Vacancy-controlled interdiffusion: Nonlinear effects

We derive the nonlinear equations governing vacancy-controlled interdiffusion in a two-component noninteracting lattice gas. We observe that when the diffusion constants of the two species are not equal, the problem cannot be reduced to a simple linear diffusion. In order to treat the strongly nonlinear limit of large kinetic asymmetry and small concentration of vacancies, we introduce an adiabatic approximation in which the "fast" species is in an equilibrium state defined by the instantaneous distribution of the "slow" species, which obeys a linear diffusion equation with a renormalized diffusion coefficient. Comparison with numerical solutions of the nonlinear equations shows that the adiabatic approximation captures the essential physics of the diffusion process.