We describe a formalism to predict diffusion coefficients of substitutional alloys from first principles. The focus is restricted to vacancy mediated diffusion in binary substitutional alloys. The approach relies on the evaluation of Kubo-Green expressions of kinetic-transport coefficients and fluctuation expressions of thermodynamic factors for a perfect crystal using Monte Carlo simulations applied to a cluster expansion of the configurational energy. We make a clear distinction between diffusion in a perfect crystal (i.e. no climbing dislocations and grain boundaries that can act as vacancy sources) and diffusion in a solid containing a continuous distribution of vacancy sources that regulate an equilibrium vacancy concentration throughout. A variety of useful metrics to characterize intermixing processes and net vacancy fluxes that can result in the Kirkendall effect are described and are analyzed in the context of thermodynamically ideal but kinetically non-ideal model alloys as well as a realistic thermodynamically non-ideal alloy. Based on continuum simulations of diffusion couples using self-consistent perfect-crystal diffusion coefficients, we show that the rate and mechanism of intermixing in kinetically non-ideal alloys is very sensitive to the density of discrete vacancy sources.
ScienceDirect - Progress in Materials Science : Vacancy mediated substitutional diffusion in binary crystalline solids