Molecular dynamics simulations are limited to very short time scales due to a need to resolve the thermal vibrations of atoms. This is a problem when attempting to model slow processes such as diffusion. A new method, called diffusive molecular dynamics (DMD), is presented for computer simulations of vacancy diffusion at the atomic scale. A variational free energy similar to that in the variational Gaussian method, with EAM potentials, of LeSar, et al. is derived in the grand canonical ensemble. A kinetic law based on the master equation is used to track vacancy diffusion over a site lattice. Static minimization of the variational free energy allows the site lattice to adjust to changes in the occupation probabilities of the sites.
Some results from applications of the DMD method are also presented. Basic verification of the model is provided by reproducing basic material properties such as the lattice constant, bulk modulus, and vacancy formation energy, as well as matching the behavior of the kinetic law to a continuum random walker model. Void formation is observed for high vacancy concentrations. Creep under nanoindentation can also be seen.
While the above verifications give confidence in the model, several issues are yet to be resolved. These are mostly related to the mean field approximation used in deriving the variational free energy. There is a disagreement in between the concentrations used in the free energy and the expectations of the kinetic law. The mean field approximation also loses information about individual vacancies leading to self-interactions. It is uncertain if the conditions of the approximation used to incorporate the embedding term of EAM potentials are always met. There is also currently no mechanism to add vacant sites to the system preventing, for example, dislocation climb by vacancy emission. In addition, the current implementation does not account for different diffusivities through the bulk and along defects.