Compressibility and absorption frequency of ionic crystals

A simple relation is derived between the compressibility and absorption frequency of ionic crystals. This relation takes into account the change which a displacement induces in the electronic configuration, and is independent of the uncertainty concerning the Lorentz force. Comparison with experimental data shows very good agreement in the case of the alkali halides. The changes in the electronic configuration of each ion are described in terms of a dipole moment and in terms of ‘local distortions’. The latter are caused by forces not included in the Lorentz force, and it is assumed that they are localized in small regions in the immediate neighbourhood of the neighbouring ions. The local distortions are responsible for the deviation of the polarization from the value given by the Lorentz force; from the sign of this deviation it is concluded that they are due mainly to the non-electrostatic repulsive forces. Although this model allows deviations from spherical charge distribution around the ions, it nevertheless permits the splitting of the energy of certain types of displacements into two-body interactions and leads to the Cauchy relations between the elastic constants.