Unified study of the lattice mechanical properties of the AgCl crystal

Abstract

The silver halide crystals have many peculiarities in their physical properties which are uncommon among the simple ionic solids. The different theoretical models used to calculate the properties of this group of solids have concentrated on explaining one or the other of them. But these calculations have one major difficulty common to all. It has not been possible to give a consistent description of the dielectric properties and the dispersion of phonons in the framework of a single model. We have shown from a microscopic analysis of the energy expression of a system of ions occupying arbitrary positions that there exist two types of short-range polarization mechanisms, one arising out of the overlap of the unperturbed wave functions and another due to the perturbation of the wave function. These two effects taken together resolve the incompatibility mentioned above. Based on this analysis we have proposed a model in terms of which we have correlated the cohesion, the stability, the phase-transition properties, the elastic and the dielectric properties, and the phonon dispersion of the AgCl crystal. It is seen that the present model broadly reproduces all the characteristic features of this crystal. Moreover, we have tried to assess in a rough way the relative importance of the different interactions envisaged and their relation to the typicalities of this solid. Finally, some of the limitations of the present calculation are also pointed out.