diffusive molecular dynamics ju li, bill cox, tom lenosky, ning ma, yunzhi wang ohio state...
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Diffusive Molecular Dynamics
Ju Li, Bill Cox, Tom Lenosky,Ning Ma, Yunzhi Wang
Ohio State University
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Traditional Molecular Dynamics
• Traditional MD numerically integrates Newton’s equation of motion over 3N degrees of freedom, the atomic positions:
• It is difficult to reach diffusive time scales using traditional MD due to timestep (~ ps / 100), which needs to resolve atomic vibrations.
, 1..i i Nx
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Diffusive MD: The Idea
Ferris wheel seen with long camera exposure time
Variational Gaussian Method
Lesar, Najafabadi and Srolovitz, Phys. Rev. Lett. 63 (1989) 624.
, , 1..i i i N x
DMD
ci: occupation probability(vacancy, solutes)
Define i for each atom,to drive diffusion
, , , 1..i i i i N x c
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3 23 2 2 2
0 0 01
Gibbs-Bogoliubov Free Energy Bound:
1exp exp | |
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3
2
(| |, , )
Nji
i i i j j j i j i ji i j
B
i j i j
F F U U u d d
k T
w
x x x x x x x x
x x
2
1
ln
2Thermal wavelength:
Ni T
i
TB
e
mk T
Variational Gaussian Method
{xi,i}true free energy
VG free energy
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Comparison with Monte Carlo
Lesar, Najafabadi and 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
10
2
1 1
The chemical potential for each atom 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
1
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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• 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 phase-field method.
• No need to pre-build event catalog. Could be competitive against kinetic Monte Carlo.