Rigorous Model and Simulations of the Kirkendall Effect Diffusion in Substitutional Binary Alloys.

Abstract

The Kirkendall effect stems from the difference between the exchange rates of the atomic species and vacancies in a substitutional alloy. Vacancies, which mediate diffusion, are generated and eliminated at their sources and sinks, resulting in lattice shift and deformation. In the conventional model, these vacancy sources and sinks are assumed to be distributed everywhere in a solid and maintain vacancy concentration at a constant, uniform equilibrium value throughout the solid. In this thesis work, we propose a new, rigorous model of interdiffusion by considering explicit and localized vacancy sources and sinks such as free surfaces and grain boundaries. Vacancy concentration only remains at its equilibrium value at these explicit sources and sinks. In the bulk of a grain, vacancies are conserved and must diffuse in the same manner as atomic species.

This model was first applied to one-dimensional planar and quasi-one-dimensional cylindrical systems. The results demonstrated that explicit consideration of vacancy diffusion leads to different dynamics and final states compared with what the conventional model would predict. Two-dimensional simulations of the concentration evolution in a solid containing a grain boundary demonstrated that the interdiffusion process changes from fast-mode diffusion to slow-mode diffusion as the interdiffusion region becomes farther away from a grain boundary. In order to simulate interdiffusion and the Kirkendall-effect-induced deformation in two dimensions, we extended a smooth boundary method to impose generalized boundary conditions at the solid surfaces. This method was first applied to the traditional interdiffusion model coupled with a linear visco-plastic deformation model. Expansion, contraction, bending, as well as a complex combination of these types of deformations were studied. The new method was also applied to our rigorous model to simulate interdiffusion and resultant shape changes of a single crystalline solid.