Theory of the Electronic Polarizabilities of Ions in Crystals: Application to the Alkali Halide Crystals

Abstract

A theoretical estimate of the polarizabilities of ions in the alkali halides is made by means of a procedure based upon the product approximation which distinguishes the ionic constituents in the crystals but allows for their overlap and mutual interaction. Analysis by means of the Thomas-Kuhn sum rule is used allowing the sum representing the ionic polarizability to be represented by one effective parameter, which is calculated for the free ions from the Pauling theoretical values. The change in this parameter when the ion is transported into the crystalline environment is estimated by an energy level analysis used previously by Seitz. It is shown that this procedure accounts for most of the quantitative features of the polarizabilities of the alkali halides. Moreover, the implications of these results are strongly at variance with the usual view concerning the polarizabilities of ionic crystals, since the additivity rule appears as an accidental result of the qualitative similarity of the interactions in many crystals, and the possibility of large fluctuations in the polarizability of a given ion in different crystalline environments is made evident.