Diffusion in concentrated lattice gases. Self-diffusion of noninteracting particles in three-dimensional lattices

Abstract

The dynamical process of the diffusion of tagged particles in concentrated lattice gases is investigated. The lattice is fcc and the particles are noninteracting except that double occupancy is forbidden. The self-diffusion coefficient and the waiting-time distributions for two consecutive jumps of a tagged particle are calculated numerically by Monte Carlo methods. The time-dependent correlations between consecutive jumps are analyzed in detail, especially the initially increased rate for backward jumps of the tagged particle. The self-correlation function of a diffusing particle is also calculated by a correlated-jump model, which represents a generalization of the usual treatment of self-diffusion to frequency dependence and to finite concentrations. The resulting diffusion coefficient agrees well with the direct numerical calculations. Some other analytical predictions are also tested. The incoherent dynamical scattering function shows the effect of correlations at small frequencies and mean-field behavior at high frequencies.