Compressibility and Absorption Frequency of Ionic Crystals

B. Szigeti
1950 Proceedings of the Royal Society A  
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
more » ... 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 twobody interactions and leads to the Cauchy relations between the elastic constants. * This paper is based on E.R .A . R eport L/T 233. [ 51 ] 4 -2 © © © F igure 4. Ions in their equilibrium positions. In this figure the distortions of the negative ions due to second neighbours are also indicated. The do tted line corre sponds to spherical shape, for th e sake of comparison. may be taken to illustrate the case when there is a small homopolar tendency in equilibrium which diminishes with decreasing distance between neighbouring ions. Possible distortions of the negative ions due to second neighbours, neglected in figures 1 to 3, are shown in figure 4 .
doi:10.1098/rspa.1950.0161 fatcat:a4q7isl4g5axha2et2iuom4fvy