using intercalation to simulate irradiation damage of
TRANSCRIPT
Using Intercalation to Simulate Irradiation
Damage of Nuclear Graphite
Lewis Luyken
2012
A thesis submitted to the University of Manchester for the
degree of Doctor of Philosophy in the Faculty of Engineering
and Physical Sciences.
School of Mechanical, Aerospace and Civil Engineering
The University of Manchester
2
Acknowledgements
I owe a huge thanks to Professor Barry Marsden for giving me the
opportunity to carry out this research. I never imagined that a blanket
email to the professors in the school searching for a supervisor for a
half baked undergraduate project would lead on to this. His support
throughout the project has been invaluable.
Secondly I am hugely indebted to Dr Abbie Jones, Dr Marc Schmidt, Dr
Med Benyezzar, Professor James Marrow, Professor Paul Mummery
and Mr Rob Stringer. Without their advice and assistance I could never
have completed this work. I also owe a big thanks to the members of
the nuclear graphite research group who have made the project an
enjoyable experience even while in the depths of research doom.
Finally Rosie Luyken whose patience and support has been invaluable, I
am so lucky to have her in my life. Most importantly I will now be able
to spend much more time causing havoc with Seumas.
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Declaration
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4
Abstract
This thesis investigates the use of bromine intercalation of graphite as a
method to simulate and investigate irradiation damage. In particular
this study investigates the effects of intercalation on dimensional
change on the macro and micro scales and how these changes combine
to affect Young’s modulus.
Highly Orientated Pyrolytic Graphite has been used to gather data as a
close approximation to single crystal graphite. Three different grades of
polycrystalline nuclear graphite have been used to investigate the
effect of different microstructure on intercalation and subsequent
property changes. The graphites have been characterized by optical
microscopy, pycnometry and x-ray powder diffraction and texture
measurements. A number of bespoke rigs were designed and
manufactured to carry out sorption, tomography and laser vibrometry
experiments.
The results indicate that the rate of dimensional change for
polycrystalline graphites is significantly lower than for single crystal
graphites. Modelling of dimensional change suggests that the
difference in expansion is due to closure of porosity. Closer
investigation of the dimensional change within the microstructure
shows that the majority of the dimensional change is driven by
expansion of filler particles.
The young’s modulus results show an initial increase in modulus
followed by a decrease, which corresponds with empirical evidence for
irradiated samples. It is postulated that the initial increase in modulus is
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due to crystal expansion and that the subsequent decrease is due to
crack growth. After experimentation some samples show significant
cracking which would appear to support this assertion.
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Contents
Acknowledgements ........................................................................................... 2
Declaration ........................................................................................................ 3
Abstract ............................................................................................................. 4
Contents ............................................................................................................ 6
List of Figures ................................................................................................... 10
List of Tables .................................................................................................... 17
Nomenclature .................................................................................................. 18
Abbreviations .................................................................................................. 20
1. INTRODUCTION ....................................................................................... 22
1.1. Development of Graphite Reactors ..................................................... 23
1.1.1. Chicago Pile Zero ...................................................................................... 23
1.1.2. Magnox Reactors ...................................................................................... 23
1.1.3. Advanced Gas Cooled Reactor .................................................................. 24
1.1.4. Very High Temperature Reactors .............................................................. 25
1.2. An Introduction to Nuclear Graphite ................................................... 26
1.2.1. Cross Section ............................................................................................ 27
1.2.2. Structure and manufacture....................................................................... 28
1.2.3. Manufacture ............................................................................................ 34
1.3. Irradiation Damage .............................................................................. 36
1.3.1. Atomic Scale Damage ............................................................................... 36
1.3.2. Dimensional Change ................................................................................. 39
1.3.3. Young’s Modulus ...................................................................................... 47
1.4. Scientific Proposal ............................................................................... 51
7
1.5. Summary ............................................................................................. 52
2. INTERCALATION ...................................................................................... 53
2.1. Intercalation Compounds .................................................................... 53
2.2. Graphite Intercalation Compounds ..................................................... 55
2.2.1. Intercalation Methods .............................................................................. 55
2.2.2. Structure of Graphite Intercalation Compounds ....................................... 57
2.2.3. The Intercalation Reaction ........................................................................ 61
2.3. Property Changes ................................................................................ 68
2.3.1. Dimensional Changes ............................................................................... 68
2.3.2. Young’s Modulus ...................................................................................... 69
2.4. Summary ............................................................................................. 71
3. MATERIALS AND METHODS .................................................................... 73
3.1. Experimental Techniques .................................................................... 73
3.1.1. McBain Spring Balance ............................................................................. 73
3.1.2. X-ray Computed Tomography ................................................................... 74
3.1.3. Laser Ultrasonics ...................................................................................... 80
3.1.4. X-ray Diffraction ....................................................................................... 85
3.2. Experimental Rigs ................................................................................ 90
3.2.1. Design of experimental rig to measure dimensional change of bulk material
................................................................................................................. 90
3.2.2. Design of experimental rig to measure microstructural dimensional change
................................................................................................................. 91
3.2.3. Design of experimental rig to measure Young’s modulus change of
brominated graphite ................................................................................ 95
3.3. Conclusions .......................................................................................... 99
4. CHARACTERISATION OF NUCLEAR GRAPHITE ....................................... 100
8
4.1. Characterisation Results .................................................................... 100
4.1.1. Polarised optical microscopy .................................................................. 100
4.1.2. Pycnometry ............................................................................................ 102
4.1.3. Powder Diffraction ................................................................................. 103
4.1.4. Textural Analysis..................................................................................... 107
4.2. Graphite Grades ................................................................................ 113
4.2.1. Pile Grade A graphite .............................................................................. 113
4.2.2. Pechiney Graphite .................................................................................. 114
4.2.3. Gilsocarbon ............................................................................................ 114
4.3. Conclusions ........................................................................................ 115
5. DIMENSIONAL CHANGE ........................................................................ 116
5.1. Dimensional Change of Nuclear Grade Graphite by Bromine
Intercalation ...................................................................................... 118
5.1.1. Calibration of the spring for sorption balance ......................................... 119
5.1.2. Dimensional change experiments ........................................................... 121
5.1.3. Dimensional Change of Highly Orientated Pyrolytic Graphite .................. 122
5.1.4. Dimensional Change of Polycrystalline Graphite ..................................... 132
5.1.5. Analysis of Dimensional Change ............................................................. 137
5.2. Microstructural Experiment .............................................................. 156
5.2.1. Two dimensional Analysis ....................................................................... 158
5.3. Conclusions ........................................................................................ 172
6. YOUNG’S MODULUS.............................................................................. 174
6.1. Measuring optimal input energy for Young’s modulus measurements
by laser impact excitation ................................................................. 176
6.1.1. Verification of Laser Impact Excitation as a suitable modification of ASTM
C769 ....................................................................................................... 179
6.2. Change in modulus of brominated graphite ...................................... 184
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6.2.1. Change in density of brominated graphite .............................................. 185
6.3. Modulus changes of brominated Graphite ........................................ 189
6.3.1. HOPG ..................................................................................................... 189
6.3.2. Modulus changes in brominated polycrystalline graphites ...................... 195
6.3.3. Possible sources of Errors ....................................................................... 204
6.4. Comparison of modulus changes due to irradiation and bromination
.......................................................................................................... 205
6.5. Conclusions ........................................................................................ 208
7. CONCLUSIONS AND FURTHER WORK .................................................... 210
7.1. Conclusions ........................................................................................ 210
7.2. Future Work ...................................................................................... 212
8. REFERENCES .......................................................................................... 214
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List of Figures Figure 1.1 Magnox Schematic[2] ....................................................................................... 24
Figure 1.2 AGR Schematic [3] ............................................................................................ 25
Figure 1.3 Very High Temperature Reactor [6] ................................................................... 26
Figure 1.4 Graphite Structure[11] 30
Figure 1.5 Atomic structure of graphite crystal[10] ............................................................ 30
Figure 1.6 Edge Dislocation [14] ....................................................................................... 31
Figure 1.7 Screw Dislocation[15] ....................................................................................... 31
Figure 1.8 TEM of Highly Orientated Pyrolytic Graphite (Image courtesy of Keyen Wen) ... 32
Figure 1.9 Gilsocarbon Microstructure (Image Abbie Jones) .............................................. 33
Figure 1.10 Binder Matrix Crystallite Structure (Image Abbie Jones) .................................. 33
Figure 1.11 Graphite manufacturing process [18] .............................................................. 34
Figure 1.12 Displacement Cascade .................................................................................... 36
Figure 1.13 Growth of interstitial loops[22] ....................................................................... 37
Figure 1.14 Frenkel Pair[1] ................................................................................................ 37
Figure 1.15 Interstitial loops created by irradiation at 1350°C to 11.7 x 1020 neutrons cm-2
[27] ................................................................................................................................... 38
Figure 1.16 Effect of dose and irradiation temperatures on dimensional change of HOPG in
the c-axis[25] .................................................................................................................... 40
Figure 1.17 Effect of dose and irradiation temperature on the dimensional change of HOPG
in the a-axis.[25] ............................................................................................................... 40
Figure 1.18 PGA Dimensional Change at low Temperature[35] .......................................... 41
Figure 1.19 PGA Dimensional Changes of PGA at High Temperatures Perpendicular to
Extrusion[36] .................................................................................................................... 42
11
Figure 1.20 Dimensional Changes at High Temperatures Parallel to Extrusion[36] ............. 42
Figure 1.21 Dimensional changes of Gilsocarbon due to irradiation damage[32] ............... 43
Figure 1.22 Schematic describing the with grain and against grain directions .................... 46
Figure 1.23 Nuclear graphite stress strain curve[50] .......................................................... 48
Figure 1.24 Orientation of unit vectors in relation to graphite layer planes........................ 49
Figure 1.25 Change in Gilsocarbon Young's modulus due to irradiation[32, 36] ................. 51
Figure 2.1 Bromine Intercalation Apparatus for weight uptake measurements[58] ........... 56
Figure 2.2 Bromine Intercalation with control of intercalant partial pressure for XRD
measurements[76] ............................................................................................................ 57
Figure 2.3 Schematic of increasing intercalation stages ..................................................... 58
Figure 2.4 TEM Image of CuCl2 (light regions) intercalated graphite (dark regions) [79] ..... 58
Figure 2.5 Distance between graphite layer planes for different intercalation species [58] 59
Figure 2.6 Graphite basal planes (black) with intercalant (white) a) stage 3 b) stage 2 ....... 59
Figure 2.7 Bromine positions at low concentrations calculated by DFT [66] ....................... 60
Figure 2.8 Unit Cell C8Br found by Neutron Diffraction [86] ............................................... 60
Figure 2.9 Intercalate clusters [24] .................................................................................... 61
Figure 2.10 Interstitial clusters caused by fast irradiation[27] ............................................ 61
Figure 2.11 Phase change induced by change in intercalant pressure. [76] ........................ 62
Figure 2.12 Intercalation Rate through sample thickness [91] ............................................ 63
Figure 2.13 Stage two and stage three Daumas Herold Domains[94] ................................. 64
Figure 2.14 Effect of crystal perfection on bromine uptake [101] ...................................... 67
Figure 2.15 Change in elastic constants of lithiated graphite[109] ..................................... 70
12
Figure 3.1 Schematic of McBain Spring Balance[113] ......................................................... 74
Figure 3.2 Tomography setup ............................................................................................ 75
Figure 3.3 Effect of sample composition on x-ray shadow ................................................. 77
Figure 3.4 Schematic of ASTM C769 experimental setup[129] ........................................... 81
Figure 3.5 Schematic of ultrasonic wave generation by laser [131] .................................... 83
Figure 3.6 Michellson interferometer ................................................................................ 85
Figure 3.7 Philips X’pert modular diffractometer ............................................................... 86
Figure 3.8 Schematic representation of diffraction by a crystal[36, 136] ............................ 86
Figure 3.9 Schematic of hkl planes[18] .............................................................................. 87
Figure 3.10 Micrometrics pycnometer ............................................................................... 90
Figure 3.11 Dimensional Change Rig .................................................................................. 91
Figure 3.12 X-ray attenuation coefficients of candidate rig materials[144] ........................ 93
Figure 3.13 Tomography sample ....................................................................................... 94
Figure 3.14 Experimental rig for tomographic scans of bromine intercalated graphite ....... 95
Figure 3.15 Reflectivity of argon coated glass[146] ............................................................ 97
Figure 3.16 Reflectivity of VIS-NIR coated glass[146] ......................................................... 97
Figure 3.17 Exploded diagram of cell to measure Young's modulus of brominated graphite
......................................................................................................................................... 98
Figure 3.18 Sample holder for polycrystalline graphite ...................................................... 99
Figure 4.1 Optical mircographs of nuclear grade graphite ................................................ 102
Figure 4.2 XRD powder diffraction spectra of PGA ........................................................... 105
Figure 4.3 XRD powder diffraction spectra of Pechinay Graphite ..................................... 105
13
Figure 4.4 XRD powder diffraction spectra of Gilsocarbon ............................................... 106
Figure 4.5 Image detailing the Full Width at Half Maximum[148] .................................... 107
Figure 4.6 PGA pole figure ............................................................................................... 110
Figure 4.7 Pechiney pole figure ....................................................................................... 111
Figure 4.8 Gilsocarbon pole figure ................................................................................... 112
Figure 5.1 Brick deformations caused by non uniform flux profiles .................................. 116
Figure 5.2 McBain Sorption Balance[58] .......................................................................... 119
Figure 5.3 Calibration of spring for weighing polycrystalline samples............................... 120
Figure 5.4 Calibration of spring for weighing HOPG samples ............................................ 120
Figure 5.5 Schematic of McBain Spring Balance ............................................................... 121
Figure 5.6 Schematic of crystal arrangement in HOPG 126
Figure 5.7 Schematic of HOPG sample with orientation of axes shown ............................ 124
Figure 5.8 Dimensional change of bromine intercalated HOPG 130
Figure 5.9 HOPG microstructure ...................................................................................... 128
Figure 5.10 Difference between theoretical and measured mass ..................................... 129
Figure 5.11 In plane expansion ........................................................................................ 130
Figure 5.12 Irradiation induced dimensional change of HOPG[33] ................................... 131
Figure 5.13 Dimensional change of extruded polycrystalline graphites ........................... 134
Figure 5.14 Dimensional change of PGA and Gilsocarbon ................................................ 135
Figure 5.15 Dimensional change due to irradiation[32] ................................................... 137
Figure 5.16 Porosity distribution base graphite[18] ......................................................... 139
Figure 5.17 XRD texture orientations .............................................................................. 142
14
Figure 5.18 Theta derived for against grain calculation ................................................... 142
Figure 5.19 Theta derived for with grain calculation ........................................................ 144
Figure 5.20 Effect of crystal orientation on dimensional change against grain ................. 145
Figure 5.21 Effect of crystal orientation on dimensional change with grain ..................... 146
Figure 5.22 PGA bromination accommodation factors ..................................................... 149
Figure 5.23 Gilsocarbon bromination accommodation factors…………………………….............149
Figure 5.24 PGA thermal expansion accommodation factors[158] ................................. 150
Figure 5.25 PGA predicted dimensional change ............................................................... 151
Figure 5.26 Modelled dimensional change of Gilsocarbon ............................................... 152
Figure 5.27 Accommodation Volume .............................................................................. 153
Figure 5.28 Prediction of Irradiated Dimensional Change using intercalation
accommodation factors; simulation of low neutron dose ................................................ 155
Figure 5.29 Prediction of irradiated dimensional change using intercalation accommodation
factors; simulation of high neutron dose ......................................................................... 156
Figure 5.30 Bromination rig in position. Highlighted are a) X-ray source b) shutter c) rig and
d) camera ........................................................................................................................ 158
Figure 5.31 Digital image correlation performed on PGA radiographs .............................. 159
Figure 5.32 Dimensional change calculated from radiographs for PGA ............................ 161
Figure 5.33 Dimensional change calculated from radiographs for Gilsocarbon................. 162
Figure 5.34 Dimensional Change calculated by digital image correlation for Pechinay ..... 162
Figure 5.35 Bicubic filter .................................................................................................. 164
Figure 5.36 Microstructure of PGA tomography sample, before bromination ................. 165
Figure 5.37 Change in grayscale of brominated samples .................................................. 171
15
Figure 6.1 Ultrasonic pulse measured with laser vibrometer ........................................... 177
Figure 6.2 Ultrasonic pulse measured with laser vibrometer ........................................... 178
Figure 6.3 Effect of Impact Energy on Measured Waveform ............................................ 179
Figure 6.4 ASTM C769 Experimental setup for piezo transducer measurement of Young's
modulus .......................................................................................................................... 180
Figure 6.5 Time of flight data for modulus measurement by piezo transducer ................. 181
Figure 6.6 Experimental setup for measurement of Young's Modulus by Laser Impact
Excitation and Laser vibrometry ...................................................................................... 182
Figure 6.7 Schematic of experimental setup for measurement of Young's Modulus by Laser
Impact Excitation and Laser vibrometry .......................................................................... 183
Figure 6.8 Comparison of sonic velocity measurements by Laser and Piezo Techniques .. 184
Figure 6.9 Change in density of HOPG ............................................................................. 188
Figure 6.10 Density change of polycrystalline graphites ................................................... 188
Figure 6.11 Laser confocal micrograph of debrominated PGA a) green scale bar 100µm area
of image b highlighted in green b) scale bar 40µm filler particle outlined in green ......... 189
Figure 6.12 Piezo setup for brominated samples. ............................................................ 190
Figure 6.13 Change in Modulus of Brominated HOPG ...................................................... 192
Figure 6.14 Change in Young's modulus of brominated Pile Grade A cut perpendicular to
extrusion (Against Grain) ................................................................................................. 198
Figure 6.15 Pile Grade A sample 1 cut against the grain (perpendicular to extrusion) after
bromination .................................................................................................................... 199
Figure 6.16 Pile Grade A sample 3 cut against the grain (perpendicular to extrusion) after
bromination .................................................................................................................... 199
16
Figure 6.17 Change in Young's Modulus of Brominated Pile Grade A cut Parallel to Extrusion
....................................................................................................................................... 200
Figure 6.18 Pile Grade A Sample after bromination ......................................................... 201
Figure 6.19 Young's modulus changes in brominated Gilsocarbon ................................... 203
Figure 6.20 Laser confocal micrograph of debrominated Gilsocarbon showing reltivly little
microstructural cracking a) scale bar 100µm b) isometric image 1280 x 1280 µm ........... 203
Figure 6.21 Comparison of changes in Young's modulus in PGA parallel to extrusion due to
irradiation and bromination ............................................................................................ 206
Figure 6.22 Comparison of changes in Young's modulus in PGA parallel to extrusion due to
irradiation and bromination ............................................................................................ 207
Figure 6.23 Comparison of changes in Young's modulus in Gilsocarbon due to irradiation
and bromination ............................................................................................................. 207
17
List of Tables Table 1.1 Moderator Cross Sections ............................................................................ 28
Table 1.2 Voight Notations .......................................................................................... 28
Table 3.1 Theoretical loss of x-ray intensity due to rig ................................................. 93
Table 3.2 Microscope objectives available on TOMCAT beamline[143] ........................ 94
Table 4.1 Powder diffraction data ............................................................................. 106
Table 5.1 Properties of ZYH HOPG ............................................................................. 124
Table 5.2 Tabulated Results of HOPG dimensional change ........................................ 126
Table 5.3 Analysis of c axis expansion ....................................................................... 128
Table 6.1 Fractional Uncertainties in Young’s modulus measurement of HOPG ......... 195
18
Nomenclature
α accommodation factor in a
β crystal CTE
γ accommodation factor in c
δ dose
η Poisson’s ratio
λ wavelength
μ x-ray absorption co-efficient
ξ unit vector
ρ density
φ tilt angle
φa wave polarization
ψ azimuth angle
B Full width at half maximum
C elastic constant
d interatomic spacing
D.C. Dimensional change
E Young’s modulus
g irradiation growth of a crystal
I intensity
k spring constant
K Bacon anisotropy factor
l length
m mass
P Pressure
T Temperature
Tαβ Stress vector
19
uστ Strain vector
20
Abbreviations
AG Against Grain
AGL Anglo Great Lakes
AGR Advanced Gas cooled Reactor
ASTM American Society for Testing and Materials
BAEL British Acheson Electrodes Ltd
CCD Charged Couple Device
CTE Co-efficient of Thermal Expansion
DFT Density Functional Theory
DIC Digital Image Correlation
DYM Dynamic Young’s Modulus
EMAT Electro Magnetic Acoustic Transducer
FWHM Full Width at Half Maximum
HOPG Highly Orientated Pyrolytic Graphite
HTR High Temperature Reactor
MBA Modified Bronnikov Algorithm
NDT Non-Destructive Testing
PGA Pile Grade A graphite
PTFE Polytetrafluoroethylene
SLS Swiss Light Source
STM Scanning Tunnel Microscope
TEM Transmission Electron Microscope
21
THTR Thorium High Temperature Reactor
VHTR Very High Temperature Reactor
WG With Grain
XCT X-ray Computed Tomography
XRD X-Ray Diffraction
22
1. Introduction
This project aims to better understand the underlying principles of
material property changes induced in graphitic components within a
nuclear reactor during operation. This will be achieved using
intercalation as a technique to simulate irradiation damage to
understand material property changes.
This work will be of use to scientists and engineers within the nuclear
industry as a deeper understanding of property changes will allow
operators to improve safety cases for continued reactor operation and
allow manufacturers to improve the design of graphite for future
reactor designs. Intercalation is an area of interest across many areas of
science in particular this research may be of interest to battery
manufactures where intercalation of graphite is also a life limiting
feature.
There are many different reactor designs in use and graphite is used as
a critical component in many of them. Graphite has a unique
combination of properties in that it absorbs few neutrons whilst
remaining structurally and chemically stable at high temperatures.
Reactor designers use these properties to achieve a sustained nuclear
reaction with components that are structurally stable across a large
range of temperatures and neutron doses. As a result there is a huge
body of research dedicated to the performance of graphite under fast
neutron irradiation. Irradiation induced material property changes to
23
bulk graphite are generally attributed to changes in the atomic
structure.
1.1. Development of Graphite Reactors
1.1.1. Chicago Pile Zero
The first self sustaining artificial nuclear fission reaction was achieved
for 28 minutes by a team lead by Enrico Fermi in December 1942. A
reactor known as Chicago Pile 1, was built in a squash court on the
University of Chicago campus. The reactor was constructed from a pile
of graphite blocks interspersed with 40 tons of uranium oxide and 6
tons of uranium metal for fuel. Compared to today’s designs it was very
low tech with ambient air cooling and a man with an axe to cut a rope
attached to a boron rod which would shut the reaction down in an
emergency [2].
1.1.2. Magnox Reactors
The next significant advance for the civilian use of nuclear power
occurred in the UK with the construction of the world’s first commercial
reactors at Calder Hall. Calder hall comprises four graphite moderated
reactors with significant technological advancements over pile type
reactors. The fuel and reactor are contained within a pressure vessel
cooled by CO2 and operated at around 390°C. This provided an output
of 200 MWe[3]. The design became known as a Magnox reactor due to
the use of a magnesium-non oxidising alloy used as fuel casing. A
schematic of the plant design is shown in Figure 1.1. The reactor used
Pile Grade A (PGA) graphite as a moderator. This moderator was
designed to take advantage of the structural properties of graphite and
24
to provide support for fuel pins, control rods and channels for a carbon
dioxide coolant[3].
Figure 1.1 Magnox Schematic[3]
1.1.3. Advanced Gas Cooled Reactor
The 2nd generation of commercial reactors commissioned and built in
the UK, was the Advanced Gas Cooled (AGR) reactors, Figure 1.2. These
reactors had a number of improved design features. Designed to
operate at ~ 650°C to improve the thermal efficiency, the AGR’s also
employed a re-entrant flow’ system which kept the graphite core
temperature below 450oC in order to avoid any thermal oxidation of
the graphite in CO2 coolant. The reactor used a semi-isotropic graphite
to improve the continued structural integrity of the associated
components. The reactor employed improved fuel and safety features.
The combined result is a significantly improved reactor design with an
output of ~ 1MWe [4].
25
Figure 1.2 AGR Schematic [4]
1.1.4. Very High Temperature Reactors
The future of gas cooled graphite moderated reactors presently lies
with the Very High Temperature Reactor (VHTR) concept[5]. Research is
currently being carried out by a number of nations under the Gen IV
consortium to realise the design. The Gen IV consortium is an
international collaborative effort to design the next generation of
commercial reactors. The VHTR is touted to be the closet Gen IV design
to realisation as it builds upon technology implemented in Germany’s
pebble bed High Temperature Reactor (HTR) and the UK’s prismatic
core HTR (DRAGON) designs from the 1960’s[6]. The VHTR concept
design is shown schematically in Figure 1.3 and aims to operate at
temperatures up to 1000°C circulating helium coolant through a heat
exchanger where a secondary circuit provides heat for electricity
generation and process heat. The coolant choice eliminates oxidation as
a significant damage mechanism, only coming into effect under
emergency conditions. The high outlet temperature is expected to give
a thermal efficiency of over 50%. The main research required is for high
26
temperature materials. This design uses a significant amount of
graphite in the fuel element, reactor core and reflectors[5].
Figure 1.3 Very High Temperature Reactor [7]
1.2. An Introduction to Nuclear Graphite
This section covers a lot of basic ground in order that the reader may
better understand the reason graphite is used in a reactor, its structure
and the reason it has this structure. Starting with the physics of
graphite on the atomic scale we see why graphite is used. Looking at
graphite at increasingly larger scales will give the reader an
understanding of the structure of graphite and a brief description of
manufacturing methods will describe the reason for certain structural
features. The structural features have a significant effect on the
material properties and the way they change under irradiation as shall
be described in section 1.3.
27
1.2.1. Cross Section
The primary reason for the presence of graphite in a reactor is to act as
a moderator. A moderator is reactor component which is used to
absorb the high energy of the neutrons emitted from a fissioning
nucleus.
Two properties known as the scatter cross section and absorption cross
section describe the probability of certain outcomes when a particle of
a given energy travels though a volume of material. The scatter cross
section describes the probability that a neutron will collide with an
atom and the absorption cross sections describe the probability of a
neutron being absorbed.
Thermal reactors require neutrons with thermal energies. A neutron
with thermal energy is defined as a neutron with an energy less than
1eV, neutrons are released from a fission event with an energy from a
few KeV to 10 MeV [8]. This is achieved by placing a moderator around
the fuel pins which reduces the energy of neutrons.
Moderators require a low absorption cross section and high scatter
cross section. There are three main choice of moderator material
typically used in nuclear technology; graphite, light water and heavy
water, The cross sections of these are shown in Table 1.1[9].
The absorption cross section of water is the highest and as such can
only be used with enriched uranium. Heavy water is the best moderator
in this respect having the lowest absorption cross section. Heavy water
is very expensive unlike graphite which is relatively cheap. Furthermore
of all the materials mentioned graphite can be heated to the highest
28
temperature before a phase change occurs, phase changes in
moderators can be catastrophic causing incidents such as Chernobyl.
Table 1.1 Moderator Cross Sections
Material Density (gcm-3) σs (b) σa (b)
H2O 1.0 49.2 0.66
D2O 1.1 10.6 0.001
Graphite 1.6 4.7 0.0045
All three materials are used in various reactor designs. Graphite has
other advantages; it is used for structural components, is chemically
inert and remains stable at high temperatures. The absorption cross
section of moderators are affected by impurities within the
material[10].
1.2.2. Structure and manufacture
Observations of graphite under increasing magnifications show that
each level is made of increasingly small constituent parts as shown in
Figure 1.4. The figure shows that the bulk material is made up of an
agglomeration of coke particles in a binder matrix. The binder matrix
and coke particles are made up of ordered and disordered graphite
crystallites respectively. The crystallites are made up of crystals of
graphite, large regions of carbon atoms in a lamellar arrangement. This
section will detail graphite at each different level.
29
Figure 1.4 Graphite Structure[11]
1.2.2.1. Atomic Structure
The hexagonal structure of carbon atoms are held together by sigma
bonds along the basal plane as shown in Figure 1.5. The sigma bonds
are strong (524 kJ/mol) and short (0.141nm) bonding three valance
electrons. The basal planes are held together by a much weaker
interaction arising from the remaining valance electron forming pi
bonds. The force is relatively weak, 7kJ/mol, and therefore long
(0.335nm). Sigma bonds are significantly stronger than pi bonds
because there is significantly more overlap of the electron orbitals. The
anisotropic nature of the bond structure gives rise to high anisotropy of
the mechanical and thermal properties, whilst dimensionally graphite
crystals are many magnitudes larger in length parallel to the basal plane
than perpendicular to the planes.
The a and c axis are shown in Figure 1.5. It is important to note that the
a axis runs parallel to the strong sigma bonds and the c axis runs
parallel to the weaker dipole interactions. The work often references
these axes.
30
Figure 1.5 Atomic structure of graphite crystal[12]
Graphite is predominantly arranged in an ABAB stacking arrangement
termed hexagonal graphite[12]. This is the thermodynamically stable
form of graphite and has a density of 2.25g/cm3.
It is rare to find large regions of perfect graphene planes organised in
an ideal lamellar structure as there are normally a number of defects
present in the graphite crystal structure. The smallest defects are point
defects, such as out of plane atoms, vacancies within the lattice
structure or a combination of the two. These can be shown to exist by
computational analysis[1] and by observing reactivity changes near
defects with electron microscopy[13]. Larger defects can include
multiple interstitials, multiple vacancies or dislocations, normally edge
dislocations as shown in Figure 1.16. Occasionally screw dislocations as
shown in Figure 1.7 are also present.
Defects have also been looked at in detail with a Scanning Tunnel
Microscope (STM) a method which has also shown the presence of
c
a
a
a
c
31
ribbons on the surface of graphite[14]. STM is an experimental
technique in which a voltage is applied between the tip and sample
surface in close proximity allowing electrons to cross the gap. The
probe tip moves across the sample surface and the change in surface
height vaires the current which can cross the gap allowing very high
resolution surface maps to be obtained[15].
Figure 1.6 Edge Dislocation [16]
Figure 1.7 Screw Dislocation[17]
1.2.2.2. Crystal Structure
The nanostructure of graphite crystallites can be seen using
Transmission Electron Microscopy (TEM), Figure 1.8. The high
resolution images obtained show basal plane stacking in graphite
crystals. The presence of nanocracks known as Mrozowski cracks which
run parallel to the basal planes can also be seen [18, 19]. These cracks
form during cooling of the graphitised block.
During manufacture as the material is cooled from the graphitisation
temperature, at a temperature around 1800°C the bulk structure
hardens and the anisotropy of the Co-efficient of Thermal Expansion
(CTE) forms long cracks to relieve stresses parallel to layer planes[20].
The difference in the thermal contraction in the a and c axis generates
32
stresses and below 1800°C there is no significant thermal creep to
relieve the stresses resulting in crack formation[21].
Figure 1.8 TEM of Highly Orientated Pyrolytic Graphite (Image courtesy of Keyen Wen)
1.2.2.3. Polycrystalline Structure
The microstructure of a polycrystalline graphite can be characterised
using polarised optical microscopy as shown in Figure 1.9. The material
is polycrystalline, made up of binder, filler and flour components.
The degree of filler particle alignment depends on the forming process
used during manufacture. Filler particles are made up of well aligned
crystallites with a high degree of crystallinity. Filler particles contain
lenticular microcracks, these are calcination cracks formed during the
calcining process. The binder matrix is characterised by the disordered
nature of the crystallites, Figure 1.10Error! Reference source not found..
Binder is composed of flour, regions of graphitised coal tar as well as
complex ungraphitised regions. Although the flour is made of crushed
filler particles, these do not necessarily align according to the forming
process.
Graphite
crystal
Morosowski
crack
33
Figure 1.9 Gilsocarbon Microstructure (Image Abbie
Jones)
Figure 1.10 Binder Matrix Crystallite Structure (Image
Abbie Jones)
Within the binder matrix a pore structure, known as gas pores develop
during the baking process. Calcination cracks and Mrozowski cracks are
isolated while gas pores may or may not be[22]. Gas pores therefore
provide accesses to the internal microstructure of graphite to gases
which may cause damage under irradiating conditions depending on
their chemical makeup.
34
1.2.3. Manufacture
Graphite for nuclear applications is manufactured to a purity up to
99.999% using the process detailed in Figure 1.11 [20].
Figure 1.11 Graphite manufacturing process [20]
Most commercially produced nuclear graphites use a petroleum coke
filler as this is an easily graphitised material. The filler particle size has
an effect on the bulk structure properties influencing the, porosity,
strength, and crack resistance[23]. Filler particles are made of large
aligned regions of crystals which have a high strength along the axis of
crystal orientation. However, increased particle size tends to increase
porosity in the microstructure and therefore decrease crack resistance
and affect the strength of the bulk material. The coke is heated to
35
remove volatile hydrocarbons. This produces lenticular cracks in the
filler particles.
The coke is mixed with a coal tar binder and formed. A number of
methods can be used to form the graphite including, isostatic moulding
and vibration moulding. In general extruded graphite results in good
strength and brittleness but poor isotropy, isostatic pressing gives
excellent strength and isotropy with poor brittleness whilst
vibromoulding gives good strength, isotropy and brittleness
characteristics[23].
The formed graphite, the green article, is then baked to drive off
further volatile products. The baking process produces gas evolution
pores throughout the binder material.
Finally the graphite is graphitised, heated to ~3000°C, to improve the
crystallinity throughout the entire block[24]. It is also possible to
improve the purity of graphite further through thermal or chemical
means at this stage.
36
1.3. Irradiation Damage
The principle reason for the using graphite in a nuclear reactor is to
slow down fast neutrons. The mechanism by which graphite slows
down neutrons is also the primary cause of damage to graphite
moderators, although thermal and radiolytic oxidation is also a concern
in some reactor designs. Irradiation damage causes changes to the
dimensional, mechanical and thermal properties of the crystals and
bulk structure.
1.3.1. Atomic Scale Damage
During reactor operation fast neutrons are released from the fuel with
a mean energy of 2MeV[25] and follow a path through the graphite
structure colliding with a large number of carbon atoms in transit. The
high energy neutrons pass on a fraction of energy to the incident
carbon atoms (held in place by a binding energy of ~5eV). The excited
carbon atoms behave like high energy projectiles displacing further
carbon atoms causing a cascade effect as shown in Figure 1.12. The
displaced atoms leave immobile vacancies.
Figure 1.12 Displacement Cascade
Neutron
Primary Knock
on Atom Secondary
Knock on Atom
~100Å
~1000eV
500eV
10Å
37
The displaced atoms are mobile and most fill vacancies [25]. Vacancies
are less mobile than single atoms as more energy is required to
rearrange the atoms for a hole to move. The remaining displaced atoms
may fill interstitial positions creating local defects that have a huge
effect on the bulk properties of the graphite. Displaced atoms tend to
coalesce forming lower energy arrangements. The coalesced atoms
force apart graphene layer planes causing an expansion in the crystal c-
axis shown schematically in Figure 1.13 [26], conversely, vacancies
result in a contraction in the a-axis.
Figure 1.13 Growth of interstitial loops[25]
Figure 1.14 Frenkel Pair[1]
There are a number of possible point defects possible, one of the most
common is the Frenkel pair, Figure 1.14. These point defects create
strong cross layer binding which have a significant effect on material
properties. By creating interlayer valance bonds dislocation glide can be
restricted. These pinning points are thought to be removed by high
energy projectiles, the breakup of these bonds rearranges the atomic
structure and releases energy[27].
Singular interstitial atoms are particularly mobile and can migrate to
form larger less mobile defects. Eventually, a large enough number of
interstitials coalesce such that they may be observed using TEM, Figure
1.15, and can be considered to form a new plane i.e. a prismatic
38
dislocation[28]. Observations using STM have found these clusters to
vary in shape from circular to linear[29].
Figure 1.15 Interstitial loops created by irradiation at 1350°C to 11.7 x 1020 neutrons cm-2 [30]
Each displaced atom leaves a corresponding vacancy. Vacancies are
considered to be mobile, however the barrier energy to such mobility is
significantly higher than for interstitial atoms because more atoms
must rearrange their position for a vacancy to move than are required
for interstitial migration. Therefore a large number of single vacancies
maybe formed. As dose increases multi-vacancies are formed[30].
Multi-vacancy interstitials may reduce or eliminate dangling bonds and
so reduce the energy of such arrangements. Multi-vacancies are closed
in two possible ways; Circular vacancies are filled by the contraction of
planes above and below the vacancy site. Linear vacancies contract in
plane closing along the line of vacancies causing shrinkage in the a-axis.
Over a core lifetime there is a significant amount of annealing, so much
so that it is likely that each atom is displaced at least once[1]. The
39
overall effects of these changes to the atomic structure cause growth in
the c-axis and shrinkage in the a-axis[31].
Recently it has been suggested that there are problems with the
standard model just described. The authors cite a lack of high
resolution microscopy evidence and discrepancies between the
theoretical and measured values of dimensional change and interstitial
migration energy[32]. Instead two mechanism are proposed, at low
temperatures buckles in the graphite plane are pinned by point defects.
At high temperatures pinning is less prevalent allowing dislocations to
interact more freely, when dislocations of opposite sign meet there is
an accumulation of matter which is accommodated by folding of the
layer plane. There is much debate around this theory, even the authors
concede that there is much experimental work required to support the
theory but that it does answer some phenomena the standard model
cannot explain.
1.3.2. Dimensional Change
Highly Orientated Pyrolytic Graphite (HOPG) crystals have been used to
investigate dimensional changes to graphite crystals from fast neutron
irradiation [33]. There is a significantly larger strain induced in the c-axis
than the a-axis as shown in Figure 1.16 and Figure 1.17. At irradiation
temperatures below 300°C there is a volume change associated with
stored energy[34]. The volume change is due to annealing of defects
which release stored energy. Increasing the irradiation temperature
decreases the dimensional change rate because of the increased
thermal annealing of the induced defects. Increasing the final heat
40
treatment temperature and therefore the crystallinity of the graphite,
has been shown to decrease the rate of dimensional change [35, 36].
Figure 1.16 Effect of dose and irradiation temperatures on dimensional change of HOPG in the c-axis[28]
Figure 1.17 Effect of dose and irradiation temperature on the dimensional change of HOPG in the a-axis.[28]
Extruded polycrystalline graphite derived from needle shaped cokes
irradiated at low temperature and dose tend to expand in all directions
41
with greater expansion parallel to the direction of extrusion. Increasing
the radiating temperature decreases dimensional change trends for a
given dose. Irradiating between 150°C and 250°C causes graphite to
expand in the c-axis and shrink in the a-axis, expansion in c-axis
decreases and contraction in the a-axis increases with temperature
[37].
Figure 1.18 PGA Dimensional Change at low Temperature[38]
Above 250°C PGA contracts in both axes with greater shrinkage in the c-
axis. Initial shrinkage is then followed by growth, Figure 1.19, Figure
1.20 and Figure 1.21[31, 33, 39]. In the case of anisotropic graphites
there is a marked difference in the dimensional change of the
perpendicular and parallel directions. The dimensions of isotropic
graphites expand at a rate similar to the perpendicular extrusion
direction of anisotropic graphites.
42
Figure 1.19 PGA Dimensional Changes of PGA at High Temperatures Perpendicular to Extrusion[39]
Figure 1.20 Dimensional Changes at High Temperatures Parallel to Extrusion[39]
43
Figure 1.21 Dimensional changes of Gilsocarbon due to irradiation damage[35]
Above 250°C, the initial contraction of Gilsocarbon is due to contraction
in the a-axis with the filler and flour. Despite the concurrent crystal
expansion in the c-axis, which is of a larger magnitude than the
shrinkage a-axis, the expansion is absorbed by Mrozowski cracks
resulting in an overall shrinkage of the bulk material [40]. Eventually the
Mrozowski cracks close and the continued expansion in the c-axis
becomes the dominant factor resulting in bulk expansion. The point at
which expansion becomes more dominant than shrinkage is known as
turnaround [41]. As the irradiation temperature increases the thermal
expansion of the crystals is larger causing the Mrozowski cracks to close
at a lower dose and by implication turnaround occurs at a lower dose
[42]. Under loading conditions dimensional change is affected by
irradiation creep[43].
44
1.3.2.1. Modelling Dimensional Change
A number of attempts have been made to model and predict
dimensional changes of graphites without the expensive and time
consuming process of using materials test reactors.
Simmons observed that a linear relationship exists between the CTE,
D.C.CTExx, and the dimensional changes due to irradiation, D.C.IRRxx, at
low doses [44].
axcxxxIrr gAgACD )1(..
1. Equation 1.1
axcxxxCTE AACD )1(.. Equation 1.2
where gc and ga denote growth due to irradiation, βa and βc are the CTE
of the crystal in the a and c axis respectively and Ax is the structure
factor relating the two equations. Ax is a function of crystal temperature
dependant CTE and describes contribution of porosity and crystal
orientation to the material expansion. The model only stays true at low
irradiation doses because it assumes that the crystallites are a loose
arrangement with no interaction between them. This model thefore
does not predict turnaround[45].
Sutton and Howard[46] investigated the role of thermal expansion of
bulk nuclear graphite grades further and considered the following three
factors to be important;
a) The thermal expansion of the highly anisotropic graphite crystal.
b) The orientation of the crystals
45
c) Accommodation porosity in the form of Mrozowski cracks and fine
pores generated between adjoining crystallites.
The equations derived from these assumptions describe the coefficient
of thermal expansion experienced by bulk graphite for a given dose and
temperature;
acGW KKCD 21.... Equation 1.3
acGA KKCD 43.... Equation 1.4
where Kx are factors describing the orientation of crystals, σa and σc
describe the single crystal coefficients of thermal expansion while α and
γ are accommodation factors[46]. D.C.W.G. and D.C.A.G. describe the
thermal expansion in the With Grain (WG) and Against Grain (AG)
direction. As shown in Figure 1. 22 WG and AG describe the
predominant grain orientation direction which is determined by the
manufacturing process.
46
Figure 1. 22 Schematic describing the with grain and against grain directions for either pressing or extrusion
forming
Focussing on thermal expansion has been but one of many different
techniques used to investigate dimensional change. Brocklehurst[47]
used the emerging field of intercalation to induce dimensional change.
The feasibility of intercalation was assessed by comparing intercalation
rates to the Simmons relationship. The study showed that it was
feasible to use bromination as a technique to investigate structural
changes[48] and he deduced that microstructural changes such as
crystal expansion and pore generation determined the change in bulk
properties.
The finite element method was used by Hall[49, 50] to create a multi-
scale model of graphite. By inputting irradiation data of HOPG into a
crystallite model and using the output as input parameters for a bulk
material model. This method was quite successful in predicting changes
seen in reactor conditions. It was concluded that to verify his model it
47
must be determined if crack closure does occur under reactor
conditions [51].
1.3.3. Young’s Modulus
Generally in engineering Young’s modulus is measured by performing
static loading experiments and observing the stress strain curve. The
stress strain curve of graphite is non-linear and this poses problems for
measuring Young’s modulus. Figure 1.23 shows that very quickly there
is plastic like deformation with hysteresis in the stress strain curve. For
nonlinear materials it is possible to define the modulus by a chord
length[52], unfortunately there has been little consistency in doing this
by graphite researchers. It is most common to measure the Young’s
modulus dynamically. Dynamic Young’s modulus (DYM) is a method of
inducing strain using ultrasound and is approximately the rate of
change at the origin[53].
DYM is measured by sending an ultrasonic elastic wave through a
material which generates small strains as it travels. Therefore static
tests only produce similar results if carried out for very small elastic
deflections. Ultrasonic elastic waves are a very versatile technique for
materials testing and further to the measuring the modulus of a
material can also be used to gain information of defects within the
material by measuring parameters such as signal attenuation and the
time for echo return.
48
Figure 1.23 Nuclear graphite stress strain curve[54]
The elastic constants of graphite are often referred to using Voight
notation as given in Table 1.2[55] and shown schematically in Figure
1.24. Figure 1.24 shows the orientation of the unit vectors in relation
to graphite layer planes. C11, C22 and C33 describe Young’s modulus in
the a, a, and c directions respectively whilst C44 describes the shear
modulus perpendicular to the layer planes and C66 describes the shear
modulus parallel to shear planes.
Table 1.2 Voight notation
2. Unit
Vector
11 22 33 23=32 31=13 12=21
Voight
Abbreviation
1 2 3 4 5 6
49
Young's modulus of graphite crystals can be calculated from elastic and
crystal compliances. The values of virgin graphite in the c-axis are
around 1024 GPa in the a-axis and 36.4 GPa in the c-axis[51]. A small
initial irradiation dose greatly increases single crystal modulus, Figure
1.25. Simmons hypothesised that this is due to pinning of the basal
planes causing an increase in the shear modulus C44. Further exposure
leaves a plateau in the modulus and it has been assumed that this is
due to a saturation of the number of pinning points created[43] [1].
Saturation is thought to occur because after a certain dose a large
number of holes exist within the structure making it likely that a
displaced atom will recombine with a vacancy. Values of the elastic
compliances S11, S12 and S13 are essentially unchanged during irradiation
[56].
31 13
21
33
32
11 23
22
12
Figure 1. 24 Orientation of unit vectors in relation to graphite layer
planes
50
Figure 1.25 Change in crystal shear modulus C44 due to irradiation at 50oC[56].
Note 1dynes/cm2 is equal to 0.1 Pa
Modulus measurements of polycrystalline graphites also exhibit the
initial increase due to the change in crystal shear modulus, Figure 1.26.
It is thought that the increase in crystal shear modulus increases the
bulk modulus of graphite, this is due to experiments which show only
C44 shows any significant change due to dose[56]. The explanation given
is that the reduction of basal plane slippage implied by a high C44
prevents graphite from deforming so readily.
At higher dose a secondary increase is observed and this is considered
to be due to closure of Mrozowski cracks[57]. The closure of cracks is
thought to increase the modulus as the decrease in internal porosity
increases the stress required to induce a given compression strain, as it
is easier to compress a porous volume than a solid volume.
After this the modulus decreases rapidly as the microstructure
disintegrates. Increasing irradiation temperature decreases the
magnitude of the secondary increase and the dose required to reach
the peak of the secondary increase. Low dose Changes in Young's
modulus can be annealed out below 1000°C corresponding to
51
aggregation and annealing of small interstitial loops [58]. Changes in
modulus are shown to be significantly affected by irradiation creep [59].
Figure 1.26 Change in Gilsocarbon Young's modulus due to irradiation[35, 39]
There have been fewer attempts to model the change in modulus
though Hall[49, 50] had success with multi-scale finite element analysis.
Using the code ABAQUS a model of a graphite crystal was created and
the effect of irradiation on the crystal properties due to irradiation such
as dimensional change and co-efficient of thermal expansion were
input. The output of this model was input into a polycrystalline model.
The results showed that an increase in young’s modulus could be
attributed to closure of microporosity and that at higher doses inducing
microcracking reduced the modulus as seen in experimental data .
1.4. Scientific Proposal
This project will use intercalation of bromine as a means of inducing
structural damage to simulate irradiation damage in nuclear grade
graphites. In particular this work will focus on the anisotropic graphite
52
PGA and semi isotropic graphite Gilsocarbon. Work shall also be carried
using HOPG to model single crystal intercalation. Investigating both
polycrystalline and single crystal graphites will provide an insight into
the interrelationship of properties in these materials. Using
intercalation as a simulation technique has the advantage over
irradiation for PhD investigations as large strains can be induced
relatively quickly, over the course of a few days rather than a few years.
This technique also means standard laboratory equipment can be used
as there is no need to accommodate radioactivity.
1.5. Summary
Nuclear graphite has been used since the very first nuclear reactors as a
moderator. This is because it has a high scatter and low absorption
cross section. When graphite is placed in an irradiating environment
severe structural damage occurs. This causes the properties of graphite
to change. The manner in which they change is affected by the
microstructure of graphite. Nuclear graphite grades have different
microstructures and this is due to the manufacturing process. This work
will use intercalation to investigate selected material property changes
in nuclear graphite.
53
2. Intercalation
The core of a nuclear reactor is an extremely hostile environment and
this poses significant problems for designers and operators. High
neutron fluxes, high temperatures and corrosive coolant gases damage
the very materials from which a reactor is constructed. A large portion
of a reactor is constructed from graphite bricks, these bricks receive
substantial atomic scale damage which induces dimensional and
material property changes to both single crystal and bulk polycrystalline
graphite. As discussed in Chapter 1 it is considered that a very
significant portion of these changes are due to the growth of interstitial
layers generated by atoms displaced during collisions[60-62].
Intercalation is another method of inducing damage into the graphite
microstructure and though there are key differences in the damage
mechanisms intercalation of bromine into graphite has been used in
previous studies to simulate irradiation damage[63]. This chapter
discusses the previous work undertaken and is aimed at understanding
intercalation compounds, the chemical process and in particular,
graphite intercalated bromine. The chapter also focuses on methods of
inducing intercalation, the structure of intercalation compounds, the
intercalation reaction and the material properties of the intercalation
compounds.
2.1. Intercalation Compounds
Intercalation has been utilized by humans for many centuries as the
process by which clay can be transformed from a plastic medium to a
54
dense and brittle material for pottery[64] with some of the oldest
known ceramic objects dated as 26000 years old[65].
The first scientific investigation into intercalation was carried out in
1841 when Schauffautel intercalated Sulphate ions in graphite[66]. The
advent of X-Ray Diffraction (XRD) made it possible to carry out more
detailed investigations into these novel materials[67]. Around the same
time the science progressed further in the development of new
intercalation compounds[68].
The definition of intercalation is insertion and literally refers to the
insertion of time into a calendar. In chemistry it refers to the reversible
insertion of a guest compound into a host structure[66] where the
intercalate fills voids in the atomic structure. There are many possible
host materials including isotropic lattices such as Zeolites[69],
Orthotropic lattices such as graphite[70] and one dimensional
structures such as DNA[66].
The intercalation of many different allotropes of carbon have been
studied including graphene[71], graphite[66, 70], diamond[72],
fullerenes[73] and carbon nanotubes[74]. Intercalated materials have
been shown to have remarkable properties including
superconductivity[75]. These materials have received such interest over
recent years as there are many realized and potential technical
applications including catalysts, gas sensors, batteries,
superconductors, micro-mechanical actuators and lubricants.
55
2.2. Graphite Intercalation Compounds
Graphite is unique among host materials in that it may be an electron
acceptor or an electron donor[76] and intercalants are classified as
such. Donor compounds include alkali metals, lanthanides and metal
alloys. Ternary donor compounds have also been prepared, normally
alkali metals bonded with molecules such as ammonia[77] or
benzene[78]. Many acceptor compounds have been prepared and are
often based on Lewis acids, that is a species that accept lone pair
electrons, such as bromine[79]. Metal halides (including metal
chlorides, bromides, fluorides) acidic oxides and acids such as sulphuric
acid may also be intercalated and likewise fall into the acceptor
category[70]. The majority of these compounds are unstable in air,
donors are easily oxidized and acceptors readily desorb. Graphite-FeCl3
and SbCl5 are relatively stable and are therefore used for many
experiments which aim to understand intercalation. The stability of
samples can be improved by cooling to liquid nitrogen
temperatures[70].
2.2.1. Intercalation Methods
Graphite can be intercalated with solids, liquids and gases [80];
however it is preferable to intercalate with the gaseous form of the
intercalant if possible as this allows the highest degree of control over
the experimental conditions and the technique is the simplest to
perform. Figure 2.1 shows an early experimental arrangement as used
by Brocklehurst[63] for investigations into intercalation of nuclear
graphite. A graphite sample is held on a calibrated spring in an
evacuated chamber. The gaseous intercalant is released by breaking
56
vials containing the appropriate gas in an adjacent chamber connected
by a stopcock. On opening the stopcock the intercalant quickly fills the
sample chamber. The stopcock is closed and a fresh vial can be added
to the intercalant chamber. As more vials are added the partial pressure
of bromine increases[63].
Figure 2.1 Bromine intercalation apparatus for weight uptake measurements[63]
There are variations on how the intercalant partial pressure is
controlled. Figure 2.2 details the experimental setup Sasa used to
investigate the staging of Graphite Intercalation Compounds (GIC’s).
57
Here the intercalant chamber is placed in a temperature controlled
water bath. Increasing the temperature of the bath increased the
partial pressure of the gaseous intercalant [81]. This method gives
much closer control of the intercalant partial pressure.
Figure 2.2 Bromine Intercalation with control of intercalant partial pressure for XRD measurements[81] (1) Glass
sample holder; (2) a hole of 1mm diameter; (3) graphite sample; (4) “Teflon” sheet (0.2mm thickness); (5)
ground-glass contact: (6) Araldite sealing; (7) bromine (8) water bath for bromine pressure control; (9) to be
joined to vacuum system
2.2.2. Structure of Graphite Intercalation Compounds
The structure of graphite intercalated with bromine was first
investigated by Rudorff [79], who found that bromine intercalated up
to a maximum ratio of C8Br. Importantly the analysis carried out by XRD
showed that galleries of bromine were created and interestingly these
galleries were very ordered. In the case of C8Br there are two graphite
58
layers followed by a layer of bromine. This is known as a second stage
intercalate as shown in Figure 2.3. It has since been shown that
graphite has further lower stages, above C16Br the third stage is created
[82] and a fourth stage exists above C28Br [83]. Different intercalation
species can be intercalated to higher and lower stages, Figure 2.4 shows
a micrograph of a stage 2 CuCl2 graphite intercalation compound. The
CuCl2 is indicated by the white lines and the graphite is indicated by the
dark lines. The image shows that ordered staging can exist over a large
range.
Figure 2.3 Schematic of increasing intercalation stages
Figure 2.4 TEM Image of CuCl2 (light regions)
intercalated graphite (dark regions) [84]
When intercalated, adjacent graphite layers retain their stacking
sequence[70]. Depending on the size of the intercalation species the
induced change in layer plane spacing differs. Brocklehurst compiled
data of a number of different intercalates from a number of different
sources, and is shown in Figure 2.5. This provided Brocklehurst with his
primary reason for using bromine as the intercalation compound for his
experiments which is that the inter-carbon layer distance is
Stage 4 Stage 3 Stage 4
59
approximately the same, 7.05Å, as if the separation was caused by
interstitial carbon atoms, 6.70Å.
Plot of Graphite C-C Interlayer Apacing Containg A Layer of
Intercalated Reactant against Ionic Radii of Reactant
4
5
6
7
8
0 1 2
Ionic Radius (A)
C-C
In
terl
ay
er
Sp
ac
ing
(A
)
Na
K
F
RbCs
Br
Figure 2.5 Distance between graphite layer planes for different intercalation species [63]
Intercalates further modify the structure of graphite by inducing basal
plane slippage. Stage two graphite has AB|BC|CA|AB stacking whilst
stage three compounds have ABA|ABA|ABA stacking where the |
denotes an intercalant layer as shown in Figure 2.6 [85]. This is shown
schematically in Figure 2.6. A similar basal plane slippage is induced by
interstitial carbon atoms[1].
a)
b)
Figure 2.6 Graphite basal planes (black) with intercalant (white) a) stage 3 b) stage 2
The arrangement of bromine at low pressure has been studied using
density functional theory (DFT) Figure 2.7. The molecular arrangements
detailed in (a), (b) and (c) show bromine molecules normal to the
graphite plane, these arrangements are only possible on the outermost
60
graphene plane. Arrangements (d) to (h) show possible bromine resting
positions in between graphene planes. The number indicates the
relative stability of each arrangement in eV (a) is actually 0.004eV [71].
The unit cell of bromine intercalated graphite has been widely studied
using electron diffraction [86], x-ray diffraction [87] and neutron
diffraction [88], [89] Figure 2.8. The in plane unit cell is base-centred
orthorhombic. When bromine is intercalated it maintains its molecular
identity, that is it maintains the bromine – bromine bond length seen in
solid bromine [90].
Figure 2.7 Bromine positions at low concentrations calculated
by DFT [71]
Figure 2.8 Unit Cell C8Br found by Neutron
Diffraction [91]
Figure 2.9 and Figure 2.10 present electron micrographs of damage
sites within brominated and irradiated graphite. The size and quantity
of irradiation clusters are strongly related to irradiation temperature.
As irradiation temperature increases irradiation clusters become more
widely separated and larger [92]. By comparison TEM has shown that
the damage sites of brominated graphite are larger than irradiated
graphite and that there are fewer damage sites per unit area. The
distribution of intercalation damage sites appears to be related to the
61
surrounding microstructure, local faults and defects [27], whereas
irradiation defects are more randomly distributed[30].
Figure 2.9 Intercalate clusters (bromine main picture
Iodine chloride inset)[27]
Figure 2.10 Interstitial clusters caused by fast
irradiation[30]
2.2.3. The Intercalation Reaction
Understanding the intercalation reaction is fundamental to
understanding intercalation as a technique to simulate irradiation. This
is particularly true when using it for microstructural investigations as
this thesis aims to do. It is important to understand where the reactant
is most likely to be located and how the nature of the host and reactant
may affect this.
The amount of reactant intercalated is related to the partial pressure of
the reactant. The most detailed study was carried out by Sasa who
performed an intricate experiment to investigate the effect of partial
pressure on the reactant/host ratio. Sasa measured the amount of
bromine intercalated for a given partial pressure and in conjunction
with xray diffraction measurements deduced the pressures required for
each phase change from pure pyrolytic graphite to a fully intercalated
compound, this is detailed in Figure 2.11.
62
The X-ray diffraction results show that as the partial pressure increases
the weight uptake increases and associated with the weight uptake is a
change in phase. A change in phase is followed by an increase in the
rate of intercalation, this is due to the intercalant arranging in
increasingly dense arrangements. On removal of the intercalant there is
a hysteresis associated with intercalant removal. On deintercalation it is
not possible to remove all of the intercalant unless the host is heated to
suitably high temperatures[20, 93].
Figure 2.11 Phase change induced by change in intercalant pressure. Open circles indicate intercalation and
closed circles denote deintercalation[81]
Ubbelohde et al[94] examined the bromination initiation process and
proposed that the intercalant atom may become adsorbed on the
graphite surface, thus forming an ionic bond with a carbon macro-
molecule. It was thought that this change in charge distribution would
“unpin” the graphite layers and allow intercalation to occur by
diffusion. Recent thermogravity experiments on graphene confirm the
importance of chemisorption [95].
Ubbelohde’s idea suggests that once graphite has adsorbed the
intercalant any layer is equally likely to intercalate. The theory was
63
shown to be incomplete by a very interesting experiment by J.G.
Hooley[96]. By taking 60mm thick piece of pyrolytic graphite with five
equally spaced marks along its height (parallel to the basal planes) he
could make strain measurements at five separate regions of a sample
as intercalation took effect. The results shown in Figure 2.12 show that
the rate of intercalation is quickest at the outermost regions of the
sample to a point of saturation with intercalation of the inner regions
being slightly delayed and that therefore not every layer was
immediately open to intercalation. Later theoretical work showed that
this effect was due to a long range elastic interaction between
intercalant layers [97, 98].
Figure 2.12 Intercalation Rate through sample thickness [96]
An interesting area of research regards the way an intercalation
compound changes from one stage to the next. The problem arises in
the higher stage compounds when the insertion or removal of an
intercalant layer will not result in the regular intercalant spacing seen
with intercalation compounds. There is a change in the XRD spectra
associated with the phase change which shows the rise and fall 00l
peaks. It is very difficult to determine from these how the intercalation
64
compound changes from one phase to another, though there are two
proposed theories.
Nixon et al studied intercalation of nitrates and interpreted their results
as showing whole layers deintercalating and intercalating at the
appropriate level. They suggest this is achieved by mobile dislocations
which are present in all layers at the edges of graphite and travel
towards the centre at the appropriate intercalate concentration. Nixon
et al reasoned that this will produce the most stable arrangement [85].
A second theory has been proposed by Daumas and Herold who found
it unlikely that whole layers of intercalate would be removed before
new layers could intercalate to achieve the next stage. Either stages
had to be missed or there was another way. Daumas proposed that
there are microscopic domains of well staged material; however the
domains may be in different layers of graphite as seen in Figure 2.13. As
the surrounding intercalates partial pressure changes, the domains
move along the layer planes such that the different stages are formed.
Theoretical work shows that a long range elastic interaction between
intercalant islands will drive the random or mixed staged compounds to
pure stage ordering[97, 98].
Figure 2.13 Stage two (left) and stage three (right) Daumas Herold Domains[99]
65
The domain model is supported experimentally with evidence collected
by Clarke et al[100]. By intercalating graphite with potassium to a stage
2 compound and applying a load, XRD measurements showed that two
stages can coexist in a sample and that there is a time dependant
change in the super lattice order. Clarke noticed that the degree of
crystalline perfection has a significant effect on the load under which
two stages can coexist, suggesting this may be from differences in
dislocation densities and the associated difference in shear modulus,
C44. Evidence of mixed stages has since been observed by TEM in
graphite samples intercalated with FeCl3 [101], K[102] and CuCl2 [84].
A TEM study on graphite with residue bromine, SbCl5 and KHg
intercalates by Timp & Dresselhaus [103] found large domains, up to
25nm x 210nm, and using diffraction contrast techniques found these
domains to be free of dislocations. By looking at the resulting
interference between electron waves which have passed through the
sample using a TEM microsope it is possible to observe dislocations in
the atomic structure. Timp and Dresselhaus looked for basal plane
dislocations which would be indicative of the Damaus and Herold
model but could not find any. This runs contrary to the domain model
and Timp & Dresselhaus suggest that while the Daumas & Herold model
may hold for other intercalates it does not for those chosen for this
experiment. They suggest the stage changes involve the intercalate
diffusing through point defects in the graphite lattice allowing the
movement of full intercalate layers. A later study into SbCl5 using a
Scanning Ion Microprobe did find domains of intercalant on freshly
cleaved sample surfaces [104].
66
Axdal and Chung[99] developed a theory that relates results from many
different intercalation experiments of different intercalation
compounds. The reaction is split up into a number of rate determining
steps. The initial step occurs while the intercalant is external to the
graphite, that is evolution of the intercalate and transport of the
intercalate to the sample. Then surface reactions occur, adsorption to
the surface and nucleation of insertion sites. This is followed by
diffusion of the intercalant through the sample. The final step is the
staging reaction. The overall rate of reaction will strongly depend on
which of these steps takes the longest. They show theoretically that in
the case of bromine, diffusion is the rate controlling mechanism. This
implies that the chemical potential for a reaction decreases towards the
centre of the sample. This agrees with experimental work carried out in
parallel by the authors[105].
Intercalation is strongly related to the degree of crystal perfection
affecting both the rate and amount of intercalant uptake. A study by
Ubbelohde et al[106] investigated how the graphitisation temperature
used in the formation of pyrolytic graphite affected the uptake of
bromine after 70 hours as shown in Figure 2.14. The study shows that
above 1900°C there is a significant decrease in the c-spacing coupled
with a decrease in stacking disorder suggesting a step change in the
number of defects present. The reduction in defects allows the graphite
to absorb bromine to its maximum ratio C8Br [106, 107]. This is
important as it indicates the degree of crystal perfection has an effect
on the uptake of intercalate and this may potentially have an effect in
polycrystalline graphite where different regions have graphitised to
different degrees.
67
Hooley[107] showed that the rate of bromine uptake was also directly
related to crystal perfection with the samples graphitised at a higher
temperature intercalating at a faster rate. It has also been shown that
intercalation is not affected by chemical impurities in a graphite lattice
[108].
Figure 2.14 Effect of crystal perfection on bromine uptake [106]
A detailed microscopy study by Heerschap[27] investigated dislocations
induced by bromine intercalation. The boundary dislocations of
intercalated bromine are sessile, that is they can only travel in the glide
plane by diffusion of the intercalant. The boundaries are highly mobile
and have a low line tension. Evidence is presented that bromine easily
travels through line defects present in the original graphite crystal,
widening the dislocation as more bromine is intercalated.
In summary the rate of bromine uptake is affected by the degree of
crystal perfection of the graphite and the partial pressure of the
surrounding intercalant with the reaction unable to initiate if either of
these two components are insufficient. The reaction is initiated by an
68
unpinning of the graphite layers by the intercalant drawing charge. The
reaction is a diffusion controlled process and is progressed by a long
range stress interaction. Staging is a phenomenon unique to
intercalation compounds where long range order is seen and it is a
matter of debate how staging progresses. Experimental work has seen
multiple stages co-exist which strongly suggests domain interactions
are the mechanisms behind stage changes. However it is disputed
whether this is the mechanism in a graphite bromine intercalation
compound.
2.3. Property Changes
2.3.1. Dimensional Changes
Dimensional changes are the most studied property change of
intercalation compounds with investigations into both single crystal and
polycrystalline compounds. A significant portion of the work which
investigated the intercalation mechanism was carried out on single
crystal graphites with dimensional change being a key measurement
[81, 85, 94, 106, 107, 109, 110].
The first studies into the intercalation of nuclear graphite were
concerned with dimensional change. Brocklehurst [63] found that
polycrystalline graphites have an initial linear growth per unit
concentration which could be modelled by Simmon’s growth
theory[111], that is the thermal expansion of graphite can be used to
predict the initial dimensional change behaviour under intercalative
conditions. The relationship held true for single crystal graphites but
not for poorly graphitised materials which were shown to intercalate
69
poorly. After the initial predictable linear expansion, polycrystalline
graphites expand at an increased rate and it is hypothesized that this is
due to opening of porosity by misaligned crystallites. The subsequent
increase in expansion was shown to be less pronounced for isotopic
graphites [63].
An interesting study has been carried out relating the microstructural
changes in battery electrodes to the bulk material dimensional changes
during intercalation of lithium. The graphite electrode material is
polycrystalline made of binder and filler components as with nuclear
graphite, although the associated filler particles and porosity are
significantly smaller, with average pore size around 25µm and 10µm
respectively [112]. This research concluded that the dimensional
changes seen in lithiated electrode graphite are large in the filler
particles and an order of magnitude lower in the bulk material. DFT
calculations show an interstitial lithium atom shares its charge with the
twelve nearest carbon atoms which strengthens interlayer bonding
causing a change in C33 and C44. At the atomic scale an increase in bond
strength is expected to increase the modulus, however at larger scales
this is complicated by the presence of porosity in the bulk structure. It
has been postulated that the change in modulus has a significant effect
causing contraction and expansion of surrounding regions of binder
which can have a different modulus [113].
2.3.2. Young’s Modulus
The data on change in elastic constants of bromine intercalated
graphite is sparse though measurements have been taken by neutron
70
diffraction reporting a decrease in the shear modulus C44 from 0.89 x
109 N/m2 to 0.18 x 109 N/m2 [88].
An interesting DFT study of lithiated graphite [114] has looked at the
effect of lithium intercalation on graphite electrodes, Figure 2.15. It has
been shown that as the stages lower, the linear elastic constant C33
increases by two and a half times and the shear elastic constant C44
increase by up to four times. By applying the results to a polycrystalline
model the Young’s modulus is calculated to increase by a factor of
three and the poisons ratio is calculated to fall from 0.31 to 0.24.
The Poisson’s ratio of nuclear graphite is lower than that of battery
electrodes measured as 0.21 for Gilsocarbon and 0.07 for PGA[35].
Measured changes due to irradiation are noisy[115] and are therefore
assumed to be unchanged by irradiation[42, 115]. As with irradiated
graphite, a change in C44 has also been attributed to the initial rise in
Young’s modulus[56].
Figure 2.15 Change in elastic constants of lithiated graphite[114]
71
Existing data on modulus changes of intercalated materials is sparse,
therefore this literature review was expanded to include intercalated
graphite fibre epoxy composites. Research shows that there is little
change in modulus between the two materials, though authors report
that these property measurements are controlled by the epoxy fibre
interface properties and so provide poor reflection on property changes
due to intercalation[116, 117].
2.4. Summary
Bromine has been used in previous studies to simulate irradiation of
graphite, chosen for its ability to produce similar layer plane spacing to
interstitial carbon atoms. Intercalation refers to the reversible insertion
of a substance in to a host material. There are a range of host materials
which require voids in their structure to accommodate the intercalant,
to which carbon based materials are particularly suitable. It is possible
to intercalate many different substances, with respect to graphite.
These intercalants can be donors or acceptors depending on charge
transfer. When materials are intercalated they form staged structures,
that is the intercalant will fill regular periodic positions perpendicular to
the layer planes.
Bromine uptake is related to the partial pressure of the surrounding
intercalant and the crystal perfection of the host. Intercalation is
initiated by an unpinning of carbon layers and progressed by elastic
interactions. It is unclear if the intercalate fills whole layers or islands
within the host; evidence has been presented for and against each idea.
Axdal and Chung[99, 105] have shown that bromine intercalation in
72
graphite is a diffusion controlled process and that therefore there is less
potential for a reaction towards the centre of a sample.
The most studied property change induced by intercalation is
dimensional change, this has also been modelled extensively on single
crystal graphites and shown to cause an expansion parallel to layer
planes. Various polycrystalline graphite grades have also been studied
by Brocklehurst[63] who showed that initial expansion could be
modelled using Simmons growth theory and he hypothesised that a
later increase in expansion rate could be due to the opening of
microporosity by misaligned crystallites.
Data on young’s modulus of intercalation compounds is sparse, neutron
diffraction investigations of brominated graphite suggest there is a drop
in the shear constant C44 of HOPG. A theoretical study of lithiated
graphite shows a significant increase in elastic constants.
73
3. Materials and Methods
This study is concerned with investigating microstructural damage in
graphite and the effect this has on the bulk material properties. This
chapter details the methods used in this investigation including the
experimental techniques used and design of experimental rigs.
3.1. Experimental Techniques
3.1.1. McBain Spring Balance
As mentioned in Chapter 2 a common piece of experimental equipment
used for intercalation experiments is the sorption balance, otherwise
known as a McBain spring balance [118]. The method is very simple
consisting of a specimen attached to a calibrated spring as shown in
Figure 3.1. A travelling micrometer is used to track the displacement of
the spring, and using Hookes law the change in mass can be calculated,
Equation 3.1.
1hkm Equation 3.1
where m is the mass, k the spring constant in g/mm and h1 is the
position of the bottom of the spring. When using this technique care
must be taken to prevent external interference with the spring.
Vibration of the rig must be prevented and the gas must enter the
chamber at a slow rate[119] to avoid turbulence.
74
Figure 3.1 Schematic of McBain Spring Balance[118]
The McBain spring balance is designed for measuring changes in
sorption with temperature so Brocklehurst [28] modified the McBain
spring balance [118] for studies into the dimensional change associated
with intercalation of graphite. The difference being that there was no
temperature control and the strain induced by sorption was measured.
This was achieved by ensuring the sample dimensions were such that
the travelling micrometer could be used to measure the top and
bottom of the samples to obtain the change in sample length.
3.1.2. X-ray Computed Tomography
X-ray Computed Tomography (XCT) is a non-destructive three
dimensional imaging technique. This study utilises micro tomography to
study the development of intercalation and associated strains within
polycrystalline graphitic microstructures. Strains are measured using
Thermometer
Thermometer
Liquid to be employed
for sorbption
Sorbent
Silica spring
Heating element
75
Digital Image Correlation (DIC). This section is divided into two; the first
part describes the experimental setup of tomography and how to
obtain good quality data; the second part describes the image analysis
techniques used to measure strains induced by intercalation.
3.1.2.1. Experimental setup
The experimental set up for an x-ray tomography experiment is shown
in Figure 3.2. An X-ray source beams photons through a sample. The
sample is rotated through at least 180° with an image taken at suitable
rotational increments. The x-rays are normally passed through a
magnifying optical set up and then converted by a scintillator into a
form which can be detected by a Charged Coupled Device (CCD) camera
[119] and recorded as radiographs. Data may then be reconstructed
and analysed by software.
Figure 3.2 Tomography setup
X-rays can be produced by laboratory sources and synchrotron sources.
Laboratory equipment produces x-rays by firing electrons at a solid
metal anode, radiation is emitted as the electrons are decelerated. This
produces photons with a range of wavelengths [120]. Synchrotrons
produce x-rays by diverting the path of an electron beam through a
magnetic field; this produces a polychromatic beam of x-rays which if
76
desired can then be passed through monochromating optics to produce
a monochromatic beam[121]. The effect of this is that Synchrotrons
have monochromatic light at high flux while laboratory equipment has
polychromatic light at low flux. The higher flux achievable with
synchrotron sources means data can be acquired at a significantly
quicker rate and so can be used for time series investigations.
X-rays are ideal for tomography as they penetrate solid materials and
by measuring x-ray attenuation it is possible to gather information
about the internal structure of a sample. The x-ray absorption cross-
section varies depending upon the atomic structure of the different
phases of the material under investigation and the energy the photons
emitted from the x-ray source. The detector picks up a shadow of a
sample which represents the difference in intensity due to variation in
attenuation across the sample. Figure 3.3 shows the effect of different
sample variations on the x-ray shadow as measured by a radiograph.
77
Figure 3.3 Effect of sample composition on x-ray shadow
When conducting an x-ray experiment a number of difficulties may
arise. The first problem is due to the statistical nature of photons, there
is a probability associated with photon production and interaction with
both sample and detector which causes a speckled effect on the
reconstructed images. There are two options for overcoming this issue,
first method is to increase the length of time for each projection, thus
increasing counting statistics; the second is to use a smoothing
algorithm. A smoothing algorithm will result in a loss of data to a
certain degree however time restrictions normally require a
compromise[122].
Another experimental difficulty may arise from beam hardening which
is a particular problem when using polychromatic light sources. One of
78
the factors which affects x-ray attenuation is the x-ray energy, generally
the lower the x-ray wavelength, the higher the attenuation is. This
results in low energy light to be disproportionately absorbed through
the sample thickness, this manifests as a darkening towards the sample
centre and may be overcome using various algorithms [122].
There are also issues related to the detectors as not all the pixels will
give the same output for a given photon count. This will show up as
light and dark regions in a radiograph. This is compensated for by
calibrating the equipment taking a series of dark and white images
[122].
Nuclear graphite has been studied extensively by tomography. The first
study investigated density variations of thermally oxidised IG110, at
that time a candidate material for Japans High Temperature Gas cooled
Reactor (HTGR)[123]. Further work was carried out at the University of
Manchester on tomography of thermally oxidised samples with
particular focus on automated porosity classification[124]. More recent
work has used synchrotron tomography with phase contrast
reconstruction algorithms to investigate crystal strain due to thermal
expansion[125], phase contrast techniques are suited to graphite
experiments due to the low absorption co-efficient of graphite[126].
3.1.2.2. Digital Image Correlation
DIC is an image analysis technique used to track movement of features
between images. The technique was developed during the 1980’s when
image correlation found use for engineering applications in particular
79
stress analysis in solid mechanics and particle image velocimetry in fluid
mechanics.
By measuring the movement of pixel patterns between two images
displacement vectors can be calculated and from this microstructural
dimensional change can be calculated [127]. In the most basic sense
this is achieved by sectioning an image and tracking the movement of
the pixel patterns and calculating the associated displacement vector.
For a good quality analysis there must be sufficient texture within the
reference window to track motion. For unmodified materials this
means increasing the size of the window. However if the window is too
large motion cannot be tracked within that window. Errors can be
further reduced by ensuring the movement between each image is as
small as possible[128].
Two Dimensional DIC was first applied to fracture mechanics problems
and there have been a number of such studies devoted to
understanding crack propagation in nuclear graphite[129-131]. More
recently three dimensional DIC has been carried out looking at strains
induced by thermal expansion of nuclear graphite. This work focused
on understanding which regions within the heterogeneous
microstructure contributed to expansion. Algorithms were written to
extract local strains from the displacement vectors measured by DIC.
The code removes rigid body motion, rotational vectors which are
induced by small rotational displacements between different
tomography scans and finally radial expansion due to the bulk
expansion. By removing the bulk displacements the remaining
displacement vectors describe the local strains and as such allow an
80
understanding of how microstructural features affect microstructural
strains. The work proved very effective in characterising local
displacements[125].
3.1.3. Laser Ultrasonics
Ultrasound refers to pressure waves with a frequency in the range of
20kHz to 2GHz and are useful for non destructive engineering
applications such as crack detection and property measurements.
Ultrasonics are commonly used for the measurement of Young’s
modulus in nuclear graphite. This section will introduce the standard
test method to perform Dynamic Young’s Modulus (DYM)
measurements and go on to describe the modifications employed to
apply the technique to the measurement of brominated graphite.
3.1.3.1. Ultrasonics
Equations defining DYM measurements differ to classical modulus
definitions because the strains induced are small. Therefore the
definition is derived from equations of motion, a full derivation can be
found in Timoshenko’s Theory of Elasticity[132] and the result is given
in Equation 3.2.
)1(
)21)(1(2
vE Equation 3.2
where E is the DYM, ρ is the sample density, η is Poisson’s ratio and ν is
the ultrasonic velocity. Though ultrasonic waves propagate through
elastic media in three modes, shear waves, longitudinal waves and
81
surface waves, for DYM measurements only the longitudinal velocity is
required[133].
3.1.3.2. ASTM standard C 769-09
The experimental method to measure the DYM of nuclear graphite is
defined by ASTM standard C 769-09. Using piezo transducers the
experimental setup is outlined in Figure 3.4. The experimental
apparatus measures the time an ultrasonic pulse takes to travel
through a sample. This standard is reported to give a result to within
10% of the result provided by other methods such as measuring
fundamental frequencies[134].
Figure 3.4 Schematic of ASTM C769 experimental setup[134]
The driving circuit should be capable of generating frequencies from 0.5
to 2.6MHz. Samples must be straight with a uniform cross section. The
end faces must be perpendicular to the cylindrical surface within to
0.125mm and the sample must be long in comparison to the probing
wavelength. The weight and dimensions of the sample are to be
weighed to 0.5% accuracy.
82
3.1.3.3. Laser Induced Ultrasound
As the principle focus of this research is aimed at understanding
property changes of brominated samples a technique was developed to
operate in harsh corrosive environments. To this end the use of laser
ultrasonics was utilised as a non contact method. Laser ultrasound has
a number of advantages over differing contact methods as the
measured sample is not held in a pre-stressed state as well as problems
associated with transducer contact couplants such as difficulties in
ensuring optimum contact conditions. Most importantly though for this
research the method can be applied for inaccessible samples in difficult
environments. Previous work has used lasers to induce ultrasound in
graphite[135].
It sounds counter intuitive that light can induce stress waves but this
can be achieved using coherent light from lasers. The non reflected
portion of light energy has a number of effects on the sample
depending on the wavelength and energy. At low power heating and
thermal and elastic waves are produced while at higher powers there
may be melting, plastic deformation and crack formation. For Non
Destructive Testing (NDT) low powered lasers are therefore required.
An elastic wave is generated by the sample absorbing electromagnetic
radiation which heats up a small region of the sample. This in turn
causes rapid thermal expansion of a small region which causes an
elastic wave to propagate through the solid as shown in Figure 3.5.
83
Figure 3.5 Schematic of ultrasonic wave generation by laser [136]
The ideal laser for generation of elastic waves is pulsed as this produces
rapid temperature changes in the sample for short periods which
generates thermoelastic stresses rather than heating of the sample. The
pulse duration should be of a magnitude such that the induced stress
waves have a suitable wavelength. A standard 20ns pulse induces a
20MHz ultrasonic wave in steel [136].
3.1.3.4. Laser Interferometry
Lasers can also be used to measure surface displacements with high
accuracy. This can be achieved by two different methods, interference
between an incident and reference beam providing instantaneous
displacement measurements or a second arrangement measuring the
change in frequency of the reflected incident beam gives good velocity
measurement. As non contact methods lasers have the advantage over
standard piezo measurements as the laser does not interact with the
ultrasonic field.
84
The basic interferometer setup used is shown in Figure 3.6. A laser
beam is fired at a beam splitter. Part of the beam is reflected off a fixed
mirror and the remaining beam is reflected off the sample surface. The
two beams are recombined and then directed to the detector surface.
As the sample surface moves the path length of the measuring wave
changes. This causes a change in the interference of the two light
beams which is measured by the detector [136].
To reduce errors associated with a laser interferometery measurements
there are a number of important factors to consider with the
experimental setup. Firstly ensure external vibrations are eliminated,
this is most easily achieved using an air table.
If the sample is measured through glass it is important to have the
window at an angle off parallel to the sample surface to reflect this
portion of the signal away from the vibrometer. However the sample
surface should be as close to perpendicular as possible as this
minimises speckle interference [137]. Speckle interference arrises from
a surface roughness on the scale of the impinging wave causing the
reflected waves to interfere. The interference pattern changes as the
surface vibrates causing the signal to fluctuate, this problem can be
reduced by slight defocusing of the beam[138].
85
Figure 3.6 Michellson interferometer
3.1.4. X-ray Diffraction
XRD is a technique used to determine the crystal structure of materials
and is used in this study to characterise different graphitic
microstructures. This study uses two x-ray techniques for
characterisation, powder diffraction and textural analysis.
Powder diffraction is a very powerful technique and can be used to
establish many aspects of crystal structure including lattice parameters,
crystal size, strains and dislocation densities. During this research
various graphite grades have been measured using XRD in order to
calculate the lattice parameters and crystal size
Textural analysis is a technique used to determine the preferred
orientation within a sample. This is important to this study to gain an
insight into how the initial arrangement of crystals affected subsequent
dimensional changes under intercalation conditions[139].
Laser
Detector
Fixed Mirror
Moving
Mirror
86
All XRD measurements conducted for this research were carried out
using the Philips X’Pert modular diffractometer shown in Figure 3.7.
This is a very versatile piece of equipment and can be setup for powder
diffraction measurements and texture measurements. The x-rays are
produced from a cobalt anode with a wavelength of 1.7902Å.
Figure 3.7 Philips X’pert modular diffractometer
3.1.4.1. Lattice Parameters
X-rays have wavelengths of a similar magnitude to interatomic spacing
and are therefore diffracted. The interaction of x-rays and atoms is
complex, however the problem has been simplified by William Bragg
[140] who proposed the schematic shown Figure 3.8 which forms the
basis of all XRD.
Figure 3.8 Schematic representation of diffraction by a crystal[39, 141]
Incident
rays
Reflected
rays
87
The schematic shown in Figure 3.8 describes the Bragg equation where
the lattice spacing of hkl planes can be calculated by measuring the
angle of peak intensity known as the Bragg angle, Equation 3.3.
Equation 3.3
where dhkl is the lattice spacing for the hkl lattice plane, lambda is the
wavelength of incident x-ray and sinθ is the angle of the reflected x-ray
[141]. Figure 3.9 details some of the important hkl planes in graphite.
Figure 3.9 Schematic of hkl planes[20]
3.1.4.2. Crystallite Size
The size of crystals can be determined to a first approximation using the
Scherrer equation [142]. The Scherrer equation given in Equation 3.4
gives the lower bound for crystal size. The crystal thickness (t) is given
by relating the incident wavelength to the broadening of a peak in the
xrd spectra. The peak broadening is quantified by measuring the peak
full width at half maximum (FWHM).
88
Peak broadening comes about from x-rays reflecting at slightly differing
Bragg angles which changes the destructive interference pattern. Peak
broadening appears due to a number of reasons; instrumental
broadening, strain broadening as well as size broadening. Instrumental
broadening can be removed by appropriate use of a standard, however
size and strain broadening are more difficult to separate. Size and strain
broadening are closely linked and therefore the Scherrer equation
should be used as a lower bound[141] for crystal size. This work utilised
a silicon standard in order to determine the instrumental broadening.
BBt
cos
9.0
Equation 3.4
3.1.4.3. Texture Analysis
The preferred crystal orientation of crystals is different for different
graphite grades and is strongly dependant on the manufacturing
process and raw materials used. The orientation can be measured by
XRD textural analysis, where the sample is rotated with respect to the
incident beam. The XRD is focused on a particular peak and the
variation in peak intensity is measured. A high peak intensity means
that a large number of crystal planes are orientated perpendicular to
this direction where as a low intensity means there are few planes in
the corresponding orientation[143]. Bacon uses this method to derive
an anisotropy factor for nuclear graphite, Equation 3.5. By focussing on
the variation in intensity of the 002 plane[144] he predicts the equation
could be used to predict the performance of graphite in irradiation
conditions.
89
2
0
2
2
0
3
..
..
.sin.cos).(
.sin).(
2
1
..
..
dI
dI
CD
CD
GW
GA Equation 3.5
Here Φ is the azimuth angle and I(Φ) is the intensity at that angle and
D.C.A.G./ D.C.W.G. is the predicted Bacon Anisotropy Factor (BAF).
3.1.4.4. Pycnometry
Pycnometry was carried out using a Micrometrics AccuPyc 1340
analysis system shown in Figure 3.10. Pycnometry is a technique which
measures the volume of a sample. This is achieved by placing a sample
in a chamber at ambient temperature and pressure, and, upon closing
the chamber, the pressure is increased. Adjacent to the sample cell is
another cell of a calibrated volume, a valve is released allowing the gas
to escape in to the second chamber. By measuring the subsequent
pressure the volume of the sample and the closed porosity can be
calculated with Equation 3.6[145].
12
1
g
g
EXPCELLSAMP
P
P
VVV
Equation 3.6
where VSAMP, VCELL and VEXP are the volume of the sample, sample cell
and expansion cell respectively. P1g is the chamber pressure at the start
90
of the experiment i.e. ambient and P2g is the pressure once the
expansion chamber has been opened.
Figure 3.10 Micrometrics pycnometer
3.2. Experimental Rigs
3.2.1. Design of experimental rig to measure dimensional change of
bulk material
Experiments to measure the dimensional change induced by
intercalation of bromine were carried out using an experimental rig
based on work by Brocklehurst[63]. The vast majority of the design
work was carried out by Miss Perrin as part of her MSc thesis[146].
Figure 3.11 shows the resulting experimental setup.
The main design aspect to this rig is the design of the spring. Previous
work of this type have used quartz springs[63, 118, 147] as quartz will
remain chemically and structurally uncompromised in the strong
oxidizing atmosphere. Unfortunately it was not possible to obtain a
suitable quartz spring, therefore it was decided that tantalum, another
material unaffected by bromine, would be used. The tantalum springs
91
were made by hand and calculations showed that a spring radius of
25mm with a wire diameter of 0.6mm and 21 turns would provide the
necessary deflection across the anticipated mass change[146].
For initial experimentation with the experimental set up, a flask heater
was used to control the temperature of the bromine. This was found to
be of little advantage experimentally whilst increasing the risks
associated with the experiment and was therefore disregarded for data
collection runs.
Figure 3.11 Dimensional Change Rig
3.2.2. Design of experimental rig to measure microstructural
dimensional change
An experimental rig was built to enable tomography scans to be made
of brominated graphite samples in order to gain an understanding of
dimensional change within the heterogeneous microstructure of
nuclear graphite. The first point to consider was the selection of a
suitable material for the sample container. For safety the rig must be
92
stable in a heavily oxidising environment; however for the best results
the rig must absorb as few x-ray photons as possible. A rig which
absorbs a high number of photons would result in noisy data at best
and no data at worst.
With this in mind there were two candidate materials for the rig, glass
and PTFE. The energy range of photons of the tomography beam line at
the Swiss Light Source (SLS) are in the 10keV range[148]. At this energy
the absorption coefficients of glass and PTFE are 1.71 cm2/g and 0.68
cm2/g respectively, Figure 3.12. The attenuation coefficient is defined in
Equation 3.7.
)/ln(/ 0
1 IIx Equation 3.7
where x = ρt is the density times the sample thickness. The thinnest
glass available for the rig was 1mm thick. Although thin layers of PTFE
have poor structural integrity it is possible to lend support by applying a
thin coating of PTFE to an aluminium support. The absorption
coefficient of aluminium at 10KeV is relatively high, 2.62 cm2/g. It was
possible to obtain aluminium tubes of 0.5mm thickness and apply a
PTFE coating of 25μm.
93
X-ray attenuation coefficients of potential rig materials
1.00E-02
1.00E-01
1.00E+00
1.00E+01
1.00E+02
1.00E+03
1.00E+04
0.00 0.01 0.10 1.00 10.00 100.00
Photon Energy (MeV)
u/p
(c
m^
2/g
)
Aluminium
PTFE
Glass
Figure 3.12 X-ray attenuation coefficients of candidate rig materials[149]
Table 3.1 shows the theoretical loss of beam intensity after travelling
though the potential candidate materials. The logarithmic relationship
between material thickness and attenuation means that it is more
important to use the thinnest materials possible rather than those with
the lowest attenuation coefficient and therefore aluminium with a PTFE
coating was used.
Table 3.1 Theoretical loss of x-ray intensity due to rig
3.
Attenuation coefficient
(cm2/g)
Material thickness
(mm)
Density
(g/cm2) I0/I
PTFE 0.68 0.5 2.2 2.11
Aluminium 2.62 1 2.7 1181
Glass 1.71 3 2.23 92958
The second aspect to consider was the sample dimensions. It was
considered important to obtain the highest resolution possible in order
94
that very small strains may be measured. The available options are
given in Table 3.2. The best option would be 0.37µm, unfortunately, it is
not possible to machine samples to such high specs. Therefore, a
compromise was reached with the area of interest of the sample being
1mmØ. A base was added to the sample to provide stability as shown in
Figure 3.13.
Table 3.2 Microscope objectives available on TOMCAT beamline[148]
Magnification Field of View
(mm2) Pixel Size
(µm2)
1.25 12.1 x 12.1 5.92 x 5.92
2 7.5 x 7.5 3.7 x 3.7
4 3.7 x 3.7 1.85 x 1.85
10 1.5 x 1.5 0.74 x 0.74
20 0.75 x 0.75 0.37 x 0.37
Figure 3.13 Tomography sample
To maximize the use of the allocated beamtime it was decided to stack
samples in the rig. The sample stage at TOMCAT has 25mm vertical
motion; therefore all samples sat within this range. Below the samples
a bromine containment vessel was located. The bromine vessel allowed
95
the bromine to be released at a time of the experimentalists’ choosing,
allowing tomographic scans of unbrominated specimens to be taken.
To allow the release of bromine to be controlled by the experimentalist
a glass vial with a stopcock was specifically manufactured for the task.
The vessel height had a strict dimensional specification of 55mm as this
was the height required for the sample when the sample stage was at
its lowest. The final design is shown in Figure 3.14. To ensure the design
did not leak the PTFE based grease Lox-8 was used to seal all joints.
Figure 3.14 Experimental rig for tomographic scans of bromine intercalated graphite
3.2.3. Design of experimental rig to measure Young’s modulus change
of brominated graphite
96
To measure the change in Young’s modulus of brominated graphite
samples it was necessary to construct a rig which would remain stable
in a highly oxidising environment whilst providing good access to the
lasers used to induce ultrasonic waves and measure their arrival on the
opposing sample surfaces. From the experience gained in previous
experiments it was decided that the bulk of the rig would be made from
PTFE and that Lox-8 grease would be used to seal the rig.
The first factor to consider was the type of laser used to induce
ultrasound. The shorter the wavelength of the impact laser the higher
the proportion of energy that is absorbed by the sample surface and
therefore the more efficient the generation of ultrasound. This is
because the reflectivity of a surface is related to the wave length of the
incoming photons [136]. Care must be taken however as shorter
wavelengths will induce ablation at lower fluence [150]. The laser
eventually chosen to induce the ultrasound was a Nd:YAG laser which
produces photons with a wavelength of 1064nm.
A coating was applied to the Nd:YAG access window to reduce the
reflection and ensure the maximum possible amount of energy reached
the sample surface. Argon coated windows for the rig were purchased
from Edmund Optics. Figure 3.15 shows that the reflectivity of Argon
coated glass for photons with a wave length of 1064nm is close to zero.
The arrival of the sonic pulse on the opposing sample surface to that of
the impact laser was measured using a HeNe laser. HeNe lasers are
often used in laser vibrometry as they have good coherence properties
and well defined wavelengths[136]. The wave length of a HeNe laser is
633 nm. It was not possible to obtain a coated window exactly to suit
97
this wavelength, though Edmund Optics VIS-NIR coated glass is
reasonably good with around 1.4% reflectivity, Figure 3.16.
Figure 3.15 Reflectivity of argon coated glass[151]
Figure 3.16 Reflectivity of VIS-NIR coated glass[151]
To reduce the number of bespoke components required for the rig, the
bromine containment vessel previously used for the tomographic rig
was utilised. Two access ports were added complete with quartz
windows to make it easy to view the sample whilst aligning the lasers.
An attempt was made to collect images for digital image correlation
through these windows. However as the chamber filled with bromine it
98
became impossible to obtain images of a suitable quality. Ports are
sealed with Lox-8 grease and PTFE seals. Figure 3.17 shows the
exploded diagram of the bromination chamber.
Figure 3.17 Exploded diagram of cell to measure Young's modulus of brominated graphite
The strain of the sample was measured using a laser displacement
detector measuring the displacement of one end of the sample surface.
This requires one end of the sample to be fixed. The sample holder for
the polycrystalline samples was a PTFE base with a tantalum wire
triangle protruding out. This allowed easy access for the impact laser
and ensured that the sample expanded in the opposing direction,
Figure 3.18. The sample was allowed to slightly overhang the sample
edge so that it rested with one end close to the optical window.
99
Figure 3.18 Sample holder for polycrystalline graphite
3.3. Conclusions
This chapter details the experimental techniques and rigs that were
used throughout this study.
Experimental techniques covered are the use of sorption balances for
bulk dimensional change experiments. Tomography and DIC for
microstructural dimensional change experiments. Dimensional change
is covered in Chapter 5. The standards and theory behind DYM
measurements are discussed which are used in Chapter 6 to investigate
changes in Young’s modulus. XRD and pycnometry are covered which
have been used in Chapter 4 for microstructural characterisation of the
graphites used in this study.
A rig has been developed based upon Brocklehurst’s rig used in for his
studies into brominated graphite [28]. The rig required some
modifications due to the current availability of components. A second
rig was designed to investigate microstructural changes due to
bromination using tomography. A third rig was designed to measure
the changes in Young’s modulus that are induced by bromination.
100
4. Characterisation of nuclear graphite
Over the course of this study a number of different grades of graphite
have been examined, all of which are currently or have been used in
the past in nuclear reactors. This chapter details a number of
experiments carried out to characterise the microstructure of these
graphites. The chapter concludes with background detail on the
graphites and a summary of the main characteristic features of the
graphites.
4.1. Characterisation Results
4.1.1. Polarised optical microscopy
Figure 4.1 presents optical micrographs of the three nuclear graphites
used in this study, PGA, Pechinay and Gilsocarbon. As discussed in
Chapter 1 there are common microstructural features seen in nuclear
graphite and these are highlighted in the images.
PGA and Pechiney graphites both have pointed ‘needle like’ filler
particles whereas Gilsocarbon has large spherical filler particles. All
three graphites exhibit the different types of porosity visible at this
level of magnification, gas evolution pores and calcination cracks. The
polarised light highlights the disorder of crystallites in the binder matrix
and the order within the filler particles.
101
a) Pile Grade A
b) Pechiney
Binder Matrix
Filler
Particle
Calcination crack
Gas evolution pore
Filler
Particle Binder
Matrix Calcination crack
Gas evolution pore
102
c) Gilsocarbon
Figure 4.1 Optical mircographs of nuclear grade graphite
4.1.2. Pycnometry
The pycnometry samples used were 10Ø x 15mm. They were
manufactured by lathe, cleaned in an ultrasonic bath and then left to
dry for 2 weeks. The volume of the sample was then calculated using
digital callipers correct to two decimal places. The mass of the sample
was measured on a 2 decimal place electronic balance.
The open porosity is found as the difference in bulk volume measured
by the pycnometer and the bulk volume measured using callipers. The
closed volume is found by taking the density of graphite as
2.25g/cm3[60], the density of a graphite crystal, and comparing it to the
measured mass of the sample using Equation 4. 1[152].
Calcination crack
Gas evolution pore
Binder Matrix Filler Particle
103
1
1
100(%) C
OpenPBulk
sample
BClosedPVV
mV
Equation 4. 1
where VClosedP, VBulk and VOpenP are the volume of closed porosity, bulk
volume and open porosity as measured by the pycnometer. ρB is the
bulk density and ρc in the crystal density.
The results shown in Table 4.1 are comparable with Standring’s results
for PGA[152]. Standring found an open pore volume of 20.1% and a
closed pore volume of 5.5%. The results show that PGA has the largest
pore volume but the lowest closed pore volume. Gilsocarbon and
Pechiney which have undergone reimpregnation during manufacture
have low overall porosity but a higher volume of closed porosity
Table 4.1 Pycnometry data for selected nuclear graphites
4.1.3. Powder Diffraction
The XRD was carried out on samples dimensioned 20 x 20 x 5mm
samples. These are relatively large sample dimensions and ensured high
104
quality data collection by limiting unwanted reflections. The data was
collected at the highest resolution time allowed which in this case was
0.025 degrees with a time step of 10 seconds. This gave a minimum of
1000 counts for the smallest peak of interest, the {110}. The other main
peak of interest is the {002} has a significantly stronger reflection.
The XRD powder diffraction data, shown in Figure 4.2, Figure 4.3, and
Figure 4.4, was used to gain an understanding of the crystal structure.
First the d spacings were calculated using Braggs equation. The results
shown in Table 4.2 show that PGA has the best layer plane stacking
indicated by the low Lc value 3.91 Å, Gilsocarbon has the widest Lc
spacing of 3.94 Å. All the graphites have very similar values for a
spacing of 1.43Å.
105
0 20 40 60 80 100 120
Bragg angle (2θ)
Inte
nsit
y (a
rbit
rary
uni
ts)
{002}
{100}
{101}
{004} {110} {112} {114}{006}
Figure 4.2 XRD powder diffraction spectra of PGA
0 20 40 60 80 100 120
Bragg angle (2θ)
Inte
nsit
y (a
rbit
rary
uni
ts)
{002}
{100}
{101}
{004} {110} {112} {114}{006}
Figure 4.3 XRD powder diffraction spectra of Pechinay Graphite
106
0 20 40 60 80 100 120
Bragg angle (2θ)
Inte
nsit
y (a
rbit
rary
uni
ts)
{002}
{100}
{101}
{004} {110} {112} {114}{006}
Figure 4.4 XRD powder diffraction spectra of Gilsocarbon
Table 4.2 Powder diffraction data
To find crystal size is slightly more involved. The size contribution to the
full width at half maximum (FWHM), B struct, is found by subtracting
the standard FWHM from the sample FWHM. The FWHM describes the
width of a peak at half of its maximum height as shown in Figure 4.5. To
calculate the crystal sizes, a silicon standard was used to remove the
instrumental broadening from the measurement.
107
Figure 4.5 Image detailing the Full Width at Half Maximum[153]
The results given in Table 4.2 show that PGA has significantly larger
crystals than the other graphites (425 x 369 Å). This figure is almost
twice that of Pechinay and Gilsocarbon with dimensions of 293 x 283 Å
and 235 x 241 Å respectively.
4.1.4. Textural Analysis
The XRD was carried out on samples dimensioned 20 x 20 x 5mm. The
samples were positioned such that the Against Grain (AG) direction ran
parallel to the sample surface and pointed to an azimuth angle of 0
degrees. The data was collected for the {002} and {110} peaks. The
{002} gives the orientation of the layer planes, the {110} gives the
orientation of the a-planes.
The measurements were carried out with a generator voltage of 40kV
and a tube current of 40mA. Figure 4.6 to Figure 4.8 show the raw pole
figures. Before any meaningful analysis could be achieved, correction
108
factors had to be applied. First a background correction must be
applied. The background error can come from a number of sources but
is particularly sensitive to changes in the tilt angle. By measuring a
nearby section of the XRD spectra which is known to contain no peaks
and is far enough away from the measured peak to allow for peak
broadening at high tilt angles, it is possible to adjust for changes to the
background[143].
The next correction to apply is the defocusing factor. This arises from
geometric considerations of the experimental setup. It is therefore
possible to correct for this by using a geometric correction function.
However, it is often better to use empirical data to obtain the
correction factor. This is achieved using a totally random sample as a
base line. As it was not possible to obtain a standard for this
experiment, the Gilsocarbon pole figure shown in Figure 4.8 was used.
The Gilsocarbon pole figure shows very random orientation. It is
sometimes necessary to also apply an absorption correction factor to
the data. The samples used for this experiment were thick enough, and
therefore this was not necessary [143].
The PGA pole figure shown in Figure 4.6, displays a strong orientation in
the {002} plane along the central axis of the pole figure. The {110}
109
shows strong orientation perpendicular to the axis where strong
orientation is seen in the {002} pole. The Gilsocarbon pole figure shown
in Figure 4.8, demonstrates almost no orientation and the intensity of
reflection shows almost no variation with azimuth angle. This is
matched by very little intensity variation in the {110} pole figure. This
can be confirmed quantitatively as the Bacon anisotropy factors given
in Table 4.3. Further analysis of texture data is carried out in the
following chapter.
Table 4.3 Bacon Anisotropy Factors
PGA Pechiney Gilsocarbon
Bacon Anisotropy Factor 1.4432 1.1908 1.0216
110
Figure 4.6 PGA pole figure
111
Figure 4.7 Pechiney pole figure
112
Figure 4.8 Gilsocarbon pole figure
113
4.2. Graphite Grades
4.2.1. Pile Grade A graphite
Pile Grade A (PGA) graphite was used in the British Magnox program.
This graphite was manufactured to a specification dictated by reactor
physicists in order to obtain good moderation properties (very low
absorption cross section ≤ 4.1millibarns and density ≥1.7g/cm3), which
required a low degree of impurity concentrations (ppm / bpm). The
result was very pure graphite with a large grain size and high degree of
crystallinity. The base materials are needle coke filler particles derived
from petroleum coke and a “low ash” coal tar binder pitch. This
graphite was formed by extrusion and this in combination with the
large grain size produced a highly anisotropic material.
Pile Grade A is characterised by long needle shaped filler coke particles
Figure 4.1(a). The filler particles contain calcination cracks and are
believed to form during the calcining process. In addition there are a
whole range of small cracks, nanometres in width by micrometres in
length. These are attributed to the large difference in the crystal
coefficient of thermal expansion perpendicular and parallel to the basal
planes. This difference leads to micro-cracking on cooling from the
graphitisation temperature [19]. These nanocracks tend to run parallel
to the crystal basal layer planes and are generally closed porosity (i.e.
not accessible to surrounding gas or air). As PGA is formed by an
extrusion process the needle type filler particles tend to align
themselves with the direction of extrusion, this direction is known as
With Grain (WG). The filler particles are surrounded by a binder matrix
114
which contains “flour”, that is small ground petroleum coke particles
randomly orientated mixed with coal tar pitch. The matrix is permeated
by gas evolution pores which form during the baking process[154, 155]
which tend to form open porosity. PGA has the largest open pore
volume of all the graphite grades studied in this work, measured by the
author as 23% , this is just above the quoted literature values around
19.8%[35]. The graphite also has the largest crystals size measured by
XRD as 42.5 x 36.9nm and the highest Bacon anisotropy factor 1.44.
4.2.2. Pechiney Graphite
Pechinay graphite was used in the French Magnox reactors[156]and is
comparable to PGA. It is a very pure extruded graphite with needle like
filler particles. The measured open pore volume is around 15%, the
crystallites are also smaller than PGA around 29.3 x 28.3nm. The
graphite is also less anisotropic than PGA with an anisotropy ratio of
1.19.
4.2.3. Gilsocarbon
Gilsocarbon was a grade manufactured by two graphite companies
Anglo Great Lakes (AGL) and British Acheson Electrodes Ltd (BAEL). It
was used in the British AGR reactors, Germanys Thorium High
Temperature Reactor (THTR) and as fuel supports in some of the French
Magnox reactors. The grade was developed for the more challenging
operating conditions of the AGR which were more highly rated than the
Magnox reactors. In particular a graphite was required that was
isotropic, more resistant to oxidation and with increased dimensional
stability under irradiation.
115
The graphite is based on the coke obtained on refining a natural asphalt
“Gilsonite” mined in Utah[157, 158]. The coke particles are spherical
with a lamina layered structure often referred to as ‘onion like’ in which
the crystallites tend to be orientated perpendicular to the sphere
radius. This gives a bulk material with near isotropic properties, with a
Bacon anisotropy factor of 1.02. Gilsocarbon has been measured by the
author to have an open porosity of 11% which agrees well with values
in the literature[35] and small crystallites compared to the anisotropic
graphite grades.
4.3. Conclusions
This chapter details microstructural characterisation experiments
carried out on the grades of nuclear graphite used for investigations
into the effect of bromination on changes to material properties. Three
graphites have been used PGA, Pechiney, and Gilsocarbon. PGA and
Pechiney are both highly anisotropic graphites as highlighted by their
high values for the BAF calculated from pole figure measurements. Both
PGA and Pechiney have needle like filler particles. Gilsocarbon is a near
isotropic graphite with spherical filler particles. PGA has the largest
volume of porosity within its structure followed by Pechiney and
Gilsocarbon. PGA is made of the largest crystallites with the smallest d
spacing whilst Gilsocarbon has the smallest crystallites and the largest d
spacing’s.
116
5. Dimensional Change
Graphite is subjected to extreme environments in nuclear
applications, with variables such as neutron flux and temperature
inducing anisotropic dimensional change in the crystals as has been
described in Chapter 1. Problems arising from dimensional change
effects are exacerbated by variations in the flux intensity around a
reactor core. The flux profile seen by a component is not uniform
across a reactor, or even a component and this causes variations in
the local dimensional change rates[34]. The different dimensional
change rates can lead to brick deformations such as bowing and
barrelling examples of which are as shown in Figure 5.1.
a)
b)
c)
Figure 5.1 Brick deformations caused by non uniform flux profiles a) bowing b) barrelling c) wheat sheafing
Bowing is caused by a flux profile across the component causing a
difference in expansion across the brick. The flux profile can be
present because of a number of factors including proximity to
absorbers, empty fuel channels or side reflectors. Bowing can cause
117
instability in the reactor core as wedge shaped gaps open between
bricks in a column.
Barrelling and wheat sheafing are caused by the radial flux profile of
a brick. The flux is higher towards the centre of a brick where it is
closer to the fuel. Initially there are tensile stresses around the bore
of the brick and compressive stresses towards the outer edges. These
stresses combined with the lack of axial restraint at the bricks ends
cause the brick to barrel. Wheat sheafing occurs later in the reactor
lifecycle as turnaround occurs earlier in crystals around the bore of
the brick creating a reversal in the radial stress profile in the brick.
Structural features such as keyway slots introduce sharp radii into
graphite components. The effect of irradiation induced strains at the
resulting stress concentration points can cause components to
fracture, gradually reducing the structural integrity of the core.
Dimensional change is therefore a key property in determining the
operational lifetime of reactors, should the effect become too
considerable the performance, structural integrity and ultimately the
safe operation of the reactor are compromised.
This chapter aims to gain an understanding into how changes in
crystal volume directly affect the graphite microstructure by using
bromine intercalation to simulate irradiation damage. The effects of
bromine intercalation on HOPG and polycrystalline graphites are
measured using Brocklehurst’s methods[63]. Here the work is
118
furthered by using x-ray tomography and modelling to gain an
understanding of microstructural changes in damaged graphite. High
resolution tomography is a powerful technique which is used to gain
an understanding of how microstructural features affect the
intercalation of bromine and how the development of the
intercalation compound drives dimensional change of the bulk
structure. The modelling based on the techniques of Sutton and
Howard[46] provides an insight into processes which are occurring
below the resolution of tomography.
5.1. Dimensional Change of Nuclear Grade Graphite by Bromine
Intercalation
Using the experimental rig shown in Figure 5.2, it was possible to
understand bromination on the bulk structure of graphite. The
bromine used was analytical reagent grade, a grade that is
sufficiently pure for chemical analysis but is by no means the purest
bromine available. The bromine is allowed to evaporate at room
temperature and pressure in a sealed glass column which will
equilibrate with a vapour pressure of 223 hPa[159].
119
Figure 5.2 McBain Sorption Balance[63]
5.1.1. Calibration of the spring for sorption balance
As described in Section 3.2.1 the experiment uses a McBain Spring
Balance[118] to measure the sorption of the sample. This is achieved
by hanging a graphite sample from a spring. The springs were
designed such that the anticipated change in mass would allow the
fullest range of the travelling micrometer to be used[146].
The springs were calibrated hanging weights of known mass off the
end of the spring. The weights were measured on a digital balance
accurate to milligrams. The spring was hung from a clamp stand and
a small piece of masking tape was stuck to the bottom of the spring
as a marker. The height of the marker was measured with a travelling
micrometer. The resulting curves given in Figure 5.3 and Figure 5.4
Travelling Microscope
Graphite
Sample
Bromine
Spring
120
show the springs to have a very linear response over the mass range
of interest with R2 values of 0.9976 and 0.9949. The curve for the
polycrystalline experiment does not lie completely within the
expected error bounds. Therefore, there has been an
underestimation of some associated errors namely the linearity of
the spring. This is most likely due to the fact that the spring was
handmade and so the coils won’t all be parallel.
Figure 5.3 Calibration of spring for weighing polycrystalline samples
Figure 5.4 Calibration of spring for weighing HOPG samples
121
5.1.2. Dimensional change experiments
The dimensional change experiments were carried out using HOPG
and polycrystalline graphites. HOPG was used as an approximation to
single crystal graphite. The polycrystalline graphites used were PGA,
Pechiney and Gilsocarbon chosen for differences in their respective
microstructures.
Measurements are carried out on the samples prior to starting the
experiment. The mass of the sample is measured on a digital balance
accurate to milligrams and the dimensions are measured with
callipers. The graphite sample is then attached to the spring and
carefully placed in the glass column. Care is taken to ensure that this
is done slowly to prevent the sample oscillating too much. As soon as
any oscillations have stopped two height measurements, highlighted
in Figure 5.5 , are taken with a travelling microscope. These
measurements are repeated at time intervals until the end of the
experiment.
Figure 5.5 Schematic of McBain Spring Balance
h1
h2
1500mm
0mm
Orientation of
travelling
micrometer scale
122
The dimensional change of the sample is calculated by comparing the
dimensions of the original sample to those of the sample at each
time increment using Equation 5.1, where h1 and h2 are the
measurements taken at each time interval and h1t0 and h2t0 are the
initial height measurements taken. For the first measurement, the
height of the sample is compared to the length measurement carried
out with callipers. This showed there was no measurable dimensional
change occurring between the sample entering the bromine chamber
and the spring stopping oscillating, Therefore h1t0 and h2t0 are taken
as the length measurements at t0.
0
0
21
2121..
tto
tto
hh
hhhhCD
Equation 5.1
The amount of bromine absorption that has occurred is calculated as
the molar ratio of bromine and carbon present in the sample.
Equation 5.2 gives the equation used to make the calculation. Here k
is the spring constant measured in Figure 5.2 or Figure 5.3, M(C) and
M(Br) are the molar masses of carbon and bromine and mt0 is the
mass of the sample measured on the digital balance.
)(
)()11(]/[
BrMm
CkMhhCBr
to
to Equation 5.2
5.1.3. Dimensional Change of Highly Orientated Pyrolytic Graphite
Single crystal measurements were carried out using 12 x 12 x 4mm
HOPG grade ZYH obtained from Momentive Performance. Selected
properties of the graphite are given in Table 5.1. HOPG is not strictly
123
speaking a single crystal, it is in fact a polycrystal made up of very
well aligned crystals. The mosaic spread is a number given to quantify
the alignment of the crystals as shown schematically in Figure 5.6.
Relative to other grades available this is a poor grade of HOPG.
However it was not possible to obtain a sample with such large
dimensions of a better grade. A higher degree of mosaicity means the
properties will slightly deviate from that of a perfect single crystal. It
was decided though, that larger dimensions rather than a better
grade would have a more significant effect on reducing the overall
error in the experiment.
The sample is shown schematically in Figure 5.7 to highlight how axes
are labelled with respect to the sample. The a-axis is parallel with the
graphite layer planes and the c-axis is perpendicular to the layer
planes.
124
Table 5.1 Properties of ZYH HOPG
ZYH grade HOPG[160]
Density 2.255-2.265g/cm3
Spacing of {002} planes 3.355-3.359Å
Thermal Expansion a axis – slightly negative
c axis – 20 x 10-6 (20 - 120°C)
Electrical Resistivity a axis – 3.5 – 4.5x10-5Ωcm
c axis – 0.15 – 0.25 Ωcm
Mosaic Spread 3.5° ±1.5°
Figure 5.6 Schematic of crystal arrangement in HOPG
Figure 5.7 Schematic of HOPG sample with
orientation of axes shown
The results of the HOPG dimensional change experiment are shown
in Figure 5.8 and tabulated in Table 5.2 . The a-axis and c-axis
measurements were recorded on two separate pieces of graphite;
unfortunately it was not possible to measure the two dimensions at
once with the available equipment.
There is a very large expansion in the c-axis with little bromine
absorbed. As discussed in Chapter 2 this is due to bromine creating
interstitial layers in the graphite. The bromine progressively opens
the graphite planes as staging progresses in the structure. The
c
a
4mm
12mm
125
outermost layers become fully brominated first as the boundary of
the sample has lower elastic restraint[96].
There are three curves plotted with the c axis expansion data. The
solid blue line is the theoretical dimensional change curve derived
from the results of Eklund [28], and shown in more detail in [28]. The
dotted red line is a linear best fit curve to all but the first data point.
The black dashed line is a binomial best fit curve including all data
points.
The theoretical curve starts at the origin and ends at the maximum
bromine to carbon ratio C8Br or 12.5%.The dimensional change
induced in a unit cell with the maximum bromine concentration is
given in Equation 5.3, where D.C.Theory is the theoretical dimensional
change, dc is the d spacing between two graphite layers and dCBr is
the spacing between two graphite layers intercalated with bromine.
100..
C
CBrCTheory
d
ddCD
Equation 5.3
The two curves which fit the data describe two different scenarios.
The red linear curve fit implies that the first data point is erroneous.
The gradient of the theoretical expansion rate and the linear curve fit
are very close. The binomial curve has a superior R2 value suggesting
a better fit to the data.
126
y = 16.33x - 5.5978
R2 = 0.9492
y = 0.1961x - 0.2179
y = 16.393x
R2 = 1
y = 3.5784x2 + 6.9335x + 0.1539
R2 = 0.99
-5
0
5
10
15
20
25
30
-2 0 2 4 6 8 10
% Br/C
% S
trai
n
c axis
a axis
c axis theory
Figure 5.8 Dimensional change of bromine intercalated HOPG
Table 5.2 Tabulated Results of HOPG dimensional change
Time
step
h1
(cm) h2 (cm)
Dimensional
Change (%) %[Br/C]
a axis 0 10.897 3.372 0 0
1 10.703 3.18 -0.02676 3.520053
2 10.638 3.005 1.444816 6.728434
3 10.52 2.885 1.471572 8.928467
c axis 0 8.032 7.488 0 0
1 8.009 7.435 11.45631 0.971681
2 8.005 7.415 14.56311 1.338353
3 8.015 7.405 18.4466 1.521689
4 8.02 7.4 20.38835 1.613357
5 8.03 7.395 23.30097 1.705025
6 8.031 7.389 24.66019 1.815027
127
The curve fitting to the data suggests two different possible physical
processes. The linear curve suggests that HOPG is very close to an
ideal crystal expanding within the bounds of error. The binomial
expression puts forward the possibility that there is porosity within
HOPG and this is accommodating some initial expansion. Figure 5.9
shows the microstructure of HOPG and there does appear to be
Mrozowski cracks present.
Table 5.3 shows the steps in calculating a theoretical value for the
mass of bromine required for the measured expansion. By taking the
dimensions of the bromine layer in a stage II bromine intercalation
compound unit cell from the work of Eklund et al[161], it is possible
to extrapolate the mass of a complete mono-layer of bromine atoms
adsorbed to the sample surface. The interlayer spacing induced by an
interstitial layer is 7.05Å[48]. By measuring the expansion of a sample
it is possible to estimate the number of bromine layers intercalated.
Given the theoretical number of bromine layers intercalated and the
mass of a mono-layer it is possible to deduce a theoretical increase in
mass.
The theoretical mass is calculated to be 6.60g which is slightly higher
than the measured value of 6.15g. The percentage difference is
plotted against bromine concentration in Figure 5.10 . The graph
shows that for a given change in mass the measured change in length
is less than the theoretical change in length. In other words there
appears to be some accommodation of expansion which decreases as
128
the bromine concentration increases. This supports the theory that
there are Mrozowski cracks present in HOPG and they do influence
the dimensional change by restricting the measured dimensional
change.
Table 5.3 Analysis of c axis expansion
Original sample height (m) 5.44E-03
Intercalated sample height (m) 6.72E-03
interlayer spacing graphite (m)[160] 6.72E-10
interlayer spacing intercalated bromine (m)[48] 7.05E-10
Number of graphite layers 1.62E+07
Number of bromine layers 3.31E+06
Area containing 4 Br atoms (m
2)[161] 3.84E-19
Area of layer (m2) 1.44E-04
Number of bromine atoms in a layer 1.50E+15
Mass of one layer of bromine atoms (g) 1.99E-07
Theoretical mass increase (g) 6.60E-01
Measured mass increase (g) 6.15E-01
Figure 5.9 HOPG microstructure
129
-60
-50
-40
-30
-20
-10
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
[Br/C]
% d
iffe
ren
ce
be
twe
en
th
eo
reti
ca
l a
nd
me
as
ure
d
mass
Figure 5.10 Difference between theoretical and measured mass
Figure 5.8 shows that a small change in the a-axis is measured, this is
an unexpected result. It is thought that the most likely explanation
for this is that misaligned crystals are expanding in the a direction.
Given the mosaic spread is 3.5° ±1.5° it is most probable that the
average graphite plane is not parallel to the sample surface but
slightly skewed. The angle created by the expansion vectors as shown
in 5.11 suggests that the true c-axis is 0.8° of the normal of the
sample surface.
130
5.11 In plane expansion
Figure 5.12 shows dimensional change data for irradiated HOPG. The
big difference to note when comparing irradiation data to
bromination data, as shown in Figure 5.8 , is that there is no
shrinkage in the a-axis for intercalated samples. Though it may be
anticipated that there would be a Poisson’s effect shrinking the a-axis
as the c-axis expands this was not measured, therefore any
occurrence of this should be considered to be very small. The
contraction in the a-axis of irradiated specimens is considered to be
due to contraction of graphite planes caused by the creation of holes
in the lattice from displaced atoms[162]. Given the understanding of
intercalation laid out in Chapter 2 it would be unexpected to see this
occur in intercalated samples.
The irradiation data as with the intercalated data has an inflection in
the expansion curves. This suggests that in both instances there are
processes at work which either inhibit early growth or enhance later
growth in the c axis. It can be seen there is also an increase in the
contraction in the a-axis of irradiated specimens as dose increases.
This change in c-axis expansion is normally ascribed to
c expansion
a expansion
131
accommodation of c axis expansion within Mrozowski cracks. This
however fails to explain the increase in the rate of contraction seen
in the a-axis of irradiated samples. It has been suggested that the
contraction in the a-axis is due to larger vacancies being less able to
capture interstitial atoms[36]. As the dose increases there will be an
increase in the number of large vacancies and therefore fewer
instances of holes and interstitials annihilating. Should this be the
case it will also affect the expansion rate in c-axis. Given that the
increase is seen in brominated and irradiated specimens, it seems
reasonable to assume that closure of porosity is at least a
contributing factor.
-15
-10
-5
0
5
10
15
20
25
30
0.0E+00 4.0E+20 8.0E+20 1.2E+21
Dose (EDN)
% S
train
600C in c
600C in a
430C in c
430C in a
Figure 5.12 Irradiation induced dimensional change of HOPG[36]
132
5.1.4. Dimensional Change of Polycrystalline Graphite
The experimental procedure for the polycrystalline experiment is
much the same as for the HOPG experiment. The samples are larger,
75mm long cylinders with a diameter of 10mm and therefore they
are also heavier. This required the use of a different spring as
described earlier in Section 5.1.1.
Three different grades of graphite were used for the polycrystalline
experiment; PGA, Pechiney, and Gilsocarbon. The microstructural
characteristics of these materials are detailed in Chapter 3. Briefly
PGA and Pechiney are two anisotropic graphites with needle like filler
particles while Gilsocarbon is a semi-isotropic graphite with spherical
filler particles.
Figure 5.13 details the results of dimensional change of the extruded
graphites. The extruded graphites have the highest Bacon anisotropy
factor and, as this implies, there is a significant difference in the WG
and AG measurements. The Bacon anisotropy factor gives a ratio
related to the proportion of crystal planes orientated in a particular
direction and as the previous experiment shows, intercalative
dimensional change is driven by c-axis expansion. In the polycrystal
experiments the layer planes are predominantly stacked along the
AG direction and it is this direction which exhibits the largest
dimensional change.
It is possible to measure the anisotropy of PGA using both Bacons
method and by finding the ratio of dimensional change induced by
133
intercalation. The anisotropy due to intercalation is 2.74 ± 0.88, this is
double the Bacon anisotropy factor of 1.44. This suggests that
intercalative expansion is affected by factors other than just plane
orientation. This could be due to microstructural features such as
porosity. There will be a general alignment of porosity with the layer
planes, this will mean that there is a larger accommodation of
expansion between the AG direction than the WG direction which
will affect the anisotropy.
The sample of Pechiney graphite came from a fuel sleeve with
dimensions such that it was only possible to extract a sample aligned
with the grain. The rate of expansion is interesting as it appears to be
too low. The Bacon anisotropy factor for Pechiney, 1.19 is lower than
PGA 1.44. It would therefore be expected that the higher proportion
of misaligned crystallites would cause a higher rate of expansion WG.
Furthermore, Pechiney has a lower porosity volume than PGA.
However the expansion rates are remarkably similar. It is unfortunate
that it was not possible to measure the expansion in the opposing
grain direction to gain a fuller understanding of Pechineys
dimensional change characteristics. This is most likely due to
accommodation of expansion by porosity as will be discussed later.
134
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3
% Br/C
% S
tra
in
PGA (AG) 1
PGA (AG) 2
PGA (WG) 1
PGA (WG) 2
Pechinay
Figure 5.13 Dimensional change of extruded polycrystalline graphites
Figure 5.14 shows the dimensional change induced in the semi
isotropic graphite Gilsocarbon and compares it with PGA (AG). It is
interesting to note that Gilsocarbon experiences a slightly higher rate
of expansion than the PGA sample cut perpendicular to extrusion
despite PGA having the denser layer plane arrangement. This could
be due to the increased porosity in the PGA samples 27% as opposed
to 19% for Gilsocarbon.
There is a marked increase in the dimensional change rate of the
graphites as the bromine content increases. This trend is also seen
with the dimensional change of HOPG when brominated, this
suggests that a closure of porosity affects both experiments. This is
because as crystallites experience dimensional change there is
initially room to accommodate some of the expansion within
135
microstructural porosity, however as the porosity closes there is less
available space within the microstructure to accommodate the
crystal expansion. This effect will be discussed in more detail in the
following section.
Figure 5.14 Dimensional change of PGA and Gilsocarbon
Figure 5.15 shows the dimensional change induced in irradiated PGA
and Gilsocarbon specimens. The PGA data presented is for AG and
WG samples irradiated at 600°C, the Gilsocarbon data presented has
been irradiated at 430°C and 600°C.
The important difference between intercalation and irradiation
damage is that intercalation damage increases in size whereas
irradiation initially causes a decrease in dimensions. There are two
important reasons for this; first intercalation adds mass to the
sample whereas irradiation damage rearranges the existing mass and
136
second the a-axis contraction of graphite crystals in irradiation
damage is not simulated with intercalation. The a-axis contraction is
a point worth considering because it implies that the stress
generated in the a-axis are considerably stronger than in the c axis.
Despite the larger dimensional changes induced in the c-axis of HOPG
specimens, the a-axis shrinkage is the dominant term. This is because
the c-axis expansion can be accommodated initially within the
Mrozowski cracks however the relief mechanism in the a-axis, creep,
has less influence.
When intercalated, Gilsocarbon expands at a higher rate than PGA
AG samples. This is opposite to what occurs under irradiative
conditions. This suggests that the a-axis shrinkage has a more
significant effect within the Gilsocarbon microstructure. Under pure
expansion conditions Gilsocarbon will expand at a higher rate than
PGA. However, introducing a-axis shrinkage causes PGA to expand
quicker. This could be the result of the spherical filler particles in
Gilsocarbon, a-axis shrinkage will generate hoop stresses which
oppose radial c-axis expansion. PGA filler particles on the other hand
expand relatively freely in the c-axis and shrink in the a-axis.
137
-10
-8
-6
-4
-2
0
2
4
0.00E+00 1.00E+22 2.00E+22 3.00E+22
Dose n cm-2 (EDN)
Dim
en
sio
nal
Ch
ange
(%
)
PGA WG 600C
PGA AG 600C
Gilsocarbon 430C
Gilsocarbon 600C
Figure 5.15 Dimensional change due to irradiation[35]
5.1.5. Analysis of Dimensional Change
As the previous section shows, dimensional change due to
intercalation and irradiation in polycrystalline graphite is a complex
process. There are many influencing factors; the accommodation of
crystal expansion in nanoscale microcracks; the shape and
orientation of filler particles and the distribution of microporosity. By
modelling these factors an insight can be gained into the relevance of
each factor.
The range of open pore volumes in a sample can be measured using
Mercury Porosimetry. Mercury porosimetry is an experimental
technique whereby a sample of graphite is placed in mercury under
138
increasing pressure. As the density increases the mercury penetrates
smaller and smaller pores. By measuring the change in bulk volume
of the mercury, it is possible to gain an insight into the range of
porosity sizes within the graphite microstructure. The plot given in
Figure 5.16 shows that graphite has a large range of pore size from
tiny lenticular nano-cracks to large pores present in the binder and
filler particles [20].
Furthermore Figure 5.16 demonstrates how the range of porosity in a
given grade of graphite can be controlled by manufacturing
processes. Grade AGOT was the graphite used in Chicago Pile 1, it has
a relatively large grain size and impregnation has been carried out.
The effect of this is a large range of porosity sizes including some very
large pores. The grade R-0018 has been baked at high temperature
and under a high pressure, producing a denser graphite with no
measurable pores above 75000 Å. The grade R-0013 is similar to R-
0018 though the grain size is smaller which has the effect of reducing
the average pore size further as well as reducing the proportion of
pores in the 30000 – 75000A range. It has already been suggested in
Section 5.1.3 that pores have an effect on the dimensional change of
HOPG. This section will examine this further.
139
Figure 5.16 Porosity distribution base graphite[20]
To try to understand the role of crystallite orientation and
accommodation on dimensional changes in bromine, a model has
been developed based on the work of Sutton and Howard[163] as
introduced in Chapter 1. Sutton and Howard proposed a model to
relate the crystal coefficient of thermal expansion to the bulk thermal
expansion of PGA graphite. Given in Equation 1.3 and Equation 1.4
they used the Bacon Anisotropy Factor in conjunction with
measurement of crystal CTE to estimate the accommodation porosity
in expansion of the bulk material.
140
acGW CDKCDKCD ...... 21.. Equation 1.3
acGA CDKCDKCD ...... 43.. Equation 1.4
The anisotropy factors used by Bacon are derived from transmission
measurements taken from a single azimuth angle. However as
equipment has improved, gathering texture data with the sample in
an Eulerian cradle has become a standard test, giving more complete
texture data. The transmission measurements used by Bacon gives
the texture data for a single tilt angle whereas the use of a Eulerian
cradle allows data to be collected for a much larger range of tilt
angles. This gives a more complete measurement of the texture in
three dimensions.
The model requires the input of three pieces of information, the
dimensional change of the crystal, the polycrystalline texture data
and the dimensional change of the polycrystalline material. Two
different sources of crystal dimensional change data are used; the
HOPG data given in Section 5.1.3, and using the unit cell dimensions
given by Eklund to derive dimensional change as also discussed in
Section 5.1.3[90]. This is because HOPG data has an intrinsic
accommodation factor. The texture data is given and discussed in
Chapter 4 and the polycrystalline dimensional change data is from
Section 5.1.4.
Equation 5.4 and Equation 5.5 give the theoretical dimensional
change curve for a crystal derived in Section 5.1.3 [28] whilst
141
Equation 5.6 and Equation 5.7 give the measured HOPG dimensional
change curves shown in Figure 5.8. The equations are used to provide
single crystal dimensional change data for the polycrystalline model.
0.. TaCD Equation 5.4
]/[393.16.. CBrCD Tc Equation 5.5
0.. MaCD Equation 5.6
1539.0]/[9335.6]/[5784.3.. 2 CBrCBrCD Mc Equation 5.7
where D.C.x is the dimensional change in the a-axis or c axis and
[Br/C] is the molar ratio of bromine to carbon content in the sample.
As discussed in Section 5.1.3 it is thought that the measured
dimensional change in the a-axis is an artefact of the HOPG sample
microstructure. Therefore the model assumes that D.C.a-HOPG is zero.
The orientation of the stacked layer planes, the c-axis, is determined
by the {002} pole figure of polycrystalline graphite grades. It is
important that the texture data is measured in the correct
orientation, the AG direction should point to zero degrees in the pole
figure.
The pole figure data is defined in polar co-ordinates and describes
the orientation of the crystal axes. The crystal axes need to be related
to a global coordinate system for further modelling. This work uses a
cartesian co-ordinate system for the global co-ordinate system.
142
Figure 5.17 shows the relationship schematically. The angle between
a and b is defined as the tilt angle ψ and the angle between b and c is
defined as the azimuth angle φ. The model also requires the
calculation of θ the angle between a and c.
Figure 5.17 XRD texture orientations
Depending on the polycrystalline orientation to be modelled, WG or
AG, a step function must be applied to the data to ensure the
calculation of theta gives a positive sign. This is because planes
orientated in a direction that would give “negative expansion” would
still have a positive effect on dimensional change. Equation 5.8 gives
the function to model the data for AG and Equation 5.9 gives the
function for modelling WG.
c b
a
Against
Grain Angle of
Measurement
b
d
a
143
360180for ,180
1800for , Equation 5.8
360270for ,270
270180for ,270
18090for ,90
900for ,90
Equation 5.9
Having modified the angles, Equation 5.10 is used to calculate the
angle θ which is the angle between the axis of the measurement and
the axis of interest.
)90()tan(tan
222
1 Equation 5.10
Figure 5.18 and Figure 5.19 show the calculated angle theta for all
instances of XRD intensity measurements. Figure 5.18 shows theta
for AG models, which shows that at azimuth angles 0° and 180° the
crystals are aligned perpendicular to the axis to be modelled. As the
tilt angle decreases all planes regardless of the azimuth angle
become less aligned.
Figure 5.19 shows theta for WG modelling. This shows that when the
azimuth angle is 90° or 270° the crystal planes are orientated
perpendicular to the axis to be modelled, again as the tilt angle
decreases the planes become less aligned.
144
Figure 5.18 Theta derived for against grain calculation
Figure 5.19 Theta derived for with grain calculation
Multiplying the cosine of theta with the proportion of crystal planes
for each theta value gives their contribution to expansion in the axis
of interest. The proportion of crystal planes facing a given angle is
defined by the normalised texture measurement.
145
Figure 5.20 and Figure 5.21 show the effect of applying the PGA pole
figure data given in Chapter 4 to the theta values. This shows how an
anisotropic material such as PGA will react to the two different theta
functions. The against grain plot, Figure 5.20 , has a large proportion
of crystals aligned with low theta angles giving a large potential for
dimensional change. Figure 5.21 on the other hand has a small
proportion of crystals aligned with the low theta angles therefore
giving low dimensional change potential.
Figure 5.20 Effect of crystal orientation on dimensional change against grain
146
Figure 5.21 Effect of crystal orientation on dimensional change with grain
Equation 5.11 predicts the dimensional change of a polycrystalline
material taking the assumption that there are no porosity effects.
Equation 5.12 applies an accommodation porosity factor to give a
more accurate prediction. Alternatively Equation 5.12 can be used
with known results for polycrystalline data to calculate the
accommodation porosity factor.
cos.... mod ICDCD cel Equation 5.11
cos.... .. ICDCD cGW Equation 5.12
Figure 5.22, Figure 5.23 and Figure 5.24 give the change in
accommodation factors with bromine concentration for PGA,
Gilsocarbon and Sutton and Howards thermal expansion results[46].
Sutton and Howards work was carried out on PGA and it can be seen
147
there is rough agreement between the initial HOPG accommodation
factors shown in Figure 5.19, both models are derived from HOPG
measurements. Sutton and Howards accommodation factor appears
to increase at a faster rate pointing to differences in the manner in
which thermal expansion interacts with pores compared to
bromination. Due to the nature of intercalation it is not possible to
calculate the α accommodation factor.
Figure 5.24 shows the accommodation factors Sutton and Howard
measured for PGA [28]. It shows the accommodation factor α to be
more significant than γ for adjusting the thermal expansion model.
This implies that there is a larger contraction in the bulk material
than the shrinkage in the a-axis of the crystal implies. This suggests
that there is a significant Poisson’s effect from the expansion in the c-
axis. There is however a large amount of scatter in the results for α
and it is likely that this is due to large errors arising from the very
small thermal strains which must be measured.
The two methods of deriving the accommodation factor, using that
derived from the unit cell or that derived from HOPG measurements
give different rates of change. Accommodation appears to decrease
with the HOPG derived value whilst it increases for the unit cell
derived values, this is true for both PGA and Gilsocarbon. This is due
to the different crystal expansion rates of the two methods. The unit
cell method says that there will be a linear increase in the crystal c-
axis with intercalated bromine whereas the measured HOPG c-axis
148
expansion value is low initially with an increasing rate of change as
bromine concentration increases.
The measured HOPG accommodation factors have an inherent
accommodation factor which increases (provides less
accommodation) as bromine content increases. The HOPG
accommodation factors for polycrystalline graphites decrease,
provide more accommodation, as the bromine concentration
increases. This suggests either there are more Mrozowski cracks in
polycrystalline graphites, or as bromine concentration increases, the
larger calcination cracks and gas evolution pores start
accommodating expansion or a combination of both.
The accommodation factor for PGA is strongly affected by
orientation. The accommodation factor is around 2.7 times larger in
the AG direction than the WG direction. This is significantly higher
than the bacon anisotropy factor of 1.44. This suggests either
Mrozowski cracks form with a preferred orientation or Mrozowski
cracks are evenly distributed around all crystals but that stresses
generated by the orientation of local crystals affects accommodation.
In other words, large regions of aligned crystals as found in filler
particles are all expanding in the same direction and are only
bounded at the outer edges of the filler particles, so easily fill internal
cracks. The HOPG (AG) curve shows no initial change in value until 0.5
[Br/C].
149
Figure 5.22 PGA bromination accommodation factors
y = 0.0177x2 - 0.1367x + 0.4994
R2 = 0.9995
y = 0.0101x + 0.2367
R2 = 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 1 2 3 4[Br/C]
Acc
om
od
atio
n F
acto
r
hopg (AG) accomodation
hopg (WG) accomodation
XRD (AG) accomodation
XRD (WG) accomodation
Figure 5.23 Gilsocarbon bromination accommodation factors
[Br/C]
150
y = 0.7196x + 0.2008
y = 0.2063x + 0.3227
0
0.5
1
1.5
2
2.5
0.1
7
0.1
9
0.2
1
0.2
3
0.2
5
0.2
7
0.2
9
0.3
1
0.3
3
Temperature equivalent [Br/C]
Ac
co
mo
da
tio
n F
ac
tor
gamma block 1
alpha block 1
gamma block 2
alpha block 2
Figure 5.24 PGA thermal expansion accommodation factors[163]
Figure 5.25 gives the predicted dimensional change rates for PGA.
The greatest dimensional change is predicted with the extrapolated
unit cell value. When HOPG data is used, the predicted dimensional
change rate is slightly lower. This is due to the intrinsic level of
accommodation associated with the HOPG data. Applying the
accommodation factor brings the model in line with the data.
151
0
2
4
6
8
10
12
14
16
18
20
0 0.5 1 1.5 2 2.5 3 3.5
[Br/C]
Dim
en
sio
nal
Ch
an
ge (
%)
Measured Data (WG)
Measured Data (AG)
Dimensional Change (WG)
Dimensional Change (AG)
XRD Dimensional Change (WG)
XRD Dimensional Change (AG)
Dimensional Change with Accomodation Factor(WG)
Dimensional Change with Accomodation Factor(AG)
Figure 5.25 PGA predicted dimensional change
Figure 5.26 shows the modelled dimensional change curves for
Gilsocarbon graphite. The curves are shown for the predicted
dimensional change utilising both the unit cell derived factor and the
measured HOPG factor. There is good agreement between the
resulting curves. The anisotropy factor for Gilsocarbon is close to
unity, therefore there is very little difference between the WG and
AG curves, though unfortunately there is insufficient data to obtain a
comparison of the WG and AG accommodation factors.
152
0
2
4
6
8
10
12
14
16
18
20
0 0.5 1 1.5 2 2.5 3 3.5
[Br/C]
Dim
en
sio
na
l C
ha
ng
e (
%)
Gilsocarbon Measured
HOPG Dimensional Change (AG)
HOPG Dimensional Change (WG)
XRD Dimensional Change (AG)
XRD Dimensional Change (WG)
HOPG dimensional change with accomodation factor (AG)
XRD dimensional change with accomodation factor (AG)
Figure 5.26 Modelled dimensional change of Gilsocarbon
As bromine penetrates the graphite microstructure an increasing
amount of porosity is filled by expanding crystals. Figure 5.27 shows
the percentage of total predicted expansion that is accommodated
within polycrystalline microstructures. It shows there is slightly more
accommodation in Gilsocarbon than in PGA (AG). This is in agreement
with the discussion in Section 5.1.5. There is a difference in the
accommodation factors for PGA (WG) and (AG) at higher bromine
concentrations. This suggests that either there is less accommodation
porosity WG than AG or the local microstructure causes the WG
cracks to close up further. The accommodation porosity in the WG
direction comes from misaligned crystals and there are fewer of
these in an anisotropic material. Therefore there will be a larger
restraining force on these layers causing the microcracks to
accommodate more expansion. It is probably a combination of both
153
factors as the microstructural features which would cause the cracks
to close further are probably the same ones that cause the cracks to
exist in the first place.
0
2
4
6
8
10
12
14
0 0.5 1 1.5 2 2.5 3 3.5
[Br/C]
% A
cco
mo
dat
ion
Vo
lum
e
Gilsocarbon
PGA (WG)
PGA (AG)
Figure 5.27 Accommodation Volume
Figure 5.28 , Figure 5.29 , and Figure 5.30 show the effect of using
bromine intercalation accommodation factors to model irradiation
data for low and high doses respectively. The bromination data has
been scaled such that the dimensional change rate of the irradiated
and brominated data are equivalent using Equation 5.13.
]/[..
]/[
..
CBr
d
CdD
CBrd
CdD
DosecIr
cBr
Equation 5.13
Figure 5.28 shows predicted dimensional change at a low irradiation
temperature of 200°C using HOPG data given in [28]. The irradiation
data used to compare the predicted dimensional change with the
154
actual dimensional change is collected in the DIDO and PLUTO
reactors [28]. The predicted curve is slightly higher than the actual
data and this can be attributed to two factors. From the difference in
temperature of the predicted and measured data it is anticipated
that the predicted data will be slightly higher as shown in Figure 1.16
[28]. Furthermore the effect of shrinkage in the a-axis cannot be
accounted for with this method. Nevertheless there is good
agreement between the model and experimental data.
Figure 5.28 Prediction of Irradiated Dimensional Change using intercalation accommodation factors;
simulation of low neutron dose[28]
At higher irradiation temperatures the model does not work so well.
At low doses there is a small amount of expansion predicted using
the bromination accommodation factors. The values are not
unexpected as it is not possible to model the a-axis accommodation
factor and it seems reasonable to assume that these two factors
155
combine to result in the small dimensional change that is seen.
However when the model is extrapolated out as shown in Figure 5.30
it is of little use. This is because of a fundamental difference in the
two processes. When irradiated to a dose of 1.37x1021 EDN at 430°C
a c-axis expansion of 24% is induced however the volume of the
sample reduces by around 5%. Compare this to bromination data
where a [Br/C] ratio of 1.81 also induces 24% expansion in the c axis
and a corresponding 24% increase in volume.
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
-1E+20 1E+20 3E+20 5E+20 7E+20 9E+20 1.1E+21 1.3E+21 1.5E+21
[Br/C] normalised to dose EDN (n cm-2)
Dim
en
sio
nal
Ch
ange
(%
)
Dimensional Change Gilsocarbon @ 430C XRDBaseDimensional Change Gilsocarbon @ 600C XRDBaseDimensional Change 430C Irradiation
Dimensional Change 600C Irradiation
Dimensional Change Gilsocarbon @ 430C HOPGBaseDimensional Change Gilsocarbon @ 600C HOPGBase
Figure 5.29 Prediction of Irradiated Dimensional Change using intercalation accommodation factors;
simulation of low neutron dose
156
-5.00
-3.00
-1.00
1.00
3.00
5.00
7.00
9.00
0 5E+21 1E+22 1.5E+22 2E+22 2.5E+22 3E+22
[Br/C] normalised to dose EDN (n cm-2)
Dim
en
sio
nal
Ch
ange
(%
)
Dimensional Change Gilsocarbon @ 430C XRDBaseDimensional Change Gilsocarbon @ 600C XRDBaseDimensional Change 430C Irradiation
Dimensional Change 600C Irradiation
Dimensional Change Gilsocarbon @ 430C HOPGBaseDimensional Change Gilsocarbon @ 600C HOPGBase
Figure 5.30 Prediction of irradiated dimensional change using intercalation accommodation factors;
simulation of high neutron dose
5.2. Microstructural Experiment
The last two sections have shown that there are key parallels
between bromination and irradiation damage. The most important
parallel being the large disparity in single crystal and polycrystalline
volume changes due to porosity in accommodating expansion and
the orientation of crystals. To investigate the behaviour further, it
was decided to observe bromination in real time using XCT to
observe the microstructural strains due to the crystallite growth. To
the authors knowledge this had not been done before.
A bromination rig was designed for use in a high resolution
tomography experiment; the setup is shown in Figure 5.31 .
Synchrotron tomography was used primarily because the fast data
157
acquisition rate meant that the small amount of expansion which was
expected to occur during each tomographic scan, around eight
minutes, would be below that of the resolution of the camera
allowing high quality reconstructions.
The samples used were 1 x 1.5 mm. This allowed a resolution of
0.7µm, which was a compromise between obtaining the highest
resolution possible and machining constraints. The synchrotron was
setup to have a beam power of 19.5KeV. The camera collected each
image in 325ms and there were 1501 projections for each data set
meaning each data set was collected in just over eight minutes.
Once the bromination rig was prepared, it was loaded onto the
sample stage. At this point there is no bromine in the sample
chamber and a scan is performed on each sample. The stop cock is
then opened releasing bromine into the sample chamber. A scan is
then performed every 30 minutes on each sample.
The data is reconstructed using in house algorithms. The machine
was setup to use the Modified Bronnikov Algorithm (MBA) for
reconstruction [164]. However, as the bromine intercalated the
sample the MBA technique became unsuitable. The MBA algorithm is
optimised for samples with little absorption contrast, virgin graphite
being a prime example. However, as bromine enters the structure
there are large differences in absorption around the sample.
Therefore, the samples were reconstructed with the standard
absorption contrast reconstruction algorithm.
158
Figure 5.31 Bromination rig in position. Highlighted are a) X-ray source b) shutter c) rig and d) camera
5.2.1. Two dimensional Analysis
Digital Image correlation was used to analyse the two-dimensional
radiographs in order to estimate the bulk dimensional change
experienced by the samples, a technique which has been used
previously in studies of rocks[165]. This was achieved using DaVis V6
from LaVision software. An example image is given in Figure 5.32 .
The overall growth was defined as the difference in expansion of the
average displacement vector at Z=200 and at Z=900. This calculation
was performed on 100 out of 1501 of the radiographs and taken as
an average.
d c b a
159
Figure 5.32 Digital image correlation performed on PGA radiographs
The results are given in Figure 5.33 , Figure 5.34 and Figure 5.35 for
PGA, Gilsocarbon and Pechiney respectively. As with the bulk
expansion experiments described in Section 5.1.4, there is an overall
general expansion. PGA achieved the largest dimensional change of
4% followed by Pechiney 0.4% and finally Gilsocarbon 0.3%. This
shows that when all samples are in the same chamber in the same
concentration of bromine, there is a difference in dimensional
change rates. Primarily this is because the larger volume of open
porosity in the graphite makes it easier for bromine to permeate the
microstructure. Further to this is the fact that PGA has larger crystals
with better crystallinity which means that once the bromine has
160
reached a crystal for intercalation it can permeate the crystal with
less difficulty[106].
In all cases there was an initial shrinkage, this may possibly be
attributed to the endothermic intercalation reaction[28]. However,
the cooling required for the contraction observed in these
experiments would need to be very large. Therefore, the author
considers that the most likely explanation is an error introduced by
the experimental technique. An initial scan was taken with no
bromine in the sample chamber then a stopcock was released for the
bromine to enter the chamber and this may have caused a significant
movement that would be recorded by the scans. If the movement
sample moves away from the x-ray source between the two scans
the sample will appear smaller and the digital image correlation
software will record an apparent contraction. Furthermore any
rotational displacements will distort the radiograph and therefore
provide erroneous results, this can be overcome by reconstructing
the data and carrying out 3D DIC.
The PGA and Pechiney samples in Figure 5.33 and Figure 5.34 appear
to have a bilinear dimensional change curve. Though it can’t be
directly correlated to the earlier measurements as it is not possible to
know the [Br/C] of the sample, it does appear to follow a similar
trend to the AG bulk samples. The bulk dimensional change is of a
similar magnitude for PGA in the microstructural experimental rig
and the polycrystal experimental rig.
161
The dimensional change curve for Gilsocarbon is a lot more
complicated. There appears to be significant noise in the data,
though the general trend appears to be more linear than the
anisotropic graphites. The noise was caused by out of plane
movement between the images causing errors in the image analysis.
-1
0
1
2
3
4
5
0 100 200 300 400 500 600
Time (mins)
Dim
en
sio
nal ch
an
ge (
%)
Figure 5.33 Dimensional change calculated from radiographs for PGA
162
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0 100 200 300 400 500 600 700
Time (mins)
Dim
en
sio
na
l c
ha
ng
e (
%)
Figure 5.34 Dimensional change calculated from radiographs for Gilsocarbon
-3.00E-01
-2.00E-01
-1.00E-01
0.00E+00
1.00E-01
2.00E-01
3.00E-01
4.00E-01
5.00E-01
0.00E+00 1.00E+02 2.00E+02 3.00E+02 4.00E+02 5.00E+02 6.00E+02 7.00E+02
Time (mins)
Dim
en
sio
nal ch
an
ge (
%)
Figure 5.35 Dimensional Change calculated by digital image correlation for Pechinay
163
5.2.2 Three Dimensional Analysis
The PGA sample was selected for further microstructural analysis as
the sample underwent similar dimensional change to the
polycrystalline experiments. This was performed using digital volume
correlation, a technique which can take into account out of plane
displacements and remove these errors from the analysis.
Before digital image correlation could be performed, some
preprocessing of the images was required. The experimental rig was
not perfect and the sample would have displacements associated
with it that weren’t due to intercalation. These rotations were
removed using the image analysis software ImageJ.
The reconstructed image stack was resliced to obtain the image stack
as slices in the XZ plane. The images were rotated so that the sample
always remained vertical. The new Image stack was resliced to obtain
images in the YZ plane. These images were also rotated to keep the
sample vertical in this orientation as well. The images were then
resliced and into the XY plane the image stacks were cropped so that
all image stacks were the same size.
Unfortunately each of the rotation step reduces the image quality.
This is because ImageJ interpolates the new greyscale value by
rotating the old pixels and calculating the greyscale value[166]. To
reduce the effect of interpolation artifacts a bicubic filter was used.
164
A bicubic filter is a method which calculates the value of a pixel in a
modified image by interpolating the value from the surrounding
pixels. Figure 5.36 describes the process in 1 dimension. By fitting a
curve to the greyscale values of the nearest neighbour pixels the
algorithm can calculate a value for the interpolated pixel value
highlighted by the red dotted line. For image analysis this is method
is applied in two dimensions and the interpolated value calculated as
a point on a surface[167].
1 2 3 4
Pixel
Figure 5.36 Bicubic filter
Figure 5.37 details a cross section through the centre of the PGA
sample. The majority of the sample is comprised of binder matrix.
This is characterised as a region of disordered crystallites permeated
with gas dendritic evolution pores. In the top right of the sample
there is a filler particle which has aligned crystallites and lenticular
calcination cracks. The sample area highlighted is 0.9 x 0.6mm. The
165
colour of the vectors highlights the magnitude of its component into
the page. Green signifies the vector is pointing into the page 1μm and
yellow indicates 1μm out of the page.
Figure 5.37 Microstructure of PGA tomography sample, before bromination
The resulting series of images are given in Figure 5.38 . The
progression of bromine through the microstructure can be observed
through the change in grey scale of the images. In the early images
the bromine first comes into contact with the graphite but no
significant intercalation has taken place.
Calcination crack
Binder
Matrix
Gas Evolution Pores
Filler
Particle
166
After two hundred and sixty minutes, there is the first sign of
intercalation in the binder matrix, highlighted by A, but it is not until
four hundred and forty minutes that there is any significant
bromination of the filler particle, highlighted by C. At this point the
binder matrix is nearly fully brominated.
The binder is clearly brominating before the filler particle. Though the
filler particle is more ordered than the binder, there is a higher partial
pressure of bromine within the binder matrix due to the pervading
open pore network within the binder. This brings to light a problem
in using bromine intercalation to simulate irradiation damage. For a
given a uniform dose profile irradiation will damage all crystals
equally. Bromine intercalation preferentially damages crystals that
are next to pores and are easy to access.
An interesting observation is that the displacement vectors also show
that the large amount of bromine intercalated causes a low level of
expansion. The binder matrix is responsible for the early expansion of
the material. On the other hand, the small amount of bromine which
penetrates the filler particles later in the series causes a large amount
of dimensional change. This implies that the aligned crystals in the
filler particles are the main driver in bulk dimensional change,
whereas intercalation of the disordered crystals has little overall
effect.
A further interesting point to note is the pore highlighted in B. This is
a calcination crack, a long lenticular crack running parallel to the WG
167
direction. As bromine intercalation occurs the pore closes, this
indicates that accommodation of crystal expansion is not limited to
Mrozowski cracks but in the case of bromine intercalation also occurs
in the larger microporosity.
168
a) t=40 mins
First bromine can be seen adsorbing at pore edges
b) t=40 mins
c) t = 100 mins d) t = 140mins
B B
B B
A A
A A
169
e) t=200 mins f) t =260 mins First signs of bromine penetrating binder
matrix
g) t = 320 mins Binder is nearly fully brominated by contrast
there is still little bromine in the filler
h) t = 380 mins
B
B B
B
A A
A A
170
i) t=440 mins First signs of significant dimensional change
in filler particle highlighted in red circle
j) t=500 mins
k) t=560 mins
Figure 5.38 Digital Volume Correlation of PGA Bromination
B B
B
A A
A
C C
C
171
Because bromine has a higher x-ray attenuation coefficient than
graphite, regions intercalated with bromine become lighter. Figure
5.39 plots the greyscale distribution for each time step. There are
three distinct peaks on the graph; the lowest value signifies the
region with the lowest absorption which is porosity; the second peak
signifies regions of virgin graphite; the highest peak on the greyscale
axis signifies regions of graphite intercalated with bromine. It can be
seen that as the time increments increase there is an increase in the
magnitude of the bromine graphite peak and a decrease in the pore
peak. This could be due to graphite intercalated with bromine
closing porosity as well as bromine condensing within the pores.
-10000
0
10000
20000
30000
40000
50000
60000
70000
80000
0 10000 20000 30000 40000 50000 60000 70000
Grey Scale Value
Co
un
ts
t10
t40
t70
t100
t140
t200
t260
t320
t380
t440
t500
t560
Figure 5.39 Change in grayscale of brominated samples
Pore
Graphite
Bromine in
Graphite
172
5.3. Conclusions
This chapter has investigated dimensional change due to
bromination, this is important as it is a very useful way of
introducing interstitial defects, which in turn induce
microstructural defects, in a laboratory setting. The results
presented in the chapter show that the dimensional change of a
bulk material is a complex process affected by many different
factors.
The work shows that bromine intercalation of single crystal
graphite produces significantly larger strains than seen in
polycrystalline graphites. This is primarily due to porosity within
graphite. Though the graphite in the binder phase is less ordered
than filler phase it is still of a high enough graphitic quality that
intercalation occurs. Therefore, the surrounding partial pressure
of bromine is the dominant factor in determining which regions of
graphite intercalate first. The microstructure of graphite is also
shown to have a significant effect on the dimensional change rate.
This work suggests that porosity, crystal orientation, and average
lattice spacing have an influence on the rate of expansion. These
microstructural factors have been combined to create a model
which gives good agreement at low irradiation temperatures,
however, at higher irradiation temperatures the model gives poor
agreement with experimental data and it is thought this is
primarily to do with a lack of information about a-axis
deformations gained from intercalation experiments.
173
A tomographic experiment has been carried out to investigate the
development of microstructural strains. The important result here
is that dimensional change is driven by interstitial damage of the
filler particles whilst the damage to the binder matrix has a rather
small affect on the overall dimensional change. There exists one
key difference between irradiation damage and intercalation
damage and which is that intercalation is a damage process which
progresses through the microstructure.
The work presented here has only scratched the surface of what is
possible with using bromination as a simulation technique. It is
suggested that future studies should try to determine the layer
spacing in the binder matrix and the filler matrix and how these
two parameters develop with bromination. This could provide key
information regarding the potential of graphite to accommodate
damage to the microstructure. Further development of techniques
such as x-ray diffraction contrast tomography would allow better
models to be built which could take into account local crystal
orientations which could be applied to three dimensional finite
element models and provide an insight into how different regions
interact as strains develop.
174
6. Young’s Modulus
When graphite is placed in an irradiating environment the Young’s
modulus will undergo a series of changes. It is generally considered
that there are two main processes contributing to the change in
modulus as given in Equation 6.1[42].
),()(0
TSTPE
Ed
Equation 6.1
The P(T) term describes “pinning” a process which causes a sharp
initial increase in modulus. The increase in modulus is induced at a
low dose. The increase can be around 50% and this has been
attributed to a change in the C44 crystal shear modulus[44].
The second term S(δ,T) is a structure factor which is influenced by
dose and temperature. The term is describing the effect of crystal
volume changes on the bulk Young’s modulus. The structure term
becomes significant at higher doses. Initially the term describes an
increase in modulus. It is thought that this is due to crystal expansion
closing porosity causing a “tightening” of the structure[57]. As dose
increases further the term describes a decrease in modulus.
Eventually at high enough dose the volume change of crystals will be
such that new porosity starts opening causing the modulus to
decrease.
175
As shown in Chapter 5, crystal expansion can be driven by
intercalation as well as irradiation. This chapter describes a series of
experiments designed to investigate the structure term and
investigate how intercalation will influence this term.
Modulus measurements of nuclear graphite are normally carried out
using dynamic testing rather than static testing. The two methods
give the same results if the static modulus is measured for low strains
0.01 – 0.05%[53, 167]. However, above this the results diverge.
Dynamic modulus measurements are normally taken using piezo
transducers as specified in the American Society for Testing and
Materials (ASTM) standard for the measurement of the graphite
modulus[134]. The work described in this thesis modified the
recommended method by using laser techniques for ultrasound
generation and measurement. This was necessary because of the
harsh environmental conditions of the bromination experiment.
This is not the first work to use laser impact excitation with graphite;
previous work used laser impact excitation in conjunction with
Electro Magnetic Acoustic Transducers (EMAT)[135] to investigate
the effect of thermal oxidation on the Young’s modulus of graphite.
An EMAT is a type of non-contact sensor that measures the
interaction of magnetic fields in a sample and the sensor. This
requires the sensor to be quite close to the sample edge.
176
Laser vibrometry is another non-contact method that can also be
used to measure surface vibrations. Vibrometry has the advantage
that it can be used relatively far away from the sample. A further
advantage particularly relevant for bromination of graphite is that
the sample dimensions can change and the vibrometer can continue
to measure a signal. There is a caveat that the sample surface
remains within the depth of field of the vibrometer, therefore large
dimensional changes require periodic refocusing of the vibrometer.
The chapter details the development of the modified dynamic
young’s modulus testing technique. The modified technique is
applied to measuring changes in brominated graphite. The overall
aim of this is to investigate how the Young’s modulus structure factor
is modified by bromine intercalation.
6.1. Measuring optimal input energy for Young’s modulus measurements by
laser impact excitation
When using lasers to induce an ultrasonic pulse, it is important to
establish the optimal input energy. At low energies the ultrasonic
wave is generated thermoelastically. However, at higher energies an
ablatic waveform is superimposed[168]. Ablation occurs when a high
energy density beam interacts with a material and causes some
material to vaporize[136]. Of the two waveforms, the lower energy
thermoelastic wave induces an amplitude proportional to the input
energy. The higher energy ablatic waveform produces a significantly
larger amplitude in the waveform but it also degrades the sample
177
surface. It is therefore preferable to carry out the experiment at the
edge of ablation regime.
To determine the optimal energy, a simple experiment was carried
out using a 50mm long PGA sample cut in the WG direction, Figure
6.1. The sample was placed on a lab jack with the impact laser and
the vibrometer focused on the opposing 20 x 5mm end surfaces. Care
was taken to ensure the surfaces remained perpendicular to the laser
beams and the two beams remained parallel. An average of five
measurements were taken for each output energy available from the
“Big Sky Nd:YAG laser”, which is 0 to 20mJ at 0.5mJ increments.
Figure 6.1 Ultrasonic pulse measured with laser vibrometer
Figure 6.2 shows the trace recorded from the laser vibrometer
measuring the surface displacement on a graphite sample which has
been struck by the Nd:YAG laser on the opposing surface. Figure 6.3
shows how increasing the input energy affects the signal recorded
with the vibrometer. To understand this graph it is best to first look
at, the captured waveform from the oscilloscope. The x axis is time
and the y axis is the output of the vibrometer measured in volts.
WG sample AG sample
50mm
5mm
20mm
178
Figure 6.3 shows what happens as the energy of the impact laser
increases. Here the x axis is the impact laser energy, time is now the y
axis and the colour map defines the wave amplitude (the y axis in
Figure 6.2). The plot shows a high energy input laser pulse induces an
ultrasonic wave with large amplitude. Though this is easy to measure
it has the undesirable effect of ablation. Therefore an energy level
should be set such that a clear signal is induced with the lowest input
energy. The optimal energy used was chosen as 7mJ.
Whilst carrying out this experiment at higher energies it was
necessary to adjust the sample position to ensure the laser beam was
not hitting a surface previously damaged by ablation. The sample was
moved perpendicular to the laser beams to achieve this. When
moving the sample it was imperative to ensure that the sample
remained perpendicular to the impact laser and vibrometer.
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
-1.00E-05 0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05
Time (s)
Am
plitu
de (
V)
Figure 6.2 Ultrasonic pulse measured with laser vibrometer
179
Figure 6.3 Effect of Impact Energy on Measured Waveform
6.1.1. Verification of Laser Impact Excitation as a suitable modification of
ASTM C769
To verify the suitability of laser measurements for the determination
of Young’s modulus of graphite, a direct comparison was made
between the standard technique and the laser technique. Two grades
of graphite were used, Gilsocarbon and PGA cut perpendicular to
extrusion. The samples were dimensioned 75 x 5 x 20mm. The end
faces of the samples were polished to produce a smooth reflective
surface using grade 4000 SiC polishing paper. This improves the
transmission of ultrasonic waves between the piezo transducers
whilst also improving the quality of the reflected signal for
vibrometry measurements.
Osc
illo
sco
pe
amp
litu
de
of
ult
raso
nic
wav
e (V
)
Energy of impact laser (mJ)
180
6.1.1.1. Standard Experimental Technique
The first modulus experiments were taken using the standard setup
shown in Figure 6.4. The equipment comprises 5MHz Olympus
transducers connected to an Olympus pulse receiver. The signal is
read by a National Instruments PCI 5124 digitizer card which samples
at 200Ms/s. Averages of three measurements were taken for each
sample. The density was calculated by measuring the sample
dimensions to three decimal places and taking a mass measurement
of four significant figures.
Figure 6.4 ASTM C769 Experimental setup for piezo transducer measurement of Young's modulus
The sample was held between the two transducers using a clamp
along its longest length. A propriety gel, (Sonagel W) was used as a
couplant. The impact wave form and the transmitted wave form are
recorded by the computer as shown in Figure 6.5.
181
The excitation pulse is convoluted with the receiving pulse. The time
of flight is measured as the time between the impact pulse reaching
10% of its maximum amplitude and the receiving pulse reaching 10%
of its maximum amplitude.
Figure 6.5 Time of flight data for modulus measurement by piezo transducer
6.1.1.2. Experimental Setup for Laser Technique
Sonic velocity measurements using the laser technique were carried
out using the experimental setup shown in Figure 6.6 and Figure 6.7.
The ultrasound was generated by focusing a 7mJ laser pulse fired for
50ns at full width half maximum from a Nd:YAG source onto the
graphite sample.
A Polytec vibrometer was mounted on a sliding plate and focused on
to the opposing sample surface. Course focusing of the vibrometer is
carried out using the sliding plate. Finer focusing was performed
using the focus on the vibrometer. The vibrometer has the ability to
182
be setup to measure the displacement or the velocity of a sample
surface. In this case it was set up for changes in surface velocity as
this method is sensitive to small surface displacements[28].
The Q Switch Sync and vibrometer signals were connected to a
500MHz LeCroy digital oscilloscope. The Q-switch is an electo-optical
device that fires the laser, the Q switch sync gives the zero time for
the experiment.
The signal used for time of flight measurement was taken as an
average of 10 pulses. The signal was smoothed further using the
oscilloscopes inbuilt Gaussian filter. The time of flight was recorded
as the time between the 10% height of the first pulse seen in the Q
switch signal and the vibrometer signal. The recorded results are an
average of three such measurements.
Figure 6.6 Experimental setup for measurement of Young's Modulus by Laser Impact Excitation and Laser
vibrometry
183
Figure 6.7 Schematic of experimental setup for measurement of Young's Modulus by Laser Impact Excitation
and Laser vibrometry
6.1.1.3. Results
The results from the two experiments are shown in Figure 6.8. The
results show general agreement though there is a small systematic
difference between the two techniques. The laser technique
produces results which are on average 0.6μs slower with a standard
deviation of 0.54 μs. This may be attributed to the delay in the
electronics of the measurement circuit. The piezo technique
accounts for this by measuring the time delay when the transducers
are brought into contact. A similar process is not possible using
lasers. When using lasers without a sample there is no ultrasonic
wave generated nor is there a signal to record for an arrival time.
The scatter in the time of flight data has been observed by previous
Sample Nd:Yag
Vibrometer
LDD
Labjac
Oscilliscope
PC
Sample Stop
184
authors[169]. They attribute it to microstructural effects in the
graphite.
Figure 6.8 Comparison of sonic velocity measurements by Laser and Piezo Techniques
6.2. Change in modulus of brominated graphite
The dynamic modulus of a material is determined by three
properties; density, Poisson’s ratio and the sonic velocity of a pulse
through the material as derived by Timoshenko[132] and given in
Equation 6.2 [134] .
)1(
)21)(1(2
vEDYM
Equation 6.2
where ρ is the sample density, v is the sonic velocity and here η is
Poisson’s ratio. The work in this thesis has focused on the change in
185
density and sonic velocity. Though the change in Poisson’s ratio has
not been measured or calculated for graphite intercalated with
bromine, it was deemed unnecessary to measure this property for
this work. This decision was based on work on lithium intercalation
which showed the change in Poisson’s ratio to be small[114]. It was
therefore decided that Poisson’s ratio was the least important of the
properties to focus upon.
The following section will present the results of experimental work
carried out to determine the change in density and sonic velocity of
brominated graphite.
6.2.1. Change in density of brominated graphite
The changes in density of brominated graphites were derived from
the measurements carried out in Section 5.1. Gilsocarbon is a semi-
isotropic material[170]. The decision was taken that the dimensional
change in one axis would be the same in the other axes. This gives
Equation 6.3 which describes the change in density of an isotropic
material given the dimensional change in one axis.
2.. xCrDl
m
Equation 6.3
Where m is the mass of the sample, l is the length of the sample for a
given level of bromination, r is the original radius of the sample and
D.C.x is the dimensional change of the sample measured at that level
of bromination.
186
The method used to measure the change in density of PGA is slightly
more complicated given its high anisotropy ratio. To do this a curve
was fitted to the dimensional change of PGA samples given in Section
5.1 giving an equation for the expansion of the sample perpendicular
to the measured direction for a given bromine concentration. This
was applied to the formula given in Equation 6.4.
2)..(
CrDl
m
Equation 6.4
All the symbols here are the same as for equation 5.1 apart from the
strain component..CD .
..CD describes the dimensional change in
the axis perpendicular to the axis from which the length (l) and mass
(m) data is taken.
To calculate the volume change of HOPG, it was assumed that there
was no dimensional change perpendicular to the planes and that all
volume change came from expansion parallel to the graphitic planes.
The justifications for these assumptions are discussed in Chapter 4.
Figure 6.9 shows that when bromine is intercalated with HOPG there
is a rapid increase in density. The density settles around 2.21g/cm3,
just under the ideal single crystal value of 2.25 g/cm3, the ideal single
crystal value. This suggests that crack closure occurs up to around
15% strain, this corresponds to a [Br/C] ratio of 1.4%. After this there
appears to be little change in density which suggests there is little
subsequent change in crack volume.
187
Figure 6.10 shows the change in density of polycrystalline graphites.
At low intercalation levels density increases up to 0.5% to 1.5% strain
depending on the graphite grade. This corresponds to a [Br/C] ratio
of approximately 1%. It is probable that Mrozowski cracks close in
polycrystalline graphites earlier than HOPG due to restraining forces
of the surrounding microstructure. It is therefore assumed that the
initial densification is caused by closure of Mrozowski cracks.
As intercalation strain increases further, the density decreases. This is
against a backdrop of increasing single crystal density, decreases in
the accommodation factors (which imply a closure of porosity) and
tomographic scans showing closure of porosity. The reason for this is
that dimensional change is driven by filler particle expansion. The
samples used for the tomographic scans showed no crack generation
because they were too small and so there was nothing restricting
filler particle expansion.
Figure 6.11 shows a laser confocal micrograph of a debrominated
PGA sample. The filler particle is highlighted in image a). The filler
particle expansion generates a crack which propagates though the
binder along the with grain direction. The generation of porosity in
the binder causes the decrease in bulk density.
188
1500
1600
1700
1800
1900
2000
2100
2200
2300
0 5 10 15 20 25 30 35
% Longitudinal Strain
De
ns
ity
(k
g/m
^3)
Figure 6.9 Change in density of HOPG
1500
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
% Longitudinal Strain
Den
sit
y (
kg
/m^
3)
Gilsocarbon
PGA (AG)
PGA (WG)
HOPG
Poly. (PGA(AG))
Figure 6.10 Density change of polycrystalline graphites
189
Figure 6.11 Laser confocal micrograph of debrominated PGA a) green scale bar 100µm area of image b
highlighted in green b) scale bar 40µm filler particle outlined in green
By fitting curves to the calculated density data curves, equations can
be found which relate density to dimensional change. This is of use
for measurement of Young’s modulus later on. The equations for
change of density are given below.
PGA (AG) )0118.1..0353.0.0133.0( 2
0 AGAG CDCD
Equation 6.5
PGA (WG) )0648.1..0135.0.0046.0( 2
0 WGWG CDCD Equation 6.6
Gilsocarbon )0137.1..0081.0.0019.0( 2
0 CDCD Equation 6.7
6.3. Modulus changes of brominated Graphite
6.3.1. HOPG
To understand modulus changes in polycrystalline graphites subject
to bromination, it is first important to understand the modulus
changes in single crystal graphite. The modulus of single crystals are
defined using the fourth order tensor Cαβστ. The can be defined by
WG
AG
190
stress – strain relations as show in Equation 6.8 or equations of
motion as given in Equation 6.9.
uCT Equation 6.8
)(2 Cv a Equation 6.9
In Equation 6.8 Tαβ describes the stress vector orientated in direction
αβ, uστ is the strain vector in direction στ. In Equation 6.9 the v is the
velocity of a plane wave with polarization φ of the three types of
waves propagated in direction of the unit vector ξ[55].
Measurements were carried out using longitudinal and shear
transducers as shown in Figure 6.4. The setup is carried out according
to ASTM C769[134] and was carried out on HOPG before and after
bromination. The brominated sample was kept separate from the
transducers using 15mm cubed PTFE blocks as shown in Figure 6.12.
Figure 6.12 Piezo setup for brominated samples.
15mm
Sample
PTFE PTFE
Piezo
Transducer
Piezo
Transducer
191
The work was carried out on ZYH grade HOPG purchased from SGI
through Momentive Performance Materials. This is the lowest grade
available which has a mosaic spread of 3.5° ± 0.5°. This made it
affordable to buy a relatively large sample of 12x12x4mm HOPG.
The results are shown in Table 6.4 and Figure 6.13. When comparing
the virgin results with literature values, there is good agreement
between the values for shear modulus C44. However, the values for
C11 and C33 are slightly low[171]. This is most likely due to the grade
of HOPG used. As earlier experiments show, this grade of HOPG has a
relatively high internal porosity which will lower the modulus. As
density calculations in section 6.2.1 show there is porosity within the
graphite which will have the effect of lowering the modulus from the
ideal value.
The calculation for the brominated modulus is carried out by
measuring the time of flight through the PTFE rods and the graphite
sample. The time of flight through the PTFE is two orders of
magnitude larger than the time of flight through the graphite sample.
Despite every effort to do the experiment quickly, a further problem
arises due to the diffusion of bromine out of the sample as the
measurements were taken. This is a rapid process once the external
partial pressure of bromine is reduced by taking the sample out of
the bromination chamber. This is particularly noticeable in the
difference between C11 and C22 measurements which are expected to
be similar, as they are for virgin measurements.
192
Overall it can be seen that there is an increase in modulus associated
with the intercalation of bromine in HOPG. This is most noticeable in
the C11, C22 & C33 modulus which could possibly be explained by
closure of Mrozowski cracks which will transfer a compression wave
faster.
The shear modulus remains relatively unchanged. This implies that
pinning is not a dominant factor when considering modulus changes
as it is thought to be in the case of irradiation.
Figure 6.13 Change in Modulus of Brominated HOPG
193
Table 6.4 Measured elastic constants of grade ZYH HOPG
Virgin HOPG
Literature Values
Brominated HOPG
Density 2.25E+03 Blakslee[171] Density 2.21E+03
Dimensions Strain Time of flight (s)
Modulus (Pa) Modulus (Pa) Dimensions Strain
Time of flight (s)
Modulus (Pa)
Zero time longitudinal 2.77E-05
C11 1.19E-02 0.00E+00 6.84E-07 6.83E+11 1.060E+12 1.20E-02 4.78E-03 2.34E-07 5.78E+12
C22 1.19E-02 0.00E+00 6.86E-07 6.80E+11 1.20E-02 4.86E-03 2.15E-07 6.91E+12
C33 3.80E-03 0.00E+00 1.08E-06 2.81E+10 3.65E+10 5.01E-03 3.19E-01 4.35E-07 6.10E+11
Zero time Shear
C44 3.80E-03 0.00E+00 1.06E-05 2.86E+08 0.18-0.35E+9 5.01E-03 3.19E-01 8.55E-06 3.34E+08
C66 1.19E-02 0.00E+00 1.12E-06 2.57E+11 1.20E-02 4.78E-03
194
6.3.1.1. Error calculation of Modulus changes in brominated single crystal
graphite
The measurement of the elastic constants of brominated HOPG was a
difficult experiment. The elastic modulus values obtained are quite
high. The change in modulus for fully lithiated graphite has an
increase of 300% for C44, 150% for C33, and a 10% decrease for C11 as
calculated by Qi using DFT[114]. By comparison, this experiment
recorded changes in value nearly an order of magnitude larger.
Equation 6.10 shows the values to be measured to arrive at a value
for the young’s modulus all of which have associated errors.
2
321
t
l
lll
mE x
d
Equation 6. 10
where Ed is the dynamic Young’s modulus, m is the mass of the
sample lx is a length measurement and t is time. The fractional
certainties are given in Table 6.6. The uncertainties for all values
except time are very low. The requirement of PTFE rods however
greatly increases the error in the time measurement. Time is
measured across the sample and rods and by subtracting the time
measured across the PTFE rods with no sample present the time
through the sample is measured. This introduces a large error as the
pulse time across the rods is 2 orders of magnitude larger than
through the sample. Therefore a 5% error in the measurement of the
pulse arrival time can result in a 650% error in the calculated time for
the pulse to travel through the graphite sample.
195
Table 6.5 Fractional Uncertainties in Young’s modulus measurement of HOPG
m 592.1
0005.0
l1 96.12
005.0
l2 98.11
005.0
l3 32.3
005.0
t
sample
samplePTFE
t
tt %5
By applying the uncertainties given in Table 6.6 to Equation 6.10 it
can be seen that the error in the time measurement is so much larger
than all other errors that they may be ignored. However as the
velocity measurement is squared the error is doubled. This means a
5% error in the time measurement propagates through to a 1300%
error in the value of Young’s modulus.
6.3.2. Modulus changes in brominated polycrystalline graphites
A series of experiments were carried out to measure the change of
sonic velocity in polycrystalline graphite. As Equation 6.2 shows, to
calculate the modulus the value of the sonic velocity is squared and it
is therefore the most dominant factor in the relationship. The change
in density of bromine with strain is introduced to the models using
the relevant equation, either Equation 6.5; Equation 6.6; or Equation
6.7. These experiments were performed on PGA and Gilsocarbon
graphite. In this section the data on change in modulus along with
196
images of the samples are used to explain the trends. The results are
also compared with various graphite irradiation data.
6.3.2.1. PGA Against Grain
The results for the change in modulus of brominated PGA measured
perpendicular to extrusion (against grain) are shown in Figure 6.14.
There is significant scatter in the results though a general trend of
increasing modulus followed by a sudden decrease can be seen.
The initial results of 9.96GPa are high compared to the literature
value of 5.4GPa. It has not been possible to determine the reason for
this discrepancy. This work is interested in changes to microstructure
that cause a change in modulus, and with this data it is still possible
to relate trends in the data to microstructural changes. Later analysis
will present the data as the ratio E/E0. This ratio is commonly used
with irradiated nuclear graphites and this allows direct comparisons
between irradiated and intercalated modulus changes to be made.
The modulus of the graphite appears to have a bilinear trend. Initially
there is a modulus increase of approximately 19%. The modulus
increases until the intercalation has progressed to between 1% and
1.5% strain. The increase in modulus is most likely due to two
reasons; closure of Mrozowski cracks causing densification of the
crystallites, and an increase in the crystal modulus.
As the strain reaches between 1% and 1.6% there is a significant drop
in modulus. This coincides with the formation of large cracks across
197
the sample as seen in Figure 6.15 and Figure 6.16. Referring back to
Figure 5.12, it is also the same region of strain when the increase in
the dimensional change rate ]/[
..
CBrd
CdD AG is observed and the drop in
density is measured, Figure 6.10.
It is postulated that the cracks are generated by well intercalated
filler particles generating large strains, the stresses of which must be
relieved through fractures propagating through the binder of the
microstructure. Investigations using confocal microscopy on the
debrominated specimen, Figure 6.11, show that the cracks run
through the binder and around the edges of the filler particle.
Coupled with knowledge gained from the synchrotron experiment in
Section 5.2 this tells us that the filler particles expand causing cracks
to propagate through the binder along the with grain direction. The
crack around the filler particle can be explained by the plastically
deformed binder matrix not returning to its original shape after the
filler particle has debrominated.
The rate of modulus drop off is lower for PGA Perp 3 than PGA Perp
1. This could be explained by differences in the cracks propagating
though the two samples. PGA Perp 1 which exhibits a sharp drop in
modulus, shows only one crack which has fractured right across the
middle of the specimen. In contrast, PGA Perp 3 shown in Figure 6.16
shows a number of smaller cracks running through the sample
contributing to a more gradual decrease in modulus.
198
The area highlighted green in Figure 6.15 and Figure 6.16 show the
sample is a slightly darker colour in this region. This means that these
regions are at a slightly higher intercalation stage than the rest of the
sample[172], and therefore the measurement technique is
influencing the sample. Fortunately the damage appears to be to the
sides so it is only a small amount of laser damaged graphite that the
ultrasonic pulse must travel through.
Figure 6.14 Change in Young's modulus of brominated Pile Grade A cut perpendicular to extrusion (Against
Grain)
199
Figure 6.15 Pile Grade A sample 1 cut against the grain (perpendicular to extrusion) after bromination
Figure 6.16 Pile Grade A sample 3 cut against the grain (perpendicular to extrusion) after bromination
6.3.2.2. PGA With Grain
The results of experiments carried out on Young’s modulus changes
in PGA cut parallel to extrusion (WG) are shown in Figure 6.17. The
initial results show good agreement with the literature data, 11.7GPa
[28] and 11.1GPa. The data shows a 25% increase in modulus at
around 1% to 1.5% strain. Again this is the region where the density
of graphite is shown to start increasing indicating porosity generation
in the binder matrix. The percentage increase in modulus is larger
with grain than against grain. This is presumably because the crystal
WG AG
WG AG
200
modulus is able to reach a higher value before cracking in the
microstructure negates the crystal increase.
The data shows a similar trend to the PGA against grain samples,
though the drop in modulus is less dramatic. This can be explained by
the same process that is used to explain the difference in the drop in
modulus for the AG samples. Figure 6.18 shows that the cracks run
along the WG direction, this results in a more gradual increase in the
porosity in an orientation that will impede the sonic pulse.
Figure 6.17 Change in Young's Modulus of Brominated Pile Grade A cut Parallel to Extrusion
201
Figure 6.18 Pile Grade A Sample after bromination
6.3.2.3. Gilsocarbon
The results for young’s modulus changes in brominated Gilsocarbon
are shown in Figure 6.19. The data shows an increase in modulus
followed by a subsequent drop when the intercalation strain reaches
1.5%. The initial increase is around 30%; this is the most significant
increase seen in all the graphites measured. The reason for this could
be the larger volume of accommodation porosity present in
Gilsocarbon as shown in Figure 5.25. This allows a larger percentage
increase in densification and therefore a bigger increase in modulus
before fracture of the binder becomes the dominant effect causing a
decrease in the modulus.
The microstructural cracks are shown in Figure 6.20, where the cracks
are much smaller in the Gilsocarbon samples than the PGA samples.
All that is left are small cracks surrounding the filler particle
presumed to have formed after debromination. This suggests that if
cracks are generated in Gilsocarbon they are much smaller. This
A
G
W
G
202
would cause a more gradual reduction in the modulus as is seen in
the data.
Gilsocarbon sample 1 given in Figure 6.19 acts somewhat differently
to the other two samples. While two of the samples show a gradual
increase followed by a gradual decrease in modulus, sample 1 shows
a rapid increase in strain, followed by a sharp drop in modulus. This
may have been be caused by a problem with the laser displacement
detector. On the other hand, confocal microscopy images, Figure
6.20, show there is very little residual cracking in the debrominated
microstructure and the data point highlighted in red in Figure 6.19 is
the debrominated Young’s modulus value. This indicates that on
debromination the modulus returns to its original or a slightly higher
value than its virgin value. This suggests any cracking which opened
up in Gilsocarbon due to intercalation closes upon debromination
and therefore it is difficult to draw conclusions as to what happened
to this particular sample without having further data to verify the
laser displacement detector values
The modulus measurements are consistently lower than the
literature values with the virgin value of Gilsocarbon as 10.85GPa [28]
compared with measured value of 5.45GPa. As with the PGA against
grain sample; it was not possible to determine the cause of the
discrepancy between the two values.
203
Change in modulus of Brominated Samples
1
2
3
4
5
6
7
8
9
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Strain (%)
Yo
un
g's
Mo
du
lus
(GP
a)
Gilso 1Gilso 4Gilso 2
Figure 6.19 Young's modulus changes in brominated Gilsocarbon
Figure 6.20 Laser confocal micrograph of debrominated Gilsocarbon showing reltivly little microstructural
cracking a) scale bar 100µm b) isometric image 1280 x 1280 µm
Rapid increase in strain
204
6.3.3. Possible sources of Errors
There are many errors associated with this experiment as highlighted
by the scatter in the data.
There is an offset error to the unknowable zero time in the
experimental apparatus. This includes electronics delays and process
delays such as the time required for a laser pulse to generate the
ultrasonic pulse. Long samples are used to reduce this error.
The quality of the signal measured using the laser vibrometer and the
laser displacement detector is noisy even with filtering of the data.
This will introduce scatter to the data.
The quality of the vibrometer wave deteriorates as the surface of the
sample becomes more damaged by the intercalant. This reduces the
reflectivity of the sample making it harder to pick up the return
signal.
The modulus measurements carried out for the initial verification
experiment and the PGA parallel experiments all show quite good
agreement with the data. However, as discussed there are consistent
and repeatable errors between two of the data sets. This points to a
mix up of the samples. However, photos were taken of the samples
as soon as they were taken out of the experimental rig using both
standard photography and laser confocal microscopy and the
microstructural features match with what was expected of the
named sample.
205
6.4. Comparison of modulus changes due to irradiation and bromination
Figure 6.21 to Figure 6.23 compare the effects of bromination with
irradiation on the change in Young’s modulus. It would have been
preferable to compare the bromination data with low temperature
irradiation data but unfortunately the data in the literature is too
sparse.
The irradiation data has been taken from Brocklehurst and Kelly’s
investigation into the Young’s modulus changes in polycrystalline
graphites[35]. The irradiation dose has been normalised to bromine
concentration by comparing the change in the c-axis of HOPG
brominated at room temperature and HOPG irradiated 430°C[36]
data to find the relationship between dose and bromination giving
1.1 x 1021EDN = 1 [Br/C].
The pinning term has been removed from the irradiation data. This is
because intercalation cannot simulate this aspect of irradiation
damage. This leaves the structural term which is thought to be due to
closure of porosity and later opening of new porosity[57].
It can be seen that all graphite grades follow the trend of increasing
then decreasing of modulus in both irradiation and bromination data
sets. As Chapter 5 shows, Mrozowski cracks are initially closed by
intercalation. As the intercalate concentration reaches higher levels
new porosity is opened as swelling filler particles fracture the
surrounding binder matrix. Density measurements show that the
206
density of brominated samples drops at a similar strain to that where
a drop in modulus is measured, both occurrences can be explained by
an increase in porosity.
When normalizing the data sets to the crystal strain they receive in
the c axis, it can be seen that irradiated graphites can experience
more damage before measureable property changes are induced.
Irradiated samples also experience larger fractional changes in
modulus. This is due to differences between the irradiation and the
bromination damage mechanisms. Irradiation creep relaxes stresses
developed by expansion of filler particles. This allows a greater
change in the volume of the filler particles and greater densification
of filler particles[43] before fracture of the microstructure occurs.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 5E+21 1E+22 1.5E+22
[Br/C] adjusted for dose (n/cm-2
)
E/E
0
PGA perp 1
PGA perp 3
PGA perp irradiated
Figure 6.21 Comparison of changes in Young's modulus in PGA parallel to extrusion due to irradiation and
bromination
207
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
0 5E+21 1E+22 1.5E+22 2E+22[Br/C] adjusted to dose (n/cm
-2)
(E/E
0)-
EP
PGA parallel 3
PGA parallel 5
PGA Irradiated at 600C
Figure 6.22 Comparison of changes in Young's modulus in PGA parallel to extrusion due to irradiation and
bromination
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
3.00E+00
3.50E+00
4.00E+00
0 5E+21 1E+22 1.5E+22 2E+22 2.5E+22
[Br/C] adjusted to Dose (n/cm-2
)
(E/E
0)-
Ep
Gilsocarbon 1
Gilsocarbon 2
Gilsocarbon 4
Gilsocarbon Irradiated at 430C
Gilsocarbon Irradiated at 600C
Figure 6.23 Comparison of changes in Young's modulus in Gilsocarbon due to irradiation and bromination
208
6.5. Conclusions
This chapter shows that there are key similarities in the mechanisms
which induce changes in Young’s modulus in irradiated and
intercalated samples.
The chapter begins by describing the experimental technique
required to carry out Young’s modulus measurements under the
unique conditions imposed by bromination experiments. The chapter
describes the standard ASTM test technique using piezo transducers
and comparing it to a modified laser technique developed for this
work. Time is taken to describe how the experimental parameters
were defined for the laser technique. Results are presented which
compare the two techniques and it shown that the results are very
similar though there is a slight decrease in the velocity measurement
taken by laser and this is attributed to delays in the measurement
technique are unable to be accounted for.
The chapter goes on to show the results obtained for change in
modulus of single crystal and polycrystalline samples. The change in
modulus seen for single crystal graphite are very high and this is
attributed to large errors in the method used to measure the travel
time for an ultrasonic pulse.
The polycrystalline samples show an increase followed by a decrease
in the modulus of graphite as bromine intercalation increases. The
increase is attributed to a closure of porosity in the microstructure.
209
The decrease is attributed to cracking induced in the microstructure
as heterogeneous strains become too large to be accommodated.
The polycrystalline results are compared to irradiation data and it can
be seen that the two methods both induce an increase followed by a
decrease in modulus and the reasons for the two changes are
thought to be the same namely an initial closure of porosity followed
by the onset of cracking in the microstructure. The magnitudes of
modulus change are much lower for brominated samples than
irradiated samples and this is attributed to fundamental differences
in the two damage processes namely the stress relief mechanism of
irradiation creep in the brominated samples.
210
7. Conclusions and further work
7.1. Conclusions
An improved understanding of property changes is required to help
nuclear operators make safety cases for reactor life time extensions
and help designers create longer lasting more efficient reactors in the
future. The work in this thesis aims to help towards these goals by
providing a better understanding of the effect of internal strains on
material properties.
This work has used intercalation as a method to induce crystal strain.
Chapter 2 discusses intercalation of graphite in detail. The
fundamental point is that intercalation can induce an interplanar
strain of a similar magnitude to that caused by irradiation. This work
has utilised this effect to induce property changes in nuclear
graphite.
Bromine is a difficult substance to work with and so two unique
experimental rigs were designed to allow insitu property
measurements during intercalation. This is an advantage of using
intercalation over irradiation as insitu measurements would not be
possible with irradiation. The rigs allowed the first tomographic scans
to observe growth of graphite crystals due to interstitial damage. The
work also provided the first empirical measurements of modulus
changes in intercalated graphites.
211
The results show that dimensional change goes through two stages.
The first stage affects the graphite crystallites at low [Br/C] ratios.
Intercalated bromine causes an expansion in the c-axis of crystals up
to a bromine concentration of 1.3 [Br/C]. The expansion causes a
closure of nanocracks; this is seen in both HOPG and polycrystalline
graphites. The closure of the cracks causes an increase in the density
of the crystallites and a corresponding increase in the density of bulk
graphite. The closure of cracks causes an increase in the modulus of
graphite polycrystalline graphites
At higher [Br/C] ratios, once crystal expansion has closed the
nanocracks the crystallites and the bulk structure start expanding at
an accelerated rate. Because intercalation initiates at the sample
surface a lot of intercalation initially occurs in the binder due to the
large surface area of binder exposed to a high partial pressure of
bromine and later on in the filler particles where it takes time for the
bromine to propogate through the crystal structure. The magnitudes
of strain induced in the microstructure by intercalation are shown by
tomography to close microcracks. As filler particle expansion occurs,
this generates strains which cause fracture in the binder matrix. This
causes fractures to propagate along the with grain direction as shown
by laser confocal microscopy and density measurements. The binder
fracturing corresponds to a decrease in the bulk modulus.
There are substantial differences between intercalation and
irradiation. There is probably no mechanism comparable to
212
irradiation creep in graphite, meaning that any property changes
occur at lower levels of intercalation damage. There is no mechanism
to cause a-axis shrinkage which reduces the volume of irradiated
crystals. This prevents the calculation of an a-axis accommodation
factor as would be required to model irradiation damage suitably.
Despite the differences, it is still possible to answer some important
questions on irradiation properties at high dose. This work gives
evidence to support the theory that the initial increase in the
structural modulus term is due to closure of nanocracks and that the
later decrease in the term is due to the opening of cracks in the
binder region[57]. The tomographic investigations support the work
of Hall[51] by showing that large scale porosity will close given the
magnitudes of strain seen in a reactor. The work shows also that filler
particle expansion is a driving force behind property changes later in
core life including dimensional change and binder matrix fracture.
7.2. Future Work
It is recommended that future studies into the intercalation of
graphite as a method to simulate irradiation damage should focus on
the following areas.
The experiment to measure the change in modulus of HOPG was
unsatisfactory. It is recommended that a theoretical approach be
taken. DFT should be used to calculate the change in elastic constants
of intercalated crystals; this could build on the work of Yaya et al [71]
213
who carried out DFT studies to find the interstitial positions of
bromine intercalated in graphite and graphene. The results of this
should be input into a finite element model to determine modulus
changes in crystallites.
It would be interesting to carry out high resolution powder diffraction
experiments. Such experiments could answer a number of questions.
How does intercalation differ between binder and filler materials? Is
there any reorientation of crystals? It could also be used to
accurately measure any a-axis contraction. If so, this would provide a
small insight into one of the mechanisms that may potentially occur
during irradiation creep[173].
If high resolution XRD were carried out and the value of Young’s
modulus of irradiated crystals were determined, it would be possible
to construct finite element meshes based on tomographic scans of
graphite, the results of which could be compared to matching
empirical data.
Given that some microstructural regions intercalate quicker than
others and therefore undergo modulus changes at different times,
the effect of this on the surrounding microstructure and bulk
material should be investigated.
214
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