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Atomistic Simulations
Ju Li, Libor Kovarik
8 nm
Mishin, Acta Mater. 52 (2004) 1451 Ardell & Ozolins, Nature Mater. 4 (2005) 309
(NT) ensemble with two vacancies
Transition pathwaysobtained using
Nudged Elastic Band (NEB) method.
Henkelman & Jonsson, J. Chem. Phys. 113 (2000) 9901;
ibid 113 (2000) 9978.
I
I IC
0.44MPa m0.75
KG G
2D activation
3D activation
sorta too long
fN
kN
A new NEB methodconnecting to unstable final state
“Free-end” algorithm:
last nodeconstrained
to move only along
energy contour
T. Zhu, J. Li, A. Samanta, H.G. Kim, S. Suresh, “Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals,” PNAS 104 (2007) 3031.
Lu et al., Acta Mater.
53 (2005)2169.
dislocationtransmission?
Lu et al., Science 287 (2000) 1463; 304 (2004) 422.
*
activationvolume v
strain-ratesensitivity m
Uniaxial tension[Lu04]
Nanoindentation[Lu05]
Atomistic calculation
Diffusion-controlled processes
Bulk forest hardening
Comparison of yield stress, activation volume and strain-rate sensitivity between experimental measurements and atomistic calculation
Nano-twinnedCopper
~ 1 GPa
*700 MPa
780 MPa
32212 b
34424 b
036.0025.0
023.0013.0
31.0~ b ~ 1
31000100 b 005.00 bulk~ b
yield stress
* extracted from measured hardness as .3
HH
*
activationvolume v
strain-ratesensitivity m
Uniaxial tension[Lu04]
Nanoindentation[Lu05]
Atomistic calculation
Diffusion-controlled processes
Bulk forest hardening
Comparison of yield stress, activation volume and strain-rate sensitivity between experimental measurements and atomistic calculation
Nano-twinnedCopper
~ 1 GPa
*700 MPa
780 MPa
32212 b
34424 b
036.0025.0
023.0013.0
31.0~ b ~ 1
31000100 b 005.00 bulk~ b
yield stress
* extracted from measured hardness as .3
HH
First time atomistic calculation provides strain-rate sensitivity information, at experimentally realistic strain rate of ~10-4/s.
avg. shear stress = 750 MPa
initial equilibrium
free-end node
node 2
node 3
node 4
3initial saddlesupercellActivation volume is estimated by 100
Qb
G
constant supercellcalculation
saddle-point configuration
[112]/6[112]/6
pseudo-twinlayer
true-twinlayer
pure Ni column
half Ni column
push inpop out
slightly tilted viewred: Al black: Ni
Libor vacancy reorderingmechanism
Vacancy-aided reordering in 2-layer pseudo-twin long behind dislocations
For comparison,VNi migration barrier
in perfect Ni3Al is 1.24 eV.
shear stress = 900 MPa
Peter Sarosi
High Tensile Strength and Ductility of Cu with Nano-Sized Twins
Lu et al., Science 287 (2000) 1463; 304 (2004) 422.
Lu et al., Acta Mater.
53 (2005)2169.
dislocationtransmission?
B
,
log 3strain-rate sensitivity activation volume *
logT
k Tm v
m
Lu et al., Acta Mater. 53 (2005) 2169.
Like other nanocrystals, nanotwinned Cu shows increased strain-rate sensitivity (~0.03) and small activation volume (~12b3)
Can atomistic calculation provide strain-rate sensitivity (m) and activation volume (v*) information of experimental relevance?
stress
Act
ivat
ion
ener
gy Q
()
athermal threshold
ath
( )dQd
activation volume
0.7eV
0eV very likely to happen in 1s
very unlikely to happen in 1s
1 2
large 2
small thermal uncertainty
small 1
large thermal uncertainty
process 1
process 2
Stress-driven activated process
Larger meansthe activation is
more “collective”,less thermal
uncertainty & the process
more “athermal”.
point defect diffusion: ~0.02-0.1b3 forest dislocation cutting: ~103b3
J. Li, “The Mechanics and Physics of Defect Nucleation,” MRS Bulletin 32 (2007) 151-159.
= 252MPaQtms=0.67eV
Qabs=0.49eV
Qdes~5eV
In experiment, stress applied is uniaxial tension, not pure shear → Taylor factor M ≈ 3.1 to convert
shear stress to uniaxial stress : = M
int( , )True activation volume:
Q
We’ve computed tms≈79b3, abs≈des≈43b3
at = 252MPa.
* * *tms abs des
3 3
,
3
44 24
A conversion factor M/ between experimentally measured * and :
b b
vv v v