Grain Boundary Diffusion in a Peierls-Nabarro Potential

We investigate the diffusion of a grain boundary in a crystalline material. We consider in particular the case of a regularly spaced low-angle grain boundary schematized as an array of dislocations that interact with each other through long-range stress fields and with the crystalline Peierls-Nabarro potential. The methodology employed to analyze the dynamics of the center of mass of the grain boundary and its spatio-temporal fluctuations is based on over-damped Langevin equations. The generality and the efficiency of this technique is proved by the agreement with molecular dynamics simulations.