A numerical method, based on the path-integral formalism, is presented to solve nonlinear Fokker-Planck equations with natural boundary conditions. For one-dimensional stochastic processes, several specific examples possessing exact analytic solutions are evaluated numerically for purposes of comparison. Various discretization prescriptions are investigated and found to be equivalent as expected. The numerical method is shown to give accurate results provided the spatial discretization and the time step satisfy certain relationships determined by the drift and the diffusion functions of the nonlinear Fokker-Planck equations.

The activation energies for self-diffusion of transition metals (Au, Ag, Cu, Ni, Pd, Pt) have been calculated with the Embedded Atom Method (EAM); the results agree well with available experimental data for both mono-vacancy and di-vacancy mechanisms. The EAM was also used to calculate activation energies for vacancy migration near dilute impurities. These energies determine the atomic jump frequencies of the classic “five-frequency formula,” which yields the diffusion rates of impurities by a mono-vacancy mechanism. These calculations were found to agree fairly well with experiment and with Neumann and Hirschwald's “Tm” model.

No abstract

No abstract