Vacancy-mediated diffusion in a binary substitutional alloy was investigated by explicitly accounting for discrete vacancy sources and sinks. The regions between sources and sinks were treated as binary crystals with a perfect lattice structure containing a dilute concentration of vacancies. The sources and sinks were assumed ideal, maintaining an equilibrium vacancy concentration in their immediate vicinity. Diffusion within the perfect lattice was described with a diffusion-coefficient matrix determined by kinetic Monte Carlo simulations for a binary, thermodynamically ideal alloy in which the components had different vacancy-exchange frequencies. Continuum simulations were performed for diffusion couples with discrete grain boundaries acting as vacancy sources and sinks. Effective grain coarsening due to the Kirkendall effect was observed even in the absence of Gibbs-Thomson driving forces. As in standard ternary systems, uphill diffusion was observed. It was also found that the drift of the lattice frame of reference as a result of the Kirkendall effect increased with the source/sink density. Upon increasing the density of vacancy sources and sinks, the conventional treatment of substitutional diffusion was recovered which assumes a dense and uniform distribution of vacancy sources and sinks that maintain an equilibrium vacancy concentration throughout the solid. The inverse Kirkendall effect, where the slower component segregates at grain boundaries acting as vacancy sinks, was also observed in the simulations.

Substitutional Diffusion and Kirkendall Effect in Binary Crystalline Solids Containing Discrete Vacancy Sources and Sinks. H.C.Yu, D.H.Yeon, A.Van der Ven, K.Thornton: Acta Materialia. 2007, 55[20], 6690-704