Precise Vibrational Frequency Distributions and the Second-Order Raman Spectrum and Specific Heat of NaCl

Abstract

Vibrational distribution functions are derived for the sodium chloride lattice for a series of increasingly dense, evenly distributed points in the Brillouin zone. The rigid-ion and the deformable-ion models are compared, and the effect of including next-nearest-neighbor repulsive interactions is considered. Calculation of the Debye characteristic temperature ${\Theta }_D\mathrm{}\left(T\right)\mathrm{}$ and the moments of the distribution ${\mu }_m$ as functions of sample density indicates that for the densest sample used the ${\Theta }_D\mathrm{}\left(T\right)\mathrm{}$ curve is established down to 2°K and the errors in the moments are insignificant for $m\ge -2.5\mathrm{}$. Singularities in the density-of-states and the combined density-of-states distributions are related to critical points and crossover features in the dispersion curves, which are also evaluated for high densities of points along certain symmetry directions. Comparison is made with the experimental second-order Raman spectrum of rocksalt, and it is shown how these measurements provide extensive indirect tests of the details of the theoretical lattice frequency spectra.