Anharmonic processes of scattering and relaxation of slow quasi-transverse phonons in cubic crystals

Abstract

Relaxation of slow quasi-transverse phonons in anharmonic processes of scattering in cubic crystals with positive (Ge, Si, diamond) and negative (KCl, NaCl) anisotropies of the second-order elastic moduli has been considered. The dependences of the relaxation rates on the direction of the wave vector of phonons in scattering processes with the participation of three quasi-transverse phonons (the TTT relaxation mechanisms) are analyzed within the anisotropic continuum model. It is shown that the TTT relaxation mechanisms in crystals are associated with their cubic anisotropy, which is responsible for the interaction between noncollinear phonons. The dominant contribution to the phonon relaxation comes from large-angle scattering. For crystals with significant anisotropy of the elastic energy (Ge, Si, KCl, NaCl), the total contribution of the TTT relaxation mechanisms to the total relaxation rate exceeds the contribution of the Landau-Rumer mechanism either by several factors or by one to two orders of magnitude depending on the direction. The dominant role of the TTT relaxation mechanisms as compared to the Landau-Rumer mechanism is governed, to a considerable extent, by the second-order elastic moduli. The total relaxation rates of slow quasi-transverse phonons are determined. It is demonstrated that, when the anharmonic processes of scattering play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the mechanisms of relaxation of the slow quasi-transverse mode by two slow or two fast modes) is insufficient for describing the anisotropy of the total relaxation rates in cubic crystals.