Drift Mobility of an Ionic Impurity in an Electric Field

Abstract

When diffusion occurs by either a vacancy or interstitialcy mechanism, an electric field has two effects on the diffusion process. First, the field exerts a direct force on the electrically charged ions. This effectively changes the energy of motion for an ion jump in the direction of the field. Secondly, the field causes a net flow of vacancies or interstitialcies. This makes vacancies or interstitialcies approach an ion more frequently from one direction and less frequently from the opposite direction. The drift mobility $\mu$ of an ionic impurity in an electric field is found from consideration of these two effects, with $\mu$ being related to $D^{*}$, the tracer diffusion coefficient of the impurity in the absence of an electric field. General equations are derived giving the value of $\frac{\mu }{D^{*}}$ in any homogeneous cubic crystal. Explicit expressions are calculated for several specific lattices. These equations apply best when the impurity ion has the same charge as the solvent ions in the sublattice of interest. Both vacancy and interstitialcy mechanisms are treated. The value of $\frac{\mu }{D^{*}}$ depends on both the diffusion mechanism and the relative values of the various jump frequencies near the impurity.