Diffusion of a grain boundary in a crystalline material was investigated. In particular, the case was considered where a regularly spaced low-angle grain boundary was schematized as an array of dislocations that interacted with each other via long-range stress fields and a crystalline Peierls–Nabarro potential. The method used to analyze the dynamics of the center of mass of the grain boundary and its spatio-temporal fluctuations was based upon over-damped Langevin equations. The generality and the efficiency of this technique was proved by its agreement with molecular dynamics simulations.

Grain Boundary Diffusion in a Peierls–Nabarro Potential. F.Leoni, S.Zapperi: Journal of Statistical Mechanics, 2007, P12004