mse 342f chapter # 4 properties part i 2014-15
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Properties of 3-D Nanomaterials
(Chapter # 4 Part I)
Uwe Erb Materials Science and Engineering,
University of Toronto, Toronto, Ontario, Canada.
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Properties of 3-D Nanomaterials
Before looking at details of properties you should consider that there are structurally three different types of 3-D nanomaterials.
1) Consolidated Powder Materials
These materials have been prepared by two-step processes. First nanopowders are made by techniques such as inert gas condensation, ball milling or chemical precipitation. In the second step these particles are consolidated under high pressures and at elevated temperatures. There is considerable residual porosity in these materials in addition to grain boundaries and tripe junctions.
2) Fully Dense Equiaxed Materials
These materials are made in one step such as electrodeposition or severe plastic deformation. The materials are usually fully dense with negligible porosity. Grain boundaries, triple junctions (and dislocations) are the main defects.
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Properties of 3-D Nanomaterials
3) Nanocrystallized Materials
The materials are produced by crystallization of amorphous precursor material. In addition to grain boundaries and triple junctions they contain residual amorphous matrix.
The properties of these materials are not always the same and direct comparisons are sometimes difficult.
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Consolidated Powder Material
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Fully Dense Equiaxed Material
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Nanocrystallized Material
amorphous
crystalline
clusters
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Thermal Stability
Nanomaterials contain very high interface contents (e.g. surfaces in 0-D nanomaterials, grain boundaries in 3-D nanomaterials). The associated interfacial energy gives the nanomaterial a very high driving force for crystal or grain growth. Therefore, for any nanomaterial, one of the key questions is their thermal stability with increasing temperature.
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Grain Growth in Conventional Materials
W.D. Callister, 6th ed., Materials Science and Engineering, Willey, NY, 2003
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Grain Growth in Conventional Materials
L.H. van Vlack, Elements of Materials Science and Engineering, 3rd ed., Addison-Wesley, Reading, MA, 1975
Larger grains grow Smaller grains shrink
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Driving Force for Grain Growth
Curvature Induced
L.H. van Vlack, Elements of Materials Science and Engineering, 3rd ed., Addison-Wesley, Reading, MA, 1975
Higher coordination number in growing grain
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Driving and Dragging Forces
Driving Force
Curvature Induced F ~ / d
Dragging Forces
Solute Drag F ~ C0 / r
Zener Drag F ~ f / R
interfacial energy r atomic radius of solute
d average grain size R particle diameter
C0 average concentration f particle volume fraction
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Normal Grain Growth Kinetics
dn – don = Kt n = 1.5 – 8
K = Ko exp (-Q/kBT)
d average grain size after time t Ko pre-exponential factor
do average starting grain size kB Boltzmann’s constant
K constant Q activation energy
T temperature
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Ex-situ TEM
Normal Grain Growth
100 nm 100 nm 250 nm
Ni – 2.5 % P
TEM bright field images of a) as-plated, b) DSC annealed, 50C/min to 4000C, c) annealed to 5000C.
a) b) c)
Y. Zhou, Ph.D. Thesis, University of Toronto, 2006
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(c) (d)
(b) (a)
300 nm
Ex-Situ TEM
Abnormal Grain Growth
Ni – 800ppm S
U. Klement, U. Erb, A.M. El-Sherik, K.T. Aust,Mat. Sci. Eng., A203 (1995) 177
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Time Exponents for Grain Growth
C. Suryanarayana & C.C. Koch, Hyperfine Interactions 130, (2000) 5
Time exponent: 1 / n
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Activation Energies
Kissinger Analysis
The curve was obtained for the Ni-P sample with starting grain size of 6.9 nm at the DSC
heating rate of 50 C/min
d = 6.9 nm
Temperature ( 0C)
0 100 200 300 400 500 600
He
at R
ele
ase
(W
/g)
0.00
0.02
0.04
0.06
0.08
0.10
DSC @ 5 to 80 0C/min 420
0 to 467
0
TP
Ni – 2.5% P
Y. Zhou, Ph.D. Thesis, University of Toronto, 2006
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Activation Energy
Modified Kissinger Analysis
where b: heating rate
Tp: peak temperature
C: constant
k: Boltzmann’s constant
T: Temperature
Q: Activation energy
L.C. Chen, F. Spaepen, Appl. Phys., 69 (1991) 679)
CkTQTb pp /)/ln(
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Peak Temperatures
280
320
360
400
440
480
0 20 40 60 80
Scanning rate (oC/min)
Pea
k t
emp
era
ture
(oC
)Ni
Ni-20%Fe
Ni-1.2%P
G.H. Hibbard, U. Erb, K.T. Aust, U. Klement, G. Palumbo, Mat. Sci. Forum, 386-388 (2002) 387
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Kissinger Analysis
Activation Energies
-5
-4.5
-4
-3.5
-3
-2.5
-2
15 16 17 18 19 20 21
1/ k B T p
Hea
tin
g r
ate
(b
/Tp )
Ni-1.2%P
2.25 eV
Ni
1.46 eV
Ni-20%Fe
2.53 eV
G.H. Hibbard, U. Erb, K.T. Aust, U. Klement, G. Palumbo, Mat. Sci. Forum, 386-388 (2002) 387
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Activation Energies
System Grain size
(nm) Tp (
0C) Q (eV)
Ni 20 290 1.36
Ni 26 266 1.20
Ni 20 269 1.22
Ni 15 293 1.42
Ni 20 296 1.46
Ni-1.2 wt% P 10 432 2.25
Ni-1.9 wt% P 9 412 2.63
Ni-2.5 wt% P 7 420 2.58
Ni-20 wt% Fe 13 379 2.53
Co 20 355 1.63
G.H. Hibbard, U. Erb, K.T. Aust, U. Klement, G. Palumbo, Mat. Sci. Forum, 386-388 (2002) 387
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Young’s Modulus
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Physical Meaning of Young’s Modulus
Young’s modulus ~ slope in force curve at a0
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Grain Boundaries
Very important for many properties of 3-D nanocrystals
W.D. Callister, 6th ed., Materials Science and Engineering, Willey, NY, 2003
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Nanocrystalline Ni and Ni-P
GRAIN SIZE (nm)
100 101 102 103 104 105
YO
UN
G'S
MO
DU
LU
S (
GP
a)
0
100
200
300
400
minor reductions
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Normalized Young’s Modulus for Nanocrystals
Region II: High Porosity
Region I: Low Porosity
Y. Zhou, U. Erb, K. T. Aust, G. Palumbo, Z. Metallk., 94 (2003) 10
major reductions
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Effect of Porosity Strong Solids (e.g., ceramics)
V. Krstic, U. Erb and G. Palumbo, Scripta Metall. Mater., 29 (1993) 1501
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Effect of Porosity Elastic Theory
V. Krstic, U. Erb and G. Palumbo, Scripta Metall. Mater., 29 (1993) 1501
1)21(41
VEE o
)57(254
)/1()57(29/1
2
3
RSRS
V : Pore volume fraction : Poisson’s ratio
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Effect of Porosity
Atomistic Modeling: Pore in Single Crystal
R. Zugic, B. Szpunar, V.D. Krstic, U. Erb, Phil. Mag., A75 (1997) 1041
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Effect of Porosity
Atomistic Modeling: Pore at 5 grain boundary
R. Zugic, B. Szpunar, V.D. Krstic, U. Erb, Phil. Mag., A75 (1997) 1041
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Effect of Porosity
Atomistic Modeling Elastic Theory
R. Zugic, B. Szpunar, V.D. Krstic, U. Erb, Phil. Mag., A75 (1997) 1041
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Effect of Porosity
data from
Region II
V. Krstic, U. Erb and G. Palumbo, Scripta Metall. Mater., 29 (1993) 1501
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Effect of Grain Size
Fully Dense Nanomaterials
Young’s modulus (normalized with respect to Young’s modulus of polycrystalline nickel, E0) of nanocrystalline Ni-2.5 wt% P alloys, pure nanocrystalline nickel and amorphous Ni-15 wt% P.
U. Erb, K. T. Aust, G. Palumbo, Z. Metallk., 94 (2003) 10
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Composite Model
f’s: Volume fractions
E’s: Modulus values
G: Grain
GB: Grain boundary
TJ: Triple junctions
TJTJGBGBGGm fEfEfEE
Y. Zhou, U. Erb, K. T. Aust, G. Palumbo, Z. Metallk., 94 (2003) 10
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Composite Model
Results for Nano Ni-2.5% P
GPaE
GPaE
GPaE
TJ
GB
G
151
157
208
Y. Zhou, U. Erb, K. T. Aust, G. Palumbo, Z. Metallk., 94 (2003) 10
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Young’s Modulus Summary
1) Grain boundaries and triple junctions have some effect on elastic properties. For the case of Ni it was shown that their Young’s Modulus is reduced by about 20% at grain sizes of ~ 5nm.
2) Fully dense 3-D nanomaterials produced by electrodeposition show some grain size dependence below 20 nm and virtually no grain size dependence above 20 nm.
3) 3-D nanomaterials produced from 1-D precursor material contain considerable porosity. Their Young’s modulus decreases rapidly with increasing porosity levels.
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Hardness, Strength, Ductility
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Vickers Hardness
Electrodeposited Ni
GRAIN SIZE (nm)
100 101 102 103 104 105
VIC
KE
R'S
HA
RD
NE
SS
(G
Pa
)
0
1
2
3
4
5
6
7
8
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Hall-Petch Relationship
regular strength
regular hardness
where d: grain size
k, k: constants
since 1989: k, k’ negative (inverse Hall-Petch)
21
0
/ dk
21
0
/ dkHH
E. O. Hall, Proc. Phys. Soc., London, B54 (1951) 747 N. J. Petch, J. Iron Steel Inst., 174 (1953) 25
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Hall-Petch Plot
Electrodeposited Ni
A. M. El-Sherik, U. Erb, G. Palumbo, K. T. Aust, Scripta Metal., 27 (1992) 1185
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Hall-Petch Plot
Electrodeposited Ni-P
G. Palumbo, U. Erb, K. T. Aust, Scripta Metal., 24 (1990) 2347
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Normal Crystalline Cu
Regular Hall-Petch
A. H. Chokshi, A. Rosen, J. Karch, H. Gleiter, Scripta Metal, 23 (1989) 1679
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Comparison with Gas Condensed Pd, Cu
Inverse Hall-Petch
A. H. Chokshi, A. Rosen, J. Karch, H. Gleiter, Scripta Metal, 23 (1989) 1679
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Hall-Petch Plot
Various Materials
R. W. Siegel, G. E. Fougere,, Nanostruct. Mat., 6 (1995) 205
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Hall-Petch Plot
Various Materials
R. W. Siegel, G. E. Fougere,, Nanostruct. Mat., 6 (1995) 205
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Yield Strength
Electrodeposited Ni
GRAIN SIZE (nm)
100 101 102 103 104 105
YIE
LD
ST
RE
NG
TH
(M
Pa
)
0
200
400
600
800
1000
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Yield Strength
Electrodeposited Ni
N. Wang, Z. Wang, K. T. Aust, U. Erb, Mat. Sci., A237 (1997) 150
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Grain Boundaries: Dislocation Barriers
S: source
At small grain size: no longer dominant deformation mechanism
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Constitutive Equations for Diffusional Mechanisms
23
5102
d
b
kT
bDx
dt
dgb
22
1
6108
d
b
kT
bDx
dt
d
n
kT
bDx
dt
d
1
510833.
12
114D
dkTdt
d
gbDdkTdt
d3
14
Nabarro-Herring
Coble creep
GB Sliding
GB Sliding
Dislocation Climb
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Constitutive Equations for Diffusional Mechanisms
strain rate
applied stress
grain size
volume of vacancy
grain boundary thickness
lattice diffusion coefficient
grain boundary diffusion coefficient
shear modulus
Burgers vector
:dt
d
:
:d
:
:1D
:gbD
:
:b
:
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Nabarro-Herring Creep, Coble Creep
Nabarro-Herring: lattice diffusion
Coble: grain boundary diffusion
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Grain Boundary Sliding
grain boundary or lattice diffusion controlled
C. R. Barrett, W. D. Nix, A. S. Tetelman, in The Principles of Engineering Materials, Prentice-Hall, Inc., Englewood Cliffs, NJ (1973)
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Ductility
Electrodeposited Ni (early results)
N. Wang, Z. Wang, K. T. Aust, U. Erb, Mat. Sci., A237 (1997) 150
very disappointing
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Ductility
Electrodeposited Ni (early results)
GRAIN SIZE (nm)
100 101 102 103 104 105
TE
NS
ILE
ELO
NG
AT
ION
(%
)
0
10
20
30
40
50
60
very disappointing
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Comparison with Gas Condensed Pd
R. W. Siegel, G. E. Fougere,, Nanostruct. Mat., 6 (1995) 205
very disappointing
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Elongation to Failure
Various Nanomaterials
C. Suryanarayana & C.C. Koch, Hyperfine Interactions 130, (2000) 5
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However: More Recently
Conventional and Nanodeposit Co
A. A. Karimpoor, Ph.D. Thesis, University of Toronto
good news
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Stress – Strain Curve
Electrodeposited Ni-Fe
H. Wei, M.A.Sc. Thesis, U of T, 2006
good news
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Hardness, Strength,Ductility
Summary
1) All 3-D nanocrystalline materials show significant increases in hardness, yield strength and tensile strength, regardless of synthesis method. Depending on the system, increases by factors of 3-10 are commonly observed.
2) All 3-D nanomaterials exhibit regular Hall-Petch behavior for larger grain sizes. Changes in the Hall-Petch slope are observed at smaller grain sizes (<100 nm). Some materials show the inverse Hall-Petch relationships at very small grain sizes(<10 nm).
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3) At very small grain sizes dislocation slip is no longer the dominant deformation mechanism.
4) The inverse Hall-Petch relationship can be explained on the basis of diffusional creep (Nabarro-Herring, Coble) and grain boundary sliding which become important at very small grain sizes even at room temperature.
Hardness, Strength,Ductility
Summary
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Hardness, Strength,Ductility
Summary
5) Early results on the ductility of 3-D nanomaterials were very disappointing. Most materials showed low ductility in tension (<5%), regardless of synthesis technique. However, these results were obtained using very small tensile samples.
6) Recent advances in electrodeposition processes have resulted in better materials and larger sample sizes for meaningful tensile tests. As a result tensile elongations in excess of 10% have been observed.
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7) Recent advances in other synthesis methods have also resulted in materials with better ductility.
8) Current efforts towards higher ductility include the synthesis of materials with much broader grain size distributions or even bimodal distributions. In these materials a compromise between high strength and reasonable ductility is achieved, whereby the smaller grains in the distribution are responsible for strengthening while the larger grains retain some ductility in the system.
Hardness, Strength,Ductility
Summary
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Summary
Changes in Hall-Petch Behavior
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50 µm
a
1) Dislocation slip
2) Twinning
Summary
Low Temperature Deformation Mechanisms
Polycrystals
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Summary
Low Temperature Deformation Mechanisms
1) Dislocation slip
2) Twinning
3) Coble
4) Nabarro-Herring
5) GB sliding
6) Grain rotation
50 nm
b
Nanocrystals