Correlated diffusion in two-dimensional systems

Abstract

An equations-of-motion procedure for calculating particle diffusion in a minimally interacting, isotropic concentrated lattice gas given by Tahir-Kheli and Elliott (TKE) is known to give moderately accurate results over a wide range of concentrations in three dimensions. In two dimensions the TKE procedure and its extension to anisotropic lattices are expected to be less accurate. To test the adequacy of these theories in two dimensions, we report a variety of precision Monte Carlo simulations which have been performed in large effective samples, both isotropic and anisotropic. We find noticeable systematic differences between the predictions of the TKE theory for the intermediate-concentration regime and the Monte Carlo results. To rectify this shortcoming, we have reanalyzed the multiple rescattering of the tracer-vacancy pair, including the ensuing spatial constraints, through a sea of background particles (and vacancies) which are distributed over a two-dimensional lattice with a coordination number z. The resultant theory is found to be in very good agreement with the precision Monte Carlo data covering a wide range of particle concentrations as well as lattice anisotropies.