The relaxation of thermal and high-frequency transverse phonons in the   semiconductor cubic crystals
  We have considered the relaxation of transverse thermal and high-frequency phonons for the Landau-Rumer mechanism in the semiconductor cubic crystals. Using the known values of these elastic moduli, the parameters determining the transverse phonon relaxation rates for the Landau-Rumer mechanism have been evaluated for the crystals under consideration. It is shown that the dependence of the relaxation rate on the wave vector of thermal and high-frequency phonons strongly differs from the classical Landau-Rumer relationship both in the isotropic medium and in the cubic crystals studied. In contrast to the isotropic medium, for Ge, Si, InSb, and GaSb crystals in the [100] direction, this dependence has an essentially non-monotonic character with two maxima, the second of which is in the range of high-frequency phonons. This anomaly in the [100] direction is most pronounced for InSb and GaSb crystals. The features of the relaxation rate are found to result from the angular dependence of the probability of anharmonic scattering and from the anisotropy of elastic properties. 
I. G. Kuleyev, I. I. Kuleyev, A. P. Tankeyev and I. Yu. Arapova