Interionic potentials and force constant models for rocksalt structure crystals

Abstract

It is suggested that the observed departure from the Cauchy relation in alkali halide structure crystals is due to ionic deformations. Interionic forces may then be taken to be central and a comparison between lattice dynamical models and interionic potential models becomes possible. In this paper attention is restricted to MgO, NaCl, LiF and KI for all of which (i) an isotropic (breathing) deformation can account for the difference C 44–C 12 and (ii) only the negative ion need be considered deformable. The interionic potential is assumed to consist of Coulombic and van der Waals terms, which are taken as known, and short range repulsive terms with an exponential dependence on separation. The constants in these repulsive terms are determined from the force constants of the lattice dynamical models. Satisfactory agreement with measured cohesive energies can be achieved only if the charge on the ions is very close to the electronic charge (2 e in the case of MgO). This leads to a sacrifice in accuracy of the lattice dynamical models but this is shown to be small so that reasonable compatibility between the two sets of models is thus demonstrated. The interionic potentials are compared with those of other workers.