Temperature Dependence of the Width of the Fundamental Lattice-Vibration Absorption Peak in Ionic Crystals. II. Approximate Numerical Results

Abstract

The results of numerical calculations of the temperature dependence of the width and position of the fundamental lattice-vibration absorption peak in NaCl and LiF are presented. The calculations are carried out in the high-temperature limit, on the basis of the Hardy-Karo deformation dipole model of these crystals. Cubic and quartic anharmonic terms are retained in the crystal Hamiltonian, but the approximation of neglecting the anharmonicity of the Coulomb forces has been made. The expressions for the Fourier-transformed anharmonic force constants have been approximated and simplified by a method suggested by Peierls. The results of the calculations show that the quartic anharmonic terms in the crystal potential energy make a contribution to the width of the fundamental absorption peak which is comparable in magnitude with the contribution from the cubic anharmonic terms, in agreement with the theoretical arguments of Gurevich and Ipatova. Since the quartic anharmonic contribution to the width is proportional to the square of the absolute temperature at high temperatures, these results provide an explanation for the experimental observations that the width increases with a power of the absolute temperature which is intermediate between the first and the second. Quantitatively, the theoretical results are in quite good agreement with the experimental data of Heilmann for the variation with temperature of the width of the fundamental absorption peak in LiF. In the case of NaCl, the agreement between theory and experiment is somewhat poorer, but the theoretical values are still within a factor of about 2 of the experimental values of Hass. The frequency dependence of the imaginary part of the dielectric constant of these two crystals has also been calculated, and is compared with experimental data.