Diffusion along the Grain Boundaries in Crystals with Dislocations

Abstract

A generalization of the Fisher model of the grain boundary diffusion is suggested, which takes into account the diffusion along short circuit diffusion paths (i.e., dislocations) in the bulk of crystalline grains. For the B-regime of the grain boundary diffusion, three different penetration modes have been found: at the short times the penetration depth of the element diffusing along the grain boundary is given by the Whipple solution of the Fisher model, but with the pipe diffusion coefficients along the dislocation cores instead of the volume diffusivities; at the intermediate times the penetration depth is a weak function of time, and at the large times the penetration depth again increases with time according to the Whipple solution, however, the rate of this increase is much smaller than in the initial period of time. The applications of the model for diffusion in nanomaterials are discussed.