Theoretical analysis of phonon dynamical behaviour of Cesium Chloride at various temperatures

Abstract

We have developed a new model to investigate the complete lattice dynamics of cesium chloride at 78 K and at room temperature (298 K). The new model, van der Waals three body force shell model (VTSM) incorporates the effect of van der Waals interactions and three-body interactions in the frame work of rigid shell model where short range interactions are effective up to the second neighbour. A good agreement has been obtained between theory and experiment for dependant properties also. Cesium halides have been given a keen interest to most of the workers in the field of lattice dynamics due to the paramount importance of such binary solids, as the nature and physical properties of such crystal reveals to an understanding of their vibrational, thermo-dynamical, elastic, optical, thermal and numerous physical properties. The availability of a lot of measured data on elastic constants (1-4), dielectric constants (5,7), phonon dispersion curves (6,7,8), Debye temperature variations (9-11), two phonon IR and Raman spectra (12-15), third and fourth order elastic constants and their pressure derivatives (16,17), for all of them (CsCl, CsBr, CsI) and their interpretations by means of theoretical models (18-25) with moderate success, has motivated the present author to the basic need for a lattice dynamical model for the satisfactory description of their interesting properties. Various experimental and theoretical workers have given evolution for the study of phonon behaviour of CsCl structure. The first and most important model considered the ions of the crystal to be rigid, undeformable and unpolarizable spherical particle is rigid ion model (RIM) of Kellermann (25) which could not interpret well the dynamical, optical and elastic properties. Further efforts have been put as deformation dipole model (DDM) of Karo and Hardy (19) and rigid shell model (RSM) of Dick and Overhauser (26) and Woods et al. (23) by two different groups of workers. The DDM allows only the redistribution of charges in deformed electron cloud while the shell model considers the relative displacement. Therefore both effects (deformation and displacement) are present in ionic crystals. A general way to remove this deficiency is to include the deformation of electron shells in the framework of RSM. The most prominent amongst them are breathing shell model (BSM) of Schroder (20), the deformable shell model (DSM) of Basu and Sengupta (21), three-body force shell model (TSM) of Verma and Singh (27) and further Singh et al. (1) used extended three-body-force shell model (ETSM) which is an amalgamation of RSM and DDM. It is emergent from the descriptions that the most realistic model for the lattice dynamics and statics of these crystals can be developed by introducing the effect of van der Waals interactions (VWI), and three body interactions (TBI) in the framework of RSM, where the short-range interactions have been considered up to the second neighbours. The development of such a lattice dynamical model is the chief aim of the present work. This model is known as van der Waals three body force shell model (VTSM). A formal description of VWI and three-body interactions in the framework of RSM has been described in section 2. The present model VTSM in a way as outline above has been applied to investigate the complete lattice dynamics of cesium halides (CsCl, CsBr, CsI). The motivation behind the choice of the present system of solids lies in the fact that they are characterized by high energy gap, some discrepancies in PDCs and Cauchy violations. The effect of TBI and VWI are quite significant and play a vital role in the description of lattice dynamics of cesium halides. The proposed investigations have been carried out by adopting a simple method to determine a consistent set of 14-parameters )