faults No evidence of a Si or C
peak was found in the XRD result This was probably due to the fact that the
additional levels of Si and C were very small (le 1at ) and it would be difficult to
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
86
identify these traces using XRD [5 19]
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
Codes H2MTCS (volvol) Additives Temperature Density (gcm3)
S1 (SiC) 10 01vol Propylene 1300 o
C 3173 + 0029
S2 (SiC+C) 10 10 vol Propylene 1300 o
C 3135 + 0034
S3 (SiC+Si) 10 -- 1300 o
C 3188 + 0002
SiC+C or SiC+Si means that nearly stoichiometric SiC with low excess C or Si less than 1 at
Productions of samples are contributed by Dr Eddie Loacutepez-Honorato
SiC coated fuel particles were hot mounted in copper-loaded conductive resin To
reduce the influence of the surface roughness the FBCVD SiC coatings were first
ground down to obtain a flat surface where the nano-indentation could be carried out
The flat surface was further polished using increasingly finer diamond suspensions
until frac14 μm and finally polished using a 003 μm colloidal silica suspension The
thickness of the coating after final polishing was estimated to be around 60 μm A
final surface roughness of lt 5 nm was detected by atomic force microscopy (AFM)
Youngrsquos modulus and hardness were measured using a nano-indenterTM
XP (MTS
System Corp USA) and a micro-indenter (CSM Instruments Switzerland)
Nano-indentation was made using a Berkovich indenter calibrated with a standard
silica specimen Before the measurement the initial contact of the indenter with the
specimen surface was checked and the compliance of the loading column was
corrected Arrays of indentations were performed on each specimen with an interval
of 20 times the indentation depth between each indentation The penetration depth for
the measurement of Youngrsquos modulus and hardness was 500 nm All data were
analysed using the Oliver and Pharr method [7] Micro-indentation was made using a
Vickers indenter at a maximum load of 3 N and the interval between each indentation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
87
was also kept to 20 times the indentation depth of ~26 μm
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
(c)
(d)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
88
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Moreover a high purity (gt999995) and fully dense polycrystalline 3C-SiC bulk
(diameter 3 cm thickness 15 cm) sample fabricated by static CVD (Rohm amp Haas
Ltd UK) was used as a reference sample in order to confirm the accurate mechanical
property measurements for FBCVD SiC coatings The Raman spectroscopy of bulk
CVD SiC was the inset in Fig 31(b) and no excess C or Si was found in it
To observe the grain morphology more clearly the finely polished (no scratch could
be seen under optical microscopes times50) cross-section (Fig 1(a)) of the coatings were
chemically etched using Murakamirsquos solution (10 g sodium hydroxide and 10 g
potassium ferricyanide in 100 ml of boiling water) The surface morphology of
coatings was characterized using scanning electron microscopy (Field emission gun
Philips XL30 FEG-SEM) A transmission electron microscope TEM (FEG-TEM
Tecnai TM
G2 F30 U-TWIN 300KV) was used to study the microstructure of the
coating layer before and after indentation For cross-sectional analysis of indentations
TEM samples were made from thin plates which are parallel to one edge and through
the center of Berkovich indentation using a focused ion beam (FIB FEI Nova 600
Dual Beam system) milling For high resolution TEM (HRTEM) the samples were
prepared using an ion beam milling method
33 Results
331 Hardness and Youngrsquos modulus
Figure 32 shows the typicl load-displacement curve of SiC coatings and the hardness
(H) and Youngrsquos modulus (E) as a function of composition of the three types of
coatings The load-displacment curve (Fig 32(a)) shows a smooth character of the
deformation process during nanoindentation There is multiple mini lsquopop-inrsquo events
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
89
reflected on the hardness curve which started at the beginning from the low
indentation load These mini lsquopop-inrsquo can not provide enough consumption of the
internal stresses induced by indenter as it was needed for the initiation and
propagation of dislocations so no well-pronounced lsquopop-inrsquo effect was observed from
the load-displacement curve
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Measurements were made on the x-z plane of SiC coatings (Fig 31(b)) and static
bulk CVD SiC for both micro- and nano-indentation to give reliable comparison with
previous studies [20-23] In the reference material the nano-hardness (36 GPa) and
Youngrsquos modulus (496 GPa) of bulk CVD SiC are nearly the same as in a previous
(c) (b)
(a)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
90
study [20] namely 36 GPa and 503 GPa respectively From Fig 32(b) it can be seen
that S1 has a higher hardness compared with S2 and S3 Further the values of
hardness obtained by nano-indentation (Fig 32(b)) are higher than by
micro-indentation for all samples
For low temperature FBCVD coatings the nano-hardness varies in the range 39 GPa
to 44 GPa whereas the micro-hardness varies between 36 GPa - 42 GPa These values
are at least 8 higher than the bulk static CVD SiC which has a nano-hardness ~36
GPa and a micro-hardness ~32 GPa (see Fig 32(b)) Moreover the low temperature
FBCVD SiC coatings have higher hardness as compared to a previous study of CVD
SiC for which the hardness values varied in the range of 25-39 GPa as measured by
nano-indentation under the similar experimental conditions [20-23]
In FBCVD SiC coatings Youngrsquos modulus of all three coatings is lower than the bulk
CVD SiC (see Fig 32(c)) which is an average Youngrsquos modulus (438 GPa) of
polycrystalline CVD SiC reported by Roy et al[24] The difference in hardness and
Youngrsquos modulus data could not be simply explained by the existence of C or Si due
to their low concentration (lt 1 at ) and location in the coatings which has been
addressed in detail in previous study [25] Therefore the difference of hardness and
modulus could be related to other microstructure such as pores which could vary
from atomic scale to micrometres which is discussed in the following session
Both nano- and micro-hardness results (Fig 32(b)) are higher than the available data
for polycrystalline CVD SiC [20-23] as discussed above and the correct measurement
of SiC coatings with small dimensions was ensured by comparing with the bulk CVD
SiC As mentioned the hardness and Youngrsquos modulus measured by
micro-indentation are slightly lower than the values measured by nano-indentation
because cracks were formed under micro-indentation due to the higher indentation
load
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
91
332 Microstructure of low temperature FBCVD SiC
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Figure 33 shows SEM images of the three etched FBCVD SiC coatings In all three
coatings the width and length of columnar grains were found to be approximately 200
nm and 1-2 μm respectively These are found to be much smaller than the SiC coating
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
92
produced at a temperature of 1500 degC which had width ~1μm and length ~4-5 μm
[17] They are also smaller than the SiC showing dislocation movement under the
indentation deformation zone which was produced at temperature of 1500-1600 degC
by FBCVD and 1500 degC by static CVD with grain size of 1-5 μm and 5-10 μm
respectively [11 16]
Although the grain size is in a similar range for three coatings (as mentioned above)
due to different deposition conditions the grain morphologies of three coatings vary
First a less laminar structure was observed in the S1 coating (see Fig 33 (a)) as
compared to the coatings with excess C or Si (Fig 33 (c) and (e)) Fig 33 (b) shows
the existence of triple junctions (dashed circle) that could resist the movement of
grain boundaries and dislocation slip [12] Pores were also observed along the laminar
structure after etching In the S2 coating it has a large amount of a laminar structure
running through a single grain (laminar structure parallel to growh direction) as
illustrated in Fig3 (d) The information of grain morphology in S2 was mostly a
laminar structure perpendicular to the growth direction after etching (Fig 33(d))
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
To get more information about the grains morphology in S2 coating a TEM image
05 μm
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
93
was taken and shown in Fig 34 Figure 34 shows that grains in S2 coating interact
(branch-like grain growth pattern on the lower-left part of Fig 34) with each other
which is similar as in sample S1 (Fig 33(b)) and grains form branch like structures
In the S3 coating (as can be seen in Fig 33 (f)) a parallel growth of grains with less
interaction among grains was observed
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
According to a previous study [25] about definition of grain boundary the grain
boundary in the S3 coating is smooth while in the S1 and S2 coating the grain
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
94
boundaries are rough which could result in branch-like grain growth pattern It could
be attributed to the different CSi ratio in reaction gas which produce SiC with
different morphologies on the (111) crystal plane which may have three different
morphologies rough smooth and pyramidal defect [26] Grains with differently
finished surfaces could lead to different grain growth morphologies because of
different surface energy For example in rough grain boundaries of S1 and S2
coatings branch like crystals were found as in Fig 33(b) and Fig 34
Figure 35 shows bright field TEM images of the S1 coating S2 and S3 coatings The
columnar grains were observed to grow perpendicular to the coating surface which
was consistent with the SEM results Further nano porous layers normal to the
coating growth direction are observed in the S2 coating (see Fig5 (b)) The formation
of porosity in thin films could be due to differences in diffusion of growth species the
incident molecule direction and deposition of secondary phases such as excess Si or C
[27]
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
BF-TEM and (b) DF-TEM
At low deposition temperatures the probability of a precursor reaching the edge of the
nucleus is considerably lower compared with that of arriving on the top due to a low
surface diffusion As these nuclei grow the areas immediately around them will suffer
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
95
from a shadowing effect blocking the arrival of new molecules and the formation of
new nuclei Since the diffusivity of atoms is low and no new nuclei are formed in
those regions gaps will be formed among grains A wrinkled like defect layer was
seen in the S3 coating (Fig 35 (c)) which could be attributed to the interruption of
the SiC crystallization growth during the deposition process such as crystal lattice
misorientation as seen in Fig 36
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
No obvious laminar defect was observed in the S1 coating by TEM this could be due
5 nm
(a) (b)
5 nm
5 nm
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
96
to less interruption during deposition process According to above observation it was
proposed that the laminar structure observed in SEM images indicates some
instability during the fabrication process resulting in the deposition of the nano- and
micro-pores and misorientation This was attributed the variations in circulation and
deposition occurring close to the nozzle or at the hot zone [5]
Stacking faults were observed for all three types of samples as shown in Fig 35 with
a higher density than for the SiC deposited at a temperature of 1500 C [11 16 17]
These stacking faults could cause an intrinsic residual stress due to the coexistence of
the partial dislocations This was supported by the high resolution TEM images
(shown in Fig 37) exhibiting wave pattern fringes and they could only be observed
in one direction which is determined by the intrinsic stress
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Since the dislocation mobility under nano-indentation deformation has not been fully
understood in hard ceramic materials therefore it is significant to study this
behaviour in FBCVD SiC coatings with a sub-micrometer grain size However it is
difficult to observe the dislocations under the two-beam or weak beam dark field
2 nm
(a)
(111)
[110]
(111)
Sessile
dislocations
(b)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
97
conditions due to the high density of defects In the present study the reversed fast
Fourier transform (FFT) images of the corresponding high resolution TEM images
was used to obtain information about the dislocations This method has been used in
many cases for dislocation observations [28]
Figure 38(a) shows a high resolution TEM image of a S1 coating which was taken as
a representative image to compare the atomic structure of all three coatings Figure
38(b) is the reverse FFT image using the marked inset diffraction pattern of Fig
37(a) in which sessile and glide dislocations can be observed The dislocation
density was calculated from the total number of glide dislocations divided by the area
in the image [29 30] From the analysis of images shown in Fig 38 the dislocation
density in S1 coatings was found to be 1013
cm2 The same magnitude of dislocations
density was found in the S2 and S3 coatings as shown in Fig 37 (three HRTEM
images were analysed for each coating)
333 Deformation behaviour under the indentation
The deformation zone under the indentation was investigated through the images of
FIB milled TEM samples in order to study the deformation mechanism of the low
temperature FBCVD SiC coatings Figure 39 shows the bright field TEM images
showing the mechanical behaviour of a S1 coating under nano-indentation on the x-z
plane (Fig 31(b)) at a maximum indentation depth of 500 nm
Figure 39(a) is an overview of the deformation area under an indentation A median
crack has formed just underneath the surface and has a direction aligned with the
indenter tip impression A higher magnification image around the elastic and plastic
interface is shown in Fig 39(b) It can be seen that a large amount of inter-granular
and trans-granular micro cracks were produced around the median crack initiation
zone This is substantially different from the dislocation-related plastic deformation
behaviour [10 11 16 31] which usually has a severe plastically deformed region
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
98
with few or no cracks Moreover the micro cracks were also observed in the C and D
zones under the indentation
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Figure 39(c) shows that micro cracks that are formed along the grain boundaries
which tend to follow the shear band direction with the formation of a few
trans-granular cracks In Fig 39(d) it can be seen that shear band micro cracks were
formed in one single grain (see inset in the left bottom corner of Fig 39(d)) This
single grain has a large amount of defects which are supposed to be the as-deposited
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
99
defects as shown in Fig 35(a) Shear band cracks were also observed just underneath
the indenter tip (right top inset in Fig 39(d)) As a result a shear band dominated
deformation zone can be seen in Fig 39(c d) under the indentation in a S1 coating
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
The S2 and S3 coatings only show a micro crack pattern which is different from S1
coating Figure 310 gives the TEM images of the S2 and S3 coatings showing the
mechanical reaction underneath the indentation It can be seen from Fig 310(a) and
Fig 310(c) that the median cracks are not always produced under the indentation for
S2 and S3 coatings However some irregular cracks in S3 coatings and lateral cracks
in S2 were produced In particular in the S3 coating (Fig 310(b)) more micro cracks
either intragrain or transgrain were found than in the S1 and S2 coatings This is due
to the fact that the most micro cracks propagate along the grain boundaries in S1 and
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
100
S2 coatings (Fig 39(b) and Fig 310(d)) A careful analysis of the TEM images
shows that only micro cracks were found under the indentation and no
dislocation-induced shear band was observed This is different from previous studies
on the deformation behaviour of polycrystalline SiC [11 16 31] For example in bulk
polycrystalline CVD SiC [11] it was found that it has more dislocation slip bands
rather than micro cracks either in grains or along grain boundaries even though the
indentation load is higher than the load used in the FBCVD SiC based materials The
possible reason of this discrepancy is discussed later Moreover no amorphous phase
and α-SiC phase was formed under the indentation observed by diffraction and bright
field TEM images which is consistent with the work of Mishra and Szlufarska [32]
34 Discussion
High hardness and Youngrsquos modulus were obtained in the sub-micrometer grain size
coatings produced at a low temperature by FBCVD In the S1 coatings the
nano-hardness is ~22 higher while the micro-hardness is ~31 higher compared to
a commercial CVD SiC The higher hardness was also obtained in S2 and S3 coatings
All the coatings retained a higher Youngrsquos modulus than those SiC materials having
high hardness in previous study (equal or higher than 40 GPa nano-hardness) [33]
making these coatings unique among polycrystalline phase brittle ceramic material
Under nano-indentation only micro cracks were found in the deformation zone The
results seem to be consistent with the conventional view of the failure mechanism of
brittle ceramics at room temperature [34] The lack of dislocation and the high Peierls
force are reasons for fracture to occur in brittle materials However
dislocation-related plastic deformation routinely occurred in hardness testing because
the indentation stress field offers conditions of stress conductive to plastic
deformation [11 13 16 34] Molecular dynamic simulations even demonstrate that
13 of the hardness-related deformation is from dislocation-related plastic deformation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
101
while 23 comes from fracture in SiC [31] It is rare to see a deformation zone
dominated by micro cracks in polycrystalline SiC such as in FBCVD SiC coatings
(Fig9 and Fig10 and see for example Ref [11 16 31]) With the above questions
we first estimated the factors controlling Youngrsquos modulus in FBCVD SiC coatings
followed by a study of the mechanism of superior hardness and deformation under an
indentation which influence the hardness in the three coatings
341 Influence of porosity on Youngrsquos modulus
Youngrsquos modulus presents a material constant for uniaxial tensile deformation which
is physically related to the atomic spacing inter atomic bond strength and bond
density In a low temperature FBCVD SiC coating it was shown from XRD
measurements that a shoulder peak was observed in addition to the β-SiC (111)
diffraction peak which corresponded to a crystal plane spacing of ~0266 nm (Fig
31(c)) Moreover we found that the XRD peak shifted to a lower diffraction angle
compared with the bulk CVD SiC According to the XRD pattern in Fig 31(c) the
crystal lattice constants of about 04366 04368 and 04368 nm for S1 S2 and S3
coatings were obtained respectively However the crystal lattice constant for bulk
CVD SiC is ~04359 nm (XRD pattern obtained by the same condition was shown in
Ref 25)
Further crystal orientation impurities and porosity may affect the Youngrsquos modulus
As the Youngrsquos modulus on the x-z plane (Fig 31(b)) was similar to the value
obtained along the cross-section (Fig 31(a)) [5 25] which meant that the orientation
has no effect on Youngrsquos modulus Moreover as discussed before the effect of C or Si
in S2 was found to have no effect on the difference of hardness and Youngrsquos modulus
Excluding these two factors (orientation and impurities) the effect of porosity on
variation of the elastic properties in three coatings was investigated The presence of
nano-pores in S2 coating as in Fig 35(b) results in a lower density Although no
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
102
pores were directly observed by TEM in the S1 and S3 coatings their density is lower
than the theoretical density of SiC Thus the elastic modulus E at room temperature
can be expressed in an exponential function of porosity pV [35] as
0 exp( )pE E CV (1)
where 0E = 496 GPa is the elastic modulus and C = 357 is a constant for a pore-free
bulk CVD SiC pV is the ratio of the relative density difference to the theoretical
density of SiC (322 gcm3)
The calculated Youngrsquos modulus for S1 S2 and S3 coatings is 465 plusmn 15 446 plusmn 17 and
473 plusmn 1 GPa respectively which follows a trend similar to the experimental data
presented in Fig 32 It was concluded that the different Youngrsquos modulus in the three
low temperature FBCVD SiC coatings is attributed to porosity although the
experimental Youngrsquos modulus data of FBCVD SiC coatings is slightly lower than the
values calculated using the Eq(1) The difference between calculated and measured
value of FBCVD SiC coatings is due to the fact that the 0E from pore-free bulk
CVD SiC instead of pore-free FBCVD SiC coatings (not available) FBCVD SiC
coatings have larger crystal lattice constant (~0437 nm) than bulk CVD SiC (~04359
nm) as discussed above Since the expanded lattice constant leads to a decrease of the
Youngrsquos modulus according to a previous study [20] the 0E of pore-free FBCVD SiC
coating is expected to be lower than bulk CVD SiC
342 Mechanism for High hardness
From previous studies [10 11 16 31] dislocation nucleation and glide is the primary
response of SiC under nano-indentation Formation of shear bands due to dislocations
has also been reported [11] which were found under the plastic deformation zone
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
103
when indentations were made on a particular grain in polycrystalline SiC and at the
grain boundaries Moreover dislocation nucleation is also correlated with the discrete
pop-ins observed in the force-displacement curve [32] No pop-ins was found due to
the presence of a large amount of dislocations in the present study Dislocation
mobility can be estimated similar to the case of a metallic material having intrinsic
dislocations Mishra and Szlufarska [32] worked on the dislocation mobility in
3C-SiC using large-scale molecular dynamics simulations The results indicated that
dislocation mobility decreased by dislocation interaction as its density reached a
saturation value This is similar to the work hardening effect in a metallic material [34]
We estimated the stress ( ) needed for dislocation to move using Taylorrsquos work
hardening equation [34] given by
1 2
0 Gb (2)
where 0 is the shear stress for a dislocation to move without any obstacle and the
value of 0 taken was 75 GPa [13] is a numerical constant depending on the
locking strength of a nod The value of taken was 8 [36] b is Burgers vector
where b = 0178 nm for a Shockley partial dislocation in SiC initiated and gliding on a
close packed (111) plane and is the density of glide dislocations G is the shear
modulus which can be written as
2(1 )
EG
(3)
where is the Poissonrsquos ratio and E is the Youngrsquos modulus The dislocation density
was ~03times1012
cm2 The calculated shear stress according to Eq (2) was ~52 GPa and
this value is much higher than the theoretical shear stress which is in the range of
295-4312 GPa obtained from previous reports [37-39] The theoretical shear stress is
the maximum stress provided for the dislocation nucleation and propagation in SiC
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
104
crystals Therefore the dislocation-related yield behaviour could not occur under the
plastic deformation zone in sub-micrometer FBCVD SiC coatings
The superior hardness value in FBCVD SiC coatings is attributed to the immobility of
the dislocations In the case of the SiC-C solid solution [40] the occurrence of a high
density of dislocations causes a strain-hardening effect Furthermore given that
dislocations could be motivated by the shear stress a phase transformation from a
crystalline phase to an amorphous could occur [32] However no amorphous phase
was observed under the nano-indentation (Fig 37 and 8) nor was dislocation
movement band observed in this study This suggests that the dislocation-related
phase transformation did not occur under the indentation
343 Deformation mechanism under nano-indentation
The hardness-related plastic deformation which occurs due to the nucleation and
propagation of micro cracks in FBCVD SiC coatings can be explained as follows
(i) The onset of plastic deformation under the indentation occurs as the maximum
shear stress approaches the yield stress [41] According to 15H Y (Y is the yield
stress H is the hardness) the yield stress in FBCVD SiC coatings is around 26 GPa
The yield stress is lower than the stress needed for the movement of dislocations and
the theoretical shear stress [37-39] This indicates that the hardness-related plastic
deformation first occurred by the nucleation of defect-induced cracks which
propagated to the indented surface (see inset (top right) in Fig 39(d)) The
deformation impression was accommodated by the densification of defects such as
the pores dislocation pile ups and grain boundaries as in Fig 33(b)
(ii) The shear stress was used to promote the movement of dislocations under the
indentation and form slip bands in previous studies [10 11 42] The highest amount
of micro cracks were observed in FBCVD SiC coatings contrary to plastic
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
105
deformation under the indentation found in previous studies [10 11 42] The micro
cracks formed in the hardness-related plastic deformation zone is the Mode-II crack)
[43] as shown in Fig 39(c) and (d) Unlike Mode-I which is dominated by the tensile
stress a Mode-II crack is the consequence of a confined shear stress [34] At the
interface of the elasticplastic deformation branch-like micro cracks were observed
as in Fig 39(b) The above discussions distinguish the hardness-related plastic
deformation mechanism in FBCVD from previous studies on ceramics which showed
dislocations are the main deformation mechanism underneath the indentation [31 44]
A unique hardness-related plastic deformation mechanism was used to explain the
difference in hardness of all three types of FBCVD SiC coatings According to Qian
et al [45] the hardness could reach an asymptotic value with the saturation of the
micro cracks growth population In three FBCVD SiC coatings studied here different
amounts of micro cracks were found (Fig 39(b) and Fig 310(b d)) and micro cracks
nucleated at stress concentration zones such as the grain boundaries or defects within
the grains Thus the difference in hardness was attributed to the grain morphologies
as shown in Fig 33 which gives different degree of resistance to the initiation and
propagation of micro cracks In the S1 coating triple junctions hamper grain
boundary shear by forming interlocks [12] which could resist and deflect the initiation
and propagation of micro cracks In the S2 coating elongated grains interact with the
surrounding small grains which could also provide interlocks (Fig 33(d) and Fig
34) The slightly lower hardness of the S2 coating as compared to the S1 coating is
due to the nano pores as seen in Fig 35(b) A lack of triple junctions and grain
interactions could be the reason for the lower hardness in the S3 coating as it has a
parallel crystalline morphology which has less constraint towards the initiation and
propagation of cracks
35 Conclusions
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
106
The microstructure and mechanical properties of three types of FBCVD SiC coatings
(SiC SiC+C and SiC+Si) were studied FBCVD SiC coatings with a sub-micrometer
grain size were deposited on simulated TRISO fuel particles by FBCVD at a low
temperature (1300 oC) The mechanical properties were studied using micro and
nano-indention The microstructures were studied using SEM and TEM It was
found that the Youngrsquos modulus of all three coatings differ which was attributed due
to the presence of nano-pores The high hardness of FBCVD SiC coatings was due to
the large amount of defects particularly the high density of dislocations It is found
that the interactions between dislocations reduced their mobility and make
dislocation-related plastic deformation unavailable We suggest that the work
hardening effect is the reason for the high hardness in the sub-micrometer grain size
FBCVD SiC coatings A hardness related-deformation mechanism was attributed to
the initiation and propagation of micro cracks The nano-indentation indent volume is
most likely be accommodated by the densification of defects such as the pores As a
result the hardness difference in FBCVD SiC coatings is due to the different grain
morphologies producing different amounts of micro cracks
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
107
36 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[2] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and
benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel
particles J Nucl Mater 317 (2003) 69-82
[3] D A Petti J Buongiorno J T Maki R R Hobbins G K Miller Key
differences in the fabrication irradiation and high temperature accident testing of
US and German TRISO-coated particle fuel and their implications on fuel
performance Nucl Eng Des 222 (2003) 281-97
[4] A C Kadak R Gnallinger M J Driscoll S Yip D G Wilson H C No J
Wang H Maclean T Galen C Wang J Lebenhaft T Zhai D A Petti W K
Terry H D Gougar A M Ougouag C H Oh R L Morre G K Miller J T
Maki G R Smolik D J Varacalle Modular pebble bed reactor Modular pebble
bed reactor project University research consortium annual report Beijing 2000
[5] E Lopez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[6] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram P Xiao Youngs modulus measurements of SiC coatings on spherical
particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[7] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[8] C H Chien S R Jian C T Wang J Y Juang J C Huang Y S Lai
Cross-sectional transmission electron microscopy observations on the Berkovich
indentation-induced deformation microstructures in GaN thin films J Phys D
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
108
Appl Phys 40 (2007) 3985-90
[9] T C Tan C A Merrill J B Orton A K Cheetham Anisotropic mechanical
properties of polymorphic hybrid inorganic-organic framework materials with
different dimensionalities Acta Mater 57 (2009) 3481-96
[10] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
related isostructural materials to nanoindentation Slip vs densification Mater
Res Soc Symp P 522 (1998) 113-18
[11] X Zhao X R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of 3C-SiC upon indentation at room temperature J Am
Ceram Soc 94 (2011) 3509-14
[12] D Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
mechanism of plastic deformation in macro- micro- and nanoindentation
processes J Phys D Appl Phys 41 (2008) 074016-24
[13] H P Chen R K Kalia A Nakano P Vashishta I Szlufarska
Multimillion-atom nanoindentation simulation of crystalline silicon carbide
Orientation dependence and anisotropic pileup J Appl Phys 102 (2007)
063514-22
[14] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[15] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[16] G Chollon J M Vallerot D Helary S Jouannigot Structural and textural
changes of CVD-SiC to indentation high temperature creep and irradiation J Eu
Ceram Soc 27 (2007) 1503-11
[17] D Heacutelary X Bourrat ODugne G Maveyraud M Peacuterez O Guillermier
Microstructures of silicon carbide and pyrocarbon coatings for fuel particles for
high temperature reactors 2nd international topical meeting on high temperature
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109
reactor technology Beijing China 2004
[18] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[19] T Fukuzaki K Tanaka K Nishimoto Y Mur K Nishio and R Tamura
Magnetic property and microstructure of Nd-Fe-B-M (M=Si C) bulk
pnanocomposite magnets prepared by spark plasma sintering method - art no
012015 J Phys Conf Ser 106 (2008) 12015-124
[20] M C Osborne J C Hay L L Snead D Steiner Mechanical- and
physical-property changes of neutron-irradiated chemical-vapor-deposited silicon
carbide J Am Ceram Soc 82 (1999) 2490-96
[21] K H Park S Kondo Y Katoh A Kohyama Mechanical properties of beta-SiC
after Si- and dual Si plus He-ion irradiation at various temperatures Fusion Sci
Technol 44 (2003) 455-59
[22] S Nagappa M Zupan C A Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
Mater 59 (2008) 995-98
[23] C Bellan J Dhers Evaluation of young modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[24] S Roy C Zorman M Mehregany R Deanna C Deeb The mechanical
properties of polycrystalline 3C-SiC films grown on polysilicon substrates by
atmospheric pressure chemical-vapor deposition J Appl Phys 99 (2006)
044108-20
[25] J Tan Mechanical properties of SiC in TRISO fuel particle Thesis University of
Manchester 2010
[26] M J Hernandez G Ferro T Chassagne J Dazord Y Monteil Study of surface
defects on 3C-SiC films grown on Si (111) by CVD J Cryst Growth 253 (2003)
95-101
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110
[27] E S Machlin Materials science in microelectronics I The relationships between
thin film processing and structure 2nd
ed Oxford Elsevier Science 2005
p206-47
[28] A Nakamura T Yamamoto Y Ikuhara Direct observation of basal dislocation
in sapphire by HRTEM Acta Mater 50 (2002) 101-08
[29] H Y Shin S K Kwon Y I Chang M J Cho K H Park Reducing
dislocation density in GaN films using a cone-shaped patterned sapphire substrate
J Cryst Growth 311 (2009) 4167-70
[30] W D Callister Materials science and engineering An introduction 7th ed
Australia John Wiley amp Sons Australia Limited 2006 p191-99
[31] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
materials with a density functional theory J Appl Phys 104 (2008) 053508-16
[32] M Mishra I Szlufarska Possibility of high-pressure transformation during
nanoindentation of SiC Acta Mater 57 (2009) 6156-65
[33] A R Beaber L J Qi J Hafiz P H Mcmurry J V R Heberlein W W
Gerberich S L Girshick Nanostructured SiC by chemical vapor deposition and
nanoparticle impaction Surf Coat Tech 202 (2007) 871-75
[34] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
p162-91
[35] R W Rice Mechanical properties of ceramics and composites 1st ed New
York Marcel Dekker 2000 p457-534
[36] U Messerschmidt Dislocation dynamics during plastic deformation Part 2
Ceramic Single Crystals Springer Series in Materials Science On line 2010
p264
[37] S Ogata J Li N Hirosaki Y Shibutani S Yip Ideal shear strain of metals and
ceramics Phys Rev B 70 (2004) 104104-10
[38] Y Umeno Y Kinoshita T Kitamura Ab initio DFT study of ideal shear
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
111
strength of polytypes of silicon carbide Strength Mater 40 (2008) 2-6
[39] Y Umeno M Cerny Effect of normal stress on the ideal shear strength in
covalent crystals Phys Rev B 77 (2008) 100101-04
[40] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
SiC-C J Mater Chem 11 (2001) 217-22
[41] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000 p139-77
[42] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[43] A A Wereszczak K E Johanns O M Jadaan Hertzian Ring Crack Initiation
in Hot-Pressed Silicon Carbides J Am Ceram Soc 92 (2009) 1788-95
[44] S L Lloyd A Castellero F Giuliani Y Long K K Mclaughlin J M
Molina-Aldareguia N A Stelmashenko L J Vandeperre W J Clegg
Observations of nanoindents via cross-sectional transmission electron microscopy
a survey of deformation mechanisms P Roy Soc a-Math Phy 461 (2005)
2521-43
[45] J Qian L L Daemen Y Zhao Hardness and fracture toughness of moissanite
Diam Relat Mater 14 (2005) 1669-72
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
112
CHAPTER 4 Vickers Indentation Fracture Toughness of
SiC Coatings
41 Introduction
Silicon carbide (SiC) layer is considered to be the most important component for
structural integrity as during the operation of a nuclear reactor it has the ability to
sustain most of the internal pressure caused by gaseous fission products produced in
the kernel and retain most of the fission products [1-4] Previous work was focused on
the investigation of mechanical properties (Youngrsquos modulus and fracture strength) of
SiC coatings on TRISO particles using different techniques such as a ring test [5 6]
a crush test [7 8] a micro-cantilever test [9] and indentation [10 11] However few
reports exist on the measurement of the fracture toughness of SiC coatings even
though it is a property used in modeling to estimate the failure probability of TRISO
fuel particles [12] For example Kadak et al [12] used a fracture toughness value of
33 plusmn 053 MPa m12
This value was obtained from bulk SiC produced by a static
CVD method The fracture toughness value may well differ for SiC coatings produced
by fluidized bed chemical vapour deposition (FBCVD) on TRISO fuel particles [10]
Because microstructure of SiC produced by static CVD and FBCVD methods could
vary significantly For example the static CVD SiC usually has larger grain size and
high density while FBCVD SiC with large grain size is usually accompanied with
porosity [13] Different grain size range and porosity fraction can lead to variation of
fracture toughness [1 2] Therefore the fracture toughness value of bulk SiC may not
be truly representative of SiC coatings used in nuclear fuel applications To our
knowledge the only available data on the fracture toughness of a SiC layer on TRISO
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
113
fuel particle is reported by Zhao et al[9] where the fracture toughness was measured
by the micro-beam method However this method is time consuming and expensive
restricting its implementation as a standard characterization technique where
repetitive measurements are required to confirm the reproducibility of experimental
data
In this Chapter micro-indentation is used to investigate the fracture behaviour of
different SiC coatings produced (on TRISO fuel particles) by FBCVD due to its
capacity to measure the mechanical properties in a small area and produce visible
cracks [14-16] The fracture behaviour under an indenter is also studied using a
transmission electron microscope (TEM) in order to give better understanding of the
fracture mechanism The characteristics of the SiC microstructures are then correlated
with their fracture behaviour
42 Experimental details
The SiC coatings used are the same as the ones in Chapter 3 and the deposition
conditions were shown in Table 31 Chapter 3
For the micro-indentation study SiC coated fuel particles were hot mounted in
copper-loaded conductive resin (to get better SEM images) and then ground to a
cross-section (as shown in Fig 31(a)) or polished a flat external surface (as shown in
Fig 31(b)) In this Chapter the y direction is called radial direction x is called
tangential direction according to Fig 31(a) and (b) The samples were then polished
using increasingly fine diamond suspensions to 14 μm Indentation fracture
toughness measurements were performed using a Vickers diamond indenter (CSM
Instruments Switzerland) Due to the through-thickness (in the radial direction)
failure behaviour of a SiC coating in a TRISO fuel particle under tensile stresses
generated from gases due to nuclear reactions similar tensile stresses could be
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
114
generated from indentation of polished external surface of TRISO particles which
could generate cracks along the radial direction (y direction in Fig 31(b)) of the
TRISO particles as well The indentations were carried out under a maximum load of
3 N (corresponding to a maximum indentation depth of ~26 μm) To avoid PyC
influence the thickness of SiC coatings (in the section as shown in Fig 31(b)) were
kept to ~60 μm after polishing which is more than 20 times the indentation depth
In this case the elastic zone has not expanded to the substrate according to the
criterion that indentation depth is less than 10 of coating thickness [17] For each
sample six indents were made on the polished external surface of SiC perpendicular
to the radial direction with a separation of 70 μm between each indent
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference [25]
The calculation of the VIF fracture toughness must account for the crack profile under
the indenter whether the cracks are of the Palmqvist mode or half-penny mode which
are illustrated in Fig 41 The halfpenny crack system is formed by the joining of
radial cracks as shown in Fig 41(a) while the Palmqvist crack system is always
shallow as shown in Fig 41(b)
To observe the crack impression under the indenter on the polished external surface
an indentation (as in Fig 42(a)) with a final indentation depth of 26 μm was
sequentially polished with 6 μm diamond suspensions The surface was polished until
the plastic deformation zone was exposed together with the radial cracks (as shown in
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
115
Fig 42(b) Afterwards polishing continued until the removal of the plastic
deformation zone (as shown in Fig 42(c)) The surface showed no cross-over
cracking present as illustrated in Fig 41(a) and this confirms the presence of the
Palmqvist mode cracks on the polished external surface of SiC coatings under the
Vickers indenter The three polished samples showed the same crack propagation
mode and this is consistent with previous reports [18 19] where a Palmqvist crack
system has been observed in SiC at low loads (lt 10 N)
The Palmqvist crack mode allows the VIF fracture toughness to be calculated using
the equation proposed by Laugier [15 16] given as
1 2 23
3 2( ) ( )IC v
a E PK
l H c
(1)
In Eq (1) the geometrical constant v is a calibrated value using the already known
fracture toughness due to the variation in use of the Vickers hardness or the
nano-hardness [14 16 20 21] The 2a and l are the lengthes of diagonal and radial
crack length of Vickers indentation (as shown later in Fig 43) respectively c=a+l
the E and H are Youngrsquos modulus and hardness measured by nano-indentation P is
the load of Vickers indentation Therefore this geometrical constant was calibrated
before it was used to calculate the VIF fracture toughness of SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
116
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
117
The only already known fracture toughness was measured on the cross-section of
extra-Si SiC coatings using a micro-beam bending method [9] so the calibration of
v was carried out on the cross section (as in Fig 31(a)) of the same coating
According to Eq(1) the hardness (H ) and Youngrsquos modulus (E) are nano-hardness
and Youngrsquos modulus as measured in a previous study [22] P is the load a is the
impression half diagonal l is the crack length and c is the half diagonal crack length
(see later in Fig 43) To get the load and dimensional values of indentations a total
of 8 indentations at different loads (3 35 and 4 N) were applied on the cross-section
of the extra-Si SiC coating
The crack lengths were measured using a scanning electron microscope (Philips XL30
FEG-SEM) FEG-TEM (Tecnai TM
G2 F30 U-TWIN 300KV) which was used to
study the fracture behaviour under the indenter For the TEM study the cross
sectional specimens for the indents were prepared using focused ion beam milling
(FIB FEI Nova 600 Dual Beam system) Note that due to the large deformation zone
(gt10 μm diameter) and radial crack length (gt15 μm) observed from micro-indent
impression it was not possible to produce a sufficiently large TEM sample by the FIB
technique This limitation restricted us to study the fracture behaviour under a sharper
indenter (Berkovich) with lower load
43 Results and discussion
431 VIF fracture toughness study
Figure 43 is the crack morphology observed in S3 (SiC + Si) coating cross-section It
shows that the fracture resistance is different in the tangential and radial directions of
the cross-section which is consistent with the previous measurements along these
directions measured by the micro beam method [9] Different crack lengths along the
tangential and radial directions observed from 8 indentations are illustrated in Table
41 Correspondingly fracture toughness values of 347 MPa m12
and 672 MPa m12
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
118
taken from Ref [9] were used as the standard values for the tangential and radial
directions of the SiC coating respectively According to Eq (1) taking into account
observed and measured parameters (KIC a c l H and E) the geometric constant
value v was calculated in each indentation for each direction (Table 41)
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for S3 SiC coatings
Table 41 illustrates the indentation parameters and the calibrated geometrical
constant v for the Palmqvist crack mode According to the results shown in Table
41 the calibrated mean value of v is 002008plusmn000273 and this value is within
the range of the geometrical constant value (0014-0023) from previous theoretical
studies [14 23] By using nano-indentation hardness and Youngrsquos modulus v was
taken as 002 for the calculation of the VIF fracture toughness in SiC layers in this
study which is the upper limit of 0016plusmn0004 used for previous studies of bulk
CVD SiC using the HE from micro-indentation [14 24-27]
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
119
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχ
v along the radial and tangential directions
Load Radial direction
Tangential direction
a (μm) c (μm) l (μm) χv a (μm) c (μm) l (μm) χv
3 N 6650 13125 6475 0020368 6685 18285 11600 0023088
6900 13090 6190 0019473 6995 15470 8475 0015013
6675 11895 5220 0015749 6120 16615 10495 0019880
6695 13130 6435 0020249 6555 15935 9380 0017057
6790 12610 5820 0017997 6425 18275 11850 0023783
35 N 7195 14970 7775 0022404 7235 20790 13555 0024930
6670 14080 7410 0020721 6715 18160 11445 0019412
4 N 7770 15855 8085 0020967 7390 20240 12850 0020187
χv 002008 plusmn 000273
Note The geometrical constantsχv presented in Table 41 were calculated using Eq(1) The fracture
toughness along the radial (672 MPa m12
) and tangential directions (347 MPa m12
) were taken from
Ref 9
Although the Vickers indentation method for fracture toughness measurement has
been discredited as a mean to obtain true fracture toughness [28] and always gives a
lower fracture toughness value than that obtained using the standard methods (such as
single edge V-norched bending)[1] the values obtained can be compared with each
other This is particular important for small samples and thin coatings since Vickers
indentation provides a method to quantify fracture behaviour when it is not feasible to
obtain true fracture toughness However to get reasonable comparison of Vickers
indentation fracture toughness in SiC coatings the following conditions should be
met
(1) SiC materials produced four regular radial cracks along the corners of the
Vickers indenter For indentation at the polished external surface of SiC
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
120
coatings deposited by FBCVD similar fracture resistance along different
orientation at the surface should be obtained
(2) The calibration of the geometrical constant should be made v was obtained
as 002 based on previous experimental results (see above)
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
Sample Grain size range (μm) Vickers toughness (MPa m12
)
S1 (SiC) 02-2 351plusmn042
S2 (SiC + C) 02-2 403plusmn043
S3 (SiC + Si) 02-2 493plusmn016
Table 42 presents the measured VIF fracture toughness on the polished external
surface using equation (1) for the SiC coatings in which the deposition conditions and
grain size were given It can be seen that the SiC coating with excess Si (S3) has
highest indentation fracture toughness followed by SiC with excess carbon (S2) and
stoichiometric SiC coatings (S1)
Vickers indentation fracture toughness values obtained in this study are slightly higher
than that of commercial CVD β-SiC which has been reported to vary from 24 to 33
MPa m12
measured by the same method [24 26 27] The VIF fracture toughness of
49 MPa m12
for extra-Si SiC measured on a polished external surface is between
347 and 672 MPa m12
when measured on a cross section by micro-beam method [9]
This is consistent with the observation of radial crack length differences ndash the crack
length on the polished external surface is between those in the tangential and radial
direction on the cross-section It is suggested that Vickers indentation is an effective
method for the characterization of fracture behaviour of FBCVD SiC coatings
Moreover the high hardness and Youngrsquos modulus of these three coatings [22] do not
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
121
cause a decrease in fracture toughness which is explained in the later part of this
paper
432 Influence of non-stoichiometries on the VIF fracture toughness
The VIF fracture toughness in S2 SiC coating is ~14 higher than the value for S1
SiC coatings and this can not be attributed to heterogeneous toughening due to the
excess carbon being at the grain boundaries Due to the low content of excess C it is
difficult to identify such an excess at the grain boundaries [29] Previous work
reported in Ref[30] showed that there was no presence of carbon at the grain
boundaries for a concentration up to 1 wt excess C In our case a similar situation
was found in S3 SiC coating where excess Si has not been found along the grain
boundaries Previous studies had [31 32] shown that excess Si in SiC was observed in
grains or near the grain boundaries by TEM only when the amount of excess Si is
high enough (such that it could be detected by XRD or a much higher Raman
spectroscopic intensity)Thus it is assumed that the excess Si could not be considered
as giving heterogeneous toughening which caused a ~43 higher VIF fracture
toughness in the S3 SiC than the S1 SiC coatings As a result the small amount of
excess carbon or silicon in SiC coatings does not seem to have influence on the VIF
fracture toughness through serving as the heterogeneous phase along the grain
boundary
The excess Si or C could be related to different grain morphologies according to
previous study [33] where it was observed that different SiC ratios in the reaction
gas produced rough smooth and irregular pyramid-like grain surfaces This further
affects the growth morphology and cohesion stress between grains For example the
smooth grain surface favours the parallel grain growth The weak grain boundary
cohesion could be the micro crack initiation zone while the strong grain boundary
could transfer the stress to stress concentration zone Here the role of grain
morphology is studied later in terms of stress concentration zone under indentation
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
122
433 Microstructural analysis of fracture behaviour under the indenter
SiC coating under nano-indentation on the polished external surface at a maximum
indentation load of 160 mN It can be seen that the median crack propagation root
deflected slightly and changed from intergranular to transgranular fracture as shown
in Fig 44(a) It is worth noticing that the median crack observed under
nano-indentation was not found under indentation because the indentation cracking
mode depends on the condition of the indenter tip [34] Higher magnification images
(Fig 44(b)) show that a large number of micro cracks were produced at the
elasticplastic interface
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
123
Both intergranular and transgranular cracks were observed near the median crack
initiation zone These cracks are under a tensile stress dominated by Mode I cracks as
the elastic-plastic stress field gives the highest tensile stress around this interface
according to a previous report (see Ref [35]) Moreover micro-cracks were observed
surrounding the median crack and also at the median crack tip as shown in Fig 44(c)
and Fig 44(d) respectively Figure 44(c) illustrates that the micro-cracks are along
the grain boundaries while the micro-cracks around the crack tip were found to both
pass through the grains and along grain boundaries (Fig 44(d))
Non-stoichiometric SiC coatings (S2 and S3) show quite different crack morphologies
under the indenter from that in the stoichiometric SiC (S1) coating as shown in Fig
310 in chapter 3 It can be seen that the propagation root of median cracks in S3 SiC
and S2 SiC coatings were affected by the microstructures as in Fig 310(a) and (c) in
chapter 3 Moreover a lateral crack was found in the S2 SiC coating The irregular
median crack propagation route in non-stoichiometric SiC coatings seems to be
related to the laminar structure
Fig 45 Cross-sectional SEM image of the S1 SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
Figure 45 shows the cross section of S1 SiC coating and the laminar structure (as
indicated by the dashed lines) is perpendicular to the grain growth direction It was
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
124
discussed in chapter 3 that the laminar structure is due to either nano-pores or a high
concentration of stacking faults and it is much less evident in the stoichiometric SiC
coating as compared to the coatings with impurities [22] In the S3 SiC coating (Fig
310(b) in chapter 3) a larger amount of micro cracks either intergranular or
transgranular were found under the indenter than in the S1 and S2 SiC coatings
The fracture mechanism of materials is influenced by their microstructure and the
fracture toughness could be enhanced by changing it For example ceramics
containing micro-cracks during fabrication could be associated with good fracture
behaviour but low strength and hardness since the micro-cracks usually serve as the
failure origins A better solution is to fabricate materials with microstructures that can
form stress induced micro-cracks under an external force [36] In FBCVD SiC a
number of micro cracks were observed under the indenter (Fig 44(b) Fig 310(b)
and (d) in chapter 3) from where the main cracks initiated and propagated away from
this zone According to a previous study although the tip of the main crack leaves the
micro-cracked zone under the indenter the wake region can provide stress shielding
against some further crack extension [37]
Thus the micro-cracks under the indentation (Fig 44(b) Fig 310(a) and (c) in
chapter 3) seem to be a mechanism for the toughening behaviour of FBCVD SiC by
dissipating the fracture energy for brittle fracture Micro-cracks were also found near
the main crack tip and surrounding the main crack for example in the stoichiometric
SiC coating (Fig 44(c) and (d)) This further confirms the toughening behaviour
through micro-cracking In CVD SiC which has a slightly lower fracture toughness
(around 33 MPa m12
) only a few micro-cracks were observed under the indentation
[38] which could be caused by indentation-induced slip bands As a result the
micro-cracks formed under the indentation near the main crack seem to be the reason
for the high VIF fracture toughness in SiC coatings when a high hardness is obtained
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
125
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a) S2
SiC (b) S3 SiC
Stress concentration zones are known to facilitate the nucleation of micro-cracks so a
large amount of micro-faults (eg pores) and weak grain boundaries (inducing the
micro-cracks under an external stress) could increase the VIF fracture toughness A
higher VIF fracture toughness in the extra-C SiC than in stoichiometric SiC coatings
may be due to the presence of the nano-pores (as shown in Fig 35(b) in chapter 3)
The S3 SiC has an even higher VIF fracture toughness than the S2 SiC coating and
this may correspond to a larger number of micro-cracks under the indentation We
assume this difference is due to their varied grain boundary morphologies as shown
in Fig 46 For example we observed different length of cracks on the cross section
(Fig 43) with cracks parallel to the grain growth direction shorter than cracks
perpendicular to the grain growth direction This is because along grain growth
direction itrsquos more likely to produce micro-cracks along the grain boundary As we see
in Fig 46 grains interact with each other in extra-C SiC (Fig 46(a)) forming branch
grains while in S3 SiC grains grow parallel (Fig 46(b)) According to a previous
study it is easier for parallel grains to form a transgranular fracture when the grain
boundaries are along the loading axis [39] This can explain the larger number of
transgranular micro-cracks under the indentation in the extra-Si SiC compared to the
extra-C coatings (Fig 310(b) in chapter 3) which caused different VIF fracture
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
126
toughness This different grain morphology could be caused by the
non-stoichiometries and further work needs to be done to study how excess C or Si
affects the microstructure of the SiC
44 Conclusions
In summary micro-indentation on the polished external surface of the SiC coating in
TRISO particles has been successfully applied to measure the VIF fracture toughness
of the silicon carbide (SiC) Three different types of SiC coatings (stoichiometric SiC
SiC with excess silicon and SiC with excess carbon) produced on spherical particles
by FBCVD were analysed The VIF fracture toughness (measured on the polished
external surface) in these three coatings investigated in this study was observed to
vary between 35 and 49 MPa m12
The results have shown that the VIF fracture
toughness is influenced by the microstructure and non-stoichiometry of SiC coatings
For FBCVD SiC coatings a high VIF fracture toughness accompanied with superior
hardness was attributed to the formation of micro-cracks The difference in VIF
fracture toughness was proposed to be dominated by the laminar defects and grain
morphologies in the SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
127
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[3] G K Miller D A Petti D J Varacalle and J T Maki Statistical approach and
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[4] D A Petti J Buongiorno J T Maki R R Hobbins and G K Miller Key
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[5] K Bongartz E Gyarmati H Schuster and K Tauber Brittle Ring Test - Method
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[6] K Bongartz E Gyarmati H Nickel H Schuster and W Winter Measurement of
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[7] M W Kim J H Kim H K Lee J Y Park W J Kim and D K Kim Strength
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[8] T S Byun J D Hunn J H Miller L L Snead and J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[9] X Zhao R M Langford J Tan and P Xiao Mechanical properties of SiC
coatings on spherical particles measured using the micro-beam method Scripta
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
128
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[10] E Lopez-Honorato P J Meadows J Tan and P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
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[11] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang
T Abram and P Xiao Youngs modulus measurements of SiC coatings on
spherical particles by using nanoindentation J Nucl Mater 393 (2009) 22-29
[12] ACKadak RGNallinger MJDriscoll SYip DGWilson HCNo JWang
HMaclean TGalen and CWang et al Modular Pebble Bed Reactor Project
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[13] J I Federer Parametric Study of Silicon-Carbide Coatings Deposited in a
Fluidized-Bed Thin Solid Films 40 (1977) 89-96
[14] G R Anstis P Chantikul B R Lawn and D B Marshall A Critical-Evaluation
of Indentation Techniques for Measuring Fracture-Toughness 1 Direct Crack
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[15] M T Laugier Palmqvist Toughness in Wc-Co Composites Viewed as a Ductile
Brittle Transition J Mater Sci Lett 6 (1987) 768-70
[16] M T Laugier Palmqvist Indentation Toughness in Wc-Co Composites J Mater
Sci Lett 6 (1987) 897-900
[17] W D Nix and R Saha Effects of the substrate on the determination of thin film
mechanical properties by nanoindentation Acta Mater 50 (2002) 23-38
[18] J Lankford and D L Davidson Crack-Initiation Threshold in Ceramic Materials
Subject to Elastic-Plastic Indentation J Mater Sci 14 (1979) 1662-68
[19] Z Li A Ghosh A S Kobayashi and R C Bradt Indentation
Fracture-Toughness of Sintered Silicon-Carbide in the Palmqvist Crack Regime J
Am CeramSoc 72 (1989) 904-11
[20] H Hatta M Zoguchi M Koyama Y Furukawa and T Sugibayashi
Micro-indentation method for evaluation of fracture toughness and thermal
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129
residual stresses of SiC coating on carboncarbon composite Adv Compos Mater
12 (2003) 155
[21] C B Ponton and R D Rawlings Vickers Indentation Fracture-Toughness Test 1
Review of Literature and Formulation of Standardized Indentation Toughness
Equations Mater Sci Tech Ser 5 (1989) 865-72
[22] H Zhang E Lopez-Honorato A Javed X Zhao and P Xiao Study of the
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Eur Ceram Soc In Press (2011)
[23] A Leonardi F Furgiuele S Syngellakis and R J K Wood Analytical
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[24] M C Osborne J C Hay L L Snead and D Steiner Mechanical- and
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[25] R D Dukino and M V Swain Comparative Measurement of Indentation
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[26] K H Park S Kondo Y Katoh and A Kohyama Mechanical properties of
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[27] S Nogami S Ohtsuka M B Toloczko A Hasegawa and K Abe Deformation
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[29] J Tan Mechanical properties of SiC in TRISO fuel particle PhDThesis
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130
[30] K Kaneko M Kawasaki T Nagano N Tamari and S Tsurekawa
Determination of the chemical width of grain boundaries of boron- and
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[31] B Reznik D Gerthsen W G Zhang and K J Huttinger Microstructure of SiC
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[32] R A Shatwell K L Dyos C Prentice Y Ward and R J Young Microstructural
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[33] M J Hernandez G Ferro T Chassagne J Dazord and Y Monteil Study of
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[34] D S Harding W C Oliver and G M Pharr Cracking during nanoindentation
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[35] ACFischer-Cripps Introduction to contact mechanics Springer New York
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[36] DJGreen An introduction to the mechanical properties of ceramics Cambridge
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[37] S B Biner A Numerical-analysis of crack-growth in microcracking brittle solids
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[38] K H Park T Hinoki and A Kohyama Influence of irradiation-induced defects
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CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
131
CHAPTER 5 Influence of Interfacial Roughness on Fracture
Strength of SiC Coatings
51 Introduction
During the irradiation process of TRI-Isotropic (TRISO) fuel particles the high
tensile stress could be accumulated at crack tips These tips were due to direct
penetration of the cracks formed in the PyC layer or the high stress concentration as a
result of the debonding of IPyCSiC interface [1 2] When the tensile stress inside of
the particle exceeded the critical fracture stress of the SiC coating it caused the
failure of the whole particle [3] Furthermore the fracture strength is a main
parameter used in modeling the probability of failure of fuel particles so it is
important to measure the fracture strength of SiC to determine their performance
which is determined from the maximum tensile stress
Different methods such as hemi-spherical bending [4] crush test [5 6] and inner
pressure [6] were introduced to measure the fracture strength of SiC coating in
TRISO fuel particle The fracture strength was in a range and could be characterised
by the Weibull distribution function [4-6] The common vague conclusion derived
from previous results is the significant effect of the IPyCSiC interface on the fracture
strength [4-6] The interface was also found to affect the primary failure mechanism
by determining if the load can transmit through the SiC [6] Previous analyses are
consistent with the well-known prescription that the fracture strength of ceramic
materials varies largely and it is dependent on the size and surface condition of the
specimen [7-9] Among these methods the latest modified crush test proposed by
Byun et al[510] showed a well controlled scatter of the fracture strength in a given
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
132
sample
Although the importance of the interface has been noticed the lack of an accurate and
scientific description of the interface has limited the further study about its
relationship with the fracture strength Roughness is a commonly used terminology to
describe the interface and it could be measured by atomic force microscope and
characterised by the standard deviation of the vertical features [11 12] However
roughness is not enough to describe the interface and to relate it to fracture strength
[13] Due to the importance of the statistical analysis for ceramic materials the
self-affine theory was used to characterise the complex interface numerically
according to previous studies [14-17] A self-affine interface is characterised by a
correlation length the saturation roughness and the roughness exponent [18] A
similarly straightforward approach was applied to demonstrate the importance of the
interfacial roughness on the mechanical properties [19] showing that interfaces with
big and sharp irregularity fail first
In this work the modified crush test was used to measure the fracture strength of a
SiC layer deposited at different temperatures The IPyCSiC interface was well
described by self-affine theory Therefore the effect of the IPyCSiC interface and
dimension of particles together with other possible influences such as porosity and
grain size on the fracture strength were discussed The improvement of this work is
being able to do statistical analysis on the interfacial roughness
52 Experimental details
521 Materials
In this Chapter the buffer pyrolytic carbon and dense pyrolytic carbon coatings were
deposited on the top of ZrO2 kernel (~ Φ500 μm) by fluidized bed chemical vapour
deposition Thirteen SiC coatings were deposited at different temperature flow rate
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
133
MTS concentration and added gas as shown in Table 51 The deposition conditions
were chosen according to previous studies to get different microstructures and more
deposition mechanisms of SiC coating can be found in Ref [20] For fracture strength
measurement the SiC particles were mounted with thermoplastic resin and ground to
about 55 portion of the sphere and polished using increasingly fine diamond
suspensions until frac14 μm SiC shells were released from surrounded PyC layers by
oxidizing at 700 ordmC for 8 hours and further washed in an ultrasonic bath with acetone
for 5 minutes
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Sample Temperature
(ordmC)
MTS
(vol )
Added gas concentration Flow rate
(LMin)
Radius
Thickness (~)
S1 1300 91 05vol C3H
6 600 72
S2 1300 91 01vol C3H
6 600 76
S3 1280 91 01vol C3H
6 600 83
S4 1300 91 -- 600 85
S5 1400 19 57vol Ar 778 87
S6 1500 22 82vol Ar 700 90
S7 1500 19 89vol Ar 778 101
S8 1500 22 79vol Ar 700 112
S9 1400 19 57vol Ar 777 117
S10 1300 19 57vol Ar 778 129
S11 1500 19 89vol Ar 777 151
S12 1500 22 76vol Ar 700 158
S13 1500 19 57vol Ar 778 190
The difference between sample S5 and S9 S7 and S11 is the thickness of the PyC layer MTS
methyltrichlorosilane Lmin the flow rate measured in liter per minute To produce SiC coatings with
particular microstructures and compositions different deposition conditions were chosen which were
contributed to Dr Eddie Lopez-Honorator
522 Test method and analysis
The crush test taking the contact area into consideration was used in this study [2 5
21] and the loading profile of the crush system is shown in Fig 51 When a partial
spherical shell (Radius R thickness t) was diametrically loaded by an external load F
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
134
concentrated on a small circular area (radius 0 ) the maximum membrane stress and
bending stress could be calculated by the equations developed by Roark and Young
[21] The combination of the maximum bending and membrane stress (Local fracture
strengthL
f ) in the inner side of the shell was the maximum fracture strength for
partially loaded shell (around 55 of the sphere)
The fracture strength of brittle SiC coating is best considered as a distribution rather
than a fixed number and the most widely used expression for characterisation is the
cumulative distribution functionmdashWeibull distribution function [7 22] In the current
study the distribution of local fracture strength and fracture strength for a full
spherical shell were characterised by the Weibull distribution The Weibull modulus m
is derived from the local fracture strength (Eq 14 in Chapter 2) The calculation of the
fracture strength for the full spherical shell (F
f ) is based on the size effect (scaling
factor mtRr 122
0 ))(4( R radius of the particle t thickness of SiC shell 0
radius of residual impression after loading) which is equal to the partial strength
divided by the scaling factor [5 7] More details about fracture strength calculation
are available in Ref [5]
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
According to a previous study [5] one reason for the difference of local fracture
10 ordm
t
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
135
strength in a given batch of coating is due to different sizes of residual impression
( 0 ) under which the distribution of defects could be different To reduce the
influence of the 0 the radius (R) at the edge of the residual impression was kept at
an angle of around 10ordm (as shown in Fig 51) from the loading axis by inserting
different kind of soft metal It varied slightly (the ratio of standard deviation to mean
value is around 10) in each batch of SiC
The crush test was carried out in a universal tensile machine INSTRON 5569
(INSTRON High Wycombe Bucks) with a 100 N maximum load cell For each batch
of SiC shell (except for S13) at least 30 specimens were tested at room temperature
with a crosshead speed of 0005 mms The failure load recorded by the tensile
machine was used as the fracture load The individual impression left on the soft
metal (Nickel alloy cold worked copper or brass) was marked under corresponding
load and its diameter was measured by optical microscope (times100 ZESIS Company
German)
523 Characterisation methods
A Philips XL30 FEG-SEM (Philips Eindhoven Netherlands) was used to characterise
IPyCSiC interfacial roughness grain size and porosity from the finely polished cross
section of SiC coatings Characterisation of the IPyCSiC interfacial roughness was
realized by editing the SEM images (in the magnification of times1600) with the Image J
software and extracted it as a line from the background SEM image The interfacial
roughness could be described by a series of pairs of x (distance tangential to the
interface) and y (distance normal to the interface) coordinates assuming the interface
is flat at a scale of 70 microm
Porosity was measured by controlling the threshold of SEM images (times1600 TIF) at a
gray level and adjusted to distinguish pores from grains with the Image J software
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
136
Pore fraction was defined as the ratio of the pores and the total area of the SEM image
Grain size of FBCVD SiC coatings varied in a range and in a columnar shape It was
characterised by measuring mean width and length of single crystals from SEM
images (times6400) and the grain size of the coatings is represented by the mean width
timeing the length of grains A FEG-TEM (TecnaiTM G2
F30 U-TWIN) was used to
observe the IPyCSiC interfacial roughness and TEM samples were prepared by
focused ion beam milling The linear regression method was used to analyze and
quantify the influences of parameters on the fracture strength and Weibull modulus
53 Results and discussions
531 Fracture strength and dimensional effect
Table 52 gives the summary of the measured and calculated parameters for all the
coatings It includes the diameter of impression (mean value 2 0 ) force (mean value
F) Weibull modulus (derived from local fracture strength m) local fracture strength
(L
fmean value) and fracture strength for the full spherical shell (
F
fmean value)
Table 52 Summary of measured and calculated parameters for all the coatings
Sample 2 0 μm F N L
f MPa Modulus (m) Scaling Factor
For Size Effect
F
f MPa
S 1 15239 2235 1784 7397 185 963
S 2 15043 1999 1599 7687 183 872
S 3 14898 1540 1446 7459 187 774
S 4 16052 2042 1620 8261 178 908
S 5 17018 2573 1810 7927 178 1018
S 6 16220 1885 1648 6953 193 855
S 7 14662 1691 1974 7755 190 1019
S 8 14905 1336 1717 7102 198 868
S 9 13040 1088 1825 6495 223 820
S10 16410 1215 1472 6801 204 722
S11 16165 1006 1430 6104 219 652
S12 14677 903 1512 6616 205 737
S13 11586 489 1762 4912 300 587
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
137
As given in Table 52 a significant difference (49-257 N) of the load among SiC
coatings was obtained According to a previous study [5] the variation is mainly
caused by different thicknesses (varied from 30 μm to 60 μm) of SiC coatings
because the relatively thin coating tends to reach higher strength concentration at
fracture
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
The Weibull modulus derived from the local fracture strength (as given in Fig 52) is
in the range of 49-86 (as shown in Table 52) and it falls into the category of moduli
for ceramics materials (from 5 to 30) This range of Weibull modulus is similar to the
values obtained from the brittle ring tests which also gave a similar range of the local
fracture strength [23 24] In different batches of SiC coatings it was found that the
Weibull modulus decreases linearly with the increase of the ratio of outer radius (R) to
the thickness of SiC coatings ( tR ) as shown in Fig 53 The ratio of Rt accounts
for up to 778 (2R from linear regression) of differences of the modulus This is
because the tR ratio is a critical dimension value for the strength distribution of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
138
SiC shell and it represents the relative thickness of SiC coating The higher the ratio
is the thinner the SiC coating So it corresponds to the larger inner surface area
resulting in larger scattering sizes of the critical flaws This observation is consistent
with the previous finite element modeling results showing that the Weibull modulus is
related to the sample dimension [10]
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
As given in Table 52 the scaling factor (effective area-parameter based on the local
fracture strength) between the local fracture strength and the fracture strength of the
full shell are in the range of 18-30 The results are consistent with Byun et alrsquos study
(19-31) [5] and it indicated the importance of the size effect on the fracture strength
of the full shell
The fracture strength for the full spherical shell of thirteen SiC coatings were given in
the form of Weibull plots as shown in Fig 54 The mean fracture strength for the full
spherical shell was in the range of 587-1019 MPa (as given in Table 52) which is
higher than the range of 330-650 MPa obtained by Byun et al [5] This is because the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
139
Rt ratio (above 11) in Ref [5] falls into the higher value categary in current work as
shown in Fig 53
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Because the Weibull modulus is dominated by the tR ratio (Fig 53) its influence on
fracture strength for a full spherical shell could also be from this ratio as shown in
Fig 55 It shows that the fracture strength for the full shell decreases nearly linearly
with the increase of the tR ratio which produces a difference of 6528 (2R derived
from linear curve fit which represents fair agreement) of differences In this work the
similar range of Rt ratio (above 11) corresponds to the fracture strength lower than
850 MPa (as shown in Fig 55) which reduced the difference from previous results
[5] Furthermore the fracture strength of about 1000 MPa was obtained when the Rt
was about 8 [25] and it is similar as the result given in Fig 55 This again
demonstrated the importance of the geometry on the fracture strength of SiC coating
Therefore it is important to eliminate the external influence and study the influences
of microstructures such as interfacial roughness porosity and grain size on fracture
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
140
strength which are discussed in the following parts
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
532 Observe and qualify the effect of interfacial roughness on fracture strength
According to Griffith fracture theory the fracture strength (L
f ) is a function of the
critical flaw size (C) and the fracture toughness ( ICK ) as shown in the following
equation [26]
12( )
L ICf
K Z
Yc (1)
Y is a loading geometrical parameter Z is the flaw size parameter The magnitude of
the critical flaw size could be related to the IPyCSiC interfacial irregularities
The interfacial flaw shape of SiC coatings is modeled from the surface morphology of
PyC coating during deposition process as shown in Fig 56(a) The crack was taken
as a semi-circular surface crack as given in Fig 56(b) where Y is 2 and Z is 16 (Y
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
141
Z are geometrical constants introduced in Eq (1) [26] The fracture toughness of SiC
coatings in TRISO fuel particle was taken to be 33 MPamiddotm12
according to previous
report [27] Taking the result of the local fracture strength from individual SiC coating
into Eq (1) the magnitude of the critical flaw size C could be obtained
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Figure 46 shows the redraws of the IPyCSiC interfacial roughness from SEM images
and the calculated critical flaw sizes according to Eq (1) (range and mean values) for
all specimens are given in the right columns If the fracture initiated at the IPyCSiC
interface as proposed in previous studies [4-6] the calculated critical flaw size range
of each type of SiC coating was expected to match the size range of the interfacial
irregularities
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
142
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
In Fig 57 most of the calculated critical flaw sizes according to Eq (1) are in the
same magnitude as the flaw size observed directly from the interfacial profile images
and this indicates that the dominant effect of the surface roughness on the local
fracture strength For example the direct observation of the biggest flaw size from the
profile is about 43 μm and 26 μm in sample S9 and S13 respectively and they are in
the range of the calculated defect sizes of 09-65 μm and 17-47 μm for S9 and S13
respectively However exceptions were found such as specimens S1 and S2 which
show slightly higher calculated surface flaw size than the observation from SEM
images Furthermore it is difficult to accurately characterise the difference of the
interfacial roughness by observing the converted images and give specific
information (such as shape) of single profile (shown in Fig 57) The estimation of
the shape of surface irregularities to be half-circular could also result in the error on
the critical flaw size calculation [7] To give a direct estimation about the influence of
interfacial roughness on local fracture strength the scaling behavior of IPyCSiC
interface need to be characterised by a statisticalnumerical method
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
143
533 Characterise and quantify the interfacial roughness
Self-affine theory has become a standard tool in the study of various rough interfaces
[18 28 29] Here it was the first time being proposed to describe the IPyCSiC
interfacial roughness accurately and scientifically and then was used to quantify the
relationship between interfacial roughness and local (intrinsic) fracture strength and
fracture strength of the full shell
5331 Self-affine theory introduction and experimental setup
In order to describe the IPyCSiC interfacial roughness with specific parameters an
easy way is using a height-height function [29 30]
2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)
where the x axis is along the IPyCSiC interface and ( )h x is the surface height profile
The amplitude of the roughness ( )h x is correlated with the length scale x and
lt gt denotes the spatial average over ( )h x in a planar reference surface If the
interfacial roughness of IPyCSiC were self-affine the correlation of x and
h should follow the power law relationship (Eq (2)) and it could be obtained by the
log-log plot of x and h The (for self-affine surface 0lt lt1) is the roughness
exponent and it describes the degree of surface roughness at short length scales [31]
This short length scale is shorter than correlation length ξ which is another parameter
used to describe the self-affine surface (besides the surface roughness h and
roughness exponent ) It is the average distance between the features in the surface
profiles within which the surface variations are correlated [28] Therefore the small
(close to 0) characterises extremely jagged or irregular interfaces while large
value characterise interface with smooth hills and valleys [32]
For all the samples the scaling properties of IPyCSiC interface (as shown in Fig 57)
are characterised by their one-dimensional height-height correlation function Eq (2)
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
144
The characteristic parameters of the digitalized IPyCSiC interfacial roughness are as
follows The resolution between two points along x axis is 020833 μm and x
changes by timing the resolution with integer (1 2 3hellip15) According to previous
self-affine theory study [16] the number of recorded points along the x axis was
taken in the range of 250-400 in this work corresponding to the length of 50-70 μm
for different IPyCSiC interfaces
5332 Results of self-affine theory
Figure 58 is a log-log plot showing the variation of h as a function of the distance
x for three SiC coatings The h varied as a power law of x (solid line ) when
x ltξ while remained nearly constant ˗ saturation roughness (σ0 dashed parallel
lines) for x gtξThese results indicated that these three IPyCSiC interfacial
roughness were self-affine with the roughness exponent of around 063-067 For the
rest of the samples the same scaling characterisation method was used Theξ σ0 and
are given in Table 53
Fig 58 Log-log representation of the height-height correlation function h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
ξ3 ξ12 ξ6
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
145
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Sample σ0 (μm) ζ ξ(μm) σ0ξ
S 1 02378 05903 06250 03804
S 2 04142 06950 08333 04971
S 3 06701 06673 16666 04021
S 4 06825 05244 14583 04680
S 5 05271 06308 14581 03615
S 6 08500 06343 20833 04080
S 7 04293 05162 14583 02944
S 8 07452 05107 14583 05110
S 9 05453 06099 12500 04362
S10 06953 05490 13044 05330
S11 05806 04949 10417 05574
S12 07584 06899 16666 04550
S13 05522 02971 18750 02945
The roughness exponent values for the 93 of IPyCSiC interface were in the range
of 05-07 (as shown in Table 53) This indicated the self-affine measurement is
reliable according to Schmittbuhl and Vilottersquos review [14] which showed that this
range of roughness exponents could have the minimum characterisation errors
Furthermore these roughness exponents are comparable except specimen S13 and it
was consistent with the observation of the interfacial roughness (Fig 57) in which
only specimen S13 showed the high degree of high frequency and short wavelength
irregularities (the dark pits in S13 profile) According to previous study [31] the
concentration of the roughness exponent values could be attributed to the same
original mechanism of the IPyCSiC interface which was produced by the FBCVD
under different conditions As a result the different roughness exponent value could
not describe the difference of the IPyCSiC interface
As shown in Table 53 the saturation roughness (σ0) and correlation length (ξ) are in
the range of 024-085 μm 063-208 μm respectively (Table 53) According to
previous studies [16 17 30] the σ0 and ξ couldnrsquot represent the interfacial
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
146
irregularities correlated with the critical flaw size Because the σ0 value range was
nearly one magnitude lower than the calculated critical flow size (mean value range of
2-4 μm) and the dimension of ξ was perpendicular to the calculated critical flaw size
direction Furthermore it was found that σ0 and ξ values were correlated to the sample
size (recorded points) [16] With the increase of the sample size for the same profile
both the ξ and the σ0 values increased and indicated these two parameters may not be
intrinsic properties of the samples However the roughness ratio σ0ξ is constant
which was found in both the current work and previous study [16]
As a result of above discussions the roughness ratio of σ0ξ was proposed to
characterise the interfacial roughness which could represent the sharpness of the
interfacial irregularities according to Ref [30] For example the low ξ value
corresponded to narrow surface irregularity when the σ0 and values were the same
With the increase of the σ0 value the surface irregularity became deep and narrow
which was hazard to the mechanical properties according to previous simulation work
on the fracture strength of SiC coatings [22] The above observations and analysis
results are supported by previous study [31] when length scale x gt ξ (shown in
Fig 58) the roughness ratio σ0ξ describes mainly the long-wavelength roughness
characteristics which could be statistically equal to the effect of the critical flaw size
on fracture strength
534 Quantify the influence of interface roughness on fracture strength
Figure 59 gives the influence of roughness ratio on the local fracture strength and it
contributes to nearly 50 (R2 from linear regression) of variation of the local fracture
strength It shows that the local fracture strength decrease linearly with the increase of
the roughness ratio This result approves previous findings about the importance of
the interfacial roughness [4-6] and is correlated with the Griffth fracture theory (Eq
(1)) about the importance of the shape and dimension of critical flaws Furthermore
the relation between interfacial roughness has been characterised quantitatively and a
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
147
linear relationship between roughness ratio and local fracture strength is proposed
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Except for the interfacial roughness the local fracture strength could also be affected
by the fracture toughness as shown in Eq (1) Although Vickers-indentation fracture
behavior of SiC coatings was different due to the laminar defects and grain
morphology [33] the fracture toughness of SiC was found to be insensitive to the
microstructure of materials [34] This could be attributed to the fact that
Vickers-indentation provided a static propagation of the crack while the real fracture
toughness was measured dynamically In this work the fast fracture process could
overtake the effect of microstructure on the different static fracture behaviour [5 25]
Since porosity and grain size were main microstructural variations in SiC coatings [1]
their effects on fracture strength were estimated
The characterisation and quantification of grain size and porosity were shown in Table
54 The grain size was found to have no effect on fracture strength according to
previous studies [5] which was also indicated from the regress analysis (R2 is close to
0) No influence was found by regressing the local fracture strength on pores
Therefore the dominant influence on the local fracture strength is from the roughness
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
148
ratio
Table 54 Results and variations influences on fracture strength for SiC coating
Specimen S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S10 S11 S12 S13
Grain size
(μm2)
04 06 06 08 20 20 20 28 20 08 20 28 25
Porosity
(Area )
0 0 0 0 05 04 12 09 03 0 08 21 20
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
Because the fracture strength for a full spherical shell is a function of the Weibull
modulus and local fracture strength [5] it was affected by factors such as the
dimension ratio of thickness to radius of the coating (as shown in Fig 55) the
roughness ratio (as shown in Fig 510) Figure 510 shows the influence of roughness
ratio on fracture strength of the full shell The linear relationship was found in 12
samples as indicated by the dashed line in Fig 510 and it could explain about 68
(2R from linear regression) of difference in fracture strength of the full particle The
high roughness ratio would decrease the fracture strength of the full shell linearly The
deviated point of sample S13 could be due to its largest Rt ratio (as shown in Fig
55) which may have over taken the effect of the roughness ratio (Work about the size
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
149
effect on the fracture strength has being carried out)
54 Conclusions
The fracture strength of SiC coatings deposited under different conditions were
measured by the modified crush test and analyzed by the statistical analysis (Weibull
function and Self-affine theory) The influences on fracture strength were studied
such as the IPyCSiC interfacial roughness specimen size and porosities Following
results were obtained
(1) Weibull modulus and fracture strength of the full shell were significantly affected
by the ratio of radius to thickness of SiC coating and both of them decrease
linearly with the increase of the ratio
(2) The dominant effect of the IPyCSiC interfacial roughness on intrinsic fracture
strength was found by matching the SEM images with the calculated critical flaw
size based on the Griffith fracture theory
(3) The interfacial roughness were successfully characterised by a
numericalstatistical method and the roughness ratio representing the shape of the
irregularities was proposed to be a unique parameter among different coatings
(4) The difference of the local fracture strength was dominated by the roughness ratio
and it decreased linearly with the increase of the roughness ratio It is been the
first time that the interfacial roughness was numerically related to the fracture
strength
(5) Microstructures such as grain boundaries and porosity were found to have
neglectable influence on fracture strength
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
150
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[26] S Gonzalez B Ferrari R Moreno C Baudin Strength analysis of
self-supported films produced by aqueous electrophoretic deposition J Am
Ceram Soc 88 (2005) 2645-48
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] B N Dev A Roy K Bhattacharjee H P Lenka D P Mahapatra Ge growth
on self-affine fractal Si surfaces influence of surface roughness J Phys D Appl
Phys 42 (2009) 145303-10
[29] J Feder Fractals Plenum New York 1988
[30] J T M De Hosson R Van Tijum Effects of self-affine surface roughness on the
adhesion of metal-polymer interfaces J Mater Sci 40 (2005) 3503-08
[31] G Palasantzas Roughness spectrum and surface width of self-affine fractal
surfaces via the K-correlation model Phys Rev B 48 (1993) 14472-78
[32] P Meakin Fractals scaling and growth far from equilibrium Cambridge
Cambridge University Press 1998
[33] H Zhang E Loacutepez-Honorato A Javed I Shapiro and P Xiao A study of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
153
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc 95 (2012) 1086-92
[34] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany and A H
Heuer Fracture toughness of polycrystalline silicon carbide thin films Apply
Phys Lett 86 (2005) 071920-22
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
154
CHAPTER 6 Effect of Thermal Treatment on
Microstructure and Fracture Strength of SiC Coatings
61 Introduction
The mechanical properties of the as-deposited SiC coatings have been widely studied
eg Youngrsquos modulus and hardness [1-3] fracture toughness [4] and fracture strength
[5] etc However after it experiences the high temperature the composition and the
microstructure of the SiC coating may change which consequently influences the
mechanical properties It has been found that mechanical properties of SiC such as
Youngrsquos modulus and hardness are less affected when experiencing the current fuel
operation temperature (less than 1600 ordmC) [1 6] even after thermal treatment
temperatures of 1980 ordmC [7] To enhance the operational temperature of the high
temperature reactor in the future design it would be necessary to understand the
evolution of microstructure and mechanical properties of SiC coatings at even higher
temperature Some research [8-10] has been carried out to study the effect of high
temperature (more than 2000 ordmC) thermal treatment on the density and microstructure
of the fuel particle Itrsquos concluded that fuel failure and fission product release
dependent on SiC thermal stability at high temperature [9] Rooyen et al[11]
measured the annealing temperature effect on the fracture strength of SiC coatings It
is found that the fracture strength increases after thermal treatment at temperature up
to 2000 ordmC decreases in strength after thermal treatment at 2100 ordmC However no
clear explanation was given on this result
Due to the importance of the SiC on the safety of this fuel it is necessary to study the
thermal stability of SiC and characterise any change in microstructure and mechanical
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
155
properties It has been previously found that SiC deposited at 1300 ordmC with the
addition of propylene and methyltrichlorosilane as gas precursors not only have good
mechanical properties such as hardness and Youngrsquos modulus [3] fracture toughness
[4] but also have high silver and palladium diffusion resistance [12 13] Therefore in
this Chapter we thermally treated SiC coatings deposited at a range of temperature
(1300-1500 ordmC) at 2000 ordmC for 1 hour in argon atmosphere The change of fracture
strength and thermal stability of SiC coating were studied in terms of composition and
microstructural change of the coatings after thermal treatment
62 Experimental details
Four batches of SiC coatings (with nearly stoichiometry) deposited by Fluidized bed
chemical vapour deposition at different tempearure were chosen to study the thermal
treatment effect on the evolution of the microstructure and fracture strength Table 61
gives the deposition conditions of coatings studied and symbols used to describe each
sample The stoichiometry was measured by the Raman spectroscopy (Renishaw 1000
Raman microprobe system with 514 nm Argon laser) The laser beam was focused on
the surface of the cross section through a times50 objective lens
Table 61 Deposition conditions of SiC coatings
Sample Temperature
(oC)
MTS concentration
(vol)
Added gas
concentration
Stoichiometry
SiC1 1280 91 01vol C3H6 SiC
SiC2 1300 91 01vol C3H6 SiC+C
SiC3 1400 19 57vol Ar SiC
SiC4 1500 22 79vol Ar SiC+C
The inner side of the coating is stoichiometric (23 of the thickness) while outside of the coating is
SiC with excess C The microstructure characterization was done in the inner side coating while the
fracture strength measurement is related to the full coating SiC+C means that the C peak around
1300-1500 cm-1
was observed in SiC coating Chosen of deposition conditions was contributed to Dr
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
156
Eddie Lopez-Honorato
The sample preparation for fracture strengths measurement is the same as described in
Chapter 5 As introduced before thermal treatment was carried out at 2000 ordmC for 1
hour in argon protected atmosphere on SiC half shells The same fracture strength test
and equipment settings as described in Chapter 5 were used in this Chapter
In addition to Raman spectroscopy the microstructure of SiC coatings before and
after thermal treatment was also characterised using X-ray diffraction (PW 1830
Philips) with a Cu Kα1 radiation source The XRD samples were the SiC segments
(fractured SiC shells without external residual stress) Scanning electron microscopy
(Philips XL30 FEG-SEM) was used to characterise the change in morphologies of
SiC coatings Porosity was measured by setting a threshold of the SEM images
(times1600 TIF) at a gray level and adjusted to distinguish pores from grains with Image
J software Three SEM images were measured for each SiC coating Average pore size
(diameter nm) and the pore fraction (area ratio of pores to the total area as observed
by SEM) were obtained For transmission electron microscopy (TEM) the specimens
were prepared by crushing the SiC shell and dispersing the fragments on a carbon
holy film copper grid and crystal structures were characterised using an FEG-TEM
(TecnaiTM G2
F30 U-TWIN)
63 Results
631 Fracture strength of SiC coatings
Figure 61 shows the Weibull distribution of the local fracture strength ( L
f ) in SiC
coatings before and after thermal treatment at 2000 ordmC It gives a direct observation on
the decrease of the local fracture strength in coating SiC2 SiC3 and SiC4 after
thermal treatment while the local fracture strength of coating SiC1 is nearly
overlapped with the as-deposited coating The magnitude of the mean local fracture
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
157
strength (as summarised in Table 62) could represent the decrease trend of the full
batch of the coating in current study
Fig 61 Weibull plots of local fracture strength ( L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
The Weibull modulus (m) was obtained by linearly fitting the curves shown in Fig 61
It shows that the Weibull modulus decreased by 14 07 and 21 in coating SiC1 SiC3
and SiC4 respectively however it increased slightly (by 12) in SiC2 after heat
treatment As shown in Fig 61 the Weibull modulus derived from linear fitting is
affected by the deviation of few points from the linear distribution of the local fracture
strength (as shown in Fig 61) For example in sample SiC3 the slightly decrease
could be attributed to the deviation of the lowest points According to previous study
[14] the slight decrease (07) of Weibull modulus in SiC3 could be neglected since
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
158
the deviated points could be caused by different failure mechanisms involved in the
fracture process [14]
Fig 62 Weibull modulus plots of fracture strength of the full shell ( F
f ) before
(black triangle) and after (red circle) thermal treatment
Figure 62 shows the Weibull plots of fracture strength of the full shell ( F
f ) before
and after thermal treatment at 2000 degC In the same batch of coatings (the same size
effect) the fracture strength of the full shell increase with the increase of the Weibull
modulus and local fracture strength according to previous study [5] Therefore the
decrease of local fracture strength and increase of the modulus in SiC2 could explain
the slight change (decreased 25 MPa obtained from Table 62) of the fracture strength
of the full shell after thermal treatment In the other three samples the fracture
strength of the full shell decreased significantly (more than 110 MPa obtained from
Table 62) after thermal treatment due to the decrease of local fracture strength and
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
159
unchanged modulus)
Table 62 summarized the results of the fracture strength measured before and after
thermal treatment at 2000 degC including the Weibull modulus (m) derived from the
distribution of the local fracture strength ( L
f ) the mean local fracture strength and
fracture strength of the full shell ( F
f ) After thermal treatment the mean local
fracture strength of coatings decreased significantly except SiC1 coating which
retained the same level as in as-deposited coating The mean fracture strength of the
full shell was reduced after thermal treatment in a different degree but the change of
Weibull modulus is more complex which shows both decreased and increased values
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the full shell before and after thermal
treatment
Sample m (from
L
f )
as deposited 2000degC
L
f MPa
as deposited 2000degC
F
f MPa
as deposited 2000degC
SiC1 75 61 1445 1421 774 660
SiC2 77 89 1599 1395 872 847
SiC3 65 58 1824 1333 820 548
SiC4 74 53 1717 1443 858 587
As concluded from Fig 61 Fig 62 and Table 62 the fracture strength decreases
less in coatings deposited at lower temperature (about 1300 degC) than those deposited
at higher temperature (1400-1500 degC) This is consistent with previous study about
high properties of SiC coatings deposited at low temperature such as the hardness
Youngrsquos modulus and resistance to the fission products [12 13 15]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
160
632 Change in morphologies
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after (c) and (d) SiC2 before and after
(e) and (f) SiC3 before and after (g) and (h) SiC4 before and after thermal treatment
Dashed and solid arrows indicate growth direction and pores respectively
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
161
Figure 63 gives the SEM images showing the microstructure of SiC coatings before
and after thermal treatment at 2000 ordmC Before thermal treatment no pores were found
in SiC1 and SiC2 coatings (Fig 63(a) and (c)) while nano-pores were found in SiC3
coating (Fig 63(e)) and even bigger (micrometres) pores were occasionally found in
SiC4 coating (Fig 63(g)) Among four as-deposited coatings SiC4 has highest area
fraction of pores (~09) followed by SiC3 (~03) coating (Fig 63 (a) (c) (e) and
(g) summarized in Table 63)
After thermal treatment at 2000 ordmC pores with different size and area fraction were
observed in all the coatings even though as-deposited SiC1 and SiC2 were free of
pores as shown in Fig 63(b) (d) (f) and (h) The amount of pores formed in treated
SiC1 coating (area fraction of ~05 ) is lower than the other three coatings which
have similar area fraction of pores (~14 ~13 and ~15 for SiC2 SiC3 and
SiC4 respectively given in Table 63) Similar to the content of the pores the pore
size (mean size of ~50 nm) in SiC1 is smaller than in the other coatings (gt 100 nm)
Among coatings SiC2 SiC3 and SiC4 much larger pores (micro-meter sized as in
Fig 63(f) and (h)) were produced in SiC3 and SiC4 coatings after thermal treatment
compared with nano-sized pores in SiC2 Furthermore it is found that most of pores
in coatings SiC2 SiC3 and SiC4 were formed along the grain boundaries and triple
junctions as we can see from Fig 63(d) (f) and (h)
The pores are uniformly distributed through the coatings and no area free of pores or
area with highly concentrated pores is observed However there are connections of
pores (2 or 3 pores formed closely) in SiC2 SiC3 and SiC4 as indicated by solid
arrows in Fig 63(d) (f) and (h) and the diameter of the porous connection zone
(black circle in Fig 63(d) (f) and (h)) could be in the magnitude of few micrometres
The connection of pores could easily become larger pores of few micrometres
diameter under external tensile strength due to the high strength concentration [14]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
162
Fig 64 The IPyCSiC interfacial roughness of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermally treated at 2000 degC (right
in each figure) The white arrow points towards to the interface irregularities (except
for thermally treated SiC4 coating (d)) black circle represents the pores in SiC
coatings
Figure 64 gives the evolution of interfacial roughness in different coatings after
thermal treatment at 2000 ordmC to study their influence on the change of fracture
strength Compared with the as-deposited coating the changes of the interfacial
roughness in SiC1 are similar to SiC3 which show the smoother interface with
interval of irregularities were observed Fig 64(a) and (c) However different from
as-deposited coatings with defects mainly at the interface defects (pores) are also
observed through the coating after thermal treatment (as seen in Fig 61(b) (f) and
Fig 64(a) (c)) Furthermore the size of pores is in the same magnitude as their
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
163
interfacial roughness (shown in Fig 64(a) and (c))
The change of the interfacial roughness in SiC2 is more significant than SiC1 and
SiC3 since pores formed as part of the interface (indicated by arrows in Fig 64(b))
and they are larger than the pores formed in the coating (circle in Fig 64(b))
Different from others three coatings the IPyCSiC interface of SiC4 becomes
smoother (Fig 64(e)) after thermal treatment compared with as-deposited coating so
the defects (pores) within the coating are bigger than surface irregularities
633 Evolution in microstructure
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermally
treated at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and
SiC2 inset shows the peak shift of as-deposited (dash line) and after thermal
treatment (solid line) (b) is SiC4 and inset is the high angle diffraction peak after
thermal treatment showing splitting while it is a single peak in as-deposited coating
Figure 65 gives XRD results of the as-deposited and thermally treated samples
which show the presence of the β-SiC in coatings The peak presents at 2θ~335ordm is
from the crystallographic errors which could either be due to the stacking faults or
the disordered α-SiC according to previous descriptions [16 17] It is found that the
intensity ratio of the 2θ~335ordm peak to the (111) plane peak (2θ~356ordm) decreased after
thermal treatment in all the coatings The coating SiC4 also shows the split of high
angle diffraction peaks (inset of the Fig 65(b) 2θ~613ordm and 713ordm) which is
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
164
attributed to the X-ray double diffraction and this implies the high crystallites after
thermal treatment
Figure 66 is the HRTEM image of sample SiC4 after thermal treatment in which the
stacking faults and micro twins could still be seen The stacking sequence of
ABCACBACBACB was observed as shown in the dashed square zone in Fig 66
According to study about crystal structure [18] this stacking sequence is supposed to
be the micro twins compared with the rest 3C stacking sequence rather than the
6H-SiC domain Furthermore the (111) peak shifted to the high angle after thermal
treatment in all the coatings as shown in the inset of Fig 65(a) which corresponded
to the decrease of the crystal constant
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Figure 67 gives the Raman spectroscopic results of SiC coatings before and after
thermal treatment The carbon peak at 1300-1600 cm-1
was found in the as-deposited
SiC2 and SiC4 coatings According to previous studies [4 19] the intensity ratio of
I1600I796 indicated that the estimated amount of excess C was less than 05 at in
this study The peak between TO and LO peaks (around 882 cm-1
) was attributed to
the stacking faults or highly disordered stacking faults cluster [3 15 20-22]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
165
After thermal treatment the weak carbon related peaks appeared at around 1395 cm-1
and 1600 cm-1
(G band) in sample SiC1 SiC2 and SiC4 The peak around 1395 cm-1
could represent the methyl group and amorphous carbon structures and G band is due
to the stretching mode of all pairs of sp2 atoms in chains and rings [23] The arising of
the 2D peak (also called G peak 2715 cm-1
) after thermal treatment was observed in
sample SiC2 SiC3 and SiC4 which is the second order of zone-boundary phonons
[24]Considering the amount of excess carbon in SiC coatings the symmetry of the
2D peak indicates that the carbon after treatment is more likely to be graphene rather
than graphite [24] which means the concentration of excess C is low in SiC coatings
It is also found that the intensity ratio of the disordered stacking faults (around 882
cm-1
) to the TO peak decreases in all samples after thermal treatment (shown in Fig
67)
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings The lower line is before thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
166
treatment and the upper line is after thermal treatment at 2000 degC in individual
sample
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
Sample Porosity ()
As 2000degC
Stoichiometry
As 2000degC
Critical Defects
As 2000degC
SiC1 0 05 0 C clusters Inter Inter+ Pore
SiC2 0 14 C clusters Ordered C Inter Inter
SiC3 03 13 0 Ordered C Inter Inter+ Pore
SiC4 09 15 C cluster Ordered C Inter Pore
First order Raman spectroscopy (1200-1600 cm-1
) Represents the carbon structure related to the
methyl group or amorphous carbon structures (contains SP2 and SP
3) [23] Second order (2700 cm
-1)
single layer grapheme related carbon materials [24]
Represents the interface irregularities
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
Furthermore the narrowing of the TO peak was found (the inset in Fig 67 (b)) in the
Raman spectroscopy Although it could be an overlap of two peaks at around 796 cm-1
and 789 cm-1
in coatings before and after thermal treatment the peak at 789 cm-1
corresponding to the stacking sequence of ABCACBhellip [25] is more likely to be
micro-twins in current study(as shown in Fig 66) Table 63 summarized the main
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
167
morphological and microstructural change of SiC coatings before and after thermal
treatment
Particularly for sample SiC3 except for the appearance of weak 2D peak after thermal
treatment without visible first order carbon peaks in the sample SiC3 the precipitates
were also observed from both inner and outside of the shell These precipitates were
demonstrated to be the single 3C-SiC crystal by Raman spectroscopy as shown in Fig
68 Raman spectra of precipitates represents the incident direction of the laser is
perpendicular to the SiC single crystal (111) plane which the LO mode at around 970
cm-1
is forbidden when Raman spectra were obtained in a backscattering geometry
[22] (The appearance of the forbidden LO band might be due to to finite collecting
angle of the spectrometer)
64 Discussion
641 Influence of interfacial roughness and pores on fracture strength
To evaluate the critical flaw size we used the equation 1
2( )
L ICf
K Z
Yc for tensile
strength (local fracture strength) and the case for the semi-circular surface crack
(Y=125 [26]) of radius c and inside holes (Y= π12
[14]) of diameter 2a When the
fracture toughness ( ICK ) of the SiC coating was taken as 33 MPa m-12
[27] the
critical surface defect radius and the diameter of the inside pores were calculated to be
in the range of 15 ndash 78 microm obtained from all the coatings The mean critical flaw
size is in the range of 30 ndash 40 microm after thermal treatment The calculated critical
flaw sizes are in the same magnitude as the defects observed at the IPyCSiC interface
and the pores in the SiC coatings after thermal treatment (see in Fig 63 and Fig 64)
Therefore the decrease of the local fracture strength after thermal treatment could be
related to the formation of these defects in SiC coatings Accordingly the sources of
critical defects were summarized in Table 63 for coatings before and after thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
168
treatment The interfacial roughness and pores within the coating compete to be the
critical flaws Once the size of interfacial irregularities is lower than critical flaw size
and rarely distributed their effect on fracture strength could be decreased or even
excluded according to previous study [14] Therefore the pores inside the coating
with the diameter of 2a would be considered as the main failure origins [14] These
could explain the decrease of local fracture strength in coatings SiC2 SiC3 and SiC4
which have micrometer pores formed within the coatings andor at the interface while
the local fracture strength is less affected in coating SiC1 due to formation of
nanometer pores
The Weibull modulus is related to the specimen size loading method and defects
distribution [5 14] In this study the specimen size and the loading morphology could
be excluded for one kind of SiC coating so the change of the modulus is due to the
degree of the scattering of the critical flaw size under the tensile strength The
interfacial irregularities in SiC2 became narrower and deeper (about 4 microm of depth as
shown in Fig 64(c)) after thermal treatment and they are also bigger than the pores
generated within the coating So the critical flaw in SiC2 after thermal treatments is
due to the interfacial irregularities (Table 62) with less scattered size under the
loading area than as-deposited coating which increased the Weibull modulus
However the critical defects in the other coatings include pores within the coatings
(shown in Fig 64 and Table 62) For example in SiC4 the critical flaw is only from
pores within the coating after thermal treatment due to the lack of interstitial
irregularities (Fig 64(h)) This enlarged the distribution of critical flaws after thermal
treatment which leads to the decrease of the Weibull modulus in different degree The
change of the fracture strength of the full shell depends on both Weibull modulus and
local fracture strength as discussed before [5] Our result showed that the SiC coating
deposited at low temperature of 1300 ordmC produced less critical flaws and smaller
decrease of the fracture strength of the full shell (see Table 63)
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
169
642 Mechanism of microstructural change
Changes in SiC coatings after thermal treatment include the formation of pores the
decreased intensity of the 2θ~335 ordm peak (crystallographic errors) in XRD the arising
of Raman peaks around 1395 cm-1
and 2715 cm-1
According to previous studies [8
10 21 25 28 29] we propose that these changes after thermal treatment could be
attributed to phase transformation or the diffusion of defects such as vacancies and
interstitials
If the 2θ~335ordm peak is from amorphous α-SiC its intensity ratio to (111) diffraction
peak would increase after heat treatment Because the presence of α-SiC phase in
β-SiC could promote the transformation of β-SiC into α-SiC [29] Conversely the
intensity of 2θ~335ordm peak decreased after thermal treatment in this work as observed
in Fig 65 and no α-SiC phase segregation (Fig 66) was found by HRTEM after
thermal treatment Furthermore the transformation from disordered α-SiC into β-SiC
after thermal treatment is also excluded because high pressure and high temperature
are needed for this process to happen [29] Therefore it is concluded that the 2θ~335ordm
peak derived from stacking faults and they could be annihilated at current
environment according to previous studies [8 28 30]
Stacking faults were surrounded by defects such as dislocations vacancies and
interstitials [10 15 31] so the high density of stacking faults in this work
corresponded to the high amount of native defects The annihilation of stacking faults
after thermal treatment indicated the reduction of these defects and it could reduce
the lattice constant In this work the decrease of the lattice constant was found after
thermal treatment as indicated by the peak shift of (111) plane in XRD results (Fig
65) and the crystallisation (ordering) was also reflected from the decreased intensity
of the 2θ~335ordm peak (Fig 65) and Raman defect peak (around 882 cm-1
) (Fig 67)
Therefore the formation of pores is due to the annealing of defects through the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
170
diffusion of vacancies or interstitials which are common even in high-purity CVD
SiC [32] However diffusion of native defects depended on their concentration which
was constrained by different composition of SiC (deviation from stoichiometry) [31]
For example for the C-rich cubic SiC the dominant defect is the CSi antisite (Si atom
site was occupied by C atom in tetrahedral structure) [31]
According to above analysis the formation mechanism of pores could be governed by
different kinds of defects In SiC1 coating the smallest and least content of pores
formed after thermal treatment is most likely caused by the annealing of stacking
faults surrounded by the dislocations and vacancies which is consistent with previous
study about the thermal treatment effect on stoichiometric SiC [28] In SiC coating
with excess carbon the microstructure evolution could be more complex as
demonstrated by the presence of the graphene layer (Raman peak at 2700 cm-1
)
According to previous studies [31 33] this is attributed to the existence of the CSi
antisite and vacancies which form the vacancy cluster and antisite clusters after
thermal treatment at 2000 degC
The microstructure change in SiC3 coating is different from SiC1 The diffusion
mechanism in SiC3 was supposed to be involved with the interstitials since the single
SiC crystal precipitate was found out of the coating(Fig 68) This also resulted in
higher amount of the pores in SiC3 than in SiC1 after thermal treatment It is
proposed that the different diffusion mechanism found in stoichiometric SiC1 (Si and
C vacancies) and SiC3 (tetragonal interstitials) could be due to different deposition
conditions which produced different kinds of dominant native defects The larger
pores formed in SiC3 and SiC4 could be due to larger grain size than SiC1 and SiC2
(different deposition temperature) because most of pores were near to the grain
boundaries and triple junctions (as shown in Fig 63(d) (f) and (h)) The diffusion of
native defects also affects the interfacial irregularities and the diffusion mechanism in
SiC coatings is being studied in our research group
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
171
65 Conclusions
The SiC coatings deposited at temperature range of 1300-1500 degC with composition
near-to the stoichiometry were thermally treated at 2000 degC in Ar atmosphere for 1
hour to study the effect of thermal treatment on microstructure and fracture strength
The following conclusions were obtained
(1) The local (intrinsic) fracture strength decreased in a varied degree after
thermal treatment and it was due to the formation of pores along the IPyCSiC
interface and in the coatings
(2) The Weibull modulus decreased once the pores have similarbigger size
asthan interfacial irregularities and distribute uniformly within coatings while
it increased with the size of pores much smaller than interfacial irregularities
after thermal treatment
(3) After thermal treatment no phase transformation was found in SiC coatings
and the crystallographic error (2θ~335 ordm) detected by XRD was demonstrated
to be stacking faults which were annihilated during this process
(4) The formation of pores after thermal treatment was attributed to the diffusion
of intrinsic defects such as vacancies interstitials and antisites Different
content and size of pores were observed in different coatings which are
presumed to have different kinds of native defects in as-deposited coatings
produced at different conditions
(5) The vacancies are supposed to be the dominant defects in stoichiometric SiC
deposited at 1280 ordmC however in other coatings the dominant defects could
be a combination of vacancies antisites and interstitials based on Raman
results before and after thermal treatment Furthermore the diffusion of native
defects also affects interfacial roughness after thermal treatment which needs
further study
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
172
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[9] D T Goodin Accident condition performance of fuels for high-temperature
gas-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[10] N Shirahata K Kijima A Nakahira K Tanaka Thermal stability of stacking
faults in Beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
173
[11] J van Rooyen J H Neethling P M van Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[12] E Loacutepez-Honorato K Fu P J Meadows J Tan and P Xiao Silicon carbide
coatings resistant to attack by palladium J Am Ceram Soc 93 (2010) 4135-41
[13] E Loacutepez-Honorato H Zhang D X Yang P Xiao Silver diffusion in silicon
carbide J Am Ceram Soc 94 (2011) 3064-71
[14] D J Green An Introduction to the Mechanical Properties of Ceramics
Cambridge University Press Cambridge 1998
[15] H Zhang E Loacutepez-Honorato A Javed X Zhao J Tan P Xiao A Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc (2012) DOI101016jjeurceramsoc201112014
[16] H Tateyama H Noma Y Adachi M Komatsu Prediction of stacking faults in
βndashSilicon carbide X-Ray and NMR studies Chem Mater 9 (1997) 766- 72
[17] K R Carduner S S Shinozaki M J Okosz C R Peters T J Whalen
Characterization of β-Silicon carbide by silicon-29 solid-state NMR transmission
electron microscopy and powder X-ray diffraction J Am Ceram Soc 73 (1990)
2281-86
[18] httptfuni-kieldematwisamatdef_enkap_6advancedt6_3_2html
[19] S M Dong G Chollon C Larbrugere M Lahaye A Guette J L Brunee M
Couzi R Naslain and D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[20] M Havel D BaronL Mazerolles P Colomban Phonon confinement in SiC
nanocrystals comparison of the size determination using transmission electron
microscopy and Raman spectroscopy Appl Spet 61 (2007) 855-59
[21] V V Pujar J D Cawley Effect of stacking faults on the X-Ray diffraction
profiles of 3C-SiC powder J Am Ceram Soc 78 (1995) 774-82
[22] Y L Ward R J Young R A Shatwell Effect of excitation wavelength on the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
174
Raman scattering from optical phonons in silicon carbide monofilaments J Appl
Phys 102 (2007) 023512 -17
[23] X J Li J Hayashi C Z Li FT-Raman spectroscopic study of the evolution of
char structure during the prolysis of a victorian brown coal Fuel 85 (2006)
1700-07
[24] A C Ferrari J C Meyer V Scardaci C Casiraghi M Lazzeri F Mauri S
Piscanec D Jiang K S Novoselov S Roth A K Geim Raman spectrum of
graphene and graphene layers Phys Rev Lett 97 (2006) 187401-04
[25] S Nakashima H Harima Raman investigation of SiC polytypes Phys Stat Sol
A-Appl Res 162 (1997) 39-64
[26] GKBasal Effect of flaw shape on strength of seramics J Am Ceram Soc 59
(1976) 87-8
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] K Koumoto S Takeda CH Pai High-resolution electron microscopy
observation of stacking faults in βndashSiC J Am Ceram Soc 72 (1989) 1985-87
[29] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J Am Ceram Soc 84 (2001) 3013-16
[30] K Koumoto S Takeda C H Pai T Sato H Yanagida High-resolution electron
microscopy observations of stacking faults in β-SiC J Am Ceram Soc 72 (1989)
1985-87
[31] C Wang J Bernholc Formation energies abundances and the electronic
structure of native defects in cubic SiC Phys Rev B 38 (1998) 12752-55
[32] E Janzen N T Son B Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[33] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-09
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
175
CHAPTER 7 Microstructure and Mechanical Properties of
Pyrolytic Carbon Coatings
71 Introduction
Pyrolytic carbon (PyC) coatings forming part of the TRI-Isotropic (TRISO) fuel
particle are important for the stability of this type of nuclear fuel Without appropriate
microstructure and mechanical properties of PyC coatings the stress generated inside
the particle due to internal gas pressure andor the dimensional change (anisotropic
shrinkage or creep) introduced in this layer during irradiation process could result in
the failure of the full particle [1-5] Fundamental understanding about relationship
between mechanical properties and microstructure of PyC coatings could help to
analyse the failure mechanism and model the probability of failure of TRISO fuel
particles [1 5] However their relations in PyC are complex [3 6-8] Kaae [7] found
that mechanical properties were related to the density crystal size and anisotropy but
they are not controlled by a single variable For example Youngrsquos modulus increased
with density for isotropic carbons with constant crystallite size but decreased with
increasing anisotropy for carbon with constant density and crystalline size In a
separate work [3] density had a dominant effect on the hardness and Youngrsquos
modulus in relative low density PyC coatings whereas no controlling factor was
given for high density PyC coatings
Nano-indentation is an effective way to study microstructural effects on mechanical
properties of PyC coatings because it could help with the understanding of the
deformation mechanism and measure Youngrsquos modulus and hardness spontaneously
Among studies on mechanical properties in carbon related materials under
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
176
depth-sensing indentation [3 9-15] few explanations about the nature of their
deformation mechanism have been discussed [9 10 13 15] First the hysteresis was
assumed to due to the slip of graphene layers in nano-meter grains and the energy
loss was attributed to the friction between graphene layers under compression stress
[9 10] Second the dislocation pileups were assumed to be responsible for energy
loss [13] but this idea failed to account for the reversible deformation [15] The most
recent theory suggested that the origin of the hysteresis was due to the formation of
(incipient) kink bands [15] This theory was found to be a universal explanation for
most laminar structured materials but the nature of initial kink band was not clear
[15]
During pressing process of TRISO fuel particles into fuel elements they experience a
final thermal treatment of 1 h above 1800 ordmC to drive off any residual impurities and
improve thermal conductivity of the fuel compact [16] The evolution of
microstructure of carbon related materials have been widely studied [17-20] Few
researches measured changes of mechanical properties after thermal treatment [19
20] but there is a lack of understanding about effect of microstructural evolution on
mechanical properties in PyC coatings Therefore in this Chapter together with the
microstructural properties the deformation mechanism under indentation influences
on mechanical properties and their change after thermal treatment in PyC coatings are
studied
72 Experimental details
Pyrolytic carbon (PyC) was coated on alumina particles (Φ 500 μm) by fluidised bed
chemical vapour deposition by Dr Eddie Loacutepez-Honorato and PyC coatings with
different density was chosen to study the mechanical properties Table 61 gives the
density and texture (orientation angle) of PyC coatings and more about deposition
mechanism could be found in Ref [21] The number of sample sequence Ci (i=1
2hellip11) starts from highest density to lowest density with density of 19 gcm3 as
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
177
border line to distinguish highlow density PyC which was measured by the
Archimedes method in ethanol For thermal treatment the coatings were first
grounded into fragments and then removed the alumina kernel The fragments of PyC
were then thermal treated at 1800 degC and 2000 degC for 1 hour in argon atmosphere For
further understanding of microstructural evolution during thermal treatment sample
C5 was thermal treated at 1300 1400 1500 and 1600 degC for 1 hour
Table 71 PyC coatings with different density and orientation angle
PyC
(High density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
PyC
(Low density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
C1 2122plusmn0059 58 C6 1855plusmn0050 63
C2 2087plusmn0183 37 C7 1738plusmn0013 73
C3 2047plusmn0030 60 C8 1635plusmn0008 71
C4 2029plusmn0015 43 C9 1603plusmn0024 71
C5 2000plusmn0061 43 C10 1414plusmn0002 85
C11 1400plusmn0024 81
Orientation angle was obtained from the full width of half maximum of azimuthal intensity scan of
SAED pattern for more information in Ref [22] Productions of PyC coatings measurement of
orientation and density measurement are contributed by Dr Eddie Loacutepez-Honorato et al
The selected area electron diffraction (SAED) patterns were obtained with the use of a
FEG-TEM (see Chapter 3) and orientation angle was measured by the azimuthal
intensity scans of SAED pattern (selected aperture diameter of 200 nm) Further
details about this measurement were shown in a previous study [22] Transmission
electron microscopy (TEM) samples were obtained by focus ion beam milling High
resolution TEM samples were prepared by dispersing the fragments on a carbon holey
film copper grid X-ray diffraction (see Chapter 3) was used to obtain domain sizes of
PyC coatings After correction of intrinsic instrumental effect the out of plane and
in-plane domain sizes (along c-axis and a-axis in graphite crystal structure) Lc and La
were qualitatively estimated from XRD data by applying the Scherrer equation to the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
178
(002) and (110) reflections respectively [23] In as-deposited PyC coatings the (110)
peak was too weak to estimate accurately on the La Raman spectroscopy (633 nm
Helium ion laser source) was performed by single spot measurements (spot size was
carefully controlled to be the same for each test) of around 2 μm diameter using a times50
objective lens The laser power of less than 05 mW (10) was used with the step
size of 60 seconds and twice accumulations For each sample 5 different positions
were measured The band fitting of the first order spectra was carried out with
GRAMS32 software
To reduce the influence of surface roughness on indentation test the PyC coatings
were ground with successive finer grades of SiC paper and polished down to a 1 microm
grid diamond paste The same nano-indentation as in Chapter 3 was used The
measurements were performed at fixed loading rate of 1 mNS reaching the
maximum load of 100 mN For each coating at least 25 indentations were conducted
on the sample surface to increase the reliability of the results The Olive and Pharr
method [24] was used to analyse all the data
73 Results
731 Microstructure of PyC coatings
In order to study the influences of microstructure on mechanical properties it is
necessary to know the nature of structure which makes one sample from another eg
disorders domain size crystallinity etc and their evolution after thermal treatment
7311 Raman spectroscopy
Figure 71 is a Raman spectroscopy for an as-deposited high density PyC coating (C5
200 gcm3) which exhibits two relatively broad Raman bands at around 1335 cm
-1
and 1600 cm-1
The first band corresponds to the D band which is attributed to double
resonant Raman scattering and represents the in-plane defects [21 25 26] The
second band is an overlap of broadened G (1580 cm-1
) and D (1620 cm-1
) bands due
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
179
to high disordered pyrolytic carbon [27] The G band is due to the stretching modes of
pairs of sp2 atoms in graphene planes whereas D represents the similar defects
structure as the D band [18 27] It is convenient to consider 1600 cm-1
band a single
G peak for practical purposes when comparing different samples or the overall
structural evolution of a given PyC coating [27]
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
According to previous studies [25-32] on fitting similar Raman spectra shown in Fig
71 a simple two-symmetric-line fit (D and G bands) could not fit it well Therefore
the Raman spectra of high density PyC coatings (C1-C5 gt 19 gcm3) were
deconvoluted into above peaks at about 1220 cm-1
1335 cm-1
1500 cm-1
and 1600
cm-1
( Fig 71) The band at about 1500 cm-1
(Drsquorsquo) is attributed to interstitial defects
which could act as coupling (covalent band) between two graphene layers or adjacent
overlapped domains [25 28] The I band at around 1220 cm-1
is due to C-C on hydro
aromatic rings [28] The Raman spectra mean the high degree of in-plane andor
out-of-plane disorders in high density PyC coatings represented mainly by the full
width at half maximum (FWHM) of the D band [28] and intensity ratio (the area ratio
of the 1500 cm-1
peak to the sum of four peaks shown in Fig 71) of the Drdquo bands
[25] respectively
D
I
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
180
Figure 72 is the Raman spectra of high density PyC coating C5 after thermal
treatment at temperature of 1300 1400 1600 and 1800 ordmC The FWHM of the D band
decreased significantly from about 150 cm-1
(as-deposited) to about 106 cm-1
(1400
ordmC) and then to about 40 cm-1
(1800 ordmC) Similarly the intensity ratio of the Drdquo was
reduced from about 0135 (as-deposited) to about 0110 (1400 ordmC) and then to about
0078 (1800 ordmC) Another change is the split of G and D bands after thermal treatment
at 1800 ordmC (Fig 72) The above changes indicate that disorders in high density PyC
coatings are low energy structural defects ie degree of disorder is low according to a
previous study [28]
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
181
After thermal treatment the degree of microstructural changes of low density PyC
coatings C6-C8 (164-186 gcm3) is slightly different from even lower density
coatings C9-C11 (140-160 gcm3) so they are described separately Figure 73 shows
Raman spectra of low density PyC coatings (a) C7 and (b) C10 before and after
thermal treatment at 1800 ordmC Similar to high density PyC the as-deposited coatings
C6-C8 contains four Raman bands After thermal treatment the FWHM of the D peak
in C7 decreased from about 120 cm-1
to 57 cm-1
and the intensity ratio of interstitial
defects was also reduced (from 0116 to 0042 Fig 73(b)) In coating C10 only
slightly decrease of FWHM of the D peak (from about 83 cm-1
to 57 cm-1
) was found
after thermal treatment at 1800 ordmC (Fig 73(b)) No split of the G and D bands was
observed in low density PyC coatings
With increase in density of PyC the FWHM of the D band the concentration of the
Drdquo band and the degree of their changes after thermal treatment increase considerably
which suggest that the disorder defects in PyC are different with variation of density
and thermal treatments change the degree of the disorder
7312 Domain sizes
Table 72 summarises the out-of-plane domain size (crystallite size perpendicular to
the graphene plane Lc) and in-plane domain size (crystallite size along the graphene
plane La) measured by XRD in PyC coatings before and after thermal treatment The
Lc is in the range of 1-3 nm in all the as-deposited coatings and it is slightly bigger in
high density (about 2-3 nm) coatings than low density (about 1-2 nm) coatings After
thermal treatment at 1800 ordmC the Lc increased significantly which is about 5 times
and 2-3 times larger than in as-deposited high density and low density PyC coatings
respectively It is 2-4 times larger in high density PyC than low density PyC coatings
The La in high density (about 6 nm) is larger than low density PyC coatings (3-4 nm)
after thermal treatment at 1800 ordmC Both Lc and La remained unchanged after thermal
treatment at 2000 ordmC in all PyC coatings (This is explained in section 741) The
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
182
increase of domain size indicated the ordering process in PyC coatings after thermal
treatment which may involve annealing of different kinds of disorders
Table 72 Domain size of as-deposited and thermal treated PyC coatings
Sample As deposited 1800 2000
Lc (nm) La (nm) Lc (nm) La (nm) Lc (nm) La (nm)
High density (gt19 gcm3)
C1 21 -- 112 -- 116 53
C2 21 -- 132 63 154 69
C3 22 -- 98 66 111 63
C4 24 -- 95 57 118 63
C5 20 -- 120 60 152 73
Low density (lt 19 gcm3)
C6 22 -- 50 42 56 44
C7 18 -- 38 36 50 34
C8 14 -- 31 33 27 39
C9 11 -- 27 32 31 34
C10 17 -- 24 33 27 35
C11 11 -- 27 35 27 33
7313 Evolution of crystallinity
Figure 74 is the TEM images of high density PyC (C5) before and after thermal
treatment The dark field TEM show bright areas (Fig 74(a) and (b)) that represent
graphene layers with similar orientation in the selected direction of the diffraction
pattern A decrease of the orientation angle from 43 ordm to 25 ordm is found after thermal
treatment at 1800 ordmC which is obtained from the full width at half maximum of
azimuthal intensity scan of SAED pattern (insets in Fig4(a) and (b)) A bright field
TEM image of a conical microstructure after thermal treatment (Fig 74(c) dashed
rectangle in Fig 74(b)) which shows the voids at the top of conical structures The
above observations show that thermal treatment increases anisotropy and results in the
volume shrinkage and generation of voids in high density PyC coatings
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
183
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Figure 75 is the typical HRTEM away from the top of conical growth feature (eg
OA=43 ordm
OA=25 ordm
Top
Voids
100 nm
(c)
(a) (b)
5 nm
Moireacute
fringes
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
184
white circle in Fig 74(c)) in high density PyC coatings (C1) before and after thermal
treatment at 1800 ordmC The wrinkled short graphene fringes in as deposited high
density PyC (Fig 75(a)) were replaced by distorted planes in a larger scale with a
bigger radius of curvature (white arrow in Fig 75(b)) The common number of
parallel layers (Fig 75(a) (002) plane white parallel lines) is 2-4 in as-deposited C1
which increased to about 30 (Fig 75(b) between white parallel lines) The moireacute
fringes were observed after thermal treatment (black arrow in Fig 75(b)) which
correspond to black bars in the bright field TEM (eg dashed black rectangle in Fig
74(c)) According to the generation mechanism of moireacute fringes [33] the on-going
ordering process along the c-axis is related to the increase of number of parallel layers
and evolution (decrease) of the inter plane distance of (002) planes
Figure 76 gives the bright field TEM and HRTEM images showing the
microstructure evolution in a low density PyC coating (C7) Globular growth features
with diameters of about 400 nm were observed in as-deposited C7 as shown in Fig
76(a) and the HRTEM image shows 2-3 layers of parallel planes (Fig 76(b)) In low
density PyC coatings the graphene fringes are longer and less oriented than in high
density coatings (reflected from orientation angle shown in Table 71 and Fig 13 in
Ref [21]]) After thermal treatment the short dark bars andor dots (as indicated by
the white arrows Fig 76(c)) were observed which is due to the moireacute fringes as
shown in Fig 76(d) The number of parallel layer increased up to 8-10 (Fig 76(d))
and it reflects the slight crystallinity after thermal treatment In the other low density
PyC coatings C9-C11 the TEM images are similar with the as-deposited low density
PyC coatings (as shown in Fig 14 and Fig 13(c) in Ref [21]) Furthermore the
orientation angle is almost the same in all low density PyC before and after thermal
treatment
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
185
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
732 Mechanical properties of PyC coatings
7321 Force-displacement curve
Figure 77 gives the force-displacement curve of PyC coatings with different density
under the maximum load of 60 mN and 100 mN by nano-indentation The unloading
curve did not completely retrace the loading curve but still returned to the origin This
process is called anelastic behaviour or hysteresis behaviour and the anelastic
reversible indentation processes with an enclosed loop are found in all the PyC
coatings
(a) (b)
100 nm 5 nm
5 nm
Sphere-like
particle
Tops
Moireacute fringes Sphere-like
particle
Top (d)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
186
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
The maximum indentation depth in low density PyC (C6-C11 lt 19 gcm3) is deeper
than in high density PyC coatings (C1-C5 gt 19 gcm3) under the same load and the
low density PyC also shows larger hysteresis loop area The ratio of the hysteresis
energy (area within the loading-unloading loop) to total loading energy (area under
loading curve) in high density PyC is lower than in low density PyC coatings For
example the ratios of sample C3 C9 and C11 are 0243 0270 and 0292 respectively
Furthermore the deformation behaviour of all PyC coatings showed the hysteresis
behaviour after thermal treatment up to 2000 ordmC The high density PyC after thermal
treatment at 1800 ordmC (red curve in Fig 77) shows anelasticity however the ratio of
its hysteresis energy (0249) is much higher than in as-deposited coating (0174)
According to previous studies [10 34] the low ratio obtained in high density PyC
coatings under pyramidal indenter corresponds to high elasticity while low density
exhibits high hysteresis (anelasticity high viscosity))
Under indentation the hardness is defined as the mean pressure the material will
support under load according to Oliver and Pharrrsquos study [24] This pressure is equal
to the load at maximum load divided by the contact area (according to eqs (7 10 11)
hc
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
187
in Chapter 2) However the residual depth hf is zero and no pleastic deformation is
observed after unloading The hardness obtained by Oliver and Pharr method does not
reflect the resistance of plastic deformation of material but it could represent the
degree of unelastic deformation qualitatively Therefore the mean pressure (P) value is
used which could reflect the anelastic properties of PyC coatings
7322 Youngrsquos modulus and the mean pressure
Figure 78 gives the Youngrsquos modulus (E) and the mean pressue (P) of as-deposited
PyC coatings as a function of density For low density PyC coatings (C6-C11 lt 19
gcm3) Youngrsquos modulus and the mean pressure increase almost linearly with the
density For high density PyC coatings (C1-C5 gt 19 gcm3) both Youngrsquos modulus
and the mean pressure reach plateaus which are independent of density It indicates
that mechanical properties of high PyC coatings are dominated by other factors
which are discussed in session 744
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
Table 73 shows the Youngrsquos modulus and the mean pressure of PyC coatings with
different density before and after thermal treatment at 1800 and 2000 ordmC After
thermal treatment at 1800 ordmC Youngrsquos modulus decreased by around 50 and the the
mean pressure is reduced by around 69 in high density PyC coatings (C1-C5 gt19
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
188
gcm3) whereas minor change is observed when thermal treatment temperature
further increased to 2000 ordmC Previous study [20] showed similar results about
changes of mechanical properties in high density PyC after thermal treatment at
different temperature In low density PyC coatings C6-C8 (164-186 gcm3) the
mean pressure and Youngrsquos modulus decreased by about 23 and 8 after thermal
treatment at 1800 ordmC respectively which is consistent with Rooyen et alrsquos results
[19] and further decreased by 18 and 15 by increasing thermal treatment
temperature to 2000 ordmC In low density coatings C9-C11 (140-160 gcm3) little
change in mechanical properties after thermal treatment up to 2000 ordmC was found and
it is similar as the isotropic low density PyC [20] Mechanical properties and their
change after thermal treatment in PyC coatings are different with different density
Table 73 Changes of mechanical properties of PyC coatings after thermal treatment
Sample As deposited Thermal treated at 1800 Thermal treated at 2000
P (GPa) E (GPa) P (GPa) E (GPa) P (GPa) E (GPa)
High density
C1 468plusmn025 2670plusmn119 103plusmn018 1482plusmn131 090plusmn013 1337plusmn093
C2 435plusmn048 2513plusmn117 132plusmn019 1091plusmn069 076plusmn021 1204plusmn126
C3 490plusmn036 2878plusmn117 -- -- 091plusmn026 1271plusmn125
C4 397plusmn019 2291plusmn076 171plusmn010 1313plusmn034 110plusmn010 1370plusmn051
C5 456plusmn010 2610plusmn036 132plusmn015 1177plusmn051 177plusmn025 1361plusmn101
Low density
C6 388plusmn035 2165plusmn191 296plusmn022 1912plusmn113 244plusmn023 1647plusmn088
C7 395plusmn053 2149plusmn200 292plusmn036 1934plusmn114 232plusmn033 1568plusmn182
C8 354plusmn027 1945plusmn070 292plusmn036 1904plusmn113 232plusmn063 1678plusmn240
C9 284plusmn040 1938plusmn094 226plusmn057 1677plusmn178 263plusmn042 1733plusmn151
C10 189plusmn009 1266plusmn035 213plusmn019 1363plusmn076 188plusmn023 1381plusmn087
C11 168plusmn017 1166plusmn082 178plusmn034 1284plusmn106 086plusmn014 1167plusmn151
74 Discussions
The main findings of this study can be summarised as follows 1) PyC with different
density show different full width at half maximum (FWHM) of the D band and
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
189
concentration of the Drsquorsquo band which suggests that they have different types of disorder
TEM observation shows longer graphene fringes with lower density PyC (Fig 13 in
Ref [21]) thermal treatments decrease the degree of disorder while PyC with higher
density (gt19 gcm3) shows higher degree of decrease 3) initial increase in PyC
density until 19 gcm3 lead to proportional increase in Youngrsquos modulus (E) and the
mean pressure (P) while further increase in density has no effect on E and P 4)
hysteresis occurred after nano-indentation of PyC while the degree of hysteresis is
controlled by the PyC density and heat treatments
741 Disorders and their changes after thermal treatment
High density PyC Coatings (C1-C5 gt 19 cmg3) The dominant in-plane disorders
are domain boundaries according to a previous study [21] which generates high
FWHM of the D band due to the low energetic disorientations (eg domains andor
graphene layers) [25 28] The Drsquorsquo band (interstitial defects) is due to the amorphous
carbon structure which is composed of mainly disordered sp2 atoms and a low
amount of sp3 atoms [27 28 35] Particularly the sp3 lines are out of plane defects
which could be formed in high density PyC coatings [36] Therefore it is assumed
that the microstructure in high density PyC is composed of disoriented nano-size
graphite domains connected by amorphous carbon
After thermal treatment the reductions of the out-of-plane defects and the tilt and
twist in graphite planes are observed which could contribute to the increase of Lc
(out-of-plane domain size) as shown in HRTEM image (Fig 75) It was supposed
that the equilibrium shear stress were generated by in-plane defects and out-of-plane
defects in PyC coatings [25] once the out-of-plane defects was reduced the in-plane
stress would tend to straighten the graphite planes Furthermore the decreases of
FWHM of the D band and the orientation angle (Fig 72 and 4) show the ordering
arrangement of graphite layers is due to the healing of in-plane disorientations The
unchanged domain size Lc could be a result of a combination of increased number of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
190
parallel graphene layers and decreased inter distance of (002) plane As a conclusion
the increase of domain size Lc could be due to the coalescence of domain size andor
graphene layers through reorientation and remove of interstitial defects which
usually started at temperature of about 900-1200 ordmC [17 25] No La (in-plane domain
size) value was obtained in as-deposited PyC and the overlap of the G and the Drsquo
bands indicates it is below 4 nm above which two bands split [37] After thermal
treatment at 1800 ordmC the La is about 6 nm in high density PyC coatings (Table 72
and splitting of G and Drsquo bands was shown in Fig 72) which demonstrates the
slightly increase of La It is attributed to the annihilation of low energetic in-plane
disorientations which could usually be removed at temperature above 1500 ordmC [25]
Since the high temperature above 2000 ordmC is needed to remove the rest high energetic
in-plane defects for high density PyC according to previously study [25 28] it could
explain the La remained nearly constant after thermal treatment further increased to
2000 ordmC The ordering of graphite layers is responsible for the formation of voids (Fig
74(c)) since the ordering could reduce the volume and increase the density of PyC
coatings after thermal treatment [38]
Low density PyC Coatings (C6-C11 lt 19 cmg3) The main defect is the
5-memebered rings in coatings C9-C11 by comparing the Raman spectroscopy (Fig
73(a)) with a previous study [21] In low density coatings C6-C8 (164-186 gcm3)
the degree of in-plane disorder is less than in high density coatings but higher than
coatings C9-C11 (140-160 gcm3 indicated by the FWHM of the D band) and the
out-of-plane defects are much higher than low density PyC coatings (Fig 73) After
thermal treatment the in-plane disorder is similar as in coatings C9-C11 Therefore
the dominant in-plane defects are supposed to be a combination of domain boundaries
and 5-membered rings The slightly increase of domain size Lc in low density PyC
coatings is due to the decrease of interfacial defects through reorientation of domains
However they have much lower degree of increase of Lc than high density coatings
this could be due to low anisotropy in low density PyC coatings which makes it
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
191
difficult to reorient domains and remove the weak defects [17 25] The domain size
La was assumed to be unchanged since ordering in-plane disorders took place at
temperature above 2400 ordmC in low density PyC due to presence of 5-member rings
[17] It is worth to notice that the graphene fringes do not represent the in-plane
domain size in low density PyC due to the curvature caused by 5-memebered rings
[21] Due to the exist of 5-membered rings in low density PyC coatings the
microstructure is lightly affected by thermal treatment
742 Hysteresis after indentation
The increase in density of PyC leads to decrease in hysteresis after indentation and
density of PyC also dominate types and degree of disorders During indentation of
PyC hysteresis is caused by the slip of graphene planes whereas the disorders such as
interstitial defects or 5-memebered rings are supposed to be responsible for the
reversible deformation The hysteresis was also observed in other carbon materials
such as single crystal graphite [15] polycrystalline graphite [15] glassy carbon [9
10] Similar explanations about the effect of slip of graphene layers on the hysteresis
behaviour under indentation were given and it suggests that the deformation
mechanism is related to a common structure in different carbon materials which are
graphene planes
The slip of graphene planes has been demonstrated available The shear modulus (micro)
of graphite is 23 GPa (between graphene layers) [39] Based on the relation of τth= micro
30 [39 40] the theoretical shear stress (τth) of graphite is estimated to be 0077 GPa
This shear stress is much lower than the yield stress under Berkovich indenter for
graphite (03-05 GPa) [15] Under indentation the slip of graphene planes consumes
energy but recovers to the original shape after unload Lower density PyC has longer
fringes than that in higher density PyC (Fig 13 Ref [21]) therefore the panes can
slip for a longer distance under shear stresses generated by nano-indentation
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
192
Reversible deformation is due to presence of interstitial defects or highly curved
5-memebered rings For indentation of crystallite graphite the kink band could be
generated during the initial indentation process then reviersible deformation occurs
under further indentation [15] similar as that shown in Fig 77 In our PyC coatings
disorder in the PyC plays a similar role as the kink band in the crystallite graphite
The slip direction is parallel to the graphene planes so the in-plane defects presents at
the tilt and twist of two adjacent domains could not stop and reflect the slip Only
those defects perpendicular to the slip direction can contribute to the reversible
deformation such as interstitial defects or the highly curved 5-memebered rings
(caused fibrous graphene planes as shown in Fig 13(c) Ref [21])
After heat treatment the growths of the in-plane fringes increase the degree of the
hysteresis in PyC coatings For example the straightened graphene fringes (Fig 75)
caused by reorientation and removes of interstitials facilitate the hysteresis
significantly (the ratio of hysteresis energy to total loading energy increased from
0174 to 0249 Fig 77)
743 Mechanical property of low density PyC coatings
In as deposited low density PyC (C6-C11 gt 19 gcm3) Youngrsquos modulus and the
mean pressure are dominated by the density which is consistent with previous studies
[3 7 41] because of the effect of porous structure [3 21] As discussed in session
741 the disorders in low density PyC coatings play an important part on the stability
of microstructure which could reflect changes of mechanical properties After thermal
treatment the mechanical properties remained almost unchanged in PyC coatings
C9-C11 (140-160 gcm3) and this could be explained by the insignificant change of
microstructures at the presence of 5-membered rings The slightly decrease of
mechanical properties were found in coatings C6-C8 (164-186 gcm3) which is due
to the ordering of graphene planes through reduction of interstitial defects which
could enhance hysteresis and decrease the mean pressure No voids and change of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
193
orientation was observed after thermal treatment in coatings C6-C8 so Youngrsquos
modulus is slightly affected It is concluded that the mean pressure and Youngrsquos
modulus are functions of density in as-deposited low density coatings and their
evolution after thermal treatment is controlled by disorders such as interstitials andor
5-membered rings
744 Mechanical Property of high density PyC coatings
In high density PyC coatings (C1-C5 gt 19 gcm3) Youngrsquos modulus and the mean
pressure are independent of density so they are discussed regarding to variation of
texture domain size and concentration of interstitial defects (the area ratio of the 1500
cm-1
peak to the sum of four peaks shown in Fig 71) Table 74 summarises
microstructure parameters and mechanical properties of high density PyC coatings
Mechanical properties are not controlled by domain size and orientation angle which
is converse to the previous study [41] It is found that Youngrsquos modulus and the mean
pressure in high density PyC coatings decrease with the reduction of concentration of
interstitial defects (as shown in Table 74)
Table 74 The parameters used to explain different mechanical properties of high
density PyC (C1-C5 gt 19 gcm3)
Sample Density
(gcm3)
Texture
OA (deg)
Domain
size (nm)
IinterstialAll Pressure
(GPa)
Modulus
(GPa)
C3 2047 plusmn0030 60 22 013955plusmn000374 490plusmn036 2878plusmn117
C1 2122 plusmn0059 58 21 013513plusmn000399 468plusmn025 2670plusmn119
C5 2000 plusmn0061 43 20 013456plusmn000561 456plusmn010 2610plusmn036
C2 2087 plusmn0183 37 21 013036plusmn000433 435plusmn048 2513plusmn117
C4 2029 plusmn0015 43 24 011823plusmn001628 397plusmn019 2291plusmn076
The physical meaning of the above observation can be explained by the effect of
interstitial defects on the deformation mechanism in high density PyC coatings First
the high concentration of interstitial defects could reduce the energy consumption by
the reversible slip of graphene planes (eg in Fig 77) and it corresponds to high the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
194
mean pressure in high density PyC coatings Second in-plane Youngrsquos modulus is
much higher than out-of plane Youngrsquos modulus in graphite so the bonding between
graphene planes becomes important when the orientation effect could be neglected in
high density PyC (Table 74) For example in sample C4 and C5 the high Youngrsquos
modulus was obtained in C5 which have high amount of covalent band (interstitial
defects sp2 and sp3 in Fig 71) in the direction perpendicular to graphene planes The
high concentration of interstitial defects in high density PyC could also reduce the
influences of orientation angle on the high Youngrsquos modulus This could explain the
similar Youngrsquos modulus in C1 and C5 which have different orientation angles
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
After thermal treatment at temperature range of 1300-1800 ordmC in C5 (about 200
gcm3) the effect of concentration of interstitial defects on mechanical properties was
again demonstrated as given in Table 75 The mechanical properties decrease
gradually with the increase of thermal treatment temperature until 1600 ordmC and then a
dramatic decrease at 1800 ordmC The decrease is related to the reduction of content of
interstitial defects (Table 75) Furthermore no other relationship between mechanical
properties and microstructural features such as FWHM of the D band intensity of D
band and G band in Raman spectroscopy is found in the current work Therefore the
concentration of interstitial defects is proposed to dominant mechanical properties of
high density PyC coatings This idea about effect of interstitial defects on mechanical
properties is similar as the cross-link theory [8] which suggested that the mechanical
properties is related to the length and number of links between domains Furthermore
Temperature (ordmC) IinterstialAll Pressure (GPa) Youngrsquos modulus (GPa)
0 013456plusmn 000561 456plusmn010 2610plusmn 036
1300 011882plusmn000906 430plusmn010 2519plusmn060
1400 011045plusmn000278 413plusmn010 2407plusmn070
1500 009598plusmn000034 406plusmn022 2439plusmn070
1600 009469plusmn000219 391plusmn016 2344plusmn036
1800 007756plusmn000199 132plusmn015 1177plusmn051
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
195
the significant decrease of the the mean pressure and Youngrsquos modulus after 1800 ordmC
could be due to the straightening of graphene layers and formation of voids (Fig
74(c)) respectively To conclude the mechanical properties in high density PyC
coatings before and after thermal treatment from 1300 to 1800 ordmC decrease with the
reduction of concentration of interstitial defects
74 Conclusions
Disorders in PyC coatings was characterised by Raman spectroscopy A
combination of high degree of in-plane (domain boundaries) and out-of plane
defects (interstitial defects) prevail in high density PyC while the 5-membered
rings are dominant defects in low density PyC coatings
In high density PyC coatings the significant increase of domain size Lc is
attributed to the coalescence of domainsgraphene layers through reorientation and
reduction of interstitial defects During this process the graphene planes were
straightened resulting in slightly increase of La
In low density PyC coatings the microstructure remained almost unchanged after
thermal treatment due to the presence of the 5-membered rings which need high
temperature to be reduced
The hysteresis deformation behaviour was found in all PyC coatings before and
after thermal treatment under nano-indentation The nature of hysteresis is
suggested to be Slip of graphene planes consumes energy (hysteresis loop) and
disorders (interstitial defects and highly curved 5-memebered rings in high density
and low density PyC coatings respectively) are responsible for the reversible
deformation (unloading curve back to origin)
The mean pressure and Youngrsquos modulus are functions of density in low density
PyC coatings and their changes after thermal treatment are insignificant which
are due to the almost unchanged microstructure
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
196
In high density PyC coatings the mean pressure and Youngrsquos modulus are
independent of density orientation angle and domain size but they are related to
the concentration of interstitial defects After thermal treatment the decrease of
mechanical properties is attributed to the reduction of interstitial defects leading
to the straightening of graphene planes and formation of voids
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
197
75 References
[1] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques thin solid films 469-70 (2004) 214-20
[2] D G Martin Considerations pertaining to the achievement of high burn-ups in
HTR fuel Nucl Eng Des 213 (2002) 241-58
[3] E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure and
mechanical properties of pyrolytic carbon produced by fluidized bed chemical
vapour deposition Nucl Eng Des 238 (2008) 3121-28
[4] G K Miller D A Petti A J Varacalle J T Maki Consideration of the effects
on fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[5] A C Kada R Gnallinger M J Driscoll S Yip D G Wilson H C No et al
Modular pebble bed reactor In Modular pebble bed reactor project University
research consortium annual report 2000
[6] G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
[7] J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[8] F G Emmerich C A Luengo Youngrsquos modulus of heat-treated carbons A
theory for nongraphitizing carbons Carbon 31 (1993) 333-39
[9] J S Field MVSwain The indentation characterisation of mechanical properties
of various carbon materials Glassy carbon coke and pyrolytic graphite Carbon
34 (1996) 1357-66
[10] N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[11] M V Swain J S Field Investigation of the mechanical properties of two glassy
carbon materials using pointed indetners Philos Mag A 74 (1996) 1085-96
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
198
[12] N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philos Mag A 82 (2002) 1873-81
[13] M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated carbons
J Am Ceram Soc 85 (2002) 1522-28
[14] A Richter R Ries R Smith MHenkel B Wolf Nanoindentation of diamond
graphite and fullerene films Diamond Relat Mater 9 (2000) 170-84
[15] MW Barsoum A Murugaiah S R Kalidindi T Zhen Y Gogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[16] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
treatment J Nucl Mater 374 (2008) 445-52
[17] F G Emmerich Evolution with heat treatment of crystallinity in carbons Carbon
33 (1995) 1709-15
[18] M A Pimenta G Dresselhaus M S Dresselhaus L G Cancado A Jorio R
Saito Studying disorder in graphite-based systems by Raman spectroscopy Phys
Chem Chem Phys 9 (2007) 1276-91
[19] I J Van Rooyen J H Neethling J Mahlangu Influence of Temperature on the
Micro-and Nanostructures of Experimental PBMR TRISO Coated Particles A
Comparative Study Proceedings of the 4th
international topical meeting on high
temperature reactor technology Washington DC USA HTR 2008-58189
[20] J C Bokros R J Price Deformation and fracture of pyrolytic carbons deposited
in a fluidized bed Carbon 3 (1966) 503-19
[21] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-I Effect of deposition conditions on microstructure
Carbon 47 (2009) 396-10
[22] P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
199
[23] S Bernard O Beyssac K Benzerara N Findling G Tzvetkov G E Brown Jr
XANES raman and XRD study of anthracene-based coke and saccharose-based
chars submitted to high-temperature pyrolysis Carbon 48 (2010) 2506-16
[24] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7 (1992) 1564-83
[25] J N Rouzaud A Oberlin C Beny-bassez Carbon films structure and
microstructure (optical and electron microscopy Raman spectroscopy) Thin solid
film 105 (1983) 75-96
[26] S Potgieter-Vermaak N Maledi N Wagner J H P Van Heerden R Van
Grieken J HPotgieter Raman spectroscopy for the analysis of coal a review J
Raman Spectrosc 42 (2011) 123-29
[27] A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-photon coupling doping and nonadiabatic effects Solid state commun
143 (2007) 47-57
[28] J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy electron
diffraction and few other techniques Carbon 44(2006) 1833-44
[29] G A Zickler B Smarsly NGierlinger H Peterlik O Paris A reconsideration
of the relationship between the crystallite size La of carbons determined by X-ray
diffraction and Raman spectroscopy Carbon 44 (2006) 3239-46
[30] A Cuesta P Dhamelincourt J Laureyns A Martinez-Alonso JMD Tascon
Raman microprobe studies on carbon materials Carbon 32 (1994) 1523-32
[31] A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
200
[32] S Yamauchi Y Kurimoto Raman spectroscopic study on pyrolyzed wood and
bark of Japanese cedar temperature dependence of Raman parameters J Wood
Sci 49 (2003) 235-40
[33] D B Williams C B Carter Transmission electron microscopy A textbook for
materials science Springer New York p 392-97
[34] M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[35] T Jawhari A Roid J Casado Raman spectroscopic characterization of some
commercially available carbon black materials Carbon 33 (1995) 1561-5
[36] G L Dong K J Huumlttinger Consideration of reaction mechanisms leading to
pyrolytic carbon of different textures Carbon 40 (2002) 2515-28
[37] A Jorio E H Martins Ferreira M V O Moutinho F Stavale C A Achete R
B Capaz Measuring disorder in graphene with the G and D bands Phys Status
Solidi B 247 (2010) 2980-82
[38] R Piat Y Lapusta T Boumlhlke M Guellali BReznik D Gerthsen TChen R
Oberacker M J Hoffmann Microstructure-induced thermal stresses in pyrolytic
carbon matrices at temperatures up to 2900 ordmC J Eur Ceram Soc 27 (2007)
4813-20
[39] J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[40] A H Cottrell Dislocations and plastic flow in crystals Clarendon Press Oxford
1972 p 162
[41] J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
CHAPTER 8 Conclusions and Future Works
201
CHAPTER 8 Conclusions and Future Works
This work provides both fundamental understanding and techniqual guidance on the
mechanical properties and their relationship with microstructures of SiC and PyC
coatings in TRISO fuel particles The measurement of hardness and Youngrsquos modulus
of SiC coatings could be used in the modelling work to study the peroperty of the
failure of the fuel particlues and these results have been published The measurement
of the fracture toughness of SiC in TRISO fuel particle has solved one of the
techniqual problems in field and the study contributes to the study of the fracture
behaviour of SiC coatings The fracture strength measurement has enriched the
strength data of SiC coatings before and after thermal treatment (related paper is
under revision) The characterisation of the interfacial roughness has provided a direct
method to correlate the relationship between fracture strength and interfacial
roughness The mechanical properties of PyC coatings provide foundamental
understanding about the deformation mechanism of the PyC coatings under
indentation The effect of thermal treatment on the mechanical properties has given a
preguidance about the behaviour of the PyC coatings at high temperature
81 Conclusions
(1) In SiC coatings deposited at 1300 ordmC by fluidised bed chemical vapour deposition
the Youngrsquos modulus was an exponential function of the porosity and the high
hardness was attributed to the high density of dislocations and their interactions
The initiation and propagation of micro cracks under the confined shear stress was
found to be responsible for the mechanism of plastic deformation Based on this
hardness-related plastic deformation mechanism the variation of hardness in the
three types of SiC coating was due to different grain morphologies
CHAPTER 8 Conclusions and Future Works
202
(2) The fracture beneath the Vickers indenter consists of Palmqvist cracks as
observed using SEM in above SiC coatings Based on this crack mode Vickers
indentation fracture toughness values of 351-493 MPa m12
were obtained It was
found that stress-induced micro-cracks seem to be a mechanism for the fracture
behaviour The presence of defects such as nano-pores and less constraint grain
boundaries could generate more micro cracks which dissipated energy from the
main cracks
(3) Fracture strength measured by modified crush test give less scattered values
within a given sample by distributing the load under a contact area It has been
found that Weibull modulus and fracture strength of the full shell were
significantly affected by the ratio of radius to thickness of the coating and both of
them decrease linearly with the increase of this ratio
(4) The numericalstatistical analysis was able to characterize the interfacial
roughness of different coatings and the roughness ratio representing the
irregularities was proposed to be a unique parameter for this description The
difference of the local (intrinsic) fracture strength was dominated by the
roughness ratio and it decrease linearly with the increase of the roughness ratio
The roughness ratio has the similar effect on the difference of fracture strength of
the full shell
(5) After heat treatment at 2000 degC the local fracture strength was reduced due to the
formation of pores in the coatings which could act as the enlarged critical flaw
size The Weibull modulus decreased when the pores in SiC coatings became
critical flaws while it increased once more uniformly distributed critical flaws
along the IPyCSiC interface were formed The formation of pores was mainly
related to the annihilation of stacking faults and diffusion of intrinsic defects such
as vacancies interstitials and antisites
CHAPTER 8 Conclusions and Future Works
203
(6) The hysteresis deformation mechanism was proposed to be due to the slip of
graphene planes which constraint by interstitial defects and highly curved
5-membered rings in high density and low density PyC coatings respectively
(7) The hardness and Youngrsquos modulus were related to the concentration of
interstitial defects and density in high density and low density PyC coatings
respectively Their changes in high density PyC is more significant than in low
density PyC coatings after heat treatment over 1800 ordmC due to the annihilation of
interstitial defects and reorientation of graphene layers
82 Suggestions for future work
(1) According to current study high amount of native defects were found in SiC
deposited at low temperature and it would be interesting to study their effects on
the thermal stability in a certain range of temperature such as from 1200-2000 ordmC
The study of the diffusion of native defects in SiC could also assist the study of
diffusion behaviour of fission products because these defects are more active and
they tend to reach the equilibrium during annealing process Due to different
deposition conditions the dominant species of native defects could be different in
different coatings therefore it is also important to study the deposition effect on
thermal stability of SiC coatings
(2) Itrsquos important to know how the microstructure change of SiC coatings deposited at
low temperature after irradiation because they showed robust mechanical
properties and high resistance to fission products It has been found they have high
amount of dislocations and stacking faults which accompanied by interstitials and
vacancies as reflected from the enlarged lattice constant According to this it is
supposed that after irradiation the volume change of SiC will be small because of
the pre-exist lattice defects Therefore study of the irradiation effect (at different
operational temperature) on SiC deposited at low temperature would be
promising
CHAPTER 8 Conclusions and Future Works
204
(3) Although current study has proposed to use self-affine theory to characterize the
interfacial roughness more work about their effects on fracture strength need to
be explored For example find out if the derived linear function between
roughness ratio and fracture strength in the current study could be used to explain
the differences of fracture strength in other tests To do further demonstration it is
necessary to reduce the geometrical influence and choose SiC coatings has
similar microstructure but different IPyCSiC interface These samples could be
prepared by just changing the deposition condition of IPyC while keep it same for
SiC coatings
Abstract
6
Abstract
Mechanical and Microstructural Study of Silicon carbide and Pyrolytic Carbon
Coatings in TRISO Fuel Particles
The University of Manchester
Huixing Zhang
Doctor of Philosophy in Materials Science
TRISO fuel particles have been developed as nuclear fuels used for a generation IV
nuclear reactor high temperature reactor Such particle consists of a fuel kernel
pyrolytic carbon (PyC) and silicon carbide (SiC) coatings This study has been carried
out to establish a relationship between mechanical properties and microstructures of
SiC coating and PyC coatings produced by fluidized bed chemical vapour deposition
Indentations were used to measure hardness Youngrsquos modulus and fracture behaviour
of SiC and PyC coatings Fracture strength of SiC coatings was measured by crush
test Microstructure of SiC and PyC was mainly characterised by transmission
scanning electron microscopy and Raman spectroscopy
For SiC coatings produced at 1300 ordmC Youngrsquos modulus is an exponential function of
relative density Hardness of SiC coatings is higher than the bulk SiC produced by
CVD and it is attributed to the high density of dislocations and their interactions The
deformation mechanism of SiC coatings under indentation is explained by presence of
defects such as grain boundaries and nano-pores The fracture of these coatings
beneath the Vickers indentation is the Palmqvist cracks and indentation fracture
toughness was in the range of 35-49 MPa m12
The stress-induced micro-cracks are
assumed to be the mechanism for the high indentation fracture toughness Different
hardness and fracture toughness in these SiC coatings are attributed to influences of
defects and grain morphology
Measurement of fracture strength was carried out on SiC coatings deposited at
1300-1500 ordmC Weibull modulus and fracture strength of the full shell are dominated
by the ratio of radius to thickness of coatings and decrease linearly with the increase
of this ratio The influence of SiCPyC interfacial roughness on fracture strength of
the SiC was quantified by self-affine theory The fracture strength decreases linearly
with the increase of the roughness ratio which is the long-wavelength roughness
characteristic After thermal treatment at 2000 ordmC fracture strength decreased in SiC
coatings due to the formation of pores which are results of diffusion of native defects
in as-deposited SiC coatings and the change of Weibull modulus is related to the size
and distribution of pores
For low density PyC coatings Youngrsquos modulus and the mean pressure increase with
the increase of the density however for high density PyC coatings they are
determined by interstitial defects The hysteresis deformation behaviour under
nano-indenation has been found be affected by density variation and thermal
treatment which is proposed to be due to the disorder structure in PyC coatings
Declaration
7
Declaration
No Portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Copyright Statment
8
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this thesis)
owns any copyright in it (the lsquolsquoCopyrightrsquorsquo) and she has given the University of
Manchester certain rights to use such Copyright including for administrative
purposes
ii Copies of this thesis either in full or in extracts and whether in hard or electronic
copy may be made only in accordance with the Copyright Desings and Patents Act
1988 (as amended) and regulations issued under it or where appropriate in
accordance with licensing agreements which the University has from time to time
This page must form part of any such copies made
iii The ownership of certain Copyright patens designs trade marks and other
intellectual property (the lsquolsquoIntellectual Property Rightsrsquorsquo) and any reproductions of
copyright works in the thesis for example graphs and tables (lsquolsquoReproductionsrsquorsquo)
which may be described in this thesis may not be owned by the author and may be
owned by third parties Such intellectual Properties Rights and Reproductions cannot
and must not be made available for use without the prior written permission of the
owner(s) of the relevant Intellectual Property Rights andor Reproductions
iv Further information on the conditions under which disclosure publication and
commercialization of this thesis the Copyright and any Intellectual Property andor
Reproductions described in it may take place is available in the University IP policy
(see httpwwwcampusmanchesteracukmedialibrarypoliciesintellectual-property
Pdf) in any relevant Thesis restriction declarations deposited in the University
Library The University Libraryrsquos regulations (see
httpwwwmanchesteracuklibraryaboutusregulations) and in the Universityrsquos
policy on presentation of Thesis
Acknowledgement
9
Acknowledgement
I will always be appreciative to Professor Ping Xiao for his support and guidance
during this project period and his enthusiasm for work and positive attitude towards
life inspired me I am thankful for what he shared about his own experience doing
research which impressed me and motivated me to make improvement
I would like to thank in particular Dr Eddie Loacutepez-Honorato for his patient guidance
on my experiments and valuable advices on my project His caution on preparing
delicate specimen infected me and helped me through my project He was always
there listening my ideas and discussing with me and he has set an example for being
a good researcher
I give my thanks to all the members in ceramic coating group old and new and I
treasure and appreciate this chance working with you
I would like to give my great gratitude to Dr Alan Harvey for his kind help on
transmission electron microscopy Mr Andrew Forest and Mr Kenneth Gyves on
nano- and micro-indentation Mr Andrew Zadoroshnyj on Raman spectroscopy Dr
Ali Gholinia and Dr Ferridon Azough on TEM sample preparation Dr Judith
Shackleton and Mr Gary Harrison on X-ray diffraction Mr Christopher Wilkins and
Mr Michael Faulkner on scanning electron microscopy and Mr Stuart Mouse on
tensile tests
I am grateful to my dear friends Yola David and Dean and you make my life more
colourful and interesting I would like to thank my beloved parents and brother for
your love care and support and you are great examples of hard work and kindness
My thanks also go to the ORS scheme the CSC grant and the F-BRIDGE for their
financial support during my PhD studies
List of Figures
10
List of Figures
CHAPTER 1 Introduction
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Fig 12 Behaviour of coated layers in fuel a particle [10]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
CHAPTER 2 Literature Review
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
List of Figures
11
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation[62]
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
List of Figures
12
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC coatings Measured by
Indentation
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
List of Figures
13
BF-TEM and (b) DF-TEM
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for extra-Si SiC coatings
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
Fig 45 Cross-sectional SEM image of stoichiometric SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
List of Figures
14
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a)
extra-C SiC (b) extra-Si SiC
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
Fig 58 Log-log representation of the height-height correlation function ∆h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
List of Figures
15
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC coatings
Fig 61 Weibull plots of local fracture strength (L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
Fig 62 Weibull modulus plots of fracture strength of the whole shell (F
f ) before
(black triangle) and after (red circle) thermal treatment
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after thermal treatment (c) and (d) SiC2
before and after thermal treatment (e) and (f) SiC3 before and after thermal treatment
(g) and (h) SiC4 before and after thermal treatment Dashed and solid arrows indicate
growth direction and pores respectively
Fig 64 The IPyCSiC interfacial morphology of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermal treated at 2000 degC (right in
each figure) The white arrow points towards to the interface irregularities (except for
thermal treated SiC4 coating (d)) black circle represents the pores in SiC coatings
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermal treated
at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and SiC2 inset
shows the peak shift of as-deposited (dash line) and after thermal treatment (solid
line) (b) is SiC4 and inset is the high angle diffraction peak after thermal treatment
showing splitting while it is a single peak in as-deposited coating
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
List of Figures
16
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
List of Tables
17
List of Tables
CHAPTER 2 Literature Review
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Table 23 Elastic tensors of 3C-SiC at room-temperature
Table 24 Vickers and nano-indentation hardness of polycrystalline CVD SiC
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Table 26 Summary of the hardness and Youngrsquos modulus for pyrolytic carbon
measured by different methods
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Measured by Indentation
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχv
along the radial and tangential directions
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC
Coatings
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Table 52 Summary of measured and calculated parameters for all the coatings
List of Tables
18
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Table 54 Results and variations influences on fracture strength for SiC coating
CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture
Strength of SiC Coatings
Table 61 Deposition conditions of SiC coatings
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the whole shell before and after thermal
treatment
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings
Table 71 PyC coatings deposition conditions and physical properties
Table 72 Domain size (XRD) of as-deposited and thermal treated PyC coatings
Table 73 Changes of mechanical properties after thermal treatment of PyC coatings
Table 74 The parameters used to explain different mechanical properties of high
density PyC
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
CHAPTER 1 Introduction
19
CHAPTER 1 Introduction
11 TRI-Isotropic (TRISO) fuel particles
A fission reaction is about that a large atomic nucleus (such as Uranium-235) is hit by
a neutron and absorbs the neutron forming a larger unstable nucleus The unstable
larger atomic nuclear breaks into two small nuclei and releases a high amount of
energy more neutrons beta and alpha particles and gamma The energy release is
much greater than for traditional fuels eg 1 g Uranium nuclear fuel releases the
same amount of energy as approximately 3 tonne of coal [1] The energy can be
transferred through the cooling system and used to boil the water to make steam to
drive a turbine and electrical generator in a nuclear power station
The high-temperature gas cooled reactor is one of the most promising candidates for
the production of nuclear energy according to its unique features For example it has
high coolant outlet temperature (850-1000 degC) which provides more efficient
electricity production due to the increased difference of the hot and cold coolant
temperatures [2] Furthermore it has the safety advantages due to the enclosure of the
fuel kernel (such as UO2 UC) within few layers of ceramic coatings Currently the
most common technique to fabricate fuels for operating the next generation
high-temperature gas cooled reactors is the TRISO fuel particles coating system [3]
The TRISO system was designed not only to retain all fission products during neutron
irradiation but also to withstand the thermo-mechanical stresses generated during
service [4]
CHAPTER 1 Introduction
20
Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block
matrix [5]
Figure 11 is the schematic of TRISO fuel particles embedded in a graphite matrix A
TRISO fuel particle consists of a fuel kernel and coating layers of porous pyrolytic
carbon (PyC) called buffer layer inner dense PyC (IPyC) silicon carbide (SiC) and an
outer dense PyC (OPyC) [5] and these layers were designed to have different
purposes The buffer layer absorbs metallic fission products recoils from kernel and
provides a space for fission product gases It also takes the volume change caused by
the kernel swelling without transmitting forces to outer layers The dense and
isotropic IPyC layer stops the chlorine from reacting with the kernel during deposition
of SiC and provides a firm substrate for the SiC layer Furthermore it protects the
SiC layer from most of the fission products and carbon monoxide during operation
The OPyC layer protects SiC layer during the remainder of the fabrication process
and provides structural stability to the particle during irradiation [3] The high
mechanical properties of SiC are needed to contain the high pressure generated in the
kernel and withstand the stress developed by the dimensional change of IPyC [3]
CHAPTER 1 Introduction
21
12 Failure mechanism
The radiation effects on the performance of the fuel particles such as fundamental
performance characteristics and fission product relsease mechanisms have been well
understood Different testing conditions (eg temperature up to 1300 degC and the does
of neutron) reflected the senariors encountered real applications [6-8]
During irradiation a number of potential failure mechanisms were revealed according
to several tests of coated fuel particles conducted in material test reactors and in
real-time operating HTR reactors [6-8] Chemically the corrosion of SiC by the
fission product palladium has been observed in almost all kinds of fuel compositions
and is considered as one of the key factors influencing the fuel performance However
this could be avoided by limiting the fuel temperature irradiation time or increase the
thickness of SiC layer [9] Mechanically the built up of the internal gas pressure (eg
CO) of irradiated particle and the neutron induced embrittlement of PyC coatings
could promote the failutre of the TRISO fuel particle The primary mechanisms which
may result in mechanical failure of TRISO fuel particles and lead ultimately to fission
product release depends significantly on the magnitude of the de-bonding strength
between IPyC and SiC layers [3 9]
121 Traditional pressure vessel failure mode
In this mode the failure was assumed to occur due to simple overload of the SiC layer
due to internal pressure build-up from fission gas [10] Both IPyC and OPyC layers
shrink during operation because of the irradiation exposure [11] This causes
compression stress in the SiC layer and tensile stress in the PyC layers Failure of the
SiC layer can only occur if the internal gas pressure is high enough to overcome the
compressive stress and critical stress of the SiC layer itself
CHAPTER 1 Introduction
22
Fig 12 Behaviour of coated layers in fuel a particle [10]
Figure 12 shows the basic behaviour modelled in a three layers standard model [10]
It shows that both IPyC and OPyC layers shrink and creep during irradiation but the
SiC layer exhibits only elastic deformation A portion of gas pressure is transmitted
through the IPyC layer to the SiC The pressure continually increases as irradiation of
the particle goes However if the PyC layer could remain in tension the failure by
fracture of SiC layer would be less likely to happen in this mode When the failure of
the PyC layer occurs a tensile hoop stress in the SiC layer is generated This leads to
the development of the stress concentration mode provided by the fracture of the inner
PyC layer
122 Stress concentration mode
In this mode it is been proposed that there is a point at which the fracture strength of
the IPyC would be exceeded during exposure When this occurs a radial crack will
form in the IPyC layer The crack could either penetrate through the SiC layer or
partially de-bonding the IPyCSiC interface This would lead to severe stress
concentration near the crack tip and it could reach the maximum of 440 MPa
according to previous simulation work [10] Once de-bonding goes through the whole
interface the source of stress in the SiC layer would be fission product gas build-up
CHAPTER 1 Introduction
23
and this case has similar failure mechanism of traditional pressure vessel failure mode
Although this process could decrease the probability of failure compared with the
stress concentration case the probability of failure may be higher than the traditional
failure mode Because the stress generated in the SiC layer after de-bonding would
increase [3]
Fig 13 A failed case of TRISO-coating observed from post-irradiation examination
[10]
All these behaviours make it easier for the SiC layer to reach its fracture strength and
lead to the radial crack and failure of the SiC results in an instantaneous release of
elastic energy that should be sufficient to cause simultaneous failure of the
pyrocarbon layer Shown in Fig 13 is a photomicrograph illustrating the failure of a
TRISO coating According to the above discussion all the carbon layers are partially
designed to support or protect the SiC layer The SiC layer serves as the main
containment barrier for gas and metallic fission products [3] and high mechanical
properties of the SiC layer are needed However without appropriate microstructure
and mechanical properties of the PyC layer the stresses or structural changes
introduced in this layer during the irradiation process could result in the failure of the
whole particle [9 12] Furthermore mechanical properties such as the hardness (It is
CHAPTER 1 Introduction
24
the resistance to plasticpermanent deformation of materials under constant load from
a sharp object) Youngrsquos modulus (It reflects the resistance to reversible deformation
of a material) fracture toughness (It describes the ability of a material containing a
crack to resist fracture) and fracture strength (It is the maximum stress at which a
specimen fails via fracture) of SiC and PyC coatings are also important factors for the
safety design and evaluation of the TRISO coating system [10]
13 Goals of dissertation
Due to the importance of mechanical properties of SiC and PyC layers in keeping the
integrity of TRISO fuel particles and providing adequate information for modelling
the probability of failure of particles a good understanding of the elastic plastic and
fracture properties and their relation with microstructure is necessary Therefore all
the work carried out in this project is aimed at studying the relationship between
microstructure and mechanical properties of these two layers aiming to provide a
fundamental understanding about the deformation mechanism and solve the practical
issues
Due to small scale of SiC and PyC coatings two main techniques used to measure
mechanical properties are micronano-indenation and crush test Furthermore to study
the effect of microstructures on mechanical properties characterization techniques
such as transmissionscanning electron microscope and Raman spectroscopy are
widely used in the current work
In this thesis Chapter 2 reviews the recent progress in microstructural characterisation
and mechanical properties of SiC and PyC related materials which provides basic
information with regard to future study about hardness Youngrsquos modulus
deformation mechanism and fracture behaviour in these
Chapter 3 studies the influences of microstructure on hardness and Youngrsquos modulus
CHAPTER 1 Introduction
25
of SiC coatings and focuses on understanding the deformation mechanism of SiC
under nano-indentation The fracture toughness of these SiC coatings is measured by
Vickers-indentation and the importance of crack modes is discussed in Chapter 4
In Chapter 5 the fracture strength of SiC coatings in TRISO fuel particles is measured
and influence of the IPyCSiC interface on fracture strength is discussed Effect of
thermal treatment on fracture strength and microstructure of SiC coatings deposited at
different conditions are introduced in Chapter 6
Chapter 7 investigates the microstructure and mechanical properties of PyC coatings
with focus on deformation mechanism under indentation and the effect of density and
disorders on mechanical properties before and after thermal treatment
At last the main results and conclusions together with suggestions on future work are
given in Chapter 8
CHAPTER 1 Introduction
26
14 References
[1] httpnuclearinfonetNuclearpowerTheScienceOfNuclearPower
[2] J J Powers Fuel performance modelling of high burnup transuranic TRISO fuels
Disertation of Master University of California Berkeley 2009
[3] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)
329-77
[4] D L Hanson J J Saurwein D W McEachern A S Shoeny Development plan
for advanced high temperature coated-particle fuels Report Nopc000513
[5] httpwwwmpafrprocessphp
[6] W Burck H Nabielek A Christ H Ragos AW Mehner HTR coated particle
fuel irradiation behaviour and performance prediction Specialists meeting on
gas-cooled reactor fuel development and spent fuel treatment IWGGCR-8 1983
174-88
[7] H Nickel H Nabielek G Pott A W Mehner Long-time experience with the
development of HTR fuel elements in Germany Nucl Eng Des 217 (2002)
141-51
[8] H Nabielek W Kuhnlein W Schenk W Heit A Christ and H Ragoss
Development of advanced HTR fuel elements Nucl Eng Des 121 (1990)
199-210
[9] K G Miller D A Petti J Varacalle T Maki Consideration of the effects on
fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[10] A C Kadak R G Ballinger M JDriscoll et al Modular pebble bed reactor
project university research consortium Annual report INEELEXT-2000-01034
MIT-ANP-PR-075
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
CHAPTER 1 Introduction
27
treatment J Nucl Mater 374 (2008) 445-52
[12] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
CHAPTER 2 Literature Review
28
CHAPTER 2 Literature Review
21 Introduction
To model the probability of failure of fuel particles a number of key mechanical
properties of silicon carbide (SiC) are needed such as Youngrsquos modulus hardness
fracture toughness and fracture strength [1 2] These properties could be affected by
the microstructure of SiC coatings such as orientation porosities grain size and
defects [1-5] The small dimensions of the SiC coating limits the techniques available
to measure its mechanical properties However the development of the
nano-indentation has provided an important tool for probing the mechanical properties
of small volumes of material From the load ndash displacement data many mechanical
properties such as hardness Youngrsquos modulus and even fracture behaviour can be
determined [6] When an indentation system is used in conjunction with a focused ion
beam system and a transmission electron microscope images of deformation under
the nano-indentation can be obtained and the 3-D crack morphology can even be
reconstructed [7] Since there is a need to explain the high mechanical properties of
SiC deposited at temperature of 1300 ordmC by fluidized-bed chemical vapour deposition
[8] this combination of techniques could provide fundamental understanding of the
deformation mechanisms during indentation Another important parameter is fracture
strength and there have always been efforts to establish one method to characterise
fracture strength of SiC for example by brittle-ring test [9] whole particle crush test
[10] and modified crush test [5] Furthermore the high temperature application of SiC
and the compact of fuel pellet could affect the microstructure of SiC [2] which would
lead to the changes of mechanical properties
CHAPTER 2 Literature Review
29
The pyrolytic carbon (PyC) has been introduced by previous studies [11-14] and is
important in helping the SiC act as the main loading bearing layer The high
mechanical properties such as Youngrsquos modulus and anelasticity of PyC are necessary
to protect from damage caused by internal stresses and by external mechanical
interactions [12] However cracking and debonding between the SiC and inner PyC
layers could increase the probability of failure of TRISO fuel particles [13 14] It was
shown that without appropriate microstructure and mechanical properties of PyC the
structural or stress changes introduced in the coating during irradiation process could
result in total failure of the particle [11 13] The microstructure of PyC varied under
different deposition conditions [15] and it dominates the mechanical properties of
PyC coatings Therefore in this Chapter we review both the microstructure of SiC
and PyC including atomic structure morphology and defects and their mechanical
properties eg hardness Youngrsquos modulus deformation behaviour etc
22 Microstructure of silicon carbide
221 Atomic structure
The basic structural unit in SiC is a covalently bonded tetrahedron a carbon atom is at
the centre of four silicon atoms (C-Si4) and vice versa (Si-C4) The length of each
bond and the local atomic environment are nearly identical while the stacking
sequence of the tetrahedral bonded Si-C bilayers could be different The different
stacking sequences give SiC more than 250 polytypes [16] of which the 3C 4H 6H
and 15R are the most common The leading number of polytypes shows the repetition
of the SindashC pair and the letter C H and R represents the cubic hexagonal and
rhombohedral crystals respectively The 3C is the only cubic polytype in which the
stacking sequence of the planar unit of Si and C in tetrahedral coordination is depicted
as ABCABC in the lt111gt direction The cubic SiC crystal is called β-SiC and all
the other polytypes are α-SiC The crystal structures of 3C- 4H- 6H- and 15R-SiC
are schematically illustrated in Fig 21(a) [17] and corresponding XRD images were
CHAPTER 2 Literature Review
30
shown in Fig 21(b) [18]
Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R
[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn
from Ref [18]
Although the transformation of SiC polytypes is primarily dependent on temperature
it could be affected by purity of the pre-existing phase pressure andor stacking faults
[19-22] The cubic form of SiC (β -SiC) is believed to be more stable than the
hexagonal structure (α-SiC eg 6H-SiC) below 2100 ordmC [19] However the polytype
of 2H-SiC which has the simplest stacking sequence is rarely observed at higher
temperature Krishna et al [20] reported that single crystals of 2H-SiC can be easily
transformed to 3C-SiC on annealing in argon at temperatures above 1400 ordmC It was
CHAPTER 2 Literature Review
31
found that the pre-existence of α-SiC (except 2H-SiC) could promote β-SiC
transformation to α-SiC while the transformation from α-SiC (6H-SiC) back to β-SiC
(3C-SiC) needs high temperature and pressure [21]
It has also been shown that the phase transformation could be closely related to
pre-existing defects such as stacking faults and their distribution [18] of which the
concentration is high even in single crystal SiC [22] Furthermore due to their low
formation energy the other intrinsic defects such as vacancies interstitials and
antisites were found to be common in SiC [23] These defects could affect mechanical
properties of SiC [8] so it is important to review their structure and properties
222 Defects in SiC
2221 Stacking faults and dislocations
A stacking fault is a disordered part of the ordered sequence in fcc crystal and the
most common stacking faults in cubic SiC are intrinsic and extrinsic stacking faults
(ISF and ESF) [24] For ISF the resulting stacking sequence is ABCACABC
if a double layer B is removed (condensation of vacancies) as for instance shown in
Fig 22[24] The ESF could be thought of as adding a double layer to the stacking
sequence (condensation of interstitials) resulting stacking sequence of
ABCACBCABChellip
Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner
stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]
CHAPTER 2 Literature Review
32
Another interpretation of the stacking faults is related to a twist of the three equivalent
bonds between two bilayers by 180deg [24] There may be an intrinsic shear stress
which could promote the glide of partial dislocations and thereby result in a faulted
crystal containing an error in stacking sequence so itrsquos reasonable to interpret
stacking faults in this way [25] Compared with dislocations and vacancies no bonds
are broken by stacking faults leading to a small energy difference between faulty and
perfect structures [26]
Table 21 The formation energy of stacking faults in SiC investigated by different
methods
[27] [28] [24] [29] [30] [31] [32]
ESF (mJ m-1
) -15 -- -28 -6 -61 -154 -323
ISF (mJ m-1
) 12 34 -34 14 138 111 -71
Table 21 lists the formation energy of stacking faults in SiC and it shows that
extrinsic stacking faults have much lower formation energy than intrinsic stacking
faults in fact the values become negative The negative formation energy of stacking
faults in 3C-SiC means they can be formed very easily even more easily than perfect
3C-SiC As a result the stacking faults in 3C-SiC are spontaneously formed and most
likely in the form of extrinsic faults in the lt111gt direction Furthermore due to the
low energy of formation the length of a stacking fault can only be limited by the size
of the crystal or the presence of other defects that act as obstacles [33]
CHAPTER 2 Literature Review
33
Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking
faults in the (111) planes viewed along the [110] direction indicated by the arrows b)
and c) represent the difference in stacking fault width [34]
The morphology of stacking faults in SiC observed by TEM is given in Fig 23 It
shows that the stacking faults could form a small domain (around 1 nm thick in Fig
23(a)) with different distances between small domains When a large concentration of
stacking faults exists in SiC it has been claimed that a conversion of cubic SiC to
hexagonal SiC on the nano-scale could happen by twinning [35] Furthermore the
stacking sequence of the faulted 3C-SiC was previously treated as random mixing of
α-type unit structures such as 6H and 4H in the 3C structure [36] Therefore it is
important to identify the properties and the microstructure of stacking faults of SiC
layers in TRISO fuel particles because the presence of α-SiC could result in reduction
of strength under irradiation which was due to enhanced possibility of anisotropic
swelling of α-SiC under irradiation compared to β-SiC [37]
(a) (b)
(c)
CHAPTER 2 Literature Review
34
Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at
different deposition temperatures (the β represents stacking faults) [8]
Figure 24 gives the XRD images of SiC in TRISO fuel particle deposited by fluidized
bed chemical vapour deposition showing the extra peak at 2θ~335ordm a high
background intensity at the peak at 2θ~353ordm and the broadening of the 3C peaks [8]
This is different from the perfect atomic structure of 3C-SiC as shown in Fig 21(b)
According to a previous simulation study [18] this kind of XRD diffraction pattern
could be caused by the existence of a high density of stacking faults and twins in the
regular cubic sequences It was demonstrated that it was unlikely to be due to the
presence of 2H-SiC or other polytypes [18] and two possible explanations were given
First two types of crystalline 3C-SiC with different populations of faults and twins
and second one type of crystal having clusters of faulted regions In SiC single
crystals although the concentration of stacking faults and twins is high the density of
dislocations is low (102-10
5cm
2) compared with metallic materials [22]
Figure 25 shows schematic images of the dislocations in face centred cubic (fcc)
crystals (β-SiC) The perfect dislocation is the (111) lt110gt system with burgers
vector of b=a2[110] (0308 nm) in SiC as shown in Fig 25(a) The perfect
dislocation could be easily dissociated into two partial dislocations of a6[121] and a6
CHAPTER 2 Literature Review
35
[21-1] as shown in Fig5 (a) and (b) because this reduces the total energy As a result
of this split a stacking fault must also be produced between the two partial
dislocations [38] Figure 25 (c) and (d) are lt110gt projections showing the Shockley
and Frank partial dislocations and their formation all related to the formation of
stacking faults
Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a
perfect dislocation split into Shockley partials is still able to glide on the same glide
plane the stacking fault just moves along (b) Schematic of perfect dislocation
dissociated into two partial dislocations forming a stacking fault (c) Shockley partial
dislocation (stacking fault is indicated in the dashed rectangle the other partial
dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial
(a)
(b)
(c) (d)
CHAPTER 2 Literature Review
36
dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by
the dashed rectangle) [38]
By comparing with previous studies [39-41] it is found that the relationship between
dislocation and stacking faults is complex The stacking faults have influences on the
mechanical properties for example enhancing the mobility of dislocations [39]
Different roles of stacking faults in II-VI heterostructures and devices have been
observed and results indicate that the stacking faults serve as the sources of misfit
dislocations [40] It is necessary to study the propagation of stacking faults or the
formation of stacking faults under stress and their influence on the properties of SiC
For example generation of stacking faults is shown to have occurred during the
fracture process together with the corresponding partial dislocation Furthermore
Agarwal et al [41] observed the growth of stacking faults from certain basal plane
dislocation within the base layer of the SiC
2222 Non-stoichiometric and point defects
Another common class of defects in SiC are non-stoichiometric (excess silicon or
carbon) and point defects [23 41 42] The purity of SiC may have effect on the
crystal structure strength corrosion resistance thermal conductivity diffusion
coefficient and other coating properties depending on its amount [43] The purity
could also affect defects in SiC eg if the stoichiometry deviates (even less than 1)
the concentrations of point defects in cubic SiC were found to be elevated [23]
Although the effect of point defects on general behaviour of nuclear fuel during
application process is not clear but their effect on microstructure evolution during
thermal treatment could be significant [44]
Silicon in SiC Stoichiometric 3C-SiC has generally been obtained at temperatures
between 1500 and 1600 [45] with carbon and silicon codeposited above and below
this temperature range By adding propylene as another carbon source the deposition
temperature of stoichiometric SiC could be reduced to about 1300 [8] The extra-Si
CHAPTER 2 Literature Review
37
SiC is less commonly investigated compared with the extra-C SiC because it has
been found that during the irradiation process the extra-Si plays a negative role in
material properties due to its low melting point [1] It has been found that the effect of
excess-Si on the Youngrsquos modulus and hardness it is more likely depending on its
amount and location [8 46]
Raman spectroscopy is an effective way to identify free Si both in amorphous and
crystalline phases eg it detected excess-Si when the XRD result showed the SiC was
stoichiometric [8] If the extra-Si is high (could be detected by XRD) TEM could be
used to detect its location and characterise the Si lattice contrast For example TEM
was carried out using both high resolution [35 47] and dark field imaging modes [48]
The HRTEM images in Fig 26 show the 3C-SiC crystallite with Si inclusions in
which nano-crystalline 3C-SiC and Si are separated by a weakly crystallized
interphase
Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a
matrix phase composed of SiC crystallites b) HRTEM image showing a
(a)
(b) (c)
β-SiC
β-SiC
β-SiC
β-SiC
Si
Si
025 nm
025 nm
025 nm
0 312 nm
0312 nm
CHAPTER 2 Literature Review
38
homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse
interphase region between the 3C-SiC and Si crystallites [35]
Figure 27 shows bright-field and dark-field images of extra-Si SiC It shows the
crystalline Si as bright points in the dark background located at the grain boundaries
[48] The above observations were carried out in SiC with more than 1 at excess Si
(by comparing the intensity of Si Raman peak) as such observations are difficult
when the amount of excess Si is low Since the Youngrsquos modulus in SiC with low
amount of excess Si was comparable to that of stoichiometric SiC[8 46] it may have
unique properties that are worth further exploitation
Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)
is a dark field image showing Si crystallites as bright points in a dark background
[48]
Carbon in SiC Excess C can also be identified by Raman spectroscopy but it is more
difficult to quantify its content and observe where this extra carbon exists due to its
small atomic number A comparative method was used to measure the content of
excess carbon by combining Raman spectroscopy auger electron spectroscopy
electron probe microanalysisand X-ray photoelectron spectroscopy [49] Once the
carbon concentration was measured (by above methods) the ratio of free excess to
SiC peak intensity (I796I1600) of Raman spectroscopy could be obtained as shown in
Fig 28 and the excess carbon concentration in the nearly stoichiometric SiC could
(a) (b)
CHAPTER 2 Literature Review
39
be estimated [49]
Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this
carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]
There are few reports regarding the location of excess C in SiC The research carried
out by KKaneko et al [50] in carbon-doped hot pressed szlig-SiC showed that grain
boundaries were found to be free of any second phase by HRTEM although excess C
is found to form the second graphite phase Mykhaylyk and Gadzira revealed that
extra-C atoms are located as planar defects [51] The C atoms in the β-SiC structure
were supposed to arrange either as diamond-like carbon interlayers or as
non-correlated point defects after sintering of the as-synthesized powder at high
pressures and high temperature Since it showed that the presence of excess C atoms
in SiC crystal structure changes the local atomic environment [52] they may exist
within the SiC crystal and be correlated with other defects
The above discussion about the excess Si and C indicates that their influences on
properties of SiC depend on their content and that they could be discussed together
with the other point defects when their amount is low (less than 1 at ) [23]
Point defects in SiC SiC has eight kinds of point defects which keep the tetrahedral
symmetry of the perfect SiC crystal [23] They are carbon vacancies (Vc) silicon
vacancies (VSi ) carbon antisites (CSi) silicon antisite (Sic) a tetrahedral interstitial
silicon atom surrounded by four Si atoms (SiTSi) a tetrahedral interstitial silicon atom
CHAPTER 2 Literature Review
40
surrounded by four C atoms (SiTC) a tetrahedral interstitial carbon atom surrounded
by four Si atoms (CTSi) and a tetrahedral interstitial carbon atom surrounded by four
C atoms (CTC) [23] The formation energies for these defects are listed in Table 22
Due to their low formation energies the individual antisites and vacancies
particularly CSi were expected to appear even in as-deposited coatings [53 54]
Table 22 Calculated formation energies for native point defects in SiC (calculated in
stoichiometric cubic SiC) [23]
Vc VSi Sic CSi SiTSi SiTC CTSi CTC
Ef (eV) 59 68 73 11 150 147 86 110
The importance of point defects for different applications of SiC was studied and
these properties were studied in the relation to the properties of the point defects
including their formation annealing and interaction with each other [53] According
to Raulsrsquos study [54] the actual results of diffusion of CSi are more likely to be the
formation of CSi clusters which could be promoted by the diffusion of vacancies For
the coexistence of self-interstitials and vacancies (eg in irradiated material) it has
been found that the annealing temperature for VSi and Vc by recombination in β-SiC
were about 500 ordmC and 750 ordmC respectively [55] For as-deposited β-SiC without
interstitials the annealing process was only dominated by the out-diffusion of
vacancies the disappearances of VSi and Vc were found at temperature of 1400 ordmC and
1600 ordmC respectively [54] It is also been found that the migration of silicon vacancies
is easier than carbon vacancies due to its lower migration energy barrier Furthermore
in the case of excess carbon inside SiC the carbon clusters may form in SiC after
annealing and the size of the cluster depends on the content of interstitial carbon [56]
The general atomic-scale microstructure of SiC was reviewed above which showed
high degree of defects such as stacking faults dislocations vacancies and antisites
CHAPTER 2 Literature Review
41
The kind and concentration of these defects could affect the mechanical properties
such as hardness Youngrsquos modulus and fracture behaviour of SiC Since variation of
mechanical properties could also be due to other microstructural factors such as grain
size and density the relationship between microstructure and mechanical properties
are further reviewed in the following session
23 Properties of silicon carbide
231 Youngrsquos modulus
Youngrsquos modulus is physically related to the atomic spacing atomic bond strength
and bond density It is accepted that high-purity SiC material eg CVD SiC exhibits
the highest elastic modulus and that a porous microstructure with a high
concentration of impurities could decrease the elastic modulus [1 57] In contrast
neither grain size nor polytype was recognized as having a significant effect on the
elastic modulus of SiC in coated fuel [1 58]
Table 23 Elastic tensors of 3C-SiC at room-temperature
C11 (GPa) C12 (GPa) C44 (GPa) Z Ref
3C-SiC a 3523 1404 2329 18196 [59]
3C-SiC b 511 128 191 10026 [1]
3C-SiC c 390 142 256 -- [60]
3C-SiC a 420 126 287 19503 [61]
a Theoretical calculations
b Sonic resonance measurement
c Raman Spectroscopy
According to the definition of Youngrsquos modulus an important factor which could
affect its value for SiC material is the texture which is the degree of anisotropy (lack
of randomness with regard to the orientation) of SiC crystals The Youngrsquos modulus is
different by a combining of elastic tensors for deformation of the crystal in different
CHAPTER 2 Literature Review
42
orientation The elastic tensors or the stiffness tensors reflect the linear stress-strain
relation of a material There are 81 elastic tensors because the stresses and strains
have 9 components each However due to the symmetries of the SiC the tensors were
reduced to 3 unknown values They could be measured by sonic resonant method [1]
and Raman spectroscopy [60] based on vibrational theory of the crystal lattice They
are defined for SiC in Table 23 and will cause the variation of Youngrsquos modulus for
anisotropic materials The elastic tensors for 3C-SiC identified by previous theoretical
and experimental results [59-61] are substantially different from the current updates
of sonic resonance data The difference could be caused by the difference of the size
of SiC mateirals which could introduce the influences of defects such as grain
boundaries and stacking faults It was proposed to be more reasonable estimation for
SiC in TRISO fuel particle [1]
A measurement of the anisotropy in β-SiC (faced centre cubic crystals) is the ratio of
the two shear moduli [3] 100 shear modulus and 110 shear modulus μ0 and μ1
respectively which is
0 44
1 11 12
2CZ
C C
(1)
the parameter Z is known as the Zener ratio or elastic anisotropy factor (given for
different elastic tensor Table 23) When Zgt1 the Youngrsquos modulus is minimum
along lt100gt and a maximum along lt111gt and the representational surfaces for
Youngrsquos modulus in cubic crystals is shown in Fig 29 For the case when Z=1 the
cubic crystal would also be isotropic and the representation surface would be
spherical
CHAPTER 2 Literature Review
43
Fig 29 Schematic image of the possible representational surface for Youngrsquos
modulus in SiC crystal with Z gt 1 [3]
If the samples were random polycrystals which means samples are isotropic the
theoretical Youngrsquos modulus can be unambiguously given by [3]
3
[1 ( 3 )]E
B
(2)
While bulk modulus and shear modulus are
11 122
3
C CB
(3)
1
0 1
1 0
52( 6 )
(4)
where 0 44C 1 11 12( ) 2C C and
01
0 0
3( 2 )
5 (3 4 )
B
B
(5)
The theoretical value can be gained when the elastic constants are known Using the
Eqs (2-5) the theoretical Youngrsquos modulus E was calculated to be 496 GPa for
isotropic SiC materials when the elastic tensor obtained by Lambrecht et al was used
The calculated value is close to the Youngrsquos modulus measured by nano-indentation
(about 527 GPa) of isotropic bulk CVD SiC [62] But this value is higher than the
Youngrsquos modulus measured by nano-indentation of SiC in TRISO fuel particle which
is about 450 GPa [8 46]
By using the elastic tensors measured by sonic resonance in Snead et alrsquos study [1]
CHAPTER 2 Literature Review
44
the calculated Z (10026) is very close to 1 and it means the Youngrsquos modulus in
TRISO coated fuel particle may show no orientation effect According to Eqs (2-5)
the calculated Youngrsquos modulus is about 459 GPa under the elastic tensors given in
Ref [1] This value is close to the Youngrsquos modulus measured by nano-indentation in
TRISO fuel particle regardless of the orientation effect [1 8 46] Therefore for
TRISO fuel particle the recommended elastic tensors measured by sonic resonances
were supposed to be appreciable due to the scale and the microstructure similarities of
SiC materials [1]
Another significant factor which affects the Youngrsquos modulus is the density The
elastic modulus E at room temperature can be empirically expressed in an exponential
function of porosity pV as [63]
0 exp( )pE E CV (6)
where 0E is the elastic modulus and C is a constant of 357 for a pore-free bulk CVD
SiC pV is the ratio of the relative density difference to the theoretical density of SiC
(322 gcm3)
The relationship between density and Youngrsquos modulus of different kinds of SiC
materials measured by different methods were summarised in a previous study [1] as
shown in Fig 210 It has been found that the standard deviation of elastic modulus of
SiC is about plusmn 10 when the density is higher than 99 and increased to plusmn 15 for
porosity higher than 1
CHAPTER 2 Literature Review
45
Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])
232 Hardness
In a brittle material indentation hardness is defined as the mean pressure the material
will support under load and it is a complex property which could involve crack
initiation and propagation and the development of new surfaces during the
indentation process [1] Furthermore the value of hardness measured by indentation
also depends on external factors Due to the difference in dimensions of materials
such as the bulk small scale and thin film materials indentation on the nano- micro-
and even macro-scale have been used to measure the hardness [64] The hardness of
β-SiC related material has mainly been investigated by Vickers and nano-indentation
techniques (introduced in the later part of this session according to Ref [65]) as
summarized in Table 24 Reviews have found that the nano-hardness is generally
higher than Vickers hardness [1] which was attributed to the indentation size effect
Although few hardness values of β-SiC are available to be compared (given in Table
24) it shows the difference of hardness within a given sample Regardless of external
influences on the measurement of hardness generally it can be affected by grain size
or grain morphology [46] density composition and defects [1 8 66] To identify the
CHAPTER 2 Literature Review
46
controlling factor for hardness it is necessary to understand the deformation
mechanism of SiC under indentation
Table 24 Vickers and nano-indentation hardness of β-SiC related materials
Deformation mechanism Research into the deformation mechanism of SiC have
shown the availability of dislocation related plasticity [70] phase transformation
(cubic phase to amorphous) [71 72] fracture mechanisms [73] and also the
combination of any two or three [62 73]
Fig 211 HRSEM image of indentation impression on single SiC crystal [70]
First the dislocation related plastic deformation was found in single crystal 6H-SiC
[70] and the propagation morphology of dislocations was observed after indentation
as shown in Fig 211 This observation confirmes that the dislocation slip is a
Materials Vickers hardness (GPa) Nano-hardness (GPa) Ref
Single β-SiC (001) 28 -- [67]
CVD β-SiC 207-32 325-406 [466668]
FBCVD β-SiC -- 36-42 [8]
Sintered β-SiC 211-239 -- [69]
500 nm
CHAPTER 2 Literature Review
47
mechanism of plastic deformation from nucleation of a few dislocation loops (at or
near the theoretical strength) to extensive dislocation plasticity
Furthermore the dislocation related plastic deformation in polycrystalline CVD β-SiC
(with micro meters grain size) was first observed by Zhao et al [62] It was found that
the initiation of the plastic deformation was reflected by the burst (pop-in) of the
force-displacement curve which is similar as the initiation of plastic deformation in
metallic materials as shown in Fig 212(a)
According to the Hertzian contact theory [74] the burst was attributed to initiation of
the dislocation glide by comparing the shear stress generated under the indentation at
that load with the theoretical shear stress in β-SiC [62] During the whole indentation
process it was shown that shear slip is the predominant deformation mechanism and
that cracks were associated with the shear faults Figure 212(b) is one of the TEM
images showing the microstructure under indentation and it shows the dislocation
induced shear bands at one side of indent [62] which depend on the orientation of
grains
Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain
size of 5-10 microm and (b) deformation behaviour under nano-indentation [62]
Second following the observations of phase transformation under indentation in
silicon [75] and the formation of SiC amorphous phase during high speed machining
(a) (b)
CHAPTER 2 Literature Review
48
process [71] the investigation of phase transformation under indentation was carried
out in SiC [7274] It has been demonstrated thermodynamically that the direct
amorphization is less likely to happen under nano-indentation [76] The
amorphization observed in single crystal SiC was attributed to the formation
propagation and accumulation of dislocations which formed the disordered phase at
the maximum stress region under a punch indentation [71] In SiC with nanometers
grain size the molecular dynamic study indicated thedominated deformation under
nano-indenation is a crossover of the indentation-induced crystallization to
disordering leading to amorphization [72] as shown in Fig 213
Fig 213 Deformation mechanism of nanocrystalline SiC (competition between
crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in
the entire range up to critical point (yield of crystalline phase within the grains)
yellow atoms disordered in the entire range blue atoms changed from disordered to
ordered brown atoms changed from ordered to disordered [72]
Further studies demonstrated that the phase transformation from β-SiC to α-SiC is not
possible under nano-indentation because a pressure of nearly 100 GPa is needed [76]
even when assisted by high dislocation density shear stress and temperature This
simulation work concluded that the primary response of β-SiC to nano-indentation is
dislocation nucleation and propagation which has been confirmed by experimental
observations [62]
Third the plastic deformation of β-SiC under indentation was divided into two parts
CHAPTER 2 Literature Review
49
which are primary dislocation initiation and propagation and the formation of micro
cracks [73] The former contributes to 13 of plastic deformation under indentation
while the later provides 23 of total deformation The hardness related plastic
deformation could be explained well by this mechanism which included above two
process as discussed in previous studies [1 46 62] Moreover considering the effect
of micro cracks the deformation mechanism under indentation could be related to
other factors which could contribute to the formation of micro cracks such as
porosity grain boundaries and stacking faults in SiC [3]
Youngrsquos modulus and hardness of coatings in TRISO fuel particle can be measured by
nanoindentation due to the limitation of small dimension A typical
load-displacement curve and the deformation pattern under nanoindentation of an
elastic-plastic sample during and after indentation are shown in Fig 214 in which the
hc is contact indentation depth and hs is the displacement of the surface at the perimeter
of the contact [65] The peak load and displacement are Pmax and hmax respectively
and the diameter of the contact circle is 2a During unloading process the elastic
displacements are recovered and when the indenter is fully withdrawn the final depth
of the residual hardness impression is hf [65]
Nanoindentation hardness is the ratio of the load to the projected contact area of the
indentation The mean pressure that the material can support under indentation is
defined as the hardness From the loadndashdisplacement curve as in Fig 214(a) hardness
can be gain when the load is at the maximum value
A
PH max (7)
where A is the projected contact area
CHAPTER 2 Literature Review
50
Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an
elastic-plastic sample during and after indentation [65]
The elastic modulus of the indented sample can be inferred from the initial unloading
contact stiffness S=dPdh ie the slope of the initial portion of the unloading curve A
geometry-independent relation involving contact stiffness contact area and elastic
modulus can be derived as follows
2A
S E
(8)
where szlig is a constant that depends on the geometry of the indenter (szlig=1034 for a
Berkovich indenter) [65] and Er is the reduced elastic modulus which accounts for the
fact that elastic deformation occurs in both the sample and the indenter Er is given by
CHAPTER 2 Literature Review
51
22 11 1 i
r i
vv
E E E
(9)
where E and υ are the elastic modulus and Poissonrsquos ratio for the sample respectively
and Ei and υi are the same quantities for the indenter For diamond Ei=1141 GPa and
υi=007[65]
For an indenter with a known geometry the projected contact area is a function of the
contact depth The area function for a perfect Berkovich indenter is given
by 2245 cA h Indenters used in practical nanoindentation testing are not ideally sharp
Therefore tip geometry calibration or area function calibration is needed A series of
indentations is made on fused quartz at depths of interest A plot of A versus hc can be
curve fit according to the following functional form
11 12 1 1282 4
1 2 3 8245 c c c c cA h C h C h C h C h (10)
where C1 through C8 are constants In some cases only the first three constants were
considered
The contact depth can be estimated from the load-displacement data using
maxmaxc
Ph h
S (11)
Where ε is a constant that depends on the indenter geometry (ε=075 for a Berkovich
indenter)
It is worth noting that high Youngrsquos modulus and hardness does not gurantee the
suitability of ceramic material to an engineering application because of the
importance of other mechanical properties such as fracture toughness and fracture
strength
CHAPTER 2 Literature Review
52
233 Fracture toughness
The definition of fracture toughness from Munz and Fett is [77] if a component or a
test specimen with a crack is loaded the stress intensity K1 increases with increasing
load until unstable crack propagation occurs at a critical value of K1 This critical
value is the fracture toughness (KIC) Therefore the measurement of fracture
toughness should be made on sample with a pre-crack however due to the small size
of SiC coating methods could be used are limited Although the most recently
developed micro-beam bending test could measure the fracture toughness of SiC in
TRISO fuel particles [78] this process is costly and time consuming because it
involves the preparation of micro-beams and notched cantilevers by focused ion beam
milling which limites the application of this technique
Indentation is now one of the most commonly used techniques to evaluate the fracture
toughness of ceramics and coating systems because it is easy to perform does not
need special samples and causes only negligible surface damage However some
researchers have declared that the indentation method is not suitable for the
measurement of fracture toughness [79 80] They concluded that the indentation
method does appear to represent some form of a complex crack arrest phenomenon
but that this occurrs in the presence of a multiple-crack path and a highly complex
residual stress field
Despite of these considerations the indentation method is an effective way to
compare the fracture behaviour of materials [80] particularly for small size specimens
and it provides information about the crack initiation and propagation Figure 215 is
the most typical characterization of the crack system generated by Vickers indentation
[81] This crack system is termed as median-radial cracking and consists of
approximately semi-circular cracks
CHAPTER 2 Literature Review
53
Fig 215 A general scheme of a plastic indentation and system of cracks formed
under an indenter [81]
The mode of crack initiation and propagation under an indenter proposed by Chiang
et al explains many of the features observed in indentation crack patterns and is the
most recent advance [82] It was found that radial cracks are the first to initiate
trigged by a combination of the highly tensile surface stress field and the availability
of surface flaws [74 82] These cracks grow on unloading and can either propagate
into the plastic zone (half penny cracks) or terminate in the elastic zone (Palmqvist
cracks) [83] depending on the microstructure of the material
For different types of crack modes such as half-penny and Palmqvist cracks different
equations were developed based on theoretical analysis of stress field and empirically
calibrations to calculate the fracture toughness under indentation For example in the
half penny crack model the Vickers indentation fracture toughness was most
frequently determined using the relationship proposed by Anstis et al [84] This
equation was first inferred based on isotropic materials and it is suitable for general
application to well-developed cracks [84]
1 2
3 2( )IC
E PK
H c (12)
Where P is the indentation load c is the radial crack length from indentation centre to
crack tip E and H are the Youngrsquos Modulus and hardness of the materialand χ
denoted as the geometrical constant which is independent of the materials The Eq
CHAPTER 2 Literature Review
54
(12) was developed on the basis of half penny cracking in homogeneous brittle
materials under high load for example in glasses [84]
The above information shows that it is possible to compare fracture toughness under
indentation in SiC coatings with different microstructures The fracture toughness of
SiC could depend on a large number of factors such as grain size porosity micro
cracks and inclusions which could dissipate the fracture energy from the main crack
[3] According to a previous review [1] fracture toughness of SiC peaks at the grain
size range of 1-5 microm So fracture toughness of SiC in TRISO fuel particle is likely to
be influenced by the grain size due to the similar range of grain size Although micro
cracks and pores could improve fracture toughness they would decrease the strength
[3] which is detrimental for the safe design of fuel particles Over several decades
studies have worked to improve the fracture toughness by introducing a
heterogeneous microstructure such as weak grain boundary phases [85] In the
heterogeneous phase toughening mechanism the cracks could initiate in or be
reflected into weak defects and thereby dissipate the fracture energy for the main
crack propagation Furthermore the distribution of grain boundary character (the
crystallagraphic type and frequency of grain boundaries) and morphology could
influence the fracture toughness [85 86] Different grain boundary orientations and
their frequency were found to affect the fracture toughness by controlling the
intergranular fracture of materials [86] Different grain morphologies such as
elongated grains could increase the fracture toughness by crack bridging or by
generating micro cracks along grain boundaries or triple junctions [85] No
heterogeneous phase is supposed to exist in SiC in TRISO fuel particles so the
fracture toughness is most likely to be affected by grain morphologies or as-deposited
defects
According to the Griffth fracture theory once the size of the critical flaw is the same
the fracture toughness is propotional to the fracture strength which is another
CHAPTER 2 Literature Review
55
parameter used in modelling of the probability of the failure of fuel particle
234 Fracture strength
For brittle materials the fracture strength is best considered as a distribution rather
than a fixed value as the flaws (such as surface cracks pores and inclusions) from
which fracture initiates vary in size and type (result in different frature strength value)
between nominally identical samples [3] The Weibull approach is a commonly used
empirical method to characterise the strength of a brittle material It assumes a simple
power-law stress function (eg in Eqs (18-20)) for the survival of the elements
which is integrated over the body volumesurface area (as shown in Eqs (19) and
(21)) In many cases this function gives results in the form of Weibull modulus (m in
Eq (19)) and characterstic strength which describe the width and magnitude of the
strength distribution [3] The Weibull modulus is the slope of Log-Log distribution
function of the survival of elements and strength (Eq (19)) For engineering
application the high Weibull modulus represents the small variation of the fracture
strengthes for a given material
Higher Weibull modulus reflects lower variability of the strength and it is typically in
the range of 5-20 [3] The commonly used strength test methods for bulk ceramics are
uniaxial tension three- and four-point bending However the small dimensions of
TRISO fuel particles make it difficult to measure the strength by those conventional
methods As a consequence some specific methods were developed in the last few
decades such as O-ring test [87 88] C-ring test [88] hemisphere bending [10]
internal pressurization [89] and crush test [5 89 90] The schematic of easily
repetitive fracture strength test geometries are given in Fig 216 and the obtained
fracture strength by different methods was shown in Table 25
CHAPTER 2 Literature Review
56
Table 25 Fracture strength of SiC in TRISO fuel particles measured by different
methods
Methods L
f (MPa) Weibull Modulus F
f (MPa) Ref
O-ring compression 596-1412 41-66 -- 87
O-ring compression 1050-1890 48-94 -- 88
C-ring Compression 980-2200 40-90 -- 88
Semi-spherical bend 720-1350 70-80 340-620 10
Inner pressurization -- 43-62 222-448 89
Crush test -- 58-75 356-427 89
Crush test 770-1324 40-73 330-647 5
Crush test 1484-1721 135-183 1045-1091 90
L
f Local fracture strength F
f Fracture strength of the full particle
The local fracture strength is in the range of 596-2200 MPa and the fracture strength
of the whole particle varies from 222 MPa to 1091 MPa Such significant variation is
tought to be caused by the differences in specimen size and loading mode which were
related to the nature of the Weibull distribution [1 3] It has been demonstrated that
specimens with larger volumesurface area (under the same loading mode) have lower
strength because there is an increased probability that a larger flaw exists in a larger
body Similarly when there is no volume difference the loading mode which stresses
larger area has lower local fracture strength [3] These discussions show the
importance of regulating the fracture strength test method and producing specimens
with regular shape and size
CHAPTER 2 Literature Review
57
Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of
inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical
loading) [89]
The modified crush test developed by Byun et al [5] is recommended for the fracture
strength measurement of SiC in TRISO fuel particles because it considered the effect
of contacting area between SiC shell and plunger which reduced the variation and
uncertainty of the stress distribution under tensile stress
Modified crush test When a partial spherical shell is diametrically loaded by an
external load F concentrated on a small circular contact area of radius 0 the
maximum membrane stress and bending stress are given by [91]
2
1 2
1membrane
FC
t
(13)
CHAPTER 2 Literature Review
58
2 2
1bending
FC
t
(14)
where ν is the Poisson ratio t is the thickness of shell and C1 and C2 were defined as
2
1 0115004022050 C (15)
)27031exp(204412 C (16)
2 2 2 1 4
0[12(1 ) ( )]r R t (17)
max membrane bending (18)
where max (L
f ) is the fracture strength for locally loaded specimens R is the outer
diameter of shell t is the thickness of the SiC shell The distribution of local fracture
strength is analysed by the Weibull distribution function which presents the
cumulative probability of failure P as [5]
mL
f
E
m
s
F
fSdAP
00
exp1exp1
(19)
where L
f m 0 and ES are the local fracture strength the Weibull modulus the
characteristic sterngth and the size effect factor respectively The size effect factor is
dAS
m
s L
f
F
f
E
Byun et al [5] used the probability estimator as follows
1
N
iPi (20)
where iP is the probability of failure for the i th-ranked strength and N is the
CHAPTER 2 Literature Review
59
sample size The increased probability that the full SiC shell has more critical flaws
compared with the stress-weighted surface is corrected by the size effect and the
fracture strength of the full shell (F
f ) is given
L
f
m
L
f
m
F
E
L
EF
ftR
r
S
S
1
2
2
0
1
)(4
(21)
After adjusting the size effect the fracture strength of the full particl of different SiC
coatings could be compared In a previou study [87] the difference of the fracture
strength was attributed to the microstructural variations which were determined by
deposition conditions [87] More detailed analysis [510] showed that the variation of
fracture strength was due to factors such as porosity roughness of the IPyCSiC
interface and grain size For example Evans et al [10] observed that the surface
roughness influenced the failure of the particle withstrength improved by reducing
the inner surface roughness According to above discussion the variation of Weibull
modulus could be attributed to the different test methods flaw distribution and sample
size [3 5]
Micostructure and mechanical properties of as-deposited SiC are reviewed above
which may change after high temperature treatment and the degree of evolution could
be different due to variational deposition conditions of SiC coatings As summarized
in a previous study [92] one of the critical properties for SiC layers in TRISO fuel
particle is that the microstructure remains unchanged after thermal treatment at 2000
ordmC for 1 hour in an inert atmosphere as determined by electron microscopy and X-ray
diffraction
235 Effect of thermal treatment on SiC
The SiC with perfect crystal structure tends to have good high temperature thermal
stability however due to the concentration and type of imperfections generated
CHAPTER 2 Literature Review
60
during deposoition process its thermal stability could be affected Defects such as
stacking faults vacancies and interstitials in as-deposited SiC coatings affect the
microstructural change after thermal treatment [93-96] For example the phase
transformation from β- to α-SiC generally happened at temperatures above 2100 ordmC
[19] but it could take place at lower temperature (gt 1700 ordmC) in special cases (eg
CVD β-SiC deposited on Si substrate with high amount of stacking faults) [93]
During high temperature thermal treatment (about 2000 ordmC) of CVD β-SiC one
significant microstructural change would be the annihilation of stacking faults [94
95] A thermodynamics study [94] has shown that the mechanism of reduction of the
stacking faults was due to the diffusion of Si or C atoms and it also demonstrated that
the migration energy of Si atoms was smaller than C atoms Considering the
abundance of intrinsic defects (section 222) there has been little investigation of
their effects on microstructure change of β-SiC after thermal treatment Furthermore
the effects of high temperature thermal treatment on mechanical properties such as
the hardness Youngrsquos modulus [97] and strength [98] have been carried out Their
results showed that mechanical properties showed little change when the treatment
temperature was lower than 2000 ordmC while there was decrease in the strength after
thermal treatment at 2100 ordmC
24 Microstructure and properties of pyrolytic carbon
In this part the microstructure of carbon related material is reviewed first which is
followed by the measurement of Youngrsquos modulus and hardness Furthermore to
know the controlling factor on mechanical properties of PyC coatings different
deformation mechanisms under indentation are introduced A brief review about effect
of thermal treatment on properties of PyC coatings is given
CHAPTER 2 Literature Review
61
241 Microstructure of pyrolytic carbon
Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features
in high density PyC (b) schematic and (d) TEM image showing the globular growth
features in low density PyC [15]
The graphite structure consists of graphene sheets having localized in-plane σ (sp2)
hybrids bonds and delocalized out of plane π (pz) orbital bonds connecting graphene
sheets The out-of-plane bond is a van der Waals interaction which is much weaker
than sp2 and sp
3 hybrids Pyrolytic carbon is a material with some covalent bonding
between its graphene layers as a result of imperfections (defects) in its structure [99]
Figure 217 gives schematics and TEM images showing different microstructures of
PyC with different densities The growth features are polyhedral or conical shape in
high density pyrolytic carbon (Fig 217 (ab)) but are globular in low density
pyrolytic carbon (Fig 217(cd)) [15] It shows that the microstructure of pyrolytic
carbon consists of growth features between 200 nm- 1000 nm in size (Fig 217 (b)
and (d)) [15] Pores were formed at the boundaries or triple junctions between growth
(a) (b)
(c) (d)
CHAPTER 2 Literature Review
62
features
According to previous studies [15101] individual growth features contain crystallites
(domains) as shown schematically in Fig 218(a) They are composed of a series of
curved graphene layers randomly rotated with respect to each other along the c-axis
[101] The dimensions of the crystal were described by La (diameter of crystal along
the χ direction) and Lc (height of the crystal perpendicular to χy plane) as shown in
Fig 218(a) Regarding the definition of the PyC there are defects within the growth
features together with crystallites A local atomic structure of less ordered graphene
layers is shown in Fig 218(b) which could reflect the plane defects in graphene
layers [102]
Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved
graphene layers (a) [101] less ordered turbostratic carbon (b) [102]
A high density of defects such as dislocation loops and kink bands were observed in
ball milled graphite by HRTEM as shown in Fig 219(a) The distorted
microstructure of graphite was also inferred from the striped diffraction points in
selected area electron diffraction image (Fig 219(b)) [103] since the diffraction
pattern gives information on orientation of crystal planes Compared with ball milled
graphite the HRTEM image of pyrolytic carbon has higher amount of defects as
shown in Fig 19(c) which is reflected from the highly distorted lattice planes and low
texture The selected area electron diffraction image of pyrolytic carbon (Fig 219(d)
with eperture diameter of 200 nm) showed arc shaped diffraction patterns [15 104]
The arc represents the overlap of diffraction patterns from different graphite domains
CHAPTER 2 Literature Review
63
with different orientations and this indicats that the microstructure is more distorted
eg smaller domain size and increased random orientation of domains In heavily
disordered PyC it is not possible to observe the individual dislocations or other
defects which is thought to be due to the numerous defects such as tilt boundaries
which obscure individual defects as described in Ref [105]
Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the
selected area electron diffraction pattern from the same sample (b) [103] the HRTEM
image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)
and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]
Raman spectroscopy is one of the most effective techniques to characterise the defects
in carbon materials and has previously been used to characterise the microstructure of
PyC [15 106] These spectra can identify even quantify the microstructure such as
crystallite boundaries and size disorders (5-memebered rings) and chemical bonding
type Figure 220 shows the evolution of the Raman spectra with the change of the
CHAPTER 2 Literature Review
64
in-plane defect types The carbon spectra of Fig 220(a-c) showed increased and
broadened D signal and the main in-plane defects observed in these structures were
supposed to be domain boundaries [15] In Fig 220(d-e) the D signal became shaper
which was attributed to the formation of five-member rings [15]
Fig 220 Schematic representation of the change of Raman spectra on PyC with
changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D
signal dominated by the presence of five-member rings in the PyC structure [15]
The high density of disorders such as in-plane domain boundaries makes the Raman
bands become broder and overlapped with each other as shown in Fig 220(c) which
inferred the structure of turbostratic or high density PyC [10 15] According to
previous studies [106 107] the broadened Raman bonds could be deconvoluted into a
number of peaks which correspond to different types of disordered structure in
carbon materials Figure 221 is an example of a first order Raman spectra fitted with
Lorentzian and Gaussian functions and it includs I (~1170 cm-1
) D (~1330 cm-1
) Drdquo
(~1500 cm-1
) G (~1580 cm-1
) and Drsquo(~1618 cm-1
) bands [106] The Drdquo peak was
CHAPTER 2 Literature Review
65
attributed to amorphous carbon with a certain amount of sp3 carbon [106108] which
could reflect the interstitial defects coupling to the graphene layers or adjacent
domains [109]
Fig 221 First order Raman spectra of one of the various pyrocarbons [106]
242 Mechanical properties of pyrolytic carbon
The different deformation mechanism of carbon materials compared to ceramic
materials results in distinct force-displacement curves which show the complete
recovery of the unloading curve [110 111] Therefore we describe the mechanical
properties of PyC coatings and deformation mechanism of carbon materials
2421 Youngrsquos modulus and hardness
Due to the importance of PyC in the nuclear industry mechanical properties were
measured by three-point bending [102 112] and nano-indentation [113-115] Table
26 gives the Youngrsquos modulus and hardness of PyC measured by different methods
In three-point bending tests the mechanical properties were functions of density
orientation angle and domain size No individual factor could clearly explain the
variation in Youngrsquos modulus strength or fracture toughness [112116] In previous
nano-indentation tests the low density PyC was found to have low hardness and
Youngrsquos modulus [114] whereas the influence on mechanical properties was
CHAPTER 2 Literature Review
66
uncertain which could be due to lack of investigation about the deformation
mechanisms
Table 26 Summary of the hardness and Youngrsquos modulus for PyC measured by
different methods
Methods Density range
(gcm3)
Youngrsquos modulus
(GPa)
Hardness
(GPa)
Ref
3-point-bending 150-212 310-427 -- 112
137-206 165-281 -- 116
Nano-indentation 185-190 255 + 2 -- 114
165-203 235-270 30-44 115
155-187 70-150 05-18 115
135-212 125-346 15-48 113
Youngrsquos modulus was changed from PSI to GPa
Figure 222 is a schematic of the typical force-displacement curve of different kinds
of materials under indentation [65110111] The curve of carbon materials shows a
completely recovery and no net displacement after unloading as shown in Fig
222(a) In carbon materials the force-displacement curve formed a closed loop and
this phenomenon was called anelastic deformation behaviour [14 117] This was
related to the internal friction of materials but there is controversy regarding the
sources of the internal friction [14105111] Since the force-displacement curve gives
information about the energy change during indentation the deformation behaviour of
carbon material can be analysed by the energy method
The energy distribution under indentation is shown in Fig 222 which includs the
hysteresis energy (Uh) and unloading energy (Uunloading) and the total energy (loading
energy Uloading) is the sum of the above two energies [110] As shown in Fig 222 the
ratio of the hysteresis energy to total loading energy could be different for different
microstructure of carbon materials [118] The ratio could be used to estimate the
CHAPTER 2 Literature Review
67
flexibility of elasticityductility [110119] For example a low ratio corresponds to
higher elasticity whist a high ratio meants higher ductility
Fig 222 The schematic figures showed the typical force-displacement curve under
indentation of carbon materials [110]
The different force-displacement curve of carbon materials was compared with the
irreversible deformation behaviour of materials with linear elasticity such as SiC as
shown in Fig 214(a) [65] In linear elastic deformation the final displacement of hf
was left after complete unloading and the unloading curve nearly followed the linear
relationship Furthermore the area between the loading and unloading curves
represents the energy consumed by the plastic deformation which could be due to the
movement of dislocations and formation of micro cracks [1 62]
2422 Deformation mechanism
Reversible slip and sliding friction theory In this theory the complete recovery of
strain was due to the reversible slip of graphene planes and the energy loss was
attributed to the friction during the slip which was caused by a compressive stress on
the graphene layers [110111] The theory was obtained by considering an arbitrary
grain located at some position in a radially declining hydrostatic stress field below a
spherical indenter as shown in Fig 223 [110111] The force was resolved into
CHAPTER 2 Literature Review
68
compressive stress perpendicular to and shear stress parallel to the slip plane By
using the equation proposed by Kelly [120] the shear component (τ τ0 shear stress
with and without friction respectively) may be expressed as τ= τ0 +μσ where μ is a
friction coefficient and σ is normal stress component To initiate slip between
graphene layers the shear stress needs to exceed some critical value Therefore the
inter-layer slip with friction was supposed to be the mechanism of anelastic
deformation The authors [110111] also concluded that the hysteresis during
unloading appeared to be a natural result of friction between the graphene layers but
additional mechanisms were supposed to be operating in the different forms of
graphitic materials Furthermore the study did not give a clear explanation about how
the reversibility of the basal plane slip was realized
Fig 223 Loading of an irregular graphite grain in the stress field below a spherical
indenter [110]
Dislocation pileup theory This idea was derived from isotropic carbon after thermal
treatment at the temperature range of 880-2600 ordmC by using micro indentation [121]
The authors attributed the unique unloadingreloading behaviour of the
well-graphitized carbons to the slip of dislocation networks on graphitic basal planes
which is partially or fully reversible It is supposed that the dislocations could pile up
at grain boundaries as in metals The stress at grain boundaries due to dislocation pile
ups could reverse the dislocation movement during indentation unloading but it did
CHAPTER 2 Literature Review
69
not explain why deformation behaviour of PyC is unlike that of metals This is also
the reason that other researches [105] doubt this theory because it fails to explain the
nature of the reversible behaviour [121]
Kink band theory It was suggested that the origin of the loops obtained in single
polycrystalline and porous carbons is the formation of incipient kink band and kink
bands [105] The kink band model was proposed by Frank and Stroh [122] as
shown in Fig 224 which showed pairs of dislocations of opposite sign nucleate and
grow at the tip of a thin elliptical kink (not clear about the nature) The stability of
kink bands depended on a shear stress [122]
Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations
of opposite polarity (b) Same as (a) but after the formation of a pair of mobile
dislocation walls (c) Formation of two IKBrsquos under the indenter [105]
In this theory since the dislocations were confined to the basal plane the hysteresis
process was attributed to the reversible movement of the dislocation along a long
distance The same mechanism was used to explain the deformation behaviour of the
bulk polycrystalline graphite The microstructural change under indentation should
first be related to the kink band initiation and then further microstructure change
could be reflected in the accumulation of other chemical bonds which could resist
dislocation glide
CHAPTER 2 Literature Review
70
2423 Effect of thermal treatment on properties of PyC
The effect of thermal treatment on the microstructure of carbon materials has been
widely studied [112 123 124] The change of the microstructure of carbon materials
during thermal treatment mainly involves the growth of the domain size (in-plane
crystal size along a axis) La and (along c axis crystal size) Lc with the increase of
temperature For different kinds of carbon materials these evolutions started at
different temperatures For example the crystal growth in-plane happened at 400-600
ordmC for graphitisable carbon and could continue up to high temperature the
coalescence of crystallites along the c-axis started above 1000-1200 ordmC the
coalescence of crystallites along ab direction occurred at temperature above 1400 ordmC
[124] For carbons with strong cross-linking (non-graphitisable) the coalescence of
domains usually happened at temperatures higher than 2400 ordmC [124] Although the
increase in anisotropy and density during processing of coated particle fuel was
reported by Hunn et al [11] no change in texture was identified on PyC due to the
post deposition of SiC shown in Lopeacutez-Honorato et alrsquos study [125] Furthermore no
significant change of mechanical properties was obtained after thermal treatment at
temperatures in the range 1000-1980 ordmC in PyC coatings with density of about 19
gcm3 [97] however a decrease of Youngrsquos modulus was observed in high density
(above 2 gcm3) PyC coatings [125] It was assumed that certain microstructures of
PyC would be less affected by thermal treatment
25 Summary
The microstructure and mechanical properties of SiC and PyC were reviewed in this
Chapter and the information obtained is summarized below
(1) It is common for SiC to have defects such as stacking fautls and dislocations
non-stoichiometry and point defects due to their low formation energy
particularly in SiC deposited by chemical vapour deposition
CHAPTER 2 Literature Review
71
(2) Defects interact with each other Stacking faults could be the result of gliding
of partial dislocations Vacancies promoted diffusion of antisites forming
antisite clusters
(3) The Youngrsquos modulus of SiC coatings in TRISO fuel particle is affected
mainly by texture and porosity
(4) Hardness related plastic deformation in single and polycrystalline (nano-meter
or micro-meter grain size) SiC is related to dislocation propagation fracture
of crystallites or phase transformation
(5) A combination of indentation together with electron microscopy is an
effective way to study the fracture behaviour of SiC coatings in TRISO fuel
particle
(6) Fracture strength of SiC coating in TRISO fuel particle varies significantly in
different measurements and the modified crush test is recommended The
interface roughness and porosity are found to be main factors controlling
fracture strength of SiC coatings
(7) The typical change of microstructure after thermal treatment in SiC is the
annihilation of stacking faults through the diffusion of vacancies
(8) The disorder in PyC coatings could be significant such as domain boundaries
and 5-membered rings Raman spectroscopy together with transmission
electron microscopy are important techniques to characterize these disorders
(9) Carbon related materials show hysteretic deformation behaviour under
indentation Different deformation mechanisms are proposed which all relate
to the slip of graphene layers
CHAPTER 2 Literature Review
72
26 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook
of SiC properties for fuel performance modeling J Nucl Mater 371 (2007)
329-77
[2] DT Goodin Accident condition performance of fuels for high-temperature gas
-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[3] D J Green An Introduction to the mechanical properties of ceramics 1st ed
Cambridge Solid State Science Series Cambridge the University Press 1998
[4] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on
fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of
Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a
Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37
[6] X Li B Bhushan A review of nanoindentation continuous stiffness
measurement technique and its applications Mater Charact 48 (2002) 11-36
[7] A Grabulov U Ziese HW Zandbergen TEMSEM investigation of
microstructural changes within the white etching area under rolling contact
fatigue and 3-D crack reconstruction by focused ion beam Scripta Matterialia 57
(2007) 635-38
[8] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
Transgranular Cleavage J Mech Phys Solids 34 (1986) 477-97
[10] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
Fuel Particles for High-Temperature Gas-Cooled Reactors J Am Ceram Soc
56 (1973) 36-41
CHAPTER 2 Literature Review
73
[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated fuel due to heat treatment J
Nucl Mater 374 (2008) 445-52
[12] D G Martin Considerations pertaining to the achievement of high burn-ups in
HTR fuel Nucl Eng Des 213 (2002) 241-58
[13] G K Miller D A Petti D J Varacalle J T Maki Consideration of the effects
on fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J
Nucl Mater 295 (2001) 205-12
[14] G K Miller D A Petti J T Maki Consideration of the effects of partial
debonding of the IPyC and particle asphericity on TRISO-coated fuel behaviour
J Nucl Mater 334 (2004) 79-89
[15] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon - I Effect of deposition conditions on
microstructure Carbon 47 (2009) 396-410
[16] R Cheung Silicon carbide microelectromechnical systems for harsh
environments Imperial College Press 2006 p 3
[17] M Iwami Silicon carbide fundamentals Nuclear instruments and methods in
physics research section A accelerators spectrometers detectors and associated
equipment 466 (2001) 406-11
[18] V V Pujar J D Cawley Effect of stacking faults on the X-ray diffraction
profiles of β-SiC powders J Am Ceram Soc 78 (1995) 774-82
[19] W F Knippenberg Growth phenomena in silicon carbide Philips Res Report
18 (1963) 161-274
[20] P Krishna RC Marshall CE Ryan The discovery of a 2H-3C solid state
transformation in silicon carbide single crystals J Crys Grow 8 (1971) 129-31
[21] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J AmCeramSoc 84 (2001) 3013-16
[22] R Stevens Defects in silicon carbide J Mater Sci 7 (1972) 517-21
CHAPTER 2 Literature Review
74
[23] C Wang J Bernholc Formation energies abundances and the electronic
structure of native defects in cubic SiC Phys Rev B 38 (1988) 12752-56
[24] P Kaumlckell JFurthmuumlller FBechstedt Stacking faults in group-IV crystals an ab
initio study Phys Rev B 58 (1998) 1326-30
[25] U Lindefelt H Iwata S Oumlberg P R Briddon Stacking faults in 3C- 4H and
6H-SiC polytypes investigated by an ab initio supercell method Phys Rev B 67
(2003) 155204-15
[26] P T B Shaffer A review of the structure of silicon carbide Acta Crystal Sec B
25 (1969) 477-88
[27] P J H Denteneer W v Haeringen Stacking-fault energies in semiconductors
from first principle calculations J Phys C Solid State Phys 20 (1987) 883-87
[28] X G Ning H Q Ye Experimental determination of the intrinsic stackingfault
energy of SiC crystals J Phy Condens Matter 2 (1990) 10223-25
[29] P J H Denteneer W v Haeringen Ground-state properties of wurtzite silicon
carbide Solid State Commun 65 (1988) 115-19
[30] P J H Denteneer Stacking-fault energies in silicon diamond and silicon
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[33] M Marinova A Mantzari E K Polychroniadis Some recent results on the
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[35] B Reznik DGerthsen W Zhang K J Huumlttinger Microstructure of SiC
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75
[36] T Mitani S Nakashima H Okumura et al Raman Scattering Analyses of
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[39] P Pirouz J W Yang Polytypic transformations in SiC the role of TEM
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[40] S Guha J M DePuydt J Qiu Role of stacking faults as misfit dislocation
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[41] AK Agarwal SKrishnaswami JRichmond et al Influence of basal plane
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[42] N W Mueggenburg H M Jaeger S R Nagel Stress transmission through
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[43] S Somiya Y Inomata Silicon carbide ceramics-2 ceramic research and
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[44] A Gali N T Son E Janzeacuten Electrical characterization of metastable carbon
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[45] C Chu Y Luand M Hon Growth characteristics of β-SiC by chemical vapour
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[46] J Tan Mechanical properties of SiC in TRISO fuel particle PhD Thesis
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[47] Z R Huang B Liang DL Jiang S H Tan Preparation of nanocrystal SiC
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[48] R A Shatwell K L Dyos C P Rentice Y Ward R J Young
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76
[49] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M
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[50] K Kaneko M Kawasaki T Nagano et al Determination of the chemical width
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[51] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution
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[52] O O Mykhaylyk YZ Khimyak JP Attfield Phase Segregation in Silicon
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[53] E Janzeacuten N T Son N Magnusson A Ellison Intrinsic defects in high-purity
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[54] E Rauls Th Frauenheim A Gali PDeaacutek Theoretical study of vacancy
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[55] N T Son P N Hai E Janzeacuten Carbon vacancy-related defect in 4H and 6H SiC
Phys Rev B 63 (2001) 201201-04
[56] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
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[58] T D Guldn H Nickel Coated particle fuels Nucl Technol 35 (1977) 206-35
[59] KB Tolpygo Optical elastic and piezoelectric properties of ionic and valence
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[60] D W Feldman J H Parker Jr J W Choyke L Patrick Phonon dispersion
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Rev 173 (1968) 787-93
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77
[61] W R L Lambrecht B Segall M Methfessel M van Schilfgaarde Calculated
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(1991) 3685-94
[62] X Zhao R M Langford I P Shapiro P Xiao Onset plastic deformation and
cracking behaviour of silicon carbide under contact load at room temperature J
Am Ceram Soc 94 (2011) 3509-14
[63] R W Rice Mechanical properties of ceramics and composites 1st ed New
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[64] O Grabco O Shikimaka E Harea Translation-rotation plasticity as basic
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[65]W C Oliver GMPharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
Mater Res 7(1992)1564-83
[66] MC Osborne JC Hay LL Snead Mechanical- and physical-property changes
of neutron-irradiated chemical-vapour-deposited silicon carbide J Am Ceram
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[67] D M Teter Computational alchemy the search for new superhard materials
MRS Bull 23 (1995) 22-27
[68] S Nagappa M Zupan CA Zorman Mechanical characterization of
chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta
Materialia 59 (2008) 995 -98
[69] M J Slavin G D Quinn Mechanical property evaluation at elevated
temperature of sintered β-silicon carbide Inter J High Tech Ceram 2 (1986)
47-63
[70] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and
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Res Soc Symp P 522 (1998) 113-18
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[71] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of
amorphization during nanoindentation of SiC A molecular dynamics study Phys
Rev B 71 (2005) 174113-23
[72] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of
nanocrystalline ceramics Science 309 (2005) 911-14
[73] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle
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[74] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical
Engineering Series 1st ed New York Springer 2000
[75] I Zarudi J Zou L C Zhang Microstructures of phases in indented silicon A
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[76] M Mishra I Szlufarska Possibility of high-pressure transformation during
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[77] D Munz T Fett Ceramics Mechcanical properties failure properties failure
behavior and materials selection Springer Verlag NewYork 1999 p 20
[78] X Zhao RM Langford J Tan P Xiao Mechanical properties of SiC coatings
on spherical particles measured using the micro-beam method Scripta Mater 59
(2008) 39ndash42
[79] G D Quinn RC Bradt On the Vickers indentation fracture toughness test J
Am Ceram Soc 90 (2007) 673-80
[80] R Morrell Fracture toughness testing for advanced technical ceramics
internationally agreed good practice Adv Appl Ceram 105 (2006)1-11
[81] R E Cook G M Pharr Direct observation and analysis of indentation cracking
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[82] S S Chiang D B Marshall AG Evans The response of solids to elasticplastic
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[83] M T Laugier Palmqvist toughness in Wc-Co composites viewed as a ductile
brittle transition J Mater Sci Lett 6 (1987) 768-70
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[84] G R Anstis P Chantikul B R Lawn D B Marshall A critical-evaluation of
indentation techniques for measuring fracture-toughness 1 Direct Crack
Measurements J Am CeramSoc 64 (1981) 533-38
[85] X F Zhang Q Yang L C D Jonghe Microstructure development in
hot-pressed silicon carbide effects of aluminium boron and carbon additives
Acta Mater 51 (2003) 3849-60
[86] T Watanabe The impact of grain boundary character distribution on fracture in
polycrystals Mater Sci Eng A 176 (1994) 39-49
[87] S J Xu J G Zhou B Yang B Z Zhang Effect of deposition temperature on
the properties of pyrolytic SiC 224 (1995) 12-16
[88] K Bongartz E Gyarmati H Schuster K Tauber Brittle ring test ndash method for
measuring strength and Youngs modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[89] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
fracture strength for silicon carbide layers in the Tri-Isotropic-Coated fuel particle
J Am Ceram Soc 90 (2007) 184-91
[90] J W Kim TSByun YKatoh Optimization of fracture strength tests for the SiC
layer of coated fuel particles by finite element analysis
[91] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[92] SDKurbakov TAMireev Deposition of high-density silicon carbide coatings
by fluidized-bed pyrolysis of chlorinated silane derivatives Solid Fuel Chem 43
(2009) 113-23
[93] M Hundhausen R Puumlsche J Roumlhrl L Ley Characterization of defects in
silicon carbide by Raman spectroscopy Phys Stat Sol 245 (2008) 1356-68
[94] N Shirahata K Kijima A Nakahira and K Tanaka Thermal stability of
stacking faults in beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
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[95] W S Seo C H Pai K Koumoto H Yanagida Microstructure development and
stacking fault annihilation in β-SiC powder compact Ceram Soc Jap 99 (1991)
443-47
[96] Z G Cambaz G N Yushin Y Gogotsi K L Vyshnyakova L N
Pereselentseva Formation of carbide-derived carbon on beta-silicon carbide
whiskers J Am Ceram Soc 89 (2006) 509-14
[97] I J V Rooyen J H Neethling J Mahlangu Influence of temperature on the
micro-and nanostructures of experimental PBMR TRISO coated particles A
comparative study Proceedings of the 4th international topical meeting on high
temperature reactor technology HTR 2008 September 28-October 1 2008
Washington DC USA HTR 2008-58189
[98] I J v Rooyen J H Neethling P M v Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[99] httpenwikipediaorgwikiPyrolytic_carbon
[100]J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
[101]Z Q Li C J Lu Z P Xia Y Zhou Z Luo X-ray diffraction patterns of
graphite and turbostratic carbon Carbon 45 (2007) 1686-95
[102]W P Hoffman W C Hurley P M Liu T W Owens The surface topography
of non-shear treated pitch and PAN carbon fibers as viewed by the STM J
Mater Res 6 (1991) 1685-94
[103]J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[104]P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
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81
[105]M W Barsoum A Murugaiah S R Kalidindi T Zhen YGogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[106]J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy
electron diffraction and few other techniques Carbon 44 (2006) 1833-44
[107]A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
[108]A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-phonon coupling doping and nonadiabatic defects Solid State
Communic 143 (2007) 47-57
[109]J N Rouzaud A Oberlin Carbon films Structure and microtexture (optical and
electron microscopy Raman spectroscopy) Thin Solid Films 105 (1983) 75-96
[110]N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[111]N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philosophical Magazine A 82 (2002) 1873-81
[112]J C Bokros R J Price Deformation and fracture of pyrolytic carbons
deposited in a fluidized bed Carbon 3 (1966) 503-19
[113]E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure
and mechanical properties of pyrolytic carbon produced by fluidized bed
chemical vapour deposition Nucl Eng Des 238 (2008) 3121-28
[114]C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by
different techniques Thin solid films 469-70 (2004) 214-20
[115]G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An
investigation of the relationship between position within coater and pyrolytic
carbon characteristic using nanoindentation Carbon 38 (2000) 645-53
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82
[116]J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[117]L M Brown In H Libelt R Talreja Fatigue and creep of composites
materials Riskilde Denmark Riso National Laboratory 1982 p 1-18
[118]M Skai The Meyer hardness A measure for plasticity J Mater Res 14 (1999)
3630-39
[119]M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics ndash adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[120]B T Kelly The physics of graphite Applied Science Publications London
1981
[121]M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated
carbons J Am Ceram Soc 85 (2002) 1522-28
[122]F C Frank A N Stroh On the theory of kinking Proc Phys Soc 65 (1952)
811-21
[123]R F Franklin Royal Society London A London 1951 209 196
[124]F G Emmerich Evolution with heat treatment of crystallinity in carbons
Carbon 33 (1995) 1709-15
[125]E Loacutepez-Honorato P J Meadows R A Shatwell P Xiao Characterization
of the anisotropy of pyrolytic carbon by Raman spectroscopy Carbon 48 (2010)
881-90
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
83
CHAPTER 3 Hardness and Youngrsquos Modulus of SiC
Coatings Measured by Indentation
31 Introduction
The silicon carbide (SiC) coating is the most important component for structural
integrity of Tri-isotropic (TRISO) fuel particles as it sustains most of the internal
pressure produced by the fission gases produced in the kernel [1-3] Youngrsquos modulus
and hardness are mechanical properties used in modeling to estimate the failure
probability of TRISO fuel particles [4] The values at room temperature are used due
to the fact that the Youngrsquos modulus slightly decreased at elevated temperature in SiC
material and the higher value could be kept until the temperature reached 2000 degC [1]
It was also found that SiC material with higher hardness at room temperature
maintains higher hardness values at temperatures up to 1600 degC [1] To achieve a
reliable fuel design a better understanding of the mechanical properties of the SiC
layer at room temperature needs to be established
It is difficult to use traditional methods to measure hardness and Youngrsquos modulus
due to the small dimension of the TRISO fuel particles (~1 mm) Nano-indentation
has made it possible to measure the hardness and Youngrsquos modulus accurately [5 6]
for a coating of such a small dimension Furthermore this method also offers the
ability to study the deformation behaviour under the indentation [7-12] as the
indentation stress field is of a localized character
Loacutepez-Honorato et alrsquos [5] study of SiC deposited at 1300 degC by fluidized bed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
84
chemical vapour deposition (FBCVD) showed that the SiC coatings produced under
those conditions had high hardness (gt 42 GPa) and Youngrsquos modulus (~455 GPa)
They found that even samples with the composition of SiC+C or SiC+Si showed high
mechanical properties It was shown that the coatings had sub-micrometer (lt1 μm
diameter) grain size but due to the complex microstructure the mechanism controlling
the hardness and Youngrsquos modulus was unknown Researchers [10 11 13-16] have
made efforts to study the deformation mechanism under indentation in SiC single
crystals and polycrystals (with a grain size lt 100 nm or grain size gt 1μm) Szlufarska
et al [15] suggested a crossover mechanism from indentation-induced crystallization
to deformation-dominated amorphization in nano-crystalline SiC
From the work reported [11 16 17] it is clear that dislocation initiation and
propagation is the primary response for the plastic deformation under an indentation
in single crystal and polycrystalline (gt 1μm) SiC Further it has also been found
while studying the microstructure [11 16 17] that defects such as stacking faults and
dislocations were present in these polycrystalline (gt 1 μm) SiC materials
(nano-indentation hardness less than 36 GPa) However the amount of defects were
lower compared to the low temperature (ie 1300 o
C vs 1500 o
C) FBCVD SiC [5]
The discrepancies in the microstructure and mechanical properties still demand
further explanation on the deformation mechanism of low temperature FBCVD SiC
This chapter focus on the fundamental study on the mechanical properties of SiC we
have investigated the Youngrsquos modulus and hardness of three sub-micrometer FBCVD
SiC coatings using the indentation method The microstructure and mechanical
properties are explained on the basis of defects observed with a transmission electron
microscope (TEM) The deformation behaviour underneath a nano-indentation is
discussed
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
85
32 Experimental details
Silicon carbide (SiC) coatings were produced on top of highly-dense pyrolytic carbon
coatings using fluidized-bed chemical vapour deposition (FBCVD) method The SiC
coatings with varied stoichiometry and deposited at low temperature of 1300 oC by
Loacutepez-Honorato et alrsquos [5] were chosen and studied in this Chapter Table 1 gives the
deposition conditions of these coatings which were found and demonstrated to give
superberb mechanical properties in prevous studies [5] Figure 31(a) and (b) show the
polished cross-section (x-y plane) and (b) polished external surface section (x-z plane)
of TRISO fuel particles (defining the directions used in the later part of this Chapter)
Densities were measured by the Archimedes method in ethanol (density is the mean
value of three tests the weight of SiC shells is 01-03 g) Composition was measured
by Raman spectroscopy (Renishaw 1000 Raman system with a 514 nm argon laser
source) with a single spot measurements of around 1 microm diameter through an times50
objective lens as shown in Fig 31 (c) Two peaks at around 794 and 970 cm-1
are for
SiC and the asymmetric peaks around 200-500 cm-1
and 1500 cm-1
are acoustic SiC
and second order SiC respectively (S1 coating) [5] Carbon peaks are around 1360
and 1600 cm-1
(S2 coating) and the peak at 520 cm-1
represents silicon (S3 coating)
[5] It was estimated that the excess C amount is less than 1 at in S2 by measuring
the intensity ratios of I1600I794 and compared to previous study [18] where Raman
spectroscopy and elemental analysis (EPMA AES and XPS) were used
The phase and composition were also analysed using X-ray diffraction (XRD PW
1830 Philips Eindhoven The Netherlands) with Cu Kα1 radiation Figure 31(d)
shows the XRD spectra of the three types of SiC coatings All three coatings exhibit
the β-SiC phase A very small shoulder peak around 2θ=345deg was also obtained from
the coatings which indicated the presence of stacking faults No evidence of a Si or C
peak was found in the XRD result This was probably due to the fact that the
additional levels of Si and C were very small (le 1at ) and it would be difficult to
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
86
identify these traces using XRD [5 19]
Table 31 Deposition conditions of the low temperature FBCVD SiC coatings
Codes H2MTCS (volvol) Additives Temperature Density (gcm3)
S1 (SiC) 10 01vol Propylene 1300 o
C 3173 + 0029
S2 (SiC+C) 10 10 vol Propylene 1300 o
C 3135 + 0034
S3 (SiC+Si) 10 -- 1300 o
C 3188 + 0002
SiC+C or SiC+Si means that nearly stoichiometric SiC with low excess C or Si less than 1 at
Productions of samples are contributed by Dr Eddie Loacutepez-Honorato
SiC coated fuel particles were hot mounted in copper-loaded conductive resin To
reduce the influence of the surface roughness the FBCVD SiC coatings were first
ground down to obtain a flat surface where the nano-indentation could be carried out
The flat surface was further polished using increasingly finer diamond suspensions
until frac14 μm and finally polished using a 003 μm colloidal silica suspension The
thickness of the coating after final polishing was estimated to be around 60 μm A
final surface roughness of lt 5 nm was detected by atomic force microscopy (AFM)
Youngrsquos modulus and hardness were measured using a nano-indenterTM
XP (MTS
System Corp USA) and a micro-indenter (CSM Instruments Switzerland)
Nano-indentation was made using a Berkovich indenter calibrated with a standard
silica specimen Before the measurement the initial contact of the indenter with the
specimen surface was checked and the compliance of the loading column was
corrected Arrays of indentations were performed on each specimen with an interval
of 20 times the indentation depth between each indentation The penetration depth for
the measurement of Youngrsquos modulus and hardness was 500 nm All data were
analysed using the Oliver and Pharr method [7] Micro-indentation was made using a
Vickers indenter at a maximum load of 3 N and the interval between each indentation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
87
was also kept to 20 times the indentation depth of ~26 μm
Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)
polished external surface section (x-z plane) of TRISO fuel particles (c) Composition
(c)
(d)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
88
of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the
inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results
of three SiC coatings
Moreover a high purity (gt999995) and fully dense polycrystalline 3C-SiC bulk
(diameter 3 cm thickness 15 cm) sample fabricated by static CVD (Rohm amp Haas
Ltd UK) was used as a reference sample in order to confirm the accurate mechanical
property measurements for FBCVD SiC coatings The Raman spectroscopy of bulk
CVD SiC was the inset in Fig 31(b) and no excess C or Si was found in it
To observe the grain morphology more clearly the finely polished (no scratch could
be seen under optical microscopes times50) cross-section (Fig 1(a)) of the coatings were
chemically etched using Murakamirsquos solution (10 g sodium hydroxide and 10 g
potassium ferricyanide in 100 ml of boiling water) The surface morphology of
coatings was characterized using scanning electron microscopy (Field emission gun
Philips XL30 FEG-SEM) A transmission electron microscope TEM (FEG-TEM
Tecnai TM
G2 F30 U-TWIN 300KV) was used to study the microstructure of the
coating layer before and after indentation For cross-sectional analysis of indentations
TEM samples were made from thin plates which are parallel to one edge and through
the center of Berkovich indentation using a focused ion beam (FIB FEI Nova 600
Dual Beam system) milling For high resolution TEM (HRTEM) the samples were
prepared using an ion beam milling method
33 Results
331 Hardness and Youngrsquos modulus
Figure 32 shows the typicl load-displacement curve of SiC coatings and the hardness
(H) and Youngrsquos modulus (E) as a function of composition of the three types of
coatings The load-displacment curve (Fig 32(a)) shows a smooth character of the
deformation process during nanoindentation There is multiple mini lsquopop-inrsquo events
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
89
reflected on the hardness curve which started at the beginning from the low
indentation load These mini lsquopop-inrsquo can not provide enough consumption of the
internal stresses induced by indenter as it was needed for the initiation and
propagation of dislocations so no well-pronounced lsquopop-inrsquo effect was observed from
the load-displacement curve
Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the
maximum indentation depth of 500 nm under a Berkovich indenter inserted is the
hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of
coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively
Measurements were made on the x-z plane of SiC coatings (Fig 31(b)) and static
bulk CVD SiC for both micro- and nano-indentation to give reliable comparison with
previous studies [20-23] In the reference material the nano-hardness (36 GPa) and
Youngrsquos modulus (496 GPa) of bulk CVD SiC are nearly the same as in a previous
(c) (b)
(a)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
90
study [20] namely 36 GPa and 503 GPa respectively From Fig 32(b) it can be seen
that S1 has a higher hardness compared with S2 and S3 Further the values of
hardness obtained by nano-indentation (Fig 32(b)) are higher than by
micro-indentation for all samples
For low temperature FBCVD coatings the nano-hardness varies in the range 39 GPa
to 44 GPa whereas the micro-hardness varies between 36 GPa - 42 GPa These values
are at least 8 higher than the bulk static CVD SiC which has a nano-hardness ~36
GPa and a micro-hardness ~32 GPa (see Fig 32(b)) Moreover the low temperature
FBCVD SiC coatings have higher hardness as compared to a previous study of CVD
SiC for which the hardness values varied in the range of 25-39 GPa as measured by
nano-indentation under the similar experimental conditions [20-23]
In FBCVD SiC coatings Youngrsquos modulus of all three coatings is lower than the bulk
CVD SiC (see Fig 32(c)) which is an average Youngrsquos modulus (438 GPa) of
polycrystalline CVD SiC reported by Roy et al[24] The difference in hardness and
Youngrsquos modulus data could not be simply explained by the existence of C or Si due
to their low concentration (lt 1 at ) and location in the coatings which has been
addressed in detail in previous study [25] Therefore the difference of hardness and
modulus could be related to other microstructure such as pores which could vary
from atomic scale to micrometres which is discussed in the following session
Both nano- and micro-hardness results (Fig 32(b)) are higher than the available data
for polycrystalline CVD SiC [20-23] as discussed above and the correct measurement
of SiC coatings with small dimensions was ensured by comparing with the bulk CVD
SiC As mentioned the hardness and Youngrsquos modulus measured by
micro-indentation are slightly lower than the values measured by nano-indentation
because cracks were formed under micro-indentation due to the higher indentation
load
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
91
332 Microstructure of low temperature FBCVD SiC
Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)
coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)
SiC coating White arrows indicate the coating growth direction
Figure 33 shows SEM images of the three etched FBCVD SiC coatings In all three
coatings the width and length of columnar grains were found to be approximately 200
nm and 1-2 μm respectively These are found to be much smaller than the SiC coating
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
92
produced at a temperature of 1500 degC which had width ~1μm and length ~4-5 μm
[17] They are also smaller than the SiC showing dislocation movement under the
indentation deformation zone which was produced at temperature of 1500-1600 degC
by FBCVD and 1500 degC by static CVD with grain size of 1-5 μm and 5-10 μm
respectively [11 16]
Although the grain size is in a similar range for three coatings (as mentioned above)
due to different deposition conditions the grain morphologies of three coatings vary
First a less laminar structure was observed in the S1 coating (see Fig 33 (a)) as
compared to the coatings with excess C or Si (Fig 33 (c) and (e)) Fig 33 (b) shows
the existence of triple junctions (dashed circle) that could resist the movement of
grain boundaries and dislocation slip [12] Pores were also observed along the laminar
structure after etching In the S2 coating it has a large amount of a laminar structure
running through a single grain (laminar structure parallel to growh direction) as
illustrated in Fig3 (d) The information of grain morphology in S2 was mostly a
laminar structure perpendicular to the growth direction after etching (Fig 33(d))
Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain
interaction with each other and the arrow indicates grain growth direction
To get more information about the grains morphology in S2 coating a TEM image
05 μm
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
93
was taken and shown in Fig 34 Figure 34 shows that grains in S2 coating interact
(branch-like grain growth pattern on the lower-left part of Fig 34) with each other
which is similar as in sample S1 (Fig 33(b)) and grains form branch like structures
In the S3 coating (as can be seen in Fig 33 (f)) a parallel growth of grains with less
interaction among grains was observed
Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with
stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the
laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)
with a wrinkled like defects layer (indicated by the black overlaid line)
According to a previous study [25] about definition of grain boundary the grain
boundary in the S3 coating is smooth while in the S1 and S2 coating the grain
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
94
boundaries are rough which could result in branch-like grain growth pattern It could
be attributed to the different CSi ratio in reaction gas which produce SiC with
different morphologies on the (111) crystal plane which may have three different
morphologies rough smooth and pyramidal defect [26] Grains with differently
finished surfaces could lead to different grain growth morphologies because of
different surface energy For example in rough grain boundaries of S1 and S2
coatings branch like crystals were found as in Fig 33(b) and Fig 34
Figure 35 shows bright field TEM images of the S1 coating S2 and S3 coatings The
columnar grains were observed to grow perpendicular to the coating surface which
was consistent with the SEM results Further nano porous layers normal to the
coating growth direction are observed in the S2 coating (see Fig5 (b)) The formation
of porosity in thin films could be due to differences in diffusion of growth species the
incident molecule direction and deposition of secondary phases such as excess Si or C
[27]
Fig 36 An example of the crystal misorientation formed during SiC deposition (a)
BF-TEM and (b) DF-TEM
At low deposition temperatures the probability of a precursor reaching the edge of the
nucleus is considerably lower compared with that of arriving on the top due to a low
surface diffusion As these nuclei grow the areas immediately around them will suffer
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
95
from a shadowing effect blocking the arrival of new molecules and the formation of
new nuclei Since the diffusivity of atoms is low and no new nuclei are formed in
those regions gaps will be formed among grains A wrinkled like defect layer was
seen in the S3 coating (Fig 35 (c)) which could be attributed to the interruption of
the SiC crystallization growth during the deposition process such as crystal lattice
misorientation as seen in Fig 36
Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)
S2 (SiC+C) and (c) S3 (SiC+Si)
No obvious laminar defect was observed in the S1 coating by TEM this could be due
5 nm
(a) (b)
5 nm
5 nm
(c)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
96
to less interruption during deposition process According to above observation it was
proposed that the laminar structure observed in SEM images indicates some
instability during the fabrication process resulting in the deposition of the nano- and
micro-pores and misorientation This was attributed the variations in circulation and
deposition occurring close to the nozzle or at the hot zone [5]
Stacking faults were observed for all three types of samples as shown in Fig 35 with
a higher density than for the SiC deposited at a temperature of 1500 C [11 16 17]
These stacking faults could cause an intrinsic residual stress due to the coexistence of
the partial dislocations This was supported by the high resolution TEM images
(shown in Fig 37) exhibiting wave pattern fringes and they could only be observed
in one direction which is determined by the intrinsic stress
Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image
with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high
density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt
projection
Since the dislocation mobility under nano-indentation deformation has not been fully
understood in hard ceramic materials therefore it is significant to study this
behaviour in FBCVD SiC coatings with a sub-micrometer grain size However it is
difficult to observe the dislocations under the two-beam or weak beam dark field
2 nm
(a)
(111)
[110]
(111)
Sessile
dislocations
(b)
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
97
conditions due to the high density of defects In the present study the reversed fast
Fourier transform (FFT) images of the corresponding high resolution TEM images
was used to obtain information about the dislocations This method has been used in
many cases for dislocation observations [28]
Figure 38(a) shows a high resolution TEM image of a S1 coating which was taken as
a representative image to compare the atomic structure of all three coatings Figure
38(b) is the reverse FFT image using the marked inset diffraction pattern of Fig
37(a) in which sessile and glide dislocations can be observed The dislocation
density was calculated from the total number of glide dislocations divided by the area
in the image [29 30] From the analysis of images shown in Fig 38 the dislocation
density in S1 coatings was found to be 1013
cm2 The same magnitude of dislocations
density was found in the S2 and S3 coatings as shown in Fig 37 (three HRTEM
images were analysed for each coating)
333 Deformation behaviour under the indentation
The deformation zone under the indentation was investigated through the images of
FIB milled TEM samples in order to study the deformation mechanism of the low
temperature FBCVD SiC coatings Figure 39 shows the bright field TEM images
showing the mechanical behaviour of a S1 coating under nano-indentation on the x-z
plane (Fig 31(b)) at a maximum indentation depth of 500 nm
Figure 39(a) is an overview of the deformation area under an indentation A median
crack has formed just underneath the surface and has a direction aligned with the
indenter tip impression A higher magnification image around the elastic and plastic
interface is shown in Fig 39(b) It can be seen that a large amount of inter-granular
and trans-granular micro cracks were produced around the median crack initiation
zone This is substantially different from the dislocation-related plastic deformation
behaviour [10 11 16 31] which usually has a severe plastically deformed region
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
98
with few or no cracks Moreover the micro cracks were also observed in the C and D
zones under the indentation
Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a
S1 (SiC) coating (a) an overview of the deformation zone higher magnification
images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)
respectively Inset in (c) shows the micro cracks in the dashed square Left bottom
inset in (d) shows a high magnification of a shear crack while right upper inset in (d)
shows a high magnification of the dashed circle under the indenter tip
Figure 39(c) shows that micro cracks that are formed along the grain boundaries
which tend to follow the shear band direction with the formation of a few
trans-granular cracks In Fig 39(d) it can be seen that shear band micro cracks were
formed in one single grain (see inset in the left bottom corner of Fig 39(d)) This
single grain has a large amount of defects which are supposed to be the as-deposited
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
99
defects as shown in Fig 35(a) Shear band cracks were also observed just underneath
the indenter tip (right top inset in Fig 39(d)) As a result a shear band dominated
deformation zone can be seen in Fig 39(c d) under the indentation in a S1 coating
Fig 310 TEM bright field images show the mechanical reaction underneath the
indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating
The S2 and S3 coatings only show a micro crack pattern which is different from S1
coating Figure 310 gives the TEM images of the S2 and S3 coatings showing the
mechanical reaction underneath the indentation It can be seen from Fig 310(a) and
Fig 310(c) that the median cracks are not always produced under the indentation for
S2 and S3 coatings However some irregular cracks in S3 coatings and lateral cracks
in S2 were produced In particular in the S3 coating (Fig 310(b)) more micro cracks
either intragrain or transgrain were found than in the S1 and S2 coatings This is due
to the fact that the most micro cracks propagate along the grain boundaries in S1 and
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
100
S2 coatings (Fig 39(b) and Fig 310(d)) A careful analysis of the TEM images
shows that only micro cracks were found under the indentation and no
dislocation-induced shear band was observed This is different from previous studies
on the deformation behaviour of polycrystalline SiC [11 16 31] For example in bulk
polycrystalline CVD SiC [11] it was found that it has more dislocation slip bands
rather than micro cracks either in grains or along grain boundaries even though the
indentation load is higher than the load used in the FBCVD SiC based materials The
possible reason of this discrepancy is discussed later Moreover no amorphous phase
and α-SiC phase was formed under the indentation observed by diffraction and bright
field TEM images which is consistent with the work of Mishra and Szlufarska [32]
34 Discussion
High hardness and Youngrsquos modulus were obtained in the sub-micrometer grain size
coatings produced at a low temperature by FBCVD In the S1 coatings the
nano-hardness is ~22 higher while the micro-hardness is ~31 higher compared to
a commercial CVD SiC The higher hardness was also obtained in S2 and S3 coatings
All the coatings retained a higher Youngrsquos modulus than those SiC materials having
high hardness in previous study (equal or higher than 40 GPa nano-hardness) [33]
making these coatings unique among polycrystalline phase brittle ceramic material
Under nano-indentation only micro cracks were found in the deformation zone The
results seem to be consistent with the conventional view of the failure mechanism of
brittle ceramics at room temperature [34] The lack of dislocation and the high Peierls
force are reasons for fracture to occur in brittle materials However
dislocation-related plastic deformation routinely occurred in hardness testing because
the indentation stress field offers conditions of stress conductive to plastic
deformation [11 13 16 34] Molecular dynamic simulations even demonstrate that
13 of the hardness-related deformation is from dislocation-related plastic deformation
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
101
while 23 comes from fracture in SiC [31] It is rare to see a deformation zone
dominated by micro cracks in polycrystalline SiC such as in FBCVD SiC coatings
(Fig9 and Fig10 and see for example Ref [11 16 31]) With the above questions
we first estimated the factors controlling Youngrsquos modulus in FBCVD SiC coatings
followed by a study of the mechanism of superior hardness and deformation under an
indentation which influence the hardness in the three coatings
341 Influence of porosity on Youngrsquos modulus
Youngrsquos modulus presents a material constant for uniaxial tensile deformation which
is physically related to the atomic spacing inter atomic bond strength and bond
density In a low temperature FBCVD SiC coating it was shown from XRD
measurements that a shoulder peak was observed in addition to the β-SiC (111)
diffraction peak which corresponded to a crystal plane spacing of ~0266 nm (Fig
31(c)) Moreover we found that the XRD peak shifted to a lower diffraction angle
compared with the bulk CVD SiC According to the XRD pattern in Fig 31(c) the
crystal lattice constants of about 04366 04368 and 04368 nm for S1 S2 and S3
coatings were obtained respectively However the crystal lattice constant for bulk
CVD SiC is ~04359 nm (XRD pattern obtained by the same condition was shown in
Ref 25)
Further crystal orientation impurities and porosity may affect the Youngrsquos modulus
As the Youngrsquos modulus on the x-z plane (Fig 31(b)) was similar to the value
obtained along the cross-section (Fig 31(a)) [5 25] which meant that the orientation
has no effect on Youngrsquos modulus Moreover as discussed before the effect of C or Si
in S2 was found to have no effect on the difference of hardness and Youngrsquos modulus
Excluding these two factors (orientation and impurities) the effect of porosity on
variation of the elastic properties in three coatings was investigated The presence of
nano-pores in S2 coating as in Fig 35(b) results in a lower density Although no
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
102
pores were directly observed by TEM in the S1 and S3 coatings their density is lower
than the theoretical density of SiC Thus the elastic modulus E at room temperature
can be expressed in an exponential function of porosity pV [35] as
0 exp( )pE E CV (1)
where 0E = 496 GPa is the elastic modulus and C = 357 is a constant for a pore-free
bulk CVD SiC pV is the ratio of the relative density difference to the theoretical
density of SiC (322 gcm3)
The calculated Youngrsquos modulus for S1 S2 and S3 coatings is 465 plusmn 15 446 plusmn 17 and
473 plusmn 1 GPa respectively which follows a trend similar to the experimental data
presented in Fig 32 It was concluded that the different Youngrsquos modulus in the three
low temperature FBCVD SiC coatings is attributed to porosity although the
experimental Youngrsquos modulus data of FBCVD SiC coatings is slightly lower than the
values calculated using the Eq(1) The difference between calculated and measured
value of FBCVD SiC coatings is due to the fact that the 0E from pore-free bulk
CVD SiC instead of pore-free FBCVD SiC coatings (not available) FBCVD SiC
coatings have larger crystal lattice constant (~0437 nm) than bulk CVD SiC (~04359
nm) as discussed above Since the expanded lattice constant leads to a decrease of the
Youngrsquos modulus according to a previous study [20] the 0E of pore-free FBCVD SiC
coating is expected to be lower than bulk CVD SiC
342 Mechanism for High hardness
From previous studies [10 11 16 31] dislocation nucleation and glide is the primary
response of SiC under nano-indentation Formation of shear bands due to dislocations
has also been reported [11] which were found under the plastic deformation zone
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
103
when indentations were made on a particular grain in polycrystalline SiC and at the
grain boundaries Moreover dislocation nucleation is also correlated with the discrete
pop-ins observed in the force-displacement curve [32] No pop-ins was found due to
the presence of a large amount of dislocations in the present study Dislocation
mobility can be estimated similar to the case of a metallic material having intrinsic
dislocations Mishra and Szlufarska [32] worked on the dislocation mobility in
3C-SiC using large-scale molecular dynamics simulations The results indicated that
dislocation mobility decreased by dislocation interaction as its density reached a
saturation value This is similar to the work hardening effect in a metallic material [34]
We estimated the stress ( ) needed for dislocation to move using Taylorrsquos work
hardening equation [34] given by
1 2
0 Gb (2)
where 0 is the shear stress for a dislocation to move without any obstacle and the
value of 0 taken was 75 GPa [13] is a numerical constant depending on the
locking strength of a nod The value of taken was 8 [36] b is Burgers vector
where b = 0178 nm for a Shockley partial dislocation in SiC initiated and gliding on a
close packed (111) plane and is the density of glide dislocations G is the shear
modulus which can be written as
2(1 )
EG
(3)
where is the Poissonrsquos ratio and E is the Youngrsquos modulus The dislocation density
was ~03times1012
cm2 The calculated shear stress according to Eq (2) was ~52 GPa and
this value is much higher than the theoretical shear stress which is in the range of
295-4312 GPa obtained from previous reports [37-39] The theoretical shear stress is
the maximum stress provided for the dislocation nucleation and propagation in SiC
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
104
crystals Therefore the dislocation-related yield behaviour could not occur under the
plastic deformation zone in sub-micrometer FBCVD SiC coatings
The superior hardness value in FBCVD SiC coatings is attributed to the immobility of
the dislocations In the case of the SiC-C solid solution [40] the occurrence of a high
density of dislocations causes a strain-hardening effect Furthermore given that
dislocations could be motivated by the shear stress a phase transformation from a
crystalline phase to an amorphous could occur [32] However no amorphous phase
was observed under the nano-indentation (Fig 37 and 8) nor was dislocation
movement band observed in this study This suggests that the dislocation-related
phase transformation did not occur under the indentation
343 Deformation mechanism under nano-indentation
The hardness-related plastic deformation which occurs due to the nucleation and
propagation of micro cracks in FBCVD SiC coatings can be explained as follows
(i) The onset of plastic deformation under the indentation occurs as the maximum
shear stress approaches the yield stress [41] According to 15H Y (Y is the yield
stress H is the hardness) the yield stress in FBCVD SiC coatings is around 26 GPa
The yield stress is lower than the stress needed for the movement of dislocations and
the theoretical shear stress [37-39] This indicates that the hardness-related plastic
deformation first occurred by the nucleation of defect-induced cracks which
propagated to the indented surface (see inset (top right) in Fig 39(d)) The
deformation impression was accommodated by the densification of defects such as
the pores dislocation pile ups and grain boundaries as in Fig 33(b)
(ii) The shear stress was used to promote the movement of dislocations under the
indentation and form slip bands in previous studies [10 11 42] The highest amount
of micro cracks were observed in FBCVD SiC coatings contrary to plastic
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
105
deformation under the indentation found in previous studies [10 11 42] The micro
cracks formed in the hardness-related plastic deformation zone is the Mode-II crack)
[43] as shown in Fig 39(c) and (d) Unlike Mode-I which is dominated by the tensile
stress a Mode-II crack is the consequence of a confined shear stress [34] At the
interface of the elasticplastic deformation branch-like micro cracks were observed
as in Fig 39(b) The above discussions distinguish the hardness-related plastic
deformation mechanism in FBCVD from previous studies on ceramics which showed
dislocations are the main deformation mechanism underneath the indentation [31 44]
A unique hardness-related plastic deformation mechanism was used to explain the
difference in hardness of all three types of FBCVD SiC coatings According to Qian
et al [45] the hardness could reach an asymptotic value with the saturation of the
micro cracks growth population In three FBCVD SiC coatings studied here different
amounts of micro cracks were found (Fig 39(b) and Fig 310(b d)) and micro cracks
nucleated at stress concentration zones such as the grain boundaries or defects within
the grains Thus the difference in hardness was attributed to the grain morphologies
as shown in Fig 33 which gives different degree of resistance to the initiation and
propagation of micro cracks In the S1 coating triple junctions hamper grain
boundary shear by forming interlocks [12] which could resist and deflect the initiation
and propagation of micro cracks In the S2 coating elongated grains interact with the
surrounding small grains which could also provide interlocks (Fig 33(d) and Fig
34) The slightly lower hardness of the S2 coating as compared to the S1 coating is
due to the nano pores as seen in Fig 35(b) A lack of triple junctions and grain
interactions could be the reason for the lower hardness in the S3 coating as it has a
parallel crystalline morphology which has less constraint towards the initiation and
propagation of cracks
35 Conclusions
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
106
The microstructure and mechanical properties of three types of FBCVD SiC coatings
(SiC SiC+C and SiC+Si) were studied FBCVD SiC coatings with a sub-micrometer
grain size were deposited on simulated TRISO fuel particles by FBCVD at a low
temperature (1300 oC) The mechanical properties were studied using micro and
nano-indention The microstructures were studied using SEM and TEM It was
found that the Youngrsquos modulus of all three coatings differ which was attributed due
to the presence of nano-pores The high hardness of FBCVD SiC coatings was due to
the large amount of defects particularly the high density of dislocations It is found
that the interactions between dislocations reduced their mobility and make
dislocation-related plastic deformation unavailable We suggest that the work
hardening effect is the reason for the high hardness in the sub-micrometer grain size
FBCVD SiC coatings A hardness related-deformation mechanism was attributed to
the initiation and propagation of micro cracks The nano-indentation indent volume is
most likely be accommodated by the densification of defects such as the pores As a
result the hardness difference in FBCVD SiC coatings is due to the different grain
morphologies producing different amounts of micro cracks
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
107
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108
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[38] Y Umeno Y Kinoshita T Kitamura Ab initio DFT study of ideal shear
CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation
111
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in Hot-Pressed Silicon Carbides J Am Ceram Soc 92 (2009) 1788-95
[44] S L Lloyd A Castellero F Giuliani Y Long K K Mclaughlin J M
Molina-Aldareguia N A Stelmashenko L J Vandeperre W J Clegg
Observations of nanoindents via cross-sectional transmission electron microscopy
a survey of deformation mechanisms P Roy Soc a-Math Phy 461 (2005)
2521-43
[45] J Qian L L Daemen Y Zhao Hardness and fracture toughness of moissanite
Diam Relat Mater 14 (2005) 1669-72
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
112
CHAPTER 4 Vickers Indentation Fracture Toughness of
SiC Coatings
41 Introduction
Silicon carbide (SiC) layer is considered to be the most important component for
structural integrity as during the operation of a nuclear reactor it has the ability to
sustain most of the internal pressure caused by gaseous fission products produced in
the kernel and retain most of the fission products [1-4] Previous work was focused on
the investigation of mechanical properties (Youngrsquos modulus and fracture strength) of
SiC coatings on TRISO particles using different techniques such as a ring test [5 6]
a crush test [7 8] a micro-cantilever test [9] and indentation [10 11] However few
reports exist on the measurement of the fracture toughness of SiC coatings even
though it is a property used in modeling to estimate the failure probability of TRISO
fuel particles [12] For example Kadak et al [12] used a fracture toughness value of
33 plusmn 053 MPa m12
This value was obtained from bulk SiC produced by a static
CVD method The fracture toughness value may well differ for SiC coatings produced
by fluidized bed chemical vapour deposition (FBCVD) on TRISO fuel particles [10]
Because microstructure of SiC produced by static CVD and FBCVD methods could
vary significantly For example the static CVD SiC usually has larger grain size and
high density while FBCVD SiC with large grain size is usually accompanied with
porosity [13] Different grain size range and porosity fraction can lead to variation of
fracture toughness [1 2] Therefore the fracture toughness value of bulk SiC may not
be truly representative of SiC coatings used in nuclear fuel applications To our
knowledge the only available data on the fracture toughness of a SiC layer on TRISO
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
113
fuel particle is reported by Zhao et al[9] where the fracture toughness was measured
by the micro-beam method However this method is time consuming and expensive
restricting its implementation as a standard characterization technique where
repetitive measurements are required to confirm the reproducibility of experimental
data
In this Chapter micro-indentation is used to investigate the fracture behaviour of
different SiC coatings produced (on TRISO fuel particles) by FBCVD due to its
capacity to measure the mechanical properties in a small area and produce visible
cracks [14-16] The fracture behaviour under an indenter is also studied using a
transmission electron microscope (TEM) in order to give better understanding of the
fracture mechanism The characteristics of the SiC microstructures are then correlated
with their fracture behaviour
42 Experimental details
The SiC coatings used are the same as the ones in Chapter 3 and the deposition
conditions were shown in Table 31 Chapter 3
For the micro-indentation study SiC coated fuel particles were hot mounted in
copper-loaded conductive resin (to get better SEM images) and then ground to a
cross-section (as shown in Fig 31(a)) or polished a flat external surface (as shown in
Fig 31(b)) In this Chapter the y direction is called radial direction x is called
tangential direction according to Fig 31(a) and (b) The samples were then polished
using increasingly fine diamond suspensions to 14 μm Indentation fracture
toughness measurements were performed using a Vickers diamond indenter (CSM
Instruments Switzerland) Due to the through-thickness (in the radial direction)
failure behaviour of a SiC coating in a TRISO fuel particle under tensile stresses
generated from gases due to nuclear reactions similar tensile stresses could be
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
114
generated from indentation of polished external surface of TRISO particles which
could generate cracks along the radial direction (y direction in Fig 31(b)) of the
TRISO particles as well The indentations were carried out under a maximum load of
3 N (corresponding to a maximum indentation depth of ~26 μm) To avoid PyC
influence the thickness of SiC coatings (in the section as shown in Fig 31(b)) were
kept to ~60 μm after polishing which is more than 20 times the indentation depth
In this case the elastic zone has not expanded to the substrate according to the
criterion that indentation depth is less than 10 of coating thickness [17] For each
sample six indents were made on the polished external surface of SiC perpendicular
to the radial direction with a separation of 70 μm between each indent
Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)
(a) half-penny crack systems and a crossed-cracks would be seen on the top view of
the dashed line (b) Palmqvist crack (or radial) system redrawn according to
reference [25]
The calculation of the VIF fracture toughness must account for the crack profile under
the indenter whether the cracks are of the Palmqvist mode or half-penny mode which
are illustrated in Fig 41 The halfpenny crack system is formed by the joining of
radial cracks as shown in Fig 41(a) while the Palmqvist crack system is always
shallow as shown in Fig 41(b)
To observe the crack impression under the indenter on the polished external surface
an indentation (as in Fig 42(a)) with a final indentation depth of 26 μm was
sequentially polished with 6 μm diamond suspensions The surface was polished until
the plastic deformation zone was exposed together with the radial cracks (as shown in
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
115
Fig 42(b) Afterwards polishing continued until the removal of the plastic
deformation zone (as shown in Fig 42(c)) The surface showed no cross-over
cracking present as illustrated in Fig 41(a) and this confirms the presence of the
Palmqvist mode cracks on the polished external surface of SiC coatings under the
Vickers indenter The three polished samples showed the same crack propagation
mode and this is consistent with previous reports [18 19] where a Palmqvist crack
system has been observed in SiC at low loads (lt 10 N)
The Palmqvist crack mode allows the VIF fracture toughness to be calculated using
the equation proposed by Laugier [15 16] given as
1 2 23
3 2( ) ( )IC v
a E PK
l H c
(1)
In Eq (1) the geometrical constant v is a calibrated value using the already known
fracture toughness due to the variation in use of the Vickers hardness or the
nano-hardness [14 16 20 21] The 2a and l are the lengthes of diagonal and radial
crack length of Vickers indentation (as shown later in Fig 43) respectively c=a+l
the E and H are Youngrsquos modulus and hardness measured by nano-indentation P is
the load of Vickers indentation Therefore this geometrical constant was calibrated
before it was used to calculate the VIF fracture toughness of SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
116
Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished
external surface of a SiC coating (a) indentation before polishing (b) image after
removal of indentation impression (c) image after removal of the plastic deformation
zone
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
117
The only already known fracture toughness was measured on the cross-section of
extra-Si SiC coatings using a micro-beam bending method [9] so the calibration of
v was carried out on the cross section (as in Fig 31(a)) of the same coating
According to Eq(1) the hardness (H ) and Youngrsquos modulus (E) are nano-hardness
and Youngrsquos modulus as measured in a previous study [22] P is the load a is the
impression half diagonal l is the crack length and c is the half diagonal crack length
(see later in Fig 43) To get the load and dimensional values of indentations a total
of 8 indentations at different loads (3 35 and 4 N) were applied on the cross-section
of the extra-Si SiC coating
The crack lengths were measured using a scanning electron microscope (Philips XL30
FEG-SEM) FEG-TEM (Tecnai TM
G2 F30 U-TWIN 300KV) which was used to
study the fracture behaviour under the indenter For the TEM study the cross
sectional specimens for the indents were prepared using focused ion beam milling
(FIB FEI Nova 600 Dual Beam system) Note that due to the large deformation zone
(gt10 μm diameter) and radial crack length (gt15 μm) observed from micro-indent
impression it was not possible to produce a sufficiently large TEM sample by the FIB
technique This limitation restricted us to study the fracture behaviour under a sharper
indenter (Berkovich) with lower load
43 Results and discussion
431 VIF fracture toughness study
Figure 43 is the crack morphology observed in S3 (SiC + Si) coating cross-section It
shows that the fracture resistance is different in the tangential and radial directions of
the cross-section which is consistent with the previous measurements along these
directions measured by the micro beam method [9] Different crack lengths along the
tangential and radial directions observed from 8 indentations are illustrated in Table
41 Correspondingly fracture toughness values of 347 MPa m12
and 672 MPa m12
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
118
taken from Ref [9] were used as the standard values for the tangential and radial
directions of the SiC coating respectively According to Eq (1) taking into account
observed and measured parameters (KIC a c l H and E) the geometric constant
value v was calculated in each indentation for each direction (Table 41)
Fig 43 Optical micrographs showing different crack lengths along the radial and
tangential directions for S3 SiC coatings
Table 41 illustrates the indentation parameters and the calibrated geometrical
constant v for the Palmqvist crack mode According to the results shown in Table
41 the calibrated mean value of v is 002008plusmn000273 and this value is within
the range of the geometrical constant value (0014-0023) from previous theoretical
studies [14 23] By using nano-indentation hardness and Youngrsquos modulus v was
taken as 002 for the calculation of the VIF fracture toughness in SiC layers in this
study which is the upper limit of 0016plusmn0004 used for previous studies of bulk
CVD SiC using the HE from micro-indentation [14 24-27]
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
119
Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχ
v along the radial and tangential directions
Load Radial direction
Tangential direction
a (μm) c (μm) l (μm) χv a (μm) c (μm) l (μm) χv
3 N 6650 13125 6475 0020368 6685 18285 11600 0023088
6900 13090 6190 0019473 6995 15470 8475 0015013
6675 11895 5220 0015749 6120 16615 10495 0019880
6695 13130 6435 0020249 6555 15935 9380 0017057
6790 12610 5820 0017997 6425 18275 11850 0023783
35 N 7195 14970 7775 0022404 7235 20790 13555 0024930
6670 14080 7410 0020721 6715 18160 11445 0019412
4 N 7770 15855 8085 0020967 7390 20240 12850 0020187
χv 002008 plusmn 000273
Note The geometrical constantsχv presented in Table 41 were calculated using Eq(1) The fracture
toughness along the radial (672 MPa m12
) and tangential directions (347 MPa m12
) were taken from
Ref 9
Although the Vickers indentation method for fracture toughness measurement has
been discredited as a mean to obtain true fracture toughness [28] and always gives a
lower fracture toughness value than that obtained using the standard methods (such as
single edge V-norched bending)[1] the values obtained can be compared with each
other This is particular important for small samples and thin coatings since Vickers
indentation provides a method to quantify fracture behaviour when it is not feasible to
obtain true fracture toughness However to get reasonable comparison of Vickers
indentation fracture toughness in SiC coatings the following conditions should be
met
(1) SiC materials produced four regular radial cracks along the corners of the
Vickers indenter For indentation at the polished external surface of SiC
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
120
coatings deposited by FBCVD similar fracture resistance along different
orientation at the surface should be obtained
(2) The calibration of the geometrical constant should be made v was obtained
as 002 based on previous experimental results (see above)
Table 42 VIF fracture toughness of SiC coatings deposited under different
conditions
Sample Grain size range (μm) Vickers toughness (MPa m12
)
S1 (SiC) 02-2 351plusmn042
S2 (SiC + C) 02-2 403plusmn043
S3 (SiC + Si) 02-2 493plusmn016
Table 42 presents the measured VIF fracture toughness on the polished external
surface using equation (1) for the SiC coatings in which the deposition conditions and
grain size were given It can be seen that the SiC coating with excess Si (S3) has
highest indentation fracture toughness followed by SiC with excess carbon (S2) and
stoichiometric SiC coatings (S1)
Vickers indentation fracture toughness values obtained in this study are slightly higher
than that of commercial CVD β-SiC which has been reported to vary from 24 to 33
MPa m12
measured by the same method [24 26 27] The VIF fracture toughness of
49 MPa m12
for extra-Si SiC measured on a polished external surface is between
347 and 672 MPa m12
when measured on a cross section by micro-beam method [9]
This is consistent with the observation of radial crack length differences ndash the crack
length on the polished external surface is between those in the tangential and radial
direction on the cross-section It is suggested that Vickers indentation is an effective
method for the characterization of fracture behaviour of FBCVD SiC coatings
Moreover the high hardness and Youngrsquos modulus of these three coatings [22] do not
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
121
cause a decrease in fracture toughness which is explained in the later part of this
paper
432 Influence of non-stoichiometries on the VIF fracture toughness
The VIF fracture toughness in S2 SiC coating is ~14 higher than the value for S1
SiC coatings and this can not be attributed to heterogeneous toughening due to the
excess carbon being at the grain boundaries Due to the low content of excess C it is
difficult to identify such an excess at the grain boundaries [29] Previous work
reported in Ref[30] showed that there was no presence of carbon at the grain
boundaries for a concentration up to 1 wt excess C In our case a similar situation
was found in S3 SiC coating where excess Si has not been found along the grain
boundaries Previous studies had [31 32] shown that excess Si in SiC was observed in
grains or near the grain boundaries by TEM only when the amount of excess Si is
high enough (such that it could be detected by XRD or a much higher Raman
spectroscopic intensity)Thus it is assumed that the excess Si could not be considered
as giving heterogeneous toughening which caused a ~43 higher VIF fracture
toughness in the S3 SiC than the S1 SiC coatings As a result the small amount of
excess carbon or silicon in SiC coatings does not seem to have influence on the VIF
fracture toughness through serving as the heterogeneous phase along the grain
boundary
The excess Si or C could be related to different grain morphologies according to
previous study [33] where it was observed that different SiC ratios in the reaction
gas produced rough smooth and irregular pyramid-like grain surfaces This further
affects the growth morphology and cohesion stress between grains For example the
smooth grain surface favours the parallel grain growth The weak grain boundary
cohesion could be the micro crack initiation zone while the strong grain boundary
could transfer the stress to stress concentration zone Here the role of grain
morphology is studied later in terms of stress concentration zone under indentation
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
122
433 Microstructural analysis of fracture behaviour under the indenter
SiC coating under nano-indentation on the polished external surface at a maximum
indentation load of 160 mN It can be seen that the median crack propagation root
deflected slightly and changed from intergranular to transgranular fracture as shown
in Fig 44(a) It is worth noticing that the median crack observed under
nano-indentation was not found under indentation because the indentation cracking
mode depends on the condition of the indenter tip [34] Higher magnification images
(Fig 44(b)) show that a large number of micro cracks were produced at the
elasticplastic interface
Fig 44 Bright field TEM images of the deformed zone under the indentation of the
S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)
(c) and (d) are higher magnification images of the median crack initiation zone (circle
B) the median crack (circle C) and the median crack tip (circle D) respectively
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
123
Both intergranular and transgranular cracks were observed near the median crack
initiation zone These cracks are under a tensile stress dominated by Mode I cracks as
the elastic-plastic stress field gives the highest tensile stress around this interface
according to a previous report (see Ref [35]) Moreover micro-cracks were observed
surrounding the median crack and also at the median crack tip as shown in Fig 44(c)
and Fig 44(d) respectively Figure 44(c) illustrates that the micro-cracks are along
the grain boundaries while the micro-cracks around the crack tip were found to both
pass through the grains and along grain boundaries (Fig 44(d))
Non-stoichiometric SiC coatings (S2 and S3) show quite different crack morphologies
under the indenter from that in the stoichiometric SiC (S1) coating as shown in Fig
310 in chapter 3 It can be seen that the propagation root of median cracks in S3 SiC
and S2 SiC coatings were affected by the microstructures as in Fig 310(a) and (c) in
chapter 3 Moreover a lateral crack was found in the S2 SiC coating The irregular
median crack propagation route in non-stoichiometric SiC coatings seems to be
related to the laminar structure
Fig 45 Cross-sectional SEM image of the S1 SiC coating showing the grain
boundary (dark arrow) and laminar structure (while arrow)
Figure 45 shows the cross section of S1 SiC coating and the laminar structure (as
indicated by the dashed lines) is perpendicular to the grain growth direction It was
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
124
discussed in chapter 3 that the laminar structure is due to either nano-pores or a high
concentration of stacking faults and it is much less evident in the stoichiometric SiC
coating as compared to the coatings with impurities [22] In the S3 SiC coating (Fig
310(b) in chapter 3) a larger amount of micro cracks either intergranular or
transgranular were found under the indenter than in the S1 and S2 SiC coatings
The fracture mechanism of materials is influenced by their microstructure and the
fracture toughness could be enhanced by changing it For example ceramics
containing micro-cracks during fabrication could be associated with good fracture
behaviour but low strength and hardness since the micro-cracks usually serve as the
failure origins A better solution is to fabricate materials with microstructures that can
form stress induced micro-cracks under an external force [36] In FBCVD SiC a
number of micro cracks were observed under the indenter (Fig 44(b) Fig 310(b)
and (d) in chapter 3) from where the main cracks initiated and propagated away from
this zone According to a previous study although the tip of the main crack leaves the
micro-cracked zone under the indenter the wake region can provide stress shielding
against some further crack extension [37]
Thus the micro-cracks under the indentation (Fig 44(b) Fig 310(a) and (c) in
chapter 3) seem to be a mechanism for the toughening behaviour of FBCVD SiC by
dissipating the fracture energy for brittle fracture Micro-cracks were also found near
the main crack tip and surrounding the main crack for example in the stoichiometric
SiC coating (Fig 44(c) and (d)) This further confirms the toughening behaviour
through micro-cracking In CVD SiC which has a slightly lower fracture toughness
(around 33 MPa m12
) only a few micro-cracks were observed under the indentation
[38] which could be caused by indentation-induced slip bands As a result the
micro-cracks formed under the indentation near the main crack seem to be the reason
for the high VIF fracture toughness in SiC coatings when a high hardness is obtained
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
125
Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a) S2
SiC (b) S3 SiC
Stress concentration zones are known to facilitate the nucleation of micro-cracks so a
large amount of micro-faults (eg pores) and weak grain boundaries (inducing the
micro-cracks under an external stress) could increase the VIF fracture toughness A
higher VIF fracture toughness in the extra-C SiC than in stoichiometric SiC coatings
may be due to the presence of the nano-pores (as shown in Fig 35(b) in chapter 3)
The S3 SiC has an even higher VIF fracture toughness than the S2 SiC coating and
this may correspond to a larger number of micro-cracks under the indentation We
assume this difference is due to their varied grain boundary morphologies as shown
in Fig 46 For example we observed different length of cracks on the cross section
(Fig 43) with cracks parallel to the grain growth direction shorter than cracks
perpendicular to the grain growth direction This is because along grain growth
direction itrsquos more likely to produce micro-cracks along the grain boundary As we see
in Fig 46 grains interact with each other in extra-C SiC (Fig 46(a)) forming branch
grains while in S3 SiC grains grow parallel (Fig 46(b)) According to a previous
study it is easier for parallel grains to form a transgranular fracture when the grain
boundaries are along the loading axis [39] This can explain the larger number of
transgranular micro-cracks under the indentation in the extra-Si SiC compared to the
extra-C coatings (Fig 310(b) in chapter 3) which caused different VIF fracture
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
126
toughness This different grain morphology could be caused by the
non-stoichiometries and further work needs to be done to study how excess C or Si
affects the microstructure of the SiC
44 Conclusions
In summary micro-indentation on the polished external surface of the SiC coating in
TRISO particles has been successfully applied to measure the VIF fracture toughness
of the silicon carbide (SiC) Three different types of SiC coatings (stoichiometric SiC
SiC with excess silicon and SiC with excess carbon) produced on spherical particles
by FBCVD were analysed The VIF fracture toughness (measured on the polished
external surface) in these three coatings investigated in this study was observed to
vary between 35 and 49 MPa m12
The results have shown that the VIF fracture
toughness is influenced by the microstructure and non-stoichiometry of SiC coatings
For FBCVD SiC coatings a high VIF fracture toughness accompanied with superior
hardness was attributed to the formation of micro-cracks The difference in VIF
fracture toughness was proposed to be dominated by the laminar defects and grain
morphologies in the SiC coatings
CHAPTER 4 Vickers indentation fracture toughness of SiC coatings
127
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on fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07
[39] H Horii and S Nematnasser Brittle failure in compression - splitting faulting
and brittle-ductile transition Philos T Roy Soc A 319 (1986) 337-74
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
131
CHAPTER 5 Influence of Interfacial Roughness on Fracture
Strength of SiC Coatings
51 Introduction
During the irradiation process of TRI-Isotropic (TRISO) fuel particles the high
tensile stress could be accumulated at crack tips These tips were due to direct
penetration of the cracks formed in the PyC layer or the high stress concentration as a
result of the debonding of IPyCSiC interface [1 2] When the tensile stress inside of
the particle exceeded the critical fracture stress of the SiC coating it caused the
failure of the whole particle [3] Furthermore the fracture strength is a main
parameter used in modeling the probability of failure of fuel particles so it is
important to measure the fracture strength of SiC to determine their performance
which is determined from the maximum tensile stress
Different methods such as hemi-spherical bending [4] crush test [5 6] and inner
pressure [6] were introduced to measure the fracture strength of SiC coating in
TRISO fuel particle The fracture strength was in a range and could be characterised
by the Weibull distribution function [4-6] The common vague conclusion derived
from previous results is the significant effect of the IPyCSiC interface on the fracture
strength [4-6] The interface was also found to affect the primary failure mechanism
by determining if the load can transmit through the SiC [6] Previous analyses are
consistent with the well-known prescription that the fracture strength of ceramic
materials varies largely and it is dependent on the size and surface condition of the
specimen [7-9] Among these methods the latest modified crush test proposed by
Byun et al[510] showed a well controlled scatter of the fracture strength in a given
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
132
sample
Although the importance of the interface has been noticed the lack of an accurate and
scientific description of the interface has limited the further study about its
relationship with the fracture strength Roughness is a commonly used terminology to
describe the interface and it could be measured by atomic force microscope and
characterised by the standard deviation of the vertical features [11 12] However
roughness is not enough to describe the interface and to relate it to fracture strength
[13] Due to the importance of the statistical analysis for ceramic materials the
self-affine theory was used to characterise the complex interface numerically
according to previous studies [14-17] A self-affine interface is characterised by a
correlation length the saturation roughness and the roughness exponent [18] A
similarly straightforward approach was applied to demonstrate the importance of the
interfacial roughness on the mechanical properties [19] showing that interfaces with
big and sharp irregularity fail first
In this work the modified crush test was used to measure the fracture strength of a
SiC layer deposited at different temperatures The IPyCSiC interface was well
described by self-affine theory Therefore the effect of the IPyCSiC interface and
dimension of particles together with other possible influences such as porosity and
grain size on the fracture strength were discussed The improvement of this work is
being able to do statistical analysis on the interfacial roughness
52 Experimental details
521 Materials
In this Chapter the buffer pyrolytic carbon and dense pyrolytic carbon coatings were
deposited on the top of ZrO2 kernel (~ Φ500 μm) by fluidized bed chemical vapour
deposition Thirteen SiC coatings were deposited at different temperature flow rate
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
133
MTS concentration and added gas as shown in Table 51 The deposition conditions
were chosen according to previous studies to get different microstructures and more
deposition mechanisms of SiC coating can be found in Ref [20] For fracture strength
measurement the SiC particles were mounted with thermoplastic resin and ground to
about 55 portion of the sphere and polished using increasingly fine diamond
suspensions until frac14 μm SiC shells were released from surrounded PyC layers by
oxidizing at 700 ordmC for 8 hours and further washed in an ultrasonic bath with acetone
for 5 minutes
Table 51 Shows the deposition conditions and dimensions of SiC coatings produced
by fluidized bed chemical vapour deposition
Sample Temperature
(ordmC)
MTS
(vol )
Added gas concentration Flow rate
(LMin)
Radius
Thickness (~)
S1 1300 91 05vol C3H
6 600 72
S2 1300 91 01vol C3H
6 600 76
S3 1280 91 01vol C3H
6 600 83
S4 1300 91 -- 600 85
S5 1400 19 57vol Ar 778 87
S6 1500 22 82vol Ar 700 90
S7 1500 19 89vol Ar 778 101
S8 1500 22 79vol Ar 700 112
S9 1400 19 57vol Ar 777 117
S10 1300 19 57vol Ar 778 129
S11 1500 19 89vol Ar 777 151
S12 1500 22 76vol Ar 700 158
S13 1500 19 57vol Ar 778 190
The difference between sample S5 and S9 S7 and S11 is the thickness of the PyC layer MTS
methyltrichlorosilane Lmin the flow rate measured in liter per minute To produce SiC coatings with
particular microstructures and compositions different deposition conditions were chosen which were
contributed to Dr Eddie Lopez-Honorator
522 Test method and analysis
The crush test taking the contact area into consideration was used in this study [2 5
21] and the loading profile of the crush system is shown in Fig 51 When a partial
spherical shell (Radius R thickness t) was diametrically loaded by an external load F
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
134
concentrated on a small circular area (radius 0 ) the maximum membrane stress and
bending stress could be calculated by the equations developed by Roark and Young
[21] The combination of the maximum bending and membrane stress (Local fracture
strengthL
f ) in the inner side of the shell was the maximum fracture strength for
partially loaded shell (around 55 of the sphere)
The fracture strength of brittle SiC coating is best considered as a distribution rather
than a fixed number and the most widely used expression for characterisation is the
cumulative distribution functionmdashWeibull distribution function [7 22] In the current
study the distribution of local fracture strength and fracture strength for a full
spherical shell were characterised by the Weibull distribution The Weibull modulus m
is derived from the local fracture strength (Eq 14 in Chapter 2) The calculation of the
fracture strength for the full spherical shell (F
f ) is based on the size effect (scaling
factor mtRr 122
0 ))(4( R radius of the particle t thickness of SiC shell 0
radius of residual impression after loading) which is equal to the partial strength
divided by the scaling factor [5 7] More details about fracture strength calculation
are available in Ref [5]
Fig 51 Schematic of the modified crush test system for SiC half shell [5]
According to a previous study [5] one reason for the difference of local fracture
10 ordm
t
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
135
strength in a given batch of coating is due to different sizes of residual impression
( 0 ) under which the distribution of defects could be different To reduce the
influence of the 0 the radius (R) at the edge of the residual impression was kept at
an angle of around 10ordm (as shown in Fig 51) from the loading axis by inserting
different kind of soft metal It varied slightly (the ratio of standard deviation to mean
value is around 10) in each batch of SiC
The crush test was carried out in a universal tensile machine INSTRON 5569
(INSTRON High Wycombe Bucks) with a 100 N maximum load cell For each batch
of SiC shell (except for S13) at least 30 specimens were tested at room temperature
with a crosshead speed of 0005 mms The failure load recorded by the tensile
machine was used as the fracture load The individual impression left on the soft
metal (Nickel alloy cold worked copper or brass) was marked under corresponding
load and its diameter was measured by optical microscope (times100 ZESIS Company
German)
523 Characterisation methods
A Philips XL30 FEG-SEM (Philips Eindhoven Netherlands) was used to characterise
IPyCSiC interfacial roughness grain size and porosity from the finely polished cross
section of SiC coatings Characterisation of the IPyCSiC interfacial roughness was
realized by editing the SEM images (in the magnification of times1600) with the Image J
software and extracted it as a line from the background SEM image The interfacial
roughness could be described by a series of pairs of x (distance tangential to the
interface) and y (distance normal to the interface) coordinates assuming the interface
is flat at a scale of 70 microm
Porosity was measured by controlling the threshold of SEM images (times1600 TIF) at a
gray level and adjusted to distinguish pores from grains with the Image J software
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
136
Pore fraction was defined as the ratio of the pores and the total area of the SEM image
Grain size of FBCVD SiC coatings varied in a range and in a columnar shape It was
characterised by measuring mean width and length of single crystals from SEM
images (times6400) and the grain size of the coatings is represented by the mean width
timeing the length of grains A FEG-TEM (TecnaiTM G2
F30 U-TWIN) was used to
observe the IPyCSiC interfacial roughness and TEM samples were prepared by
focused ion beam milling The linear regression method was used to analyze and
quantify the influences of parameters on the fracture strength and Weibull modulus
53 Results and discussions
531 Fracture strength and dimensional effect
Table 52 gives the summary of the measured and calculated parameters for all the
coatings It includes the diameter of impression (mean value 2 0 ) force (mean value
F) Weibull modulus (derived from local fracture strength m) local fracture strength
(L
fmean value) and fracture strength for the full spherical shell (
F
fmean value)
Table 52 Summary of measured and calculated parameters for all the coatings
Sample 2 0 μm F N L
f MPa Modulus (m) Scaling Factor
For Size Effect
F
f MPa
S 1 15239 2235 1784 7397 185 963
S 2 15043 1999 1599 7687 183 872
S 3 14898 1540 1446 7459 187 774
S 4 16052 2042 1620 8261 178 908
S 5 17018 2573 1810 7927 178 1018
S 6 16220 1885 1648 6953 193 855
S 7 14662 1691 1974 7755 190 1019
S 8 14905 1336 1717 7102 198 868
S 9 13040 1088 1825 6495 223 820
S10 16410 1215 1472 6801 204 722
S11 16165 1006 1430 6104 219 652
S12 14677 903 1512 6616 205 737
S13 11586 489 1762 4912 300 587
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
137
As given in Table 52 a significant difference (49-257 N) of the load among SiC
coatings was obtained According to a previous study [5] the variation is mainly
caused by different thicknesses (varied from 30 μm to 60 μm) of SiC coatings
because the relatively thin coating tends to reach higher strength concentration at
fracture
Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull
distribution
The Weibull modulus derived from the local fracture strength (as given in Fig 52) is
in the range of 49-86 (as shown in Table 52) and it falls into the category of moduli
for ceramics materials (from 5 to 30) This range of Weibull modulus is similar to the
values obtained from the brittle ring tests which also gave a similar range of the local
fracture strength [23 24] In different batches of SiC coatings it was found that the
Weibull modulus decreases linearly with the increase of the ratio of outer radius (R) to
the thickness of SiC coatings ( tR ) as shown in Fig 53 The ratio of Rt accounts
for up to 778 (2R from linear regression) of differences of the modulus This is
because the tR ratio is a critical dimension value for the strength distribution of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
138
SiC shell and it represents the relative thickness of SiC coating The higher the ratio
is the thinner the SiC coating So it corresponds to the larger inner surface area
resulting in larger scattering sizes of the critical flaws This observation is consistent
with the previous finite element modeling results showing that the Weibull modulus is
related to the sample dimension [10]
Fig 53 The relationship between the modulus (y) derived from local fracture
strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed
line represents linear fit data with fitted equation y=945-022x
As given in Table 52 the scaling factor (effective area-parameter based on the local
fracture strength) between the local fracture strength and the fracture strength of the
full shell are in the range of 18-30 The results are consistent with Byun et alrsquos study
(19-31) [5] and it indicated the importance of the size effect on the fracture strength
of the full shell
The fracture strength for the full spherical shell of thirteen SiC coatings were given in
the form of Weibull plots as shown in Fig 54 The mean fracture strength for the full
spherical shell was in the range of 587-1019 MPa (as given in Table 52) which is
higher than the range of 330-650 MPa obtained by Byun et al [5] This is because the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
139
Rt ratio (above 11) in Ref [5] falls into the higher value categary in current work as
shown in Fig 53
Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the
SiC coatings
Because the Weibull modulus is dominated by the tR ratio (Fig 53) its influence on
fracture strength for a full spherical shell could also be from this ratio as shown in
Fig 55 It shows that the fracture strength for the full shell decreases nearly linearly
with the increase of the tR ratio which produces a difference of 6528 (2R derived
from linear curve fit which represents fair agreement) of differences In this work the
similar range of Rt ratio (above 11) corresponds to the fracture strength lower than
850 MPa (as shown in Fig 55) which reduced the difference from previous results
[5] Furthermore the fracture strength of about 1000 MPa was obtained when the Rt
was about 8 [25] and it is similar as the result given in Fig 55 This again
demonstrated the importance of the geometry on the fracture strength of SiC coating
Therefore it is important to eliminate the external influence and study the influences
of microstructures such as interfacial roughness porosity and grain size on fracture
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
140
strength which are discussed in the following parts
Fig 55 The relationship between the fracture strength for a full spherical shell (y)
and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed
line is linear fit data with fitted equation y=1144-286x
532 Observe and qualify the effect of interfacial roughness on fracture strength
According to Griffith fracture theory the fracture strength (L
f ) is a function of the
critical flaw size (C) and the fracture toughness ( ICK ) as shown in the following
equation [26]
12( )
L ICf
K Z
Yc (1)
Y is a loading geometrical parameter Z is the flaw size parameter The magnitude of
the critical flaw size could be related to the IPyCSiC interfacial irregularities
The interfacial flaw shape of SiC coatings is modeled from the surface morphology of
PyC coating during deposition process as shown in Fig 56(a) The crack was taken
as a semi-circular surface crack as given in Fig 56(b) where Y is 2 and Z is 16 (Y
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
141
Z are geometrical constants introduced in Eq (1) [26] The fracture toughness of SiC
coatings in TRISO fuel particle was taken to be 33 MPamiddotm12
according to previous
report [27] Taking the result of the local fracture strength from individual SiC coating
into Eq (1) the magnitude of the critical flaw size C could be obtained
Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)
TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification
TEM image showing the spherical shape of IPyC surface
Figure 46 shows the redraws of the IPyCSiC interfacial roughness from SEM images
and the calculated critical flaw sizes according to Eq (1) (range and mean values) for
all specimens are given in the right columns If the fracture initiated at the IPyCSiC
interface as proposed in previous studies [4-6] the calculated critical flaw size range
of each type of SiC coating was expected to match the size range of the interfacial
irregularities
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
142
Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness
profile (the measured flaw sizes are randomly given in the profile of each interface as
seen the information in blue) with the calculated critical flaw size according to the Eq
(1)
In Fig 57 most of the calculated critical flaw sizes according to Eq (1) are in the
same magnitude as the flaw size observed directly from the interfacial profile images
and this indicates that the dominant effect of the surface roughness on the local
fracture strength For example the direct observation of the biggest flaw size from the
profile is about 43 μm and 26 μm in sample S9 and S13 respectively and they are in
the range of the calculated defect sizes of 09-65 μm and 17-47 μm for S9 and S13
respectively However exceptions were found such as specimens S1 and S2 which
show slightly higher calculated surface flaw size than the observation from SEM
images Furthermore it is difficult to accurately characterise the difference of the
interfacial roughness by observing the converted images and give specific
information (such as shape) of single profile (shown in Fig 57) The estimation of
the shape of surface irregularities to be half-circular could also result in the error on
the critical flaw size calculation [7] To give a direct estimation about the influence of
interfacial roughness on local fracture strength the scaling behavior of IPyCSiC
interface need to be characterised by a statisticalnumerical method
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
143
533 Characterise and quantify the interfacial roughness
Self-affine theory has become a standard tool in the study of various rough interfaces
[18 28 29] Here it was the first time being proposed to describe the IPyCSiC
interfacial roughness accurately and scientifically and then was used to quantify the
relationship between interfacial roughness and local (intrinsic) fracture strength and
fracture strength of the full shell
5331 Self-affine theory introduction and experimental setup
In order to describe the IPyCSiC interfacial roughness with specific parameters an
easy way is using a height-height function [29 30]
2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)
where the x axis is along the IPyCSiC interface and ( )h x is the surface height profile
The amplitude of the roughness ( )h x is correlated with the length scale x and
lt gt denotes the spatial average over ( )h x in a planar reference surface If the
interfacial roughness of IPyCSiC were self-affine the correlation of x and
h should follow the power law relationship (Eq (2)) and it could be obtained by the
log-log plot of x and h The (for self-affine surface 0lt lt1) is the roughness
exponent and it describes the degree of surface roughness at short length scales [31]
This short length scale is shorter than correlation length ξ which is another parameter
used to describe the self-affine surface (besides the surface roughness h and
roughness exponent ) It is the average distance between the features in the surface
profiles within which the surface variations are correlated [28] Therefore the small
(close to 0) characterises extremely jagged or irregular interfaces while large
value characterise interface with smooth hills and valleys [32]
For all the samples the scaling properties of IPyCSiC interface (as shown in Fig 57)
are characterised by their one-dimensional height-height correlation function Eq (2)
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
144
The characteristic parameters of the digitalized IPyCSiC interfacial roughness are as
follows The resolution between two points along x axis is 020833 μm and x
changes by timing the resolution with integer (1 2 3hellip15) According to previous
self-affine theory study [16] the number of recorded points along the x axis was
taken in the range of 250-400 in this work corresponding to the length of 50-70 μm
for different IPyCSiC interfaces
5332 Results of self-affine theory
Figure 58 is a log-log plot showing the variation of h as a function of the distance
x for three SiC coatings The h varied as a power law of x (solid line ) when
x ltξ while remained nearly constant ˗ saturation roughness (σ0 dashed parallel
lines) for x gtξThese results indicated that these three IPyCSiC interfacial
roughness were self-affine with the roughness exponent of around 063-067 For the
rest of the samples the same scaling characterisation method was used Theξ σ0 and
are given in Table 53
Fig 58 Log-log representation of the height-height correlation function h
computed along the x axis for three representative samples The solid line represents
the linear regression of slops of three samples and the dashed short lines represent
saturation roughness
ξ3 ξ12 ξ6
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
145
Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness
self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)
Sample σ0 (μm) ζ ξ(μm) σ0ξ
S 1 02378 05903 06250 03804
S 2 04142 06950 08333 04971
S 3 06701 06673 16666 04021
S 4 06825 05244 14583 04680
S 5 05271 06308 14581 03615
S 6 08500 06343 20833 04080
S 7 04293 05162 14583 02944
S 8 07452 05107 14583 05110
S 9 05453 06099 12500 04362
S10 06953 05490 13044 05330
S11 05806 04949 10417 05574
S12 07584 06899 16666 04550
S13 05522 02971 18750 02945
The roughness exponent values for the 93 of IPyCSiC interface were in the range
of 05-07 (as shown in Table 53) This indicated the self-affine measurement is
reliable according to Schmittbuhl and Vilottersquos review [14] which showed that this
range of roughness exponents could have the minimum characterisation errors
Furthermore these roughness exponents are comparable except specimen S13 and it
was consistent with the observation of the interfacial roughness (Fig 57) in which
only specimen S13 showed the high degree of high frequency and short wavelength
irregularities (the dark pits in S13 profile) According to previous study [31] the
concentration of the roughness exponent values could be attributed to the same
original mechanism of the IPyCSiC interface which was produced by the FBCVD
under different conditions As a result the different roughness exponent value could
not describe the difference of the IPyCSiC interface
As shown in Table 53 the saturation roughness (σ0) and correlation length (ξ) are in
the range of 024-085 μm 063-208 μm respectively (Table 53) According to
previous studies [16 17 30] the σ0 and ξ couldnrsquot represent the interfacial
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
146
irregularities correlated with the critical flaw size Because the σ0 value range was
nearly one magnitude lower than the calculated critical flow size (mean value range of
2-4 μm) and the dimension of ξ was perpendicular to the calculated critical flaw size
direction Furthermore it was found that σ0 and ξ values were correlated to the sample
size (recorded points) [16] With the increase of the sample size for the same profile
both the ξ and the σ0 values increased and indicated these two parameters may not be
intrinsic properties of the samples However the roughness ratio σ0ξ is constant
which was found in both the current work and previous study [16]
As a result of above discussions the roughness ratio of σ0ξ was proposed to
characterise the interfacial roughness which could represent the sharpness of the
interfacial irregularities according to Ref [30] For example the low ξ value
corresponded to narrow surface irregularity when the σ0 and values were the same
With the increase of the σ0 value the surface irregularity became deep and narrow
which was hazard to the mechanical properties according to previous simulation work
on the fracture strength of SiC coatings [22] The above observations and analysis
results are supported by previous study [31] when length scale x gt ξ (shown in
Fig 58) the roughness ratio σ0ξ describes mainly the long-wavelength roughness
characteristics which could be statistically equal to the effect of the critical flaw size
on fracture strength
534 Quantify the influence of interface roughness on fracture strength
Figure 59 gives the influence of roughness ratio on the local fracture strength and it
contributes to nearly 50 (R2 from linear regression) of variation of the local fracture
strength It shows that the local fracture strength decrease linearly with the increase of
the roughness ratio This result approves previous findings about the importance of
the interfacial roughness [4-6] and is correlated with the Griffth fracture theory (Eq
(1)) about the importance of the shape and dimension of critical flaws Furthermore
the relation between interfacial roughness has been characterised quantitatively and a
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
147
linear relationship between roughness ratio and local fracture strength is proposed
Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from
experiment dashed line is linear fitted data with the equation y=2265-1396x
Except for the interfacial roughness the local fracture strength could also be affected
by the fracture toughness as shown in Eq (1) Although Vickers-indentation fracture
behavior of SiC coatings was different due to the laminar defects and grain
morphology [33] the fracture toughness of SiC was found to be insensitive to the
microstructure of materials [34] This could be attributed to the fact that
Vickers-indentation provided a static propagation of the crack while the real fracture
toughness was measured dynamically In this work the fast fracture process could
overtake the effect of microstructure on the different static fracture behaviour [5 25]
Since porosity and grain size were main microstructural variations in SiC coatings [1]
their effects on fracture strength were estimated
The characterisation and quantification of grain size and porosity were shown in Table
54 The grain size was found to have no effect on fracture strength according to
previous studies [5] which was also indicated from the regress analysis (R2 is close to
0) No influence was found by regressing the local fracture strength on pores
Therefore the dominant influence on the local fracture strength is from the roughness
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
148
ratio
Table 54 Results and variations influences on fracture strength for SiC coating
Specimen S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S10 S11 S12 S13
Grain size
(μm2)
04 06 06 08 20 20 20 28 20 08 20 28 25
Porosity
(Area )
0 0 0 0 05 04 12 09 03 0 08 21 20
Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell
(y) circle is from experiment dashed line is linear fitted data with the equation
y=1351-1150x
Because the fracture strength for a full spherical shell is a function of the Weibull
modulus and local fracture strength [5] it was affected by factors such as the
dimension ratio of thickness to radius of the coating (as shown in Fig 55) the
roughness ratio (as shown in Fig 510) Figure 510 shows the influence of roughness
ratio on fracture strength of the full shell The linear relationship was found in 12
samples as indicated by the dashed line in Fig 510 and it could explain about 68
(2R from linear regression) of difference in fracture strength of the full particle The
high roughness ratio would decrease the fracture strength of the full shell linearly The
deviated point of sample S13 could be due to its largest Rt ratio (as shown in Fig
55) which may have over taken the effect of the roughness ratio (Work about the size
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
149
effect on the fracture strength has being carried out)
54 Conclusions
The fracture strength of SiC coatings deposited under different conditions were
measured by the modified crush test and analyzed by the statistical analysis (Weibull
function and Self-affine theory) The influences on fracture strength were studied
such as the IPyCSiC interfacial roughness specimen size and porosities Following
results were obtained
(1) Weibull modulus and fracture strength of the full shell were significantly affected
by the ratio of radius to thickness of SiC coating and both of them decrease
linearly with the increase of the ratio
(2) The dominant effect of the IPyCSiC interfacial roughness on intrinsic fracture
strength was found by matching the SEM images with the calculated critical flaw
size based on the Griffith fracture theory
(3) The interfacial roughness were successfully characterised by a
numericalstatistical method and the roughness ratio representing the shape of the
irregularities was proposed to be a unique parameter among different coatings
(4) The difference of the local fracture strength was dominated by the roughness ratio
and it decreased linearly with the increase of the roughness ratio It is been the
first time that the interfacial roughness was numerically related to the fracture
strength
(5) Microstructures such as grain boundaries and porosity were found to have
neglectable influence on fracture strength
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
150
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[2] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the
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[3] T Nozawa L L Snead Y Katoh J H Miller E Lara-Curzio Determining the
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[4] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of
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[7] D J Green An introduction to the mechanical properties of ceramics Cambridge
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[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by
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CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
151
[11] W N W Chen X Nie A A Wereszczak D W Templeton Effect of Loading
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[12] R T Wu X Wang A Atkinson On the interfacial degradation mechanisms of
thermal barrier coating systems Effects of bond coat composition Acta Mater 58
(2010) 5578-85
[13] X Nie W N W Chen A A Wereszczak D W Templeton Effect of Loading
Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am
Ceram Soc 92 (2009) 1287-95
[14] J Schmittbuhl J P Vilotte S Roux Reliability of Self-Affine Measurements
Phys Rev E 51 (1995) 131-47
[15] J T M De Hosson G Palasantzas Roughness effect on the measurement of
interface stress Acta Mater 48 (2000) 3641-45
[16] L Ponson H Auradou M Pessel V Lazarus J P Hulin Failure mechanisms
and surface roughness statistics of fractured Fontainebleau sandstone Phys Rev
E 76 (2007) 036108-14
[17] L Ponson H Auradou P Vie J P Hulin Low self-affine exponents of
fractured glass ceramics surfaces Phys Rev Lett 97 (2006) 125501-4
[18] F Spaepen Interfaces and stresses in thin films Acta Mater 48 (2000) 31-42
[19] W G Sloof T S Hille T J Nijdam A S J Suiker S Turteltaub Damage
growth triggered by interface irregularities in thermal barrier coatings Acta Mater
57 (2009) 2624-30
[20] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidized
bed chemical vapor deposition J Mater Res 23 (2008) 1785-96
[21] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York
1974
[22] G K Miller D A Petti J T Maki D L Knudson An evaluation of the effects
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
152
of SiC layer thinning on failure of TRISO-coated fuel particles J Nucl Mater
355 (2006) 150-62
[23] K Bongartz E Gyarmati H Schuster KTauber The brittle ring test A method
for measuring strength and Youngrsquos modulus on coatings of HTR fuel particles J
Nucl Mater 62 (1976) 123-37
[24] K Minato K Fukuda K Ikawa Strength of silicon-carbide coating layers of
fuel Pparticles for high-temperature gas-cooled reactors J Nucl Sci Tech 19
(1982) 69-77
[25] J W Kim T S Byun Y T Katoh Optimization of fracture tests for the SiC
layer of coated fuel particles by finite element analysis Ceram Nucl Appl DOI
1010029780470584002 ch13 2010
[26] S Gonzalez B Ferrari R Moreno C Baudin Strength analysis of
self-supported films produced by aqueous electrophoretic deposition J Am
Ceram Soc 88 (2005) 2645-48
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] B N Dev A Roy K Bhattacharjee H P Lenka D P Mahapatra Ge growth
on self-affine fractal Si surfaces influence of surface roughness J Phys D Appl
Phys 42 (2009) 145303-10
[29] J Feder Fractals Plenum New York 1988
[30] J T M De Hosson R Van Tijum Effects of self-affine surface roughness on the
adhesion of metal-polymer interfaces J Mater Sci 40 (2005) 3503-08
[31] G Palasantzas Roughness spectrum and surface width of self-affine fractal
surfaces via the K-correlation model Phys Rev B 48 (1993) 14472-78
[32] P Meakin Fractals scaling and growth far from equilibrium Cambridge
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[33] H Zhang E Loacutepez-Honorato A Javed I Shapiro and P Xiao A study of the
CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC
153
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc 95 (2012) 1086-92
[34] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany and A H
Heuer Fracture toughness of polycrystalline silicon carbide thin films Apply
Phys Lett 86 (2005) 071920-22
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
154
CHAPTER 6 Effect of Thermal Treatment on
Microstructure and Fracture Strength of SiC Coatings
61 Introduction
The mechanical properties of the as-deposited SiC coatings have been widely studied
eg Youngrsquos modulus and hardness [1-3] fracture toughness [4] and fracture strength
[5] etc However after it experiences the high temperature the composition and the
microstructure of the SiC coating may change which consequently influences the
mechanical properties It has been found that mechanical properties of SiC such as
Youngrsquos modulus and hardness are less affected when experiencing the current fuel
operation temperature (less than 1600 ordmC) [1 6] even after thermal treatment
temperatures of 1980 ordmC [7] To enhance the operational temperature of the high
temperature reactor in the future design it would be necessary to understand the
evolution of microstructure and mechanical properties of SiC coatings at even higher
temperature Some research [8-10] has been carried out to study the effect of high
temperature (more than 2000 ordmC) thermal treatment on the density and microstructure
of the fuel particle Itrsquos concluded that fuel failure and fission product release
dependent on SiC thermal stability at high temperature [9] Rooyen et al[11]
measured the annealing temperature effect on the fracture strength of SiC coatings It
is found that the fracture strength increases after thermal treatment at temperature up
to 2000 ordmC decreases in strength after thermal treatment at 2100 ordmC However no
clear explanation was given on this result
Due to the importance of the SiC on the safety of this fuel it is necessary to study the
thermal stability of SiC and characterise any change in microstructure and mechanical
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
155
properties It has been previously found that SiC deposited at 1300 ordmC with the
addition of propylene and methyltrichlorosilane as gas precursors not only have good
mechanical properties such as hardness and Youngrsquos modulus [3] fracture toughness
[4] but also have high silver and palladium diffusion resistance [12 13] Therefore in
this Chapter we thermally treated SiC coatings deposited at a range of temperature
(1300-1500 ordmC) at 2000 ordmC for 1 hour in argon atmosphere The change of fracture
strength and thermal stability of SiC coating were studied in terms of composition and
microstructural change of the coatings after thermal treatment
62 Experimental details
Four batches of SiC coatings (with nearly stoichiometry) deposited by Fluidized bed
chemical vapour deposition at different tempearure were chosen to study the thermal
treatment effect on the evolution of the microstructure and fracture strength Table 61
gives the deposition conditions of coatings studied and symbols used to describe each
sample The stoichiometry was measured by the Raman spectroscopy (Renishaw 1000
Raman microprobe system with 514 nm Argon laser) The laser beam was focused on
the surface of the cross section through a times50 objective lens
Table 61 Deposition conditions of SiC coatings
Sample Temperature
(oC)
MTS concentration
(vol)
Added gas
concentration
Stoichiometry
SiC1 1280 91 01vol C3H6 SiC
SiC2 1300 91 01vol C3H6 SiC+C
SiC3 1400 19 57vol Ar SiC
SiC4 1500 22 79vol Ar SiC+C
The inner side of the coating is stoichiometric (23 of the thickness) while outside of the coating is
SiC with excess C The microstructure characterization was done in the inner side coating while the
fracture strength measurement is related to the full coating SiC+C means that the C peak around
1300-1500 cm-1
was observed in SiC coating Chosen of deposition conditions was contributed to Dr
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
156
Eddie Lopez-Honorato
The sample preparation for fracture strengths measurement is the same as described in
Chapter 5 As introduced before thermal treatment was carried out at 2000 ordmC for 1
hour in argon protected atmosphere on SiC half shells The same fracture strength test
and equipment settings as described in Chapter 5 were used in this Chapter
In addition to Raman spectroscopy the microstructure of SiC coatings before and
after thermal treatment was also characterised using X-ray diffraction (PW 1830
Philips) with a Cu Kα1 radiation source The XRD samples were the SiC segments
(fractured SiC shells without external residual stress) Scanning electron microscopy
(Philips XL30 FEG-SEM) was used to characterise the change in morphologies of
SiC coatings Porosity was measured by setting a threshold of the SEM images
(times1600 TIF) at a gray level and adjusted to distinguish pores from grains with Image
J software Three SEM images were measured for each SiC coating Average pore size
(diameter nm) and the pore fraction (area ratio of pores to the total area as observed
by SEM) were obtained For transmission electron microscopy (TEM) the specimens
were prepared by crushing the SiC shell and dispersing the fragments on a carbon
holy film copper grid and crystal structures were characterised using an FEG-TEM
(TecnaiTM G2
F30 U-TWIN)
63 Results
631 Fracture strength of SiC coatings
Figure 61 shows the Weibull distribution of the local fracture strength ( L
f ) in SiC
coatings before and after thermal treatment at 2000 ordmC It gives a direct observation on
the decrease of the local fracture strength in coating SiC2 SiC3 and SiC4 after
thermal treatment while the local fracture strength of coating SiC1 is nearly
overlapped with the as-deposited coating The magnitude of the mean local fracture
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
157
strength (as summarised in Table 62) could represent the decrease trend of the full
batch of the coating in current study
Fig 61 Weibull plots of local fracture strength ( L
f ) before (black triangle) and after
(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given
black and red lines are before and after thermal treatment
The Weibull modulus (m) was obtained by linearly fitting the curves shown in Fig 61
It shows that the Weibull modulus decreased by 14 07 and 21 in coating SiC1 SiC3
and SiC4 respectively however it increased slightly (by 12) in SiC2 after heat
treatment As shown in Fig 61 the Weibull modulus derived from linear fitting is
affected by the deviation of few points from the linear distribution of the local fracture
strength (as shown in Fig 61) For example in sample SiC3 the slightly decrease
could be attributed to the deviation of the lowest points According to previous study
[14] the slight decrease (07) of Weibull modulus in SiC3 could be neglected since
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
158
the deviated points could be caused by different failure mechanisms involved in the
fracture process [14]
Fig 62 Weibull modulus plots of fracture strength of the full shell ( F
f ) before
(black triangle) and after (red circle) thermal treatment
Figure 62 shows the Weibull plots of fracture strength of the full shell ( F
f ) before
and after thermal treatment at 2000 degC In the same batch of coatings (the same size
effect) the fracture strength of the full shell increase with the increase of the Weibull
modulus and local fracture strength according to previous study [5] Therefore the
decrease of local fracture strength and increase of the modulus in SiC2 could explain
the slight change (decreased 25 MPa obtained from Table 62) of the fracture strength
of the full shell after thermal treatment In the other three samples the fracture
strength of the full shell decreased significantly (more than 110 MPa obtained from
Table 62) after thermal treatment due to the decrease of local fracture strength and
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
159
unchanged modulus)
Table 62 summarized the results of the fracture strength measured before and after
thermal treatment at 2000 degC including the Weibull modulus (m) derived from the
distribution of the local fracture strength ( L
f ) the mean local fracture strength and
fracture strength of the full shell ( F
f ) After thermal treatment the mean local
fracture strength of coatings decreased significantly except SiC1 coating which
retained the same level as in as-deposited coating The mean fracture strength of the
full shell was reduced after thermal treatment in a different degree but the change of
Weibull modulus is more complex which shows both decreased and increased values
Table 62 Summary of the modulus derived from the local fracture strength mean
local fracture strength and fracture strength of the full shell before and after thermal
treatment
Sample m (from
L
f )
as deposited 2000degC
L
f MPa
as deposited 2000degC
F
f MPa
as deposited 2000degC
SiC1 75 61 1445 1421 774 660
SiC2 77 89 1599 1395 872 847
SiC3 65 58 1824 1333 820 548
SiC4 74 53 1717 1443 858 587
As concluded from Fig 61 Fig 62 and Table 62 the fracture strength decreases
less in coatings deposited at lower temperature (about 1300 degC) than those deposited
at higher temperature (1400-1500 degC) This is consistent with previous study about
high properties of SiC coatings deposited at low temperature such as the hardness
Youngrsquos modulus and resistance to the fission products [12 13 15]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
160
632 Change in morphologies
Fig 63 SEM images showing the change in microstructure after thermal treatment at
2000 ordmC for 1 hr (a) and (b) SiC1 before and after (c) and (d) SiC2 before and after
(e) and (f) SiC3 before and after (g) and (h) SiC4 before and after thermal treatment
Dashed and solid arrows indicate growth direction and pores respectively
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
161
Figure 63 gives the SEM images showing the microstructure of SiC coatings before
and after thermal treatment at 2000 ordmC Before thermal treatment no pores were found
in SiC1 and SiC2 coatings (Fig 63(a) and (c)) while nano-pores were found in SiC3
coating (Fig 63(e)) and even bigger (micrometres) pores were occasionally found in
SiC4 coating (Fig 63(g)) Among four as-deposited coatings SiC4 has highest area
fraction of pores (~09) followed by SiC3 (~03) coating (Fig 63 (a) (c) (e) and
(g) summarized in Table 63)
After thermal treatment at 2000 ordmC pores with different size and area fraction were
observed in all the coatings even though as-deposited SiC1 and SiC2 were free of
pores as shown in Fig 63(b) (d) (f) and (h) The amount of pores formed in treated
SiC1 coating (area fraction of ~05 ) is lower than the other three coatings which
have similar area fraction of pores (~14 ~13 and ~15 for SiC2 SiC3 and
SiC4 respectively given in Table 63) Similar to the content of the pores the pore
size (mean size of ~50 nm) in SiC1 is smaller than in the other coatings (gt 100 nm)
Among coatings SiC2 SiC3 and SiC4 much larger pores (micro-meter sized as in
Fig 63(f) and (h)) were produced in SiC3 and SiC4 coatings after thermal treatment
compared with nano-sized pores in SiC2 Furthermore it is found that most of pores
in coatings SiC2 SiC3 and SiC4 were formed along the grain boundaries and triple
junctions as we can see from Fig 63(d) (f) and (h)
The pores are uniformly distributed through the coatings and no area free of pores or
area with highly concentrated pores is observed However there are connections of
pores (2 or 3 pores formed closely) in SiC2 SiC3 and SiC4 as indicated by solid
arrows in Fig 63(d) (f) and (h) and the diameter of the porous connection zone
(black circle in Fig 63(d) (f) and (h)) could be in the magnitude of few micrometres
The connection of pores could easily become larger pores of few micrometres
diameter under external tensile strength due to the high strength concentration [14]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
162
Fig 64 The IPyCSiC interfacial roughness of coating SiC1 (a) SiC2 (b) SiC3 (c)
and SiC4 (d) as deposited (left in each figure) and thermally treated at 2000 degC (right
in each figure) The white arrow points towards to the interface irregularities (except
for thermally treated SiC4 coating (d)) black circle represents the pores in SiC
coatings
Figure 64 gives the evolution of interfacial roughness in different coatings after
thermal treatment at 2000 ordmC to study their influence on the change of fracture
strength Compared with the as-deposited coating the changes of the interfacial
roughness in SiC1 are similar to SiC3 which show the smoother interface with
interval of irregularities were observed Fig 64(a) and (c) However different from
as-deposited coatings with defects mainly at the interface defects (pores) are also
observed through the coating after thermal treatment (as seen in Fig 61(b) (f) and
Fig 64(a) (c)) Furthermore the size of pores is in the same magnitude as their
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
163
interfacial roughness (shown in Fig 64(a) and (c))
The change of the interfacial roughness in SiC2 is more significant than SiC1 and
SiC3 since pores formed as part of the interface (indicated by arrows in Fig 64(b))
and they are larger than the pores formed in the coating (circle in Fig 64(b))
Different from others three coatings the IPyCSiC interface of SiC4 becomes
smoother (Fig 64(e)) after thermal treatment compared with as-deposited coating so
the defects (pores) within the coating are bigger than surface irregularities
633 Evolution in microstructure
Fig 65 XRD results of as-deposited SiC coatings and coatings after thermally
treated at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and
SiC2 inset shows the peak shift of as-deposited (dash line) and after thermal
treatment (solid line) (b) is SiC4 and inset is the high angle diffraction peak after
thermal treatment showing splitting while it is a single peak in as-deposited coating
Figure 65 gives XRD results of the as-deposited and thermally treated samples
which show the presence of the β-SiC in coatings The peak presents at 2θ~335ordm is
from the crystallographic errors which could either be due to the stacking faults or
the disordered α-SiC according to previous descriptions [16 17] It is found that the
intensity ratio of the 2θ~335ordm peak to the (111) plane peak (2θ~356ordm) decreased after
thermal treatment in all the coatings The coating SiC4 also shows the split of high
angle diffraction peaks (inset of the Fig 65(b) 2θ~613ordm and 713ordm) which is
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
164
attributed to the X-ray double diffraction and this implies the high crystallites after
thermal treatment
Figure 66 is the HRTEM image of sample SiC4 after thermal treatment in which the
stacking faults and micro twins could still be seen The stacking sequence of
ABCACBACBACB was observed as shown in the dashed square zone in Fig 66
According to study about crystal structure [18] this stacking sequence is supposed to
be the micro twins compared with the rest 3C stacking sequence rather than the
6H-SiC domain Furthermore the (111) peak shifted to the high angle after thermal
treatment in all the coatings as shown in the inset of Fig 65(a) which corresponded
to the decrease of the crystal constant
Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows
indicate stacking faults and micro twins
Figure 67 gives the Raman spectroscopic results of SiC coatings before and after
thermal treatment The carbon peak at 1300-1600 cm-1
was found in the as-deposited
SiC2 and SiC4 coatings According to previous studies [4 19] the intensity ratio of
I1600I796 indicated that the estimated amount of excess C was less than 05 at in
this study The peak between TO and LO peaks (around 882 cm-1
) was attributed to
the stacking faults or highly disordered stacking faults cluster [3 15 20-22]
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
165
After thermal treatment the weak carbon related peaks appeared at around 1395 cm-1
and 1600 cm-1
(G band) in sample SiC1 SiC2 and SiC4 The peak around 1395 cm-1
could represent the methyl group and amorphous carbon structures and G band is due
to the stretching mode of all pairs of sp2 atoms in chains and rings [23] The arising of
the 2D peak (also called G peak 2715 cm-1
) after thermal treatment was observed in
sample SiC2 SiC3 and SiC4 which is the second order of zone-boundary phonons
[24]Considering the amount of excess carbon in SiC coatings the symmetry of the
2D peak indicates that the carbon after treatment is more likely to be graphene rather
than graphite [24] which means the concentration of excess C is low in SiC coatings
It is also found that the intensity ratio of the disordered stacking faults (around 882
cm-1
) to the TO peak decreases in all samples after thermal treatment (shown in Fig
67)
Fig 67 Change of SiC before and after thermal treatment measured by Raman
spectroscopy carried out at the polished cross section of the coatings (a-d) are
specimen SiC1 SiC2 SiC3 and SiC4 coatings The lower line is before thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
166
treatment and the upper line is after thermal treatment at 2000 degC in individual
sample
Table 63 Summary of microstructural changes of SiC coatings before and after
thermal treatment
Sample Porosity ()
As 2000degC
Stoichiometry
As 2000degC
Critical Defects
As 2000degC
SiC1 0 05 0 C clusters Inter Inter+ Pore
SiC2 0 14 C clusters Ordered C Inter Inter
SiC3 03 13 0 Ordered C Inter Inter+ Pore
SiC4 09 15 C cluster Ordered C Inter Pore
First order Raman spectroscopy (1200-1600 cm-1
) Represents the carbon structure related to the
methyl group or amorphous carbon structures (contains SP2 and SP
3) [23] Second order (2700 cm
-1)
single layer grapheme related carbon materials [24]
Represents the interface irregularities
Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates
microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off
surface precipitates are taken from site A and B shown in (a)
Furthermore the narrowing of the TO peak was found (the inset in Fig 67 (b)) in the
Raman spectroscopy Although it could be an overlap of two peaks at around 796 cm-1
and 789 cm-1
in coatings before and after thermal treatment the peak at 789 cm-1
corresponding to the stacking sequence of ABCACBhellip [25] is more likely to be
micro-twins in current study(as shown in Fig 66) Table 63 summarized the main
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
167
morphological and microstructural change of SiC coatings before and after thermal
treatment
Particularly for sample SiC3 except for the appearance of weak 2D peak after thermal
treatment without visible first order carbon peaks in the sample SiC3 the precipitates
were also observed from both inner and outside of the shell These precipitates were
demonstrated to be the single 3C-SiC crystal by Raman spectroscopy as shown in Fig
68 Raman spectra of precipitates represents the incident direction of the laser is
perpendicular to the SiC single crystal (111) plane which the LO mode at around 970
cm-1
is forbidden when Raman spectra were obtained in a backscattering geometry
[22] (The appearance of the forbidden LO band might be due to to finite collecting
angle of the spectrometer)
64 Discussion
641 Influence of interfacial roughness and pores on fracture strength
To evaluate the critical flaw size we used the equation 1
2( )
L ICf
K Z
Yc for tensile
strength (local fracture strength) and the case for the semi-circular surface crack
(Y=125 [26]) of radius c and inside holes (Y= π12
[14]) of diameter 2a When the
fracture toughness ( ICK ) of the SiC coating was taken as 33 MPa m-12
[27] the
critical surface defect radius and the diameter of the inside pores were calculated to be
in the range of 15 ndash 78 microm obtained from all the coatings The mean critical flaw
size is in the range of 30 ndash 40 microm after thermal treatment The calculated critical
flaw sizes are in the same magnitude as the defects observed at the IPyCSiC interface
and the pores in the SiC coatings after thermal treatment (see in Fig 63 and Fig 64)
Therefore the decrease of the local fracture strength after thermal treatment could be
related to the formation of these defects in SiC coatings Accordingly the sources of
critical defects were summarized in Table 63 for coatings before and after thermal
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
168
treatment The interfacial roughness and pores within the coating compete to be the
critical flaws Once the size of interfacial irregularities is lower than critical flaw size
and rarely distributed their effect on fracture strength could be decreased or even
excluded according to previous study [14] Therefore the pores inside the coating
with the diameter of 2a would be considered as the main failure origins [14] These
could explain the decrease of local fracture strength in coatings SiC2 SiC3 and SiC4
which have micrometer pores formed within the coatings andor at the interface while
the local fracture strength is less affected in coating SiC1 due to formation of
nanometer pores
The Weibull modulus is related to the specimen size loading method and defects
distribution [5 14] In this study the specimen size and the loading morphology could
be excluded for one kind of SiC coating so the change of the modulus is due to the
degree of the scattering of the critical flaw size under the tensile strength The
interfacial irregularities in SiC2 became narrower and deeper (about 4 microm of depth as
shown in Fig 64(c)) after thermal treatment and they are also bigger than the pores
generated within the coating So the critical flaw in SiC2 after thermal treatments is
due to the interfacial irregularities (Table 62) with less scattered size under the
loading area than as-deposited coating which increased the Weibull modulus
However the critical defects in the other coatings include pores within the coatings
(shown in Fig 64 and Table 62) For example in SiC4 the critical flaw is only from
pores within the coating after thermal treatment due to the lack of interstitial
irregularities (Fig 64(h)) This enlarged the distribution of critical flaws after thermal
treatment which leads to the decrease of the Weibull modulus in different degree The
change of the fracture strength of the full shell depends on both Weibull modulus and
local fracture strength as discussed before [5] Our result showed that the SiC coating
deposited at low temperature of 1300 ordmC produced less critical flaws and smaller
decrease of the fracture strength of the full shell (see Table 63)
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
169
642 Mechanism of microstructural change
Changes in SiC coatings after thermal treatment include the formation of pores the
decreased intensity of the 2θ~335 ordm peak (crystallographic errors) in XRD the arising
of Raman peaks around 1395 cm-1
and 2715 cm-1
According to previous studies [8
10 21 25 28 29] we propose that these changes after thermal treatment could be
attributed to phase transformation or the diffusion of defects such as vacancies and
interstitials
If the 2θ~335ordm peak is from amorphous α-SiC its intensity ratio to (111) diffraction
peak would increase after heat treatment Because the presence of α-SiC phase in
β-SiC could promote the transformation of β-SiC into α-SiC [29] Conversely the
intensity of 2θ~335ordm peak decreased after thermal treatment in this work as observed
in Fig 65 and no α-SiC phase segregation (Fig 66) was found by HRTEM after
thermal treatment Furthermore the transformation from disordered α-SiC into β-SiC
after thermal treatment is also excluded because high pressure and high temperature
are needed for this process to happen [29] Therefore it is concluded that the 2θ~335ordm
peak derived from stacking faults and they could be annihilated at current
environment according to previous studies [8 28 30]
Stacking faults were surrounded by defects such as dislocations vacancies and
interstitials [10 15 31] so the high density of stacking faults in this work
corresponded to the high amount of native defects The annihilation of stacking faults
after thermal treatment indicated the reduction of these defects and it could reduce
the lattice constant In this work the decrease of the lattice constant was found after
thermal treatment as indicated by the peak shift of (111) plane in XRD results (Fig
65) and the crystallisation (ordering) was also reflected from the decreased intensity
of the 2θ~335ordm peak (Fig 65) and Raman defect peak (around 882 cm-1
) (Fig 67)
Therefore the formation of pores is due to the annealing of defects through the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
170
diffusion of vacancies or interstitials which are common even in high-purity CVD
SiC [32] However diffusion of native defects depended on their concentration which
was constrained by different composition of SiC (deviation from stoichiometry) [31]
For example for the C-rich cubic SiC the dominant defect is the CSi antisite (Si atom
site was occupied by C atom in tetrahedral structure) [31]
According to above analysis the formation mechanism of pores could be governed by
different kinds of defects In SiC1 coating the smallest and least content of pores
formed after thermal treatment is most likely caused by the annealing of stacking
faults surrounded by the dislocations and vacancies which is consistent with previous
study about the thermal treatment effect on stoichiometric SiC [28] In SiC coating
with excess carbon the microstructure evolution could be more complex as
demonstrated by the presence of the graphene layer (Raman peak at 2700 cm-1
)
According to previous studies [31 33] this is attributed to the existence of the CSi
antisite and vacancies which form the vacancy cluster and antisite clusters after
thermal treatment at 2000 degC
The microstructure change in SiC3 coating is different from SiC1 The diffusion
mechanism in SiC3 was supposed to be involved with the interstitials since the single
SiC crystal precipitate was found out of the coating(Fig 68) This also resulted in
higher amount of the pores in SiC3 than in SiC1 after thermal treatment It is
proposed that the different diffusion mechanism found in stoichiometric SiC1 (Si and
C vacancies) and SiC3 (tetragonal interstitials) could be due to different deposition
conditions which produced different kinds of dominant native defects The larger
pores formed in SiC3 and SiC4 could be due to larger grain size than SiC1 and SiC2
(different deposition temperature) because most of pores were near to the grain
boundaries and triple junctions (as shown in Fig 63(d) (f) and (h)) The diffusion of
native defects also affects the interfacial irregularities and the diffusion mechanism in
SiC coatings is being studied in our research group
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
171
65 Conclusions
The SiC coatings deposited at temperature range of 1300-1500 degC with composition
near-to the stoichiometry were thermally treated at 2000 degC in Ar atmosphere for 1
hour to study the effect of thermal treatment on microstructure and fracture strength
The following conclusions were obtained
(1) The local (intrinsic) fracture strength decreased in a varied degree after
thermal treatment and it was due to the formation of pores along the IPyCSiC
interface and in the coatings
(2) The Weibull modulus decreased once the pores have similarbigger size
asthan interfacial irregularities and distribute uniformly within coatings while
it increased with the size of pores much smaller than interfacial irregularities
after thermal treatment
(3) After thermal treatment no phase transformation was found in SiC coatings
and the crystallographic error (2θ~335 ordm) detected by XRD was demonstrated
to be stacking faults which were annihilated during this process
(4) The formation of pores after thermal treatment was attributed to the diffusion
of intrinsic defects such as vacancies interstitials and antisites Different
content and size of pores were observed in different coatings which are
presumed to have different kinds of native defects in as-deposited coatings
produced at different conditions
(5) The vacancies are supposed to be the dominant defects in stoichiometric SiC
deposited at 1280 ordmC however in other coatings the dominant defects could
be a combination of vacancies antisites and interstitials based on Raman
results before and after thermal treatment Furthermore the diffusion of native
defects also affects interfacial roughness after thermal treatment which needs
further study
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
172
66 References
[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook of
SiC properties for fuel performance modeling J Nucl Mater 371 (2007) 329-77
[2] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different
techniques Thin Solid Films 469-70 (2004) 214-20
[3] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry
microstructure and mechanical properties in SiC coatings produced by fluidised
bed chemical vapour deposition J Mater Res 23 (2008) 1785-96
[4] H Zhang E Loacutepez-Honorato A Javed I Shapiro P Xiao A study of the
microstructure and indentation fracture toughness of silicon carbide (SiC) coatings
on TRISO fuel particles J Am Ceram Soc (2011) DOI
101111j1551-2916201105044x
[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of fracture
stress for the SiC Layer of TRISO-Coated fuel particles using a modified crush
test method Int J Appl Ceram Tech 7 (2010) 327-37
[6] G H Lohnert H Nabielek W Schenk The fuel-element of the Htr-module a
prerequisite of an inherently safe reactor Nucl Eng Des 109 (1988) 257-63
[7] I J Van Rooyen J H Neethling J Mahlangu Influence of temperature on the
micro-and nanostructures of experimental PBMR TRISO coated particles A
comparative study Proceedings of the 4th
international topical meeting on high
temperature reactor technology HTR 2008 September 28-October 1 2008
Washington DC USA HTR 2008-58189
[8] Y Kurata K Ikawa K Iwamoto The effect of heat-treatment on density and
structure of SiC J Nucl Mater 92 (1980) 351-53
[9] D T Goodin Accident condition performance of fuels for high-temperature
gas-cooled reactors J Am Ceram Soc 65 (1982) 238-42
[10] N Shirahata K Kijima A Nakahira K Tanaka Thermal stability of stacking
faults in Beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
173
[11] J van Rooyen J H Neethling P M van Rooyen The influence of annealing
temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)
136-46
[12] E Loacutepez-Honorato K Fu P J Meadows J Tan and P Xiao Silicon carbide
coatings resistant to attack by palladium J Am Ceram Soc 93 (2010) 4135-41
[13] E Loacutepez-Honorato H Zhang D X Yang P Xiao Silver diffusion in silicon
carbide J Am Ceram Soc 94 (2011) 3064-71
[14] D J Green An Introduction to the Mechanical Properties of Ceramics
Cambridge University Press Cambridge 1998
[15] H Zhang E Loacutepez-Honorato A Javed X Zhao J Tan P Xiao A Study of the
microstructure and mechanical properties of SiC coatings on spherical particles J
Eur Ceram Soc (2012) DOI101016jjeurceramsoc201112014
[16] H Tateyama H Noma Y Adachi M Komatsu Prediction of stacking faults in
βndashSilicon carbide X-Ray and NMR studies Chem Mater 9 (1997) 766- 72
[17] K R Carduner S S Shinozaki M J Okosz C R Peters T J Whalen
Characterization of β-Silicon carbide by silicon-29 solid-state NMR transmission
electron microscopy and powder X-ray diffraction J Am Ceram Soc 73 (1990)
2281-86
[18] httptfuni-kieldematwisamatdef_enkap_6advancedt6_3_2html
[19] S M Dong G Chollon C Larbrugere M Lahaye A Guette J L Brunee M
Couzi R Naslain and D L Jiang Characterization of nearly stoichiometric SiC
ceramic fibres J Mater Sci 36 (2001) 2371-81
[20] M Havel D BaronL Mazerolles P Colomban Phonon confinement in SiC
nanocrystals comparison of the size determination using transmission electron
microscopy and Raman spectroscopy Appl Spet 61 (2007) 855-59
[21] V V Pujar J D Cawley Effect of stacking faults on the X-Ray diffraction
profiles of 3C-SiC powder J Am Ceram Soc 78 (1995) 774-82
[22] Y L Ward R J Young R A Shatwell Effect of excitation wavelength on the
CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment
174
Raman scattering from optical phonons in silicon carbide monofilaments J Appl
Phys 102 (2007) 023512 -17
[23] X J Li J Hayashi C Z Li FT-Raman spectroscopic study of the evolution of
char structure during the prolysis of a victorian brown coal Fuel 85 (2006)
1700-07
[24] A C Ferrari J C Meyer V Scardaci C Casiraghi M Lazzeri F Mauri S
Piscanec D Jiang K S Novoselov S Roth A K Geim Raman spectrum of
graphene and graphene layers Phys Rev Lett 97 (2006) 187401-04
[25] S Nakashima H Harima Raman investigation of SiC polytypes Phys Stat Sol
A-Appl Res 162 (1997) 39-64
[26] GKBasal Effect of flaw shape on strength of seramics J Am Ceram Soc 59
(1976) 87-8
[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer
Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett
86 (2005) 071920-22
[28] K Koumoto S Takeda CH Pai High-resolution electron microscopy
observation of stacking faults in βndashSiC J Am Ceram Soc 72 (1989) 1985-87
[29] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide
at high pressure and high temperature J Am Ceram Soc 84 (2001) 3013-16
[30] K Koumoto S Takeda C H Pai T Sato H Yanagida High-resolution electron
microscopy observations of stacking faults in β-SiC J Am Ceram Soc 72 (1989)
1985-87
[31] C Wang J Bernholc Formation energies abundances and the electronic
structure of native defects in cubic SiC Phys Rev B 38 (1998) 12752-55
[32] E Janzen N T Son B Magnusson A Ellison Intrinsic defects in high-purity
SiC Microelectronic Eng 83 (2006) 130-34
[33] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides
Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-09
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
175
CHAPTER 7 Microstructure and Mechanical Properties of
Pyrolytic Carbon Coatings
71 Introduction
Pyrolytic carbon (PyC) coatings forming part of the TRI-Isotropic (TRISO) fuel
particle are important for the stability of this type of nuclear fuel Without appropriate
microstructure and mechanical properties of PyC coatings the stress generated inside
the particle due to internal gas pressure andor the dimensional change (anisotropic
shrinkage or creep) introduced in this layer during irradiation process could result in
the failure of the full particle [1-5] Fundamental understanding about relationship
between mechanical properties and microstructure of PyC coatings could help to
analyse the failure mechanism and model the probability of failure of TRISO fuel
particles [1 5] However their relations in PyC are complex [3 6-8] Kaae [7] found
that mechanical properties were related to the density crystal size and anisotropy but
they are not controlled by a single variable For example Youngrsquos modulus increased
with density for isotropic carbons with constant crystallite size but decreased with
increasing anisotropy for carbon with constant density and crystalline size In a
separate work [3] density had a dominant effect on the hardness and Youngrsquos
modulus in relative low density PyC coatings whereas no controlling factor was
given for high density PyC coatings
Nano-indentation is an effective way to study microstructural effects on mechanical
properties of PyC coatings because it could help with the understanding of the
deformation mechanism and measure Youngrsquos modulus and hardness spontaneously
Among studies on mechanical properties in carbon related materials under
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
176
depth-sensing indentation [3 9-15] few explanations about the nature of their
deformation mechanism have been discussed [9 10 13 15] First the hysteresis was
assumed to due to the slip of graphene layers in nano-meter grains and the energy
loss was attributed to the friction between graphene layers under compression stress
[9 10] Second the dislocation pileups were assumed to be responsible for energy
loss [13] but this idea failed to account for the reversible deformation [15] The most
recent theory suggested that the origin of the hysteresis was due to the formation of
(incipient) kink bands [15] This theory was found to be a universal explanation for
most laminar structured materials but the nature of initial kink band was not clear
[15]
During pressing process of TRISO fuel particles into fuel elements they experience a
final thermal treatment of 1 h above 1800 ordmC to drive off any residual impurities and
improve thermal conductivity of the fuel compact [16] The evolution of
microstructure of carbon related materials have been widely studied [17-20] Few
researches measured changes of mechanical properties after thermal treatment [19
20] but there is a lack of understanding about effect of microstructural evolution on
mechanical properties in PyC coatings Therefore in this Chapter together with the
microstructural properties the deformation mechanism under indentation influences
on mechanical properties and their change after thermal treatment in PyC coatings are
studied
72 Experimental details
Pyrolytic carbon (PyC) was coated on alumina particles (Φ 500 μm) by fluidised bed
chemical vapour deposition by Dr Eddie Loacutepez-Honorato and PyC coatings with
different density was chosen to study the mechanical properties Table 61 gives the
density and texture (orientation angle) of PyC coatings and more about deposition
mechanism could be found in Ref [21] The number of sample sequence Ci (i=1
2hellip11) starts from highest density to lowest density with density of 19 gcm3 as
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
177
border line to distinguish highlow density PyC which was measured by the
Archimedes method in ethanol For thermal treatment the coatings were first
grounded into fragments and then removed the alumina kernel The fragments of PyC
were then thermal treated at 1800 degC and 2000 degC for 1 hour in argon atmosphere For
further understanding of microstructural evolution during thermal treatment sample
C5 was thermal treated at 1300 1400 1500 and 1600 degC for 1 hour
Table 71 PyC coatings with different density and orientation angle
PyC
(High density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
PyC
(Low density)
Density
(gcm3)
Texture(Orient-
ation angle deg)
C1 2122plusmn0059 58 C6 1855plusmn0050 63
C2 2087plusmn0183 37 C7 1738plusmn0013 73
C3 2047plusmn0030 60 C8 1635plusmn0008 71
C4 2029plusmn0015 43 C9 1603plusmn0024 71
C5 2000plusmn0061 43 C10 1414plusmn0002 85
C11 1400plusmn0024 81
Orientation angle was obtained from the full width of half maximum of azimuthal intensity scan of
SAED pattern for more information in Ref [22] Productions of PyC coatings measurement of
orientation and density measurement are contributed by Dr Eddie Loacutepez-Honorato et al
The selected area electron diffraction (SAED) patterns were obtained with the use of a
FEG-TEM (see Chapter 3) and orientation angle was measured by the azimuthal
intensity scans of SAED pattern (selected aperture diameter of 200 nm) Further
details about this measurement were shown in a previous study [22] Transmission
electron microscopy (TEM) samples were obtained by focus ion beam milling High
resolution TEM samples were prepared by dispersing the fragments on a carbon holey
film copper grid X-ray diffraction (see Chapter 3) was used to obtain domain sizes of
PyC coatings After correction of intrinsic instrumental effect the out of plane and
in-plane domain sizes (along c-axis and a-axis in graphite crystal structure) Lc and La
were qualitatively estimated from XRD data by applying the Scherrer equation to the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
178
(002) and (110) reflections respectively [23] In as-deposited PyC coatings the (110)
peak was too weak to estimate accurately on the La Raman spectroscopy (633 nm
Helium ion laser source) was performed by single spot measurements (spot size was
carefully controlled to be the same for each test) of around 2 μm diameter using a times50
objective lens The laser power of less than 05 mW (10) was used with the step
size of 60 seconds and twice accumulations For each sample 5 different positions
were measured The band fitting of the first order spectra was carried out with
GRAMS32 software
To reduce the influence of surface roughness on indentation test the PyC coatings
were ground with successive finer grades of SiC paper and polished down to a 1 microm
grid diamond paste The same nano-indentation as in Chapter 3 was used The
measurements were performed at fixed loading rate of 1 mNS reaching the
maximum load of 100 mN For each coating at least 25 indentations were conducted
on the sample surface to increase the reliability of the results The Olive and Pharr
method [24] was used to analyse all the data
73 Results
731 Microstructure of PyC coatings
In order to study the influences of microstructure on mechanical properties it is
necessary to know the nature of structure which makes one sample from another eg
disorders domain size crystallinity etc and their evolution after thermal treatment
7311 Raman spectroscopy
Figure 71 is a Raman spectroscopy for an as-deposited high density PyC coating (C5
200 gcm3) which exhibits two relatively broad Raman bands at around 1335 cm
-1
and 1600 cm-1
The first band corresponds to the D band which is attributed to double
resonant Raman scattering and represents the in-plane defects [21 25 26] The
second band is an overlap of broadened G (1580 cm-1
) and D (1620 cm-1
) bands due
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
179
to high disordered pyrolytic carbon [27] The G band is due to the stretching modes of
pairs of sp2 atoms in graphene planes whereas D represents the similar defects
structure as the D band [18 27] It is convenient to consider 1600 cm-1
band a single
G peak for practical purposes when comparing different samples or the overall
structural evolution of a given PyC coating [27]
Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200
gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during
fitting to limit the uncertainty in spectral parameters) The green line represents the
difference between the calculated curve and the experimental curve
According to previous studies [25-32] on fitting similar Raman spectra shown in Fig
71 a simple two-symmetric-line fit (D and G bands) could not fit it well Therefore
the Raman spectra of high density PyC coatings (C1-C5 gt 19 gcm3) were
deconvoluted into above peaks at about 1220 cm-1
1335 cm-1
1500 cm-1
and 1600
cm-1
( Fig 71) The band at about 1500 cm-1
(Drsquorsquo) is attributed to interstitial defects
which could act as coupling (covalent band) between two graphene layers or adjacent
overlapped domains [25 28] The I band at around 1220 cm-1
is due to C-C on hydro
aromatic rings [28] The Raman spectra mean the high degree of in-plane andor
out-of-plane disorders in high density PyC coatings represented mainly by the full
width at half maximum (FWHM) of the D band [28] and intensity ratio (the area ratio
of the 1500 cm-1
peak to the sum of four peaks shown in Fig 71) of the Drdquo bands
[25] respectively
D
I
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
180
Figure 72 is the Raman spectra of high density PyC coating C5 after thermal
treatment at temperature of 1300 1400 1600 and 1800 ordmC The FWHM of the D band
decreased significantly from about 150 cm-1
(as-deposited) to about 106 cm-1
(1400
ordmC) and then to about 40 cm-1
(1800 ordmC) Similarly the intensity ratio of the Drdquo was
reduced from about 0135 (as-deposited) to about 0110 (1400 ordmC) and then to about
0078 (1800 ordmC) Another change is the split of G and D bands after thermal treatment
at 1800 ordmC (Fig 72) The above changes indicate that disorders in high density PyC
coatings are low energy structural defects ie degree of disorder is low according to a
previous study [28]
Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of
temperatures
Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)
C10 (141 gcm3) before and after thermal treatment at 1800 ordmC
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
181
After thermal treatment the degree of microstructural changes of low density PyC
coatings C6-C8 (164-186 gcm3) is slightly different from even lower density
coatings C9-C11 (140-160 gcm3) so they are described separately Figure 73 shows
Raman spectra of low density PyC coatings (a) C7 and (b) C10 before and after
thermal treatment at 1800 ordmC Similar to high density PyC the as-deposited coatings
C6-C8 contains four Raman bands After thermal treatment the FWHM of the D peak
in C7 decreased from about 120 cm-1
to 57 cm-1
and the intensity ratio of interstitial
defects was also reduced (from 0116 to 0042 Fig 73(b)) In coating C10 only
slightly decrease of FWHM of the D peak (from about 83 cm-1
to 57 cm-1
) was found
after thermal treatment at 1800 ordmC (Fig 73(b)) No split of the G and D bands was
observed in low density PyC coatings
With increase in density of PyC the FWHM of the D band the concentration of the
Drdquo band and the degree of their changes after thermal treatment increase considerably
which suggest that the disorder defects in PyC are different with variation of density
and thermal treatments change the degree of the disorder
7312 Domain sizes
Table 72 summarises the out-of-plane domain size (crystallite size perpendicular to
the graphene plane Lc) and in-plane domain size (crystallite size along the graphene
plane La) measured by XRD in PyC coatings before and after thermal treatment The
Lc is in the range of 1-3 nm in all the as-deposited coatings and it is slightly bigger in
high density (about 2-3 nm) coatings than low density (about 1-2 nm) coatings After
thermal treatment at 1800 ordmC the Lc increased significantly which is about 5 times
and 2-3 times larger than in as-deposited high density and low density PyC coatings
respectively It is 2-4 times larger in high density PyC than low density PyC coatings
The La in high density (about 6 nm) is larger than low density PyC coatings (3-4 nm)
after thermal treatment at 1800 ordmC Both Lc and La remained unchanged after thermal
treatment at 2000 ordmC in all PyC coatings (This is explained in section 741) The
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
182
increase of domain size indicated the ordering process in PyC coatings after thermal
treatment which may involve annealing of different kinds of disorders
Table 72 Domain size of as-deposited and thermal treated PyC coatings
Sample As deposited 1800 2000
Lc (nm) La (nm) Lc (nm) La (nm) Lc (nm) La (nm)
High density (gt19 gcm3)
C1 21 -- 112 -- 116 53
C2 21 -- 132 63 154 69
C3 22 -- 98 66 111 63
C4 24 -- 95 57 118 63
C5 20 -- 120 60 152 73
Low density (lt 19 gcm3)
C6 22 -- 50 42 56 44
C7 18 -- 38 36 50 34
C8 14 -- 31 33 27 39
C9 11 -- 27 32 31 34
C10 17 -- 24 33 27 35
C11 11 -- 27 35 27 33
7313 Evolution of crystallinity
Figure 74 is the TEM images of high density PyC (C5) before and after thermal
treatment The dark field TEM show bright areas (Fig 74(a) and (b)) that represent
graphene layers with similar orientation in the selected direction of the diffraction
pattern A decrease of the orientation angle from 43 ordm to 25 ordm is found after thermal
treatment at 1800 ordmC which is obtained from the full width at half maximum of
azimuthal intensity scan of SAED pattern (insets in Fig4(a) and (b)) A bright field
TEM image of a conical microstructure after thermal treatment (Fig 74(c) dashed
rectangle in Fig 74(b)) which shows the voids at the top of conical structures The
above observations show that thermal treatment increases anisotropy and results in the
volume shrinkage and generation of voids in high density PyC coatings
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
183
Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after
thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical
structure after thermal treatment insets are the SAED images with aperture diameter
of 200 nm
Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)
after thermal treatment at 1800 ordmC
Figure 75 is the typical HRTEM away from the top of conical growth feature (eg
OA=43 ordm
OA=25 ordm
Top
Voids
100 nm
(c)
(a) (b)
5 nm
Moireacute
fringes
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
184
white circle in Fig 74(c)) in high density PyC coatings (C1) before and after thermal
treatment at 1800 ordmC The wrinkled short graphene fringes in as deposited high
density PyC (Fig 75(a)) were replaced by distorted planes in a larger scale with a
bigger radius of curvature (white arrow in Fig 75(b)) The common number of
parallel layers (Fig 75(a) (002) plane white parallel lines) is 2-4 in as-deposited C1
which increased to about 30 (Fig 75(b) between white parallel lines) The moireacute
fringes were observed after thermal treatment (black arrow in Fig 75(b)) which
correspond to black bars in the bright field TEM (eg dashed black rectangle in Fig
74(c)) According to the generation mechanism of moireacute fringes [33] the on-going
ordering process along the c-axis is related to the increase of number of parallel layers
and evolution (decrease) of the inter plane distance of (002) planes
Figure 76 gives the bright field TEM and HRTEM images showing the
microstructure evolution in a low density PyC coating (C7) Globular growth features
with diameters of about 400 nm were observed in as-deposited C7 as shown in Fig
76(a) and the HRTEM image shows 2-3 layers of parallel planes (Fig 76(b)) In low
density PyC coatings the graphene fringes are longer and less oriented than in high
density coatings (reflected from orientation angle shown in Table 71 and Fig 13 in
Ref [21]]) After thermal treatment the short dark bars andor dots (as indicated by
the white arrows Fig 76(c)) were observed which is due to the moireacute fringes as
shown in Fig 76(d) The number of parallel layer increased up to 8-10 (Fig 76(d))
and it reflects the slight crystallinity after thermal treatment In the other low density
PyC coatings C9-C11 the TEM images are similar with the as-deposited low density
PyC coatings (as shown in Fig 14 and Fig 13(c) in Ref [21]) Furthermore the
orientation angle is almost the same in all low density PyC before and after thermal
treatment
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
185
Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7
174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal
treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment
732 Mechanical properties of PyC coatings
7321 Force-displacement curve
Figure 77 gives the force-displacement curve of PyC coatings with different density
under the maximum load of 60 mN and 100 mN by nano-indentation The unloading
curve did not completely retrace the loading curve but still returned to the origin This
process is called anelastic behaviour or hysteresis behaviour and the anelastic
reversible indentation processes with an enclosed loop are found in all the PyC
coatings
(a) (b)
100 nm 5 nm
5 nm
Sphere-like
particle
Tops
Moireacute fringes Sphere-like
particle
Top (d)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
186
Fig 77 Force-displacement curves for PyC coatings of different density with the
maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal
treatment at 1800 ordmC The contact depth of hc derived from the power law function of
the unloading curve [24]
The maximum indentation depth in low density PyC (C6-C11 lt 19 gcm3) is deeper
than in high density PyC coatings (C1-C5 gt 19 gcm3) under the same load and the
low density PyC also shows larger hysteresis loop area The ratio of the hysteresis
energy (area within the loading-unloading loop) to total loading energy (area under
loading curve) in high density PyC is lower than in low density PyC coatings For
example the ratios of sample C3 C9 and C11 are 0243 0270 and 0292 respectively
Furthermore the deformation behaviour of all PyC coatings showed the hysteresis
behaviour after thermal treatment up to 2000 ordmC The high density PyC after thermal
treatment at 1800 ordmC (red curve in Fig 77) shows anelasticity however the ratio of
its hysteresis energy (0249) is much higher than in as-deposited coating (0174)
According to previous studies [10 34] the low ratio obtained in high density PyC
coatings under pyramidal indenter corresponds to high elasticity while low density
exhibits high hysteresis (anelasticity high viscosity))
Under indentation the hardness is defined as the mean pressure the material will
support under load according to Oliver and Pharrrsquos study [24] This pressure is equal
to the load at maximum load divided by the contact area (according to eqs (7 10 11)
hc
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
187
in Chapter 2) However the residual depth hf is zero and no pleastic deformation is
observed after unloading The hardness obtained by Oliver and Pharr method does not
reflect the resistance of plastic deformation of material but it could represent the
degree of unelastic deformation qualitatively Therefore the mean pressure (P) value is
used which could reflect the anelastic properties of PyC coatings
7322 Youngrsquos modulus and the mean pressure
Figure 78 gives the Youngrsquos modulus (E) and the mean pressue (P) of as-deposited
PyC coatings as a function of density For low density PyC coatings (C6-C11 lt 19
gcm3) Youngrsquos modulus and the mean pressure increase almost linearly with the
density For high density PyC coatings (C1-C5 gt 19 gcm3) both Youngrsquos modulus
and the mean pressure reach plateaus which are independent of density It indicates
that mechanical properties of high PyC coatings are dominated by other factors
which are discussed in session 744
Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings
as functions of density
Table 73 shows the Youngrsquos modulus and the mean pressure of PyC coatings with
different density before and after thermal treatment at 1800 and 2000 ordmC After
thermal treatment at 1800 ordmC Youngrsquos modulus decreased by around 50 and the the
mean pressure is reduced by around 69 in high density PyC coatings (C1-C5 gt19
(a) (b)
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
188
gcm3) whereas minor change is observed when thermal treatment temperature
further increased to 2000 ordmC Previous study [20] showed similar results about
changes of mechanical properties in high density PyC after thermal treatment at
different temperature In low density PyC coatings C6-C8 (164-186 gcm3) the
mean pressure and Youngrsquos modulus decreased by about 23 and 8 after thermal
treatment at 1800 ordmC respectively which is consistent with Rooyen et alrsquos results
[19] and further decreased by 18 and 15 by increasing thermal treatment
temperature to 2000 ordmC In low density coatings C9-C11 (140-160 gcm3) little
change in mechanical properties after thermal treatment up to 2000 ordmC was found and
it is similar as the isotropic low density PyC [20] Mechanical properties and their
change after thermal treatment in PyC coatings are different with different density
Table 73 Changes of mechanical properties of PyC coatings after thermal treatment
Sample As deposited Thermal treated at 1800 Thermal treated at 2000
P (GPa) E (GPa) P (GPa) E (GPa) P (GPa) E (GPa)
High density
C1 468plusmn025 2670plusmn119 103plusmn018 1482plusmn131 090plusmn013 1337plusmn093
C2 435plusmn048 2513plusmn117 132plusmn019 1091plusmn069 076plusmn021 1204plusmn126
C3 490plusmn036 2878plusmn117 -- -- 091plusmn026 1271plusmn125
C4 397plusmn019 2291plusmn076 171plusmn010 1313plusmn034 110plusmn010 1370plusmn051
C5 456plusmn010 2610plusmn036 132plusmn015 1177plusmn051 177plusmn025 1361plusmn101
Low density
C6 388plusmn035 2165plusmn191 296plusmn022 1912plusmn113 244plusmn023 1647plusmn088
C7 395plusmn053 2149plusmn200 292plusmn036 1934plusmn114 232plusmn033 1568plusmn182
C8 354plusmn027 1945plusmn070 292plusmn036 1904plusmn113 232plusmn063 1678plusmn240
C9 284plusmn040 1938plusmn094 226plusmn057 1677plusmn178 263plusmn042 1733plusmn151
C10 189plusmn009 1266plusmn035 213plusmn019 1363plusmn076 188plusmn023 1381plusmn087
C11 168plusmn017 1166plusmn082 178plusmn034 1284plusmn106 086plusmn014 1167plusmn151
74 Discussions
The main findings of this study can be summarised as follows 1) PyC with different
density show different full width at half maximum (FWHM) of the D band and
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
189
concentration of the Drsquorsquo band which suggests that they have different types of disorder
TEM observation shows longer graphene fringes with lower density PyC (Fig 13 in
Ref [21]) thermal treatments decrease the degree of disorder while PyC with higher
density (gt19 gcm3) shows higher degree of decrease 3) initial increase in PyC
density until 19 gcm3 lead to proportional increase in Youngrsquos modulus (E) and the
mean pressure (P) while further increase in density has no effect on E and P 4)
hysteresis occurred after nano-indentation of PyC while the degree of hysteresis is
controlled by the PyC density and heat treatments
741 Disorders and their changes after thermal treatment
High density PyC Coatings (C1-C5 gt 19 cmg3) The dominant in-plane disorders
are domain boundaries according to a previous study [21] which generates high
FWHM of the D band due to the low energetic disorientations (eg domains andor
graphene layers) [25 28] The Drsquorsquo band (interstitial defects) is due to the amorphous
carbon structure which is composed of mainly disordered sp2 atoms and a low
amount of sp3 atoms [27 28 35] Particularly the sp3 lines are out of plane defects
which could be formed in high density PyC coatings [36] Therefore it is assumed
that the microstructure in high density PyC is composed of disoriented nano-size
graphite domains connected by amorphous carbon
After thermal treatment the reductions of the out-of-plane defects and the tilt and
twist in graphite planes are observed which could contribute to the increase of Lc
(out-of-plane domain size) as shown in HRTEM image (Fig 75) It was supposed
that the equilibrium shear stress were generated by in-plane defects and out-of-plane
defects in PyC coatings [25] once the out-of-plane defects was reduced the in-plane
stress would tend to straighten the graphite planes Furthermore the decreases of
FWHM of the D band and the orientation angle (Fig 72 and 4) show the ordering
arrangement of graphite layers is due to the healing of in-plane disorientations The
unchanged domain size Lc could be a result of a combination of increased number of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
190
parallel graphene layers and decreased inter distance of (002) plane As a conclusion
the increase of domain size Lc could be due to the coalescence of domain size andor
graphene layers through reorientation and remove of interstitial defects which
usually started at temperature of about 900-1200 ordmC [17 25] No La (in-plane domain
size) value was obtained in as-deposited PyC and the overlap of the G and the Drsquo
bands indicates it is below 4 nm above which two bands split [37] After thermal
treatment at 1800 ordmC the La is about 6 nm in high density PyC coatings (Table 72
and splitting of G and Drsquo bands was shown in Fig 72) which demonstrates the
slightly increase of La It is attributed to the annihilation of low energetic in-plane
disorientations which could usually be removed at temperature above 1500 ordmC [25]
Since the high temperature above 2000 ordmC is needed to remove the rest high energetic
in-plane defects for high density PyC according to previously study [25 28] it could
explain the La remained nearly constant after thermal treatment further increased to
2000 ordmC The ordering of graphite layers is responsible for the formation of voids (Fig
74(c)) since the ordering could reduce the volume and increase the density of PyC
coatings after thermal treatment [38]
Low density PyC Coatings (C6-C11 lt 19 cmg3) The main defect is the
5-memebered rings in coatings C9-C11 by comparing the Raman spectroscopy (Fig
73(a)) with a previous study [21] In low density coatings C6-C8 (164-186 gcm3)
the degree of in-plane disorder is less than in high density coatings but higher than
coatings C9-C11 (140-160 gcm3 indicated by the FWHM of the D band) and the
out-of-plane defects are much higher than low density PyC coatings (Fig 73) After
thermal treatment the in-plane disorder is similar as in coatings C9-C11 Therefore
the dominant in-plane defects are supposed to be a combination of domain boundaries
and 5-membered rings The slightly increase of domain size Lc in low density PyC
coatings is due to the decrease of interfacial defects through reorientation of domains
However they have much lower degree of increase of Lc than high density coatings
this could be due to low anisotropy in low density PyC coatings which makes it
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
191
difficult to reorient domains and remove the weak defects [17 25] The domain size
La was assumed to be unchanged since ordering in-plane disorders took place at
temperature above 2400 ordmC in low density PyC due to presence of 5-member rings
[17] It is worth to notice that the graphene fringes do not represent the in-plane
domain size in low density PyC due to the curvature caused by 5-memebered rings
[21] Due to the exist of 5-membered rings in low density PyC coatings the
microstructure is lightly affected by thermal treatment
742 Hysteresis after indentation
The increase in density of PyC leads to decrease in hysteresis after indentation and
density of PyC also dominate types and degree of disorders During indentation of
PyC hysteresis is caused by the slip of graphene planes whereas the disorders such as
interstitial defects or 5-memebered rings are supposed to be responsible for the
reversible deformation The hysteresis was also observed in other carbon materials
such as single crystal graphite [15] polycrystalline graphite [15] glassy carbon [9
10] Similar explanations about the effect of slip of graphene layers on the hysteresis
behaviour under indentation were given and it suggests that the deformation
mechanism is related to a common structure in different carbon materials which are
graphene planes
The slip of graphene planes has been demonstrated available The shear modulus (micro)
of graphite is 23 GPa (between graphene layers) [39] Based on the relation of τth= micro
30 [39 40] the theoretical shear stress (τth) of graphite is estimated to be 0077 GPa
This shear stress is much lower than the yield stress under Berkovich indenter for
graphite (03-05 GPa) [15] Under indentation the slip of graphene planes consumes
energy but recovers to the original shape after unload Lower density PyC has longer
fringes than that in higher density PyC (Fig 13 Ref [21]) therefore the panes can
slip for a longer distance under shear stresses generated by nano-indentation
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
192
Reversible deformation is due to presence of interstitial defects or highly curved
5-memebered rings For indentation of crystallite graphite the kink band could be
generated during the initial indentation process then reviersible deformation occurs
under further indentation [15] similar as that shown in Fig 77 In our PyC coatings
disorder in the PyC plays a similar role as the kink band in the crystallite graphite
The slip direction is parallel to the graphene planes so the in-plane defects presents at
the tilt and twist of two adjacent domains could not stop and reflect the slip Only
those defects perpendicular to the slip direction can contribute to the reversible
deformation such as interstitial defects or the highly curved 5-memebered rings
(caused fibrous graphene planes as shown in Fig 13(c) Ref [21])
After heat treatment the growths of the in-plane fringes increase the degree of the
hysteresis in PyC coatings For example the straightened graphene fringes (Fig 75)
caused by reorientation and removes of interstitials facilitate the hysteresis
significantly (the ratio of hysteresis energy to total loading energy increased from
0174 to 0249 Fig 77)
743 Mechanical property of low density PyC coatings
In as deposited low density PyC (C6-C11 gt 19 gcm3) Youngrsquos modulus and the
mean pressure are dominated by the density which is consistent with previous studies
[3 7 41] because of the effect of porous structure [3 21] As discussed in session
741 the disorders in low density PyC coatings play an important part on the stability
of microstructure which could reflect changes of mechanical properties After thermal
treatment the mechanical properties remained almost unchanged in PyC coatings
C9-C11 (140-160 gcm3) and this could be explained by the insignificant change of
microstructures at the presence of 5-membered rings The slightly decrease of
mechanical properties were found in coatings C6-C8 (164-186 gcm3) which is due
to the ordering of graphene planes through reduction of interstitial defects which
could enhance hysteresis and decrease the mean pressure No voids and change of
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
193
orientation was observed after thermal treatment in coatings C6-C8 so Youngrsquos
modulus is slightly affected It is concluded that the mean pressure and Youngrsquos
modulus are functions of density in as-deposited low density coatings and their
evolution after thermal treatment is controlled by disorders such as interstitials andor
5-membered rings
744 Mechanical Property of high density PyC coatings
In high density PyC coatings (C1-C5 gt 19 gcm3) Youngrsquos modulus and the mean
pressure are independent of density so they are discussed regarding to variation of
texture domain size and concentration of interstitial defects (the area ratio of the 1500
cm-1
peak to the sum of four peaks shown in Fig 71) Table 74 summarises
microstructure parameters and mechanical properties of high density PyC coatings
Mechanical properties are not controlled by domain size and orientation angle which
is converse to the previous study [41] It is found that Youngrsquos modulus and the mean
pressure in high density PyC coatings decrease with the reduction of concentration of
interstitial defects (as shown in Table 74)
Table 74 The parameters used to explain different mechanical properties of high
density PyC (C1-C5 gt 19 gcm3)
Sample Density
(gcm3)
Texture
OA (deg)
Domain
size (nm)
IinterstialAll Pressure
(GPa)
Modulus
(GPa)
C3 2047 plusmn0030 60 22 013955plusmn000374 490plusmn036 2878plusmn117
C1 2122 plusmn0059 58 21 013513plusmn000399 468plusmn025 2670plusmn119
C5 2000 plusmn0061 43 20 013456plusmn000561 456plusmn010 2610plusmn036
C2 2087 plusmn0183 37 21 013036plusmn000433 435plusmn048 2513plusmn117
C4 2029 plusmn0015 43 24 011823plusmn001628 397plusmn019 2291plusmn076
The physical meaning of the above observation can be explained by the effect of
interstitial defects on the deformation mechanism in high density PyC coatings First
the high concentration of interstitial defects could reduce the energy consumption by
the reversible slip of graphene planes (eg in Fig 77) and it corresponds to high the
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
194
mean pressure in high density PyC coatings Second in-plane Youngrsquos modulus is
much higher than out-of plane Youngrsquos modulus in graphite so the bonding between
graphene planes becomes important when the orientation effect could be neglected in
high density PyC (Table 74) For example in sample C4 and C5 the high Youngrsquos
modulus was obtained in C5 which have high amount of covalent band (interstitial
defects sp2 and sp3 in Fig 71) in the direction perpendicular to graphene planes The
high concentration of interstitial defects in high density PyC could also reduce the
influences of orientation angle on the high Youngrsquos modulus This could explain the
similar Youngrsquos modulus in C1 and C5 which have different orientation angles
Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of
sample C5 (200 gcm3)
After thermal treatment at temperature range of 1300-1800 ordmC in C5 (about 200
gcm3) the effect of concentration of interstitial defects on mechanical properties was
again demonstrated as given in Table 75 The mechanical properties decrease
gradually with the increase of thermal treatment temperature until 1600 ordmC and then a
dramatic decrease at 1800 ordmC The decrease is related to the reduction of content of
interstitial defects (Table 75) Furthermore no other relationship between mechanical
properties and microstructural features such as FWHM of the D band intensity of D
band and G band in Raman spectroscopy is found in the current work Therefore the
concentration of interstitial defects is proposed to dominant mechanical properties of
high density PyC coatings This idea about effect of interstitial defects on mechanical
properties is similar as the cross-link theory [8] which suggested that the mechanical
properties is related to the length and number of links between domains Furthermore
Temperature (ordmC) IinterstialAll Pressure (GPa) Youngrsquos modulus (GPa)
0 013456plusmn 000561 456plusmn010 2610plusmn 036
1300 011882plusmn000906 430plusmn010 2519plusmn060
1400 011045plusmn000278 413plusmn010 2407plusmn070
1500 009598plusmn000034 406plusmn022 2439plusmn070
1600 009469plusmn000219 391plusmn016 2344plusmn036
1800 007756plusmn000199 132plusmn015 1177plusmn051
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
195
the significant decrease of the the mean pressure and Youngrsquos modulus after 1800 ordmC
could be due to the straightening of graphene layers and formation of voids (Fig
74(c)) respectively To conclude the mechanical properties in high density PyC
coatings before and after thermal treatment from 1300 to 1800 ordmC decrease with the
reduction of concentration of interstitial defects
74 Conclusions
Disorders in PyC coatings was characterised by Raman spectroscopy A
combination of high degree of in-plane (domain boundaries) and out-of plane
defects (interstitial defects) prevail in high density PyC while the 5-membered
rings are dominant defects in low density PyC coatings
In high density PyC coatings the significant increase of domain size Lc is
attributed to the coalescence of domainsgraphene layers through reorientation and
reduction of interstitial defects During this process the graphene planes were
straightened resulting in slightly increase of La
In low density PyC coatings the microstructure remained almost unchanged after
thermal treatment due to the presence of the 5-membered rings which need high
temperature to be reduced
The hysteresis deformation behaviour was found in all PyC coatings before and
after thermal treatment under nano-indentation The nature of hysteresis is
suggested to be Slip of graphene planes consumes energy (hysteresis loop) and
disorders (interstitial defects and highly curved 5-memebered rings in high density
and low density PyC coatings respectively) are responsible for the reversible
deformation (unloading curve back to origin)
The mean pressure and Youngrsquos modulus are functions of density in low density
PyC coatings and their changes after thermal treatment are insignificant which
are due to the almost unchanged microstructure
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
196
In high density PyC coatings the mean pressure and Youngrsquos modulus are
independent of density orientation angle and domain size but they are related to
the concentration of interstitial defects After thermal treatment the decrease of
mechanical properties is attributed to the reduction of interstitial defects leading
to the straightening of graphene planes and formation of voids
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
197
75 References
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[2] D G Martin Considerations pertaining to the achievement of high burn-ups in
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[3] E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure and
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[4] G K Miller D A Petti A J Varacalle J T Maki Consideration of the effects
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[5] A C Kada R Gnallinger M J Driscoll S Yip D G Wilson H C No et al
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[7] J L Kaae Relations between the structure and the mechanical properties of
fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99
[8] F G Emmerich C A Luengo Youngrsquos modulus of heat-treated carbons A
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[9] J S Field MVSwain The indentation characterisation of mechanical properties
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[10] N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at
different temperatures Carbon 39 (2001) 1525-32
[11] M V Swain J S Field Investigation of the mechanical properties of two glassy
carbon materials using pointed indetners Philos Mag A 74 (1996) 1085-96
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
198
[12] N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon
materials Philos Mag A 82 (2002) 1873-81
[13] M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated carbons
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[14] A Richter R Ries R Smith MHenkel B Wolf Nanoindentation of diamond
graphite and fullerene films Diamond Relat Mater 9 (2000) 170-84
[15] MW Barsoum A Murugaiah S R Kalidindi T Zhen Y Gogotsi Kink bands
nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45
[16] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical
anisotropy and density during processing of coated particle fuel due to heat
treatment J Nucl Mater 374 (2008) 445-52
[17] F G Emmerich Evolution with heat treatment of crystallinity in carbons Carbon
33 (1995) 1709-15
[18] M A Pimenta G Dresselhaus M S Dresselhaus L G Cancado A Jorio R
Saito Studying disorder in graphite-based systems by Raman spectroscopy Phys
Chem Chem Phys 9 (2007) 1276-91
[19] I J Van Rooyen J H Neethling J Mahlangu Influence of Temperature on the
Micro-and Nanostructures of Experimental PBMR TRISO Coated Particles A
Comparative Study Proceedings of the 4th
international topical meeting on high
temperature reactor technology Washington DC USA HTR 2008-58189
[20] J C Bokros R J Price Deformation and fracture of pyrolytic carbons deposited
in a fluidized bed Carbon 3 (1966) 503-19
[21] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-I Effect of deposition conditions on microstructure
Carbon 47 (2009) 396-10
[22] P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour
deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy
Carbon 47 (2009) 251-62
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
199
[23] S Bernard O Beyssac K Benzerara N Findling G Tzvetkov G E Brown Jr
XANES raman and XRD study of anthracene-based coke and saccharose-based
chars submitted to high-temperature pyrolysis Carbon 48 (2010) 2506-16
[24] W C Oliver G M Pharr An improved technique for determining hardness and
elastic-modulus using load and displacement sensing indentation experiments J
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[25] J N Rouzaud A Oberlin C Beny-bassez Carbon films structure and
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[26] S Potgieter-Vermaak N Maledi N Wagner J H P Van Heerden R Van
Grieken J HPotgieter Raman spectroscopy for the analysis of coal a review J
Raman Spectrosc 42 (2011) 123-29
[27] A C Ferrari Raman spectroscopy of graphene and graphite Disorder
electron-photon coupling doping and nonadiabatic effects Solid state commun
143 (2007) 47-57
[28] J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and
textural assessment of laminar pyrocarbons through Raman spectroscopy electron
diffraction and few other techniques Carbon 44(2006) 1833-44
[29] G A Zickler B Smarsly NGierlinger H Peterlik O Paris A reconsideration
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diffraction and Raman spectroscopy Carbon 44 (2006) 3239-46
[30] A Cuesta P Dhamelincourt J Laureyns A Martinez-Alonso JMD Tascon
Raman microprobe studies on carbon materials Carbon 32 (1994) 1523-32
[31] A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman
microspectroscopy of soot and related carbonaceous materials spectral analysis
and structural information Carbon 43 (2005) 1731-42
CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings
200
[32] S Yamauchi Y Kurimoto Raman spectroscopic study on pyrolyzed wood and
bark of Japanese cedar temperature dependence of Raman parameters J Wood
Sci 49 (2003) 235-40
[33] D B Williams C B Carter Transmission electron microscopy A textbook for
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[34] M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics adding
the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31
[35] T Jawhari A Roid J Casado Raman spectroscopic characterization of some
commercially available carbon black materials Carbon 33 (1995) 1561-5
[36] G L Dong K J Huumlttinger Consideration of reaction mechanisms leading to
pyrolytic carbon of different textures Carbon 40 (2002) 2515-28
[37] A Jorio E H Martins Ferreira M V O Moutinho F Stavale C A Achete R
B Capaz Measuring disorder in graphene with the G and D bands Phys Status
Solidi B 247 (2010) 2980-82
[38] R Piat Y Lapusta T Boumlhlke M Guellali BReznik D Gerthsen TChen R
Oberacker M J Hoffmann Microstructure-induced thermal stresses in pyrolytic
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4813-20
[39] J Y Huang HRTEM and EELS studies of defects structure and amorphous-like
graphite induced by ball-milling Acta Mater 47 (1999) 1801-08
[40] A H Cottrell Dislocations and plastic flow in crystals Clarendon Press Oxford
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[41] J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)
55-62
CHAPTER 8 Conclusions and Future Works
201
CHAPTER 8 Conclusions and Future Works
This work provides both fundamental understanding and techniqual guidance on the
mechanical properties and their relationship with microstructures of SiC and PyC
coatings in TRISO fuel particles The measurement of hardness and Youngrsquos modulus
of SiC coatings could be used in the modelling work to study the peroperty of the
failure of the fuel particlues and these results have been published The measurement
of the fracture toughness of SiC in TRISO fuel particle has solved one of the
techniqual problems in field and the study contributes to the study of the fracture
behaviour of SiC coatings The fracture strength measurement has enriched the
strength data of SiC coatings before and after thermal treatment (related paper is
under revision) The characterisation of the interfacial roughness has provided a direct
method to correlate the relationship between fracture strength and interfacial
roughness The mechanical properties of PyC coatings provide foundamental
understanding about the deformation mechanism of the PyC coatings under
indentation The effect of thermal treatment on the mechanical properties has given a
preguidance about the behaviour of the PyC coatings at high temperature
81 Conclusions
(1) In SiC coatings deposited at 1300 ordmC by fluidised bed chemical vapour deposition
the Youngrsquos modulus was an exponential function of the porosity and the high
hardness was attributed to the high density of dislocations and their interactions
The initiation and propagation of micro cracks under the confined shear stress was
found to be responsible for the mechanism of plastic deformation Based on this
hardness-related plastic deformation mechanism the variation of hardness in the
three types of SiC coating was due to different grain morphologies
CHAPTER 8 Conclusions and Future Works
202
(2) The fracture beneath the Vickers indenter consists of Palmqvist cracks as
observed using SEM in above SiC coatings Based on this crack mode Vickers
indentation fracture toughness values of 351-493 MPa m12
were obtained It was
found that stress-induced micro-cracks seem to be a mechanism for the fracture
behaviour The presence of defects such as nano-pores and less constraint grain
boundaries could generate more micro cracks which dissipated energy from the
main cracks
(3) Fracture strength measured by modified crush test give less scattered values
within a given sample by distributing the load under a contact area It has been
found that Weibull modulus and fracture strength of the full shell were
significantly affected by the ratio of radius to thickness of the coating and both of
them decrease linearly with the increase of this ratio
(4) The numericalstatistical analysis was able to characterize the interfacial
roughness of different coatings and the roughness ratio representing the
irregularities was proposed to be a unique parameter for this description The
difference of the local (intrinsic) fracture strength was dominated by the
roughness ratio and it decrease linearly with the increase of the roughness ratio
The roughness ratio has the similar effect on the difference of fracture strength of
the full shell
(5) After heat treatment at 2000 degC the local fracture strength was reduced due to the
formation of pores in the coatings which could act as the enlarged critical flaw
size The Weibull modulus decreased when the pores in SiC coatings became
critical flaws while it increased once more uniformly distributed critical flaws
along the IPyCSiC interface were formed The formation of pores was mainly
related to the annihilation of stacking faults and diffusion of intrinsic defects such
as vacancies interstitials and antisites
CHAPTER 8 Conclusions and Future Works
203
(6) The hysteresis deformation mechanism was proposed to be due to the slip of
graphene planes which constraint by interstitial defects and highly curved
5-membered rings in high density and low density PyC coatings respectively
(7) The hardness and Youngrsquos modulus were related to the concentration of
interstitial defects and density in high density and low density PyC coatings
respectively Their changes in high density PyC is more significant than in low
density PyC coatings after heat treatment over 1800 ordmC due to the annihilation of
interstitial defects and reorientation of graphene layers
82 Suggestions for future work
(1) According to current study high amount of native defects were found in SiC
deposited at low temperature and it would be interesting to study their effects on
the thermal stability in a certain range of temperature such as from 1200-2000 ordmC
The study of the diffusion of native defects in SiC could also assist the study of
diffusion behaviour of fission products because these defects are more active and
they tend to reach the equilibrium during annealing process Due to different
deposition conditions the dominant species of native defects could be different in
different coatings therefore it is also important to study the deposition effect on
thermal stability of SiC coatings
(2) Itrsquos important to know how the microstructure change of SiC coatings deposited at
low temperature after irradiation because they showed robust mechanical
properties and high resistance to fission products It has been found they have high
amount of dislocations and stacking faults which accompanied by interstitials and
vacancies as reflected from the enlarged lattice constant According to this it is
supposed that after irradiation the volume change of SiC will be small because of
the pre-exist lattice defects Therefore study of the irradiation effect (at different
operational temperature) on SiC deposited at low temperature would be
promising
CHAPTER 8 Conclusions and Future Works
204
(3) Although current study has proposed to use self-affine theory to characterize the
interfacial roughness more work about their effects on fracture strength need to
be explored For example find out if the derived linear function between
roughness ratio and fracture strength in the current study could be used to explain
the differences of fracture strength in other tests To do further demonstration it is
necessary to reduce the geometrical influence and choose SiC coatings has
similar microstructure but different IPyCSiC interface These samples could be
prepared by just changing the deposition condition of IPyC while keep it same for
SiC coatings