The polarization catastrophe in defect calculations in ionic crystals

Abstract

The nature of the polarization catastrophe previously reported in several defect calculations is analysed. For the commonly used polarizable point dipole model it is shown that a necessary condition for the avoidance of such catastrophes is that the separation of all ion pairs, i, j must be greater than r_crit=(4 alpha _i alpha _j)^1/6 where the alpha _i's are the electronic polarizabilities. This requirement is independent of the form of the interionic potential function. This condition is identical with that previously derived by Tosi and Doyama for alkali halide molecules, but it is shown that it applies to all ion pairs in the solid. The effect of these inherent instabilities on the calculated energies of defects and of alkali halide molecules is discussed. It is concluded that the most realistic physical extension of the model which avoids these instabilities is the inclusion of the reduction of polarizability with ionic overlap.