Drift Mobility and Diffusion for Impurities in Ionic Crystals

Abstract

An electric field exerts a force on the charged ions in an ionic crystal and causes a net flow of ions and vacancies. In calculations of the drift mobility $\mu$ and diffusion coefficient $D$, it has been customary to assume that the vacancy flow does not alter the average vacancy concentrations at sites that are second-nearest neighbors or farther from the impurity. In the present treatment, this approximation is avoided. Instead vacancies are presumed to be at equilibrium only at vacancy sources and sinks and on the symmetry plane containing the impurity. The resulting equations for $\frac{\mu }{D}$ include terms $\Sigma i^{}{k}_i\Delta w_i$. Here $\Delta w_i$ is the difference between the vacancy-jump frequencies in the positive and negative $x$ directions from site $i$ in the absence of a field, and the $k_i$ are coefficients. The summation, which is over all sites in the crystal, simplifies in a number of special cases. Whenever the vacancy-jump frequency for association of a vacancy-impurity complex differs from the vacancy-jump frequency far from an impurity, extra terms which have not appeared in previous expressions for $\frac{\mu }{D}$ are obtained.