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 being binary crystals, with a perfect lattice structure, which contained a dilute concentration of vacancies. The sources and sinks were assumed to be ideal and to maintain an equilibrium vacancy concentration in their immediate vicinity. Diffusion within the perfect lattice was described by using a diffusion-coefficient matrix which was determined by kinetic Monte Carlo simulations for a binary thermodynamically ideal alloy in which the components had differing vacancy-exchange frequencies. Continuum simulations were performed for diffusion couples having discrete grain boundaries which acted 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, up-hill 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. This assumed a dense and uniform distribution of vacancy sources and sinks that maintained an equilibrium vacancy concentration throughout the solid. The inverse Kirkendall effect, where the slower component segregated 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