Mobility and diffusivity for vacancy-solute diffusion in a simple cubic edge dislocation

Abstract

An edge dislocation in a simple cubic crystal is considered as the basis for a model for vacancy-induced transport. The Burgers vector for the dislocation is [01̄0], and a solute atom moves along the compressed region of the core by vacancy exchanges along the edge of the extra half plane of atoms. The length of the dislocation is carried to the limit of an infinite number of lattice sites. Consequently, when the vacancy is tightly bound to the dislocation, that limit of tight binding becomes exact. In the tight binding limit, the correlation factor goes to zero for self-diffusion as expected. With vacancy solute tight binding, this result is not altered. Vacancy-solute repulsion can override vacancy-dislocation attraction and change the limit. In the case of dislocation and solute binding to the vacancy, the diffusivity becomes indefinitely large due to the abundance of defects increasing the jump frequency at a rate faster than the correlation factor decreases it. The mobility for electromigration also shows unusual limits. When the solute and dislocation both bind the vacancy, the ratio of the mobility to diffusivity becomes indefinitely large. So long as there is large dislocation vacancy binding, the ratio remains large even with solute vacancy repulsion.