Lattice Dynamics, Mode Grüneisen Parameters, and Coefficient of Thermal Expansion of CsCl, CsBr, and CsI

Abstract

The phonon dispersion curves for CsCl, CsBr, and CsI have been obtained using a rigid-ion model with an appropriate effective ionic charge. The five model parameters for each crystal are obtained from three elastic constants and the two long-wavelength optic-mode frequencies, reliable data for which exist for all three crystals. Our results are in agreement with those of more elaborate models. The phonon density of states and the Debye characteristic temperatures are also calculated. A Born-Mayer-type potential is used to calculate long-wavelength LO and TO mode frequencies as functions of pressure from pressure dependence of bulk modulus. The result for TO of CsBr agrees well with a recent experimental determination. Next, using the values of the elastic constants and LO and TO frequencies at various pressures, $\omega -\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{s}-\overrightarrow{\mathrm{k}}$ curves in selected directions are generated as functions of pressure. Mode Grüneisen parameters are then calculated as functions of $\overrightarrow{\mathrm{k}}$. Finally, the Grüneisen constant and the volume coefficient of thermal expansion are obtained as functions of temperature. They agree very well with available experimental data.