A mean field theory for diffusion in a dilute multi-component alloy: a new model for the effect of solutes on self-diffusion

A new extension of the self-consistent mean field (SCMF) theory is developed to describe diffusion in dilute alloys, special attention being paid to the problem of self-diffusion in the presence of solute atoms. We start from a microscopic model of the atom-vacancy exchange frequency including nearest neighbour (nm) interactions and derive kinetic equations from a Master equation. The non-equilibrium distribution function is expressed through time-dependent effective interactions. Their range of interaction is controlling the level of description of the paths of a vacancy after a first exchange. In contrast to the previous diffusion models devoted to concentrated alloys, the present formulation makes appear into the final result several exchange frequencies associated to a given atom depending on the chemical species of the atoms nearby. A first approximation restricted to nn effective interactions yields analytical expressions of the transport coefficients of a face centered cubic dilute binary alloy. The phenomenological coefficients are equivalent to the ones obtained using the five-frequency model within the first shell approximation. A new expression of the self-diffusion coefficient is proposed and compared to Monte Carlo (MC) simulations using the same atomic diffusion model. The SCMF theory reproduces the main tendencies of the MC simulations, in particular within the random alloy region where the recent five-frequency model was not satisfying. The limitations and future improvements of the SCMF approach are easily related to the range of the effective interactions considered.