Modeling diffusion on heterogeneous lattices: Derivation of general analytical expressions and verification for a two-dimensional square lattice

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In order to model diffusion for real crystals, it is necessary to acknowledge that for many chemically and physically interesting classes of compounds (e.g., semiconductors, ionic solids, alloys), there are several different binding sites of possibly widely different character. In contrast to the majority of existing lattice-gas models, which ignore this aspect by assuming equivalent lattice sites, we investigate the diffusion of particles on a heterogeneous lattice with two kinds of nonequivalent sites. General analytical expressions for the chemical and jump diffusion coefficients have been derived in the case of strong inhomogeneity for lattices of different symmetries and dimensionality. It is shown that the character of the particle migration depends crucially on the relative jump frequencies of particles sitting in deep and shallow sites. If these frequencies differ insignificantly, particle diffusion proceeds by single uncorrelated jumps. In the opposite case of widely differing jump frequencies, particles perform pairs of strongly correlated jumps. We have calculated density dependencies of the diffusion coefficients and some thermodynamic quantities for different temperatures and signs of the lateral pairwise interaction between the particles. The analytical data obtained by the real-space renormalization-group method have been compared with the numerical data obtained by Monte Carlo simulations. Almost perfect agreement between the respective results has been found.