Random Walk Model of Interstitial Thermal Diffusion in Crystals

Abstract

We have developed a random walk model of interstitial diffusion of light impurity atoms in a host lattice of heavy atoms in the presence of a thermal gradient. To take account of the effect of the thermal gradient on the flux of impurity atoms we introduce a bias in the jump direction of the interstitial impurity. We assume that this bias is due to the temperature dependence of the excluded volume effects which arise during the jump of the impurity atom between interstitial sites. The resulting random walk equation for thermal diffusion is consistent with both positive and negative heats of transport in agreement with experimental data. Using a cell model approach and the assumption of local equilibrium, we then develop equations which permit the calculation of the bias in jump direction. The theory of interstitial diffusion developed here clarifies and supports the classic Wirtz model for interstitial thermal diffusion.