1. Diffusive Molecular Dynamics Ju Li, William T. Cox, Thomas J. Lenosky, Ning Ma, Yunzhi Wang

2. 2 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.

3. 3 Diffusive MD: Basic Idea Ferris wheel seen with long camera exposure time Variational Gaussian Method Lesar, Najafabadi, Srolovitz, Phys. Rev. Lett. 63 (1989) 624. DMD c i : occupation probability (vacancy, solutes) Define  i for each atomic site, to drive diffusion 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

4. 4 Variational Gaussian Method {x i,  i } true free energy VG free energy

5. 5 Comparison with Exact Solution Lesar, Najafabadi, Srolovitz, Phys. Rev. Lett. 63 (1989) 624.

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7. 7 DMD thermodynamics VG view DMD view

8. 8 DMD kinetics nearest-neighbor network

9. 9 log(D) Atomic Environment-Dependent Diffusivity Atomic coordination number 12 (perfect crystal) 9 (surface) 10,11 (dislocation core) experimental or first-principles diffusivities

10. 10 Particle on surface (large particle)

11. 11 Particle on surface (small particle)

12. 12 Sintering by hot isostatic pressing (porosity reduction in nanoparticles superlattice)

13. 13 Sintering by Hot Isostatic Pressing (random powders)

14. 14 Nanoindentation (only atoms with coordination number ≠ 12 are shown)

15. 15 Small Contact Radius, High Temperature

16. 16 Indenter accommodation by purely diffusional creep

17. 17 coordination number coloring, showing edge dislocation Dislocation Climb vacancy occupation > 0.1

18. 18 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.

19. 19 Quasicontinuum - DMD? image taken from Knap and Ortiz, Phys. Rev. Lett. 90 (2003) 226102. DMD region? continuum diffusion equation solver region, with adaptive meshing?

20. 20 Stress-Induced Bain Transformation FCC BCC

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