Local fields near a point-charge defect in cubic ionic crystals

Local fields ($E_{\mathrm{loc}}$) at ions near a point-charge defect in some cubic ionic crystals have been accurately calculated with a polarizable-rigid-ion model. The ratio $\frac{E_{\mathrm{loc}}}{r^2}$ for ions at a distance $r$ from the defect, plotted as a function of $r$, shows interesting oscillations about a horizontal line derived from the Clausius-Mossotti relation. For small $r$ the orientations of $E_{\mathrm{loc}}$ also fluctuate about the radial directions. Both the oscillations and angular fluctuations diminish rapidly with $r$ and become negligible when $r$ is beyond 20 Å. The implications of the results for defect-formation and diffusion-energy calculations for ionic crystals are discussed.