The temperature dependence of the fundamental lattice vibration absorption by localized modes

Abstract

A calculation of the fundamental lattice absorption by localized vibration modes associated with impurity ions in crystals, with particular reference to U-centers in alkali-halide crystals of the rocksalt structure, is carried out utilizing two different approaches to this problem. The first method of calculation of the localized mode contribution to the absorption coefficient of an impure crystal is based on an adiabatic theory of the localized modes, in which the localized modes and the band modes are regarded as two systems which interact through the anharmonic terms in the crystal potential energy. The second approach to the calculation is through many body perturbation theory and proceeds from the Kubo expression for the imaginary part of the dielectric function. The results of both of these calculations show that the strength of the absorption by localized modes has a temperature dependence which is described by a factor exp(−2 M( T)), where T is the absolute temperature, and a microscopic theory for the function 2 M( T) is presented.