Master equation approach to the theory of diffusion in alloys and calculations of enhancement factors for tracer solvent and tracer solute diffusion in FCC alloys

The earlier-suggested master equation approach is used to develop the consistent statistical theory of diffusion in alloys using the five-frequency model of FCC alloys as an example. Expressions for the Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are presented. We discuss methods of calculations of these averages using both the mean-field and the pair-cluster approximation to describe influence of vacancy-solute and solute-solute interactions, and both the nearest-neighbor and the second-shell approximation to describe vacancy correlation effects. The methods developed are used for calculations of enhancement factors which determine the concentration dependence of tracer self-diffusion and tracer solute diffusion in dilute FCC alloys. For the tracer self-diffusion, we show that some significant contribution to the enhancement factor related to the thermodynamic activity of vacancies was missed in the previous treatments of this problem. It implies that the most of existing estimates of parameters of the five-frequency model for real alloys should be revised. For the tracer solute diffusion, the expression for the enhancement factor seems to be presented for the first time. The results obtained are used to estimate the microscopic parameters important for diffusion, including the vacancy-solute interaction, in several FCC alloys for which necessary experimental data are available.