Calculation of Defect-Formation Energies in Alkaline-Earth Oxides: Interionic Forces

Abstract

A model potential for the alkaline-earth oxides was developed and tested. The interionic potential contains the usual Coulombic and two-body short-range terms, such as those which have been used in previous alkali halide calculations, plus many-body terms which are incorporated by means of the Lundquist three-body approximation in which only the spherically symmetric term in the overlap-charge-density expansion is retained. The three-body interactions contribute to both the long-range and the short-range forces. Additional short-range central-force interactions between nearest-neighbor ions and next-nearest-neighbor ions are included; these are modeled by means of a Born-Mayer plus van der Waals potential. The electronic polarizabilities of the ions are described by a shell model. Parameters in the model potential and in the shell model are evaluated using the elastic constants and their pressure derivatives, the low- and high-frequency dielectric constants, the infrared dispersion frequency, and the equilibrium interionic separation. Three constraints on thw shell model are required. The model does not give satisfactory results in that (1) the trend in an effective charge parameter, χo, through this family of oxides runs counter to that for the Phillips ionicities and (2) the Born-Mayer potential parameters appear to be highly anomalous compared with those for other ionic crystals. The principal weakness of the model apparently resides in tis neglect of bond-bending (noncentral force) terms, which results in an overestimate of the overlap contribution to the bond-stretching terms, in excessive deviations in the effective charges from the classical valences, and in departures of the Born-Mayer potential parameters from the values found in alkali halide and alkaline-earth fluorides.