Diffusive Molecular Dynamics Ju Li, William T. Cox, Thomas J. Lenosky, Ning Ma, Yunzhi Wang.
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Transcript of Diffusive Molecular Dynamics Ju Li, William T. Cox, Thomas J. Lenosky, Ning Ma, Yunzhi Wang.
Diffusive Molecular Dynamics
Ju Li, William T. Cox,
Thomas J. Lenosky, Ning Ma, Yunzhi Wang
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Traditional Molecular Dynamics
• Numerically integrate Newton’s equation of motion with 3N degrees of freedom, the atomic positions:
• Difficult to reach diffusive time scales due to timestep (~ ps/100) required to resolve atomic vibrations.
, 1..i i Nx
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Diffusive MD: Basic Idea
Ferris wheel seen with long camera exposure time
Variational Gaussian Method
Lesar, Najafabadi, Srolovitz, Phys. Rev. Lett. 63 (1989) 624.
, , 1..i i i N x
DMD
ci: occupation probability(vacancy, solutes)
Define i for each atomic site,to drive diffusion
, , , 1..i i i i N x c
Phase-Field Crystal: Elder, Grant, et al. Phys. Rev. Lett. 88 (2002) 245701
Phys. Rev. E 70 (2004) 051605 Phys. Rev. B 75 (2007) 064107
change of basis: planewave → Gaussian
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0 0 0
3 23 2 2 2
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Gibbs-Bogoliubov Free Energy Bound:
1exp exp | |
2
(| |, , )
Nji
i i i j j j i j i ji i j
i j i j
F F U U
u d d
w
x x x x x x x x
x x
2
1
3 2ln thermal wavelength
2
Ni T
B Ti B
k Te mk T
Variational Gaussian Method
{xi,i}true free energy
VG free energy
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Comparison with Exact Solution
Lesar, Najafabadi, Srolovitz, Phys. Rev. Lett. 63 (1989) 624.
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DMD thermodynamics
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1 1
1 3(| |, , ) ln ln 1 ln 1
2 2
N Ni
i j i j i j B i i i i ii i j i
F c c w k T c c c c ce
x x
Add occupation order parameters to sites: , , , 1..i i i i N x c
VG view DMD view
0
1
c
1
0
c
8
2
1 1
The chemical potential for each atomic site is easily derived:
1 3(| |, , ) ln ln
2 2 1
N Ni i
i j i j i j Bi i j ii i
A cc w k T
c e c
x x
DMD kinetics
nearest-neighbor network
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1 , if and are nearest neighbors2
0 otherwise
Ni
ij j ij
i j
ij
ck
t
c ck i j
k
2B 0
calibrate against experimental diffusivity:
Dk
k T a Z
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log(D)
Atomic Environment-Dependent Diffusivity
Atomic coordination
number
12(perfect crystal)
9(surface)
10,11(dislocation core)
experimental or first-principles
diffusivities
10
Particleon surface
(largeparticle)
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Particleon surface
(smallparticle)
12
Sinteringby hot
isostatic pressing
(porosityreduction in nanoparticlessuperlattice)
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Sinteringby Hot
Isostatic Pressing
(randompowders)
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Nanoindentation
(only atomswith coordination
number ≠ 12are shown)
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Small Contact Radius, High Temperature
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Indenter accommodation by purely diffusional creep
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coordination number coloring, showing edge dislocation
Dislocation Climb
vacancy occupation > 0.1
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• DMD is atomistic realization of regular solution model, with gradient thermo, long-range elastic interaction, and short-range coordination interactions all included.
• DMD kinetics is “solving Cahn-Hilliard equation on a moving atom grid”, with atomic spatial resolution, but at diffusive timescales.
• The “quasi-continuum” version of DMD can be coupled to well-established diffusion - microelasticity equation solvers such as finite element method.
• No need to pre-build event catalog. Could be competitive against kinetic Monte Carlo.
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Quasicontinuum - DMD?
image taken from Knap and Ortiz, Phys. Rev. Lett. 90 (2003) 226102.
DMDregion?
continuum diffusion
equation solver region,
with adaptive meshing?
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Stress-Induced Bain Transformation
FCC
BCC
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