Anharmonic processes of scattering and absorption of slow quasi-transverse modes in cubic crystals with positive and negative anisotropies of second-order elastic moduli

The quasi-transverse ultrasound absorption during anharmonic processes of the scattering in cubic crystals with positive (Ge, Si, diamond and InSb) and negative (KCl and NaCl) anisotropies of the second-order elastic moduli is studied. Mechanisms underlying the relaxation of the slow quasi-transverse mode by two slow (the SSS mechanism) or two fast (the SFF) modes are discussed in the long-wavelength approximation. Angular dependences of the ultrasound absorption for the SSS, SFF and Landau-Rumer relaxation mechanisms are analyzed in terms of the anisotropic continuum model. The full absorption of the slow quasi-transverse mode is determined. It is shown that the SSS and SFF relaxation mechanisms are due to the cubic anisotropy of the crystals, leading to the interaction between noncollinear phonons. Two most important cases-the wavevectors of phonons are in the cube face plane or the diagonal planes-are considered. In crystals with a considerable anisotropy of the elastic energy (Ge, Si, InSb, KCl and NaCl) the total contribution of the SSS and SFF relaxation mechanisms to the full absorption is either several times or one to two orders of magnitude larger than the contribution from the Landau-Rumer mechanism depending on the direction. Much of the dominance of the former relaxation mechanisms over the Landau-Rumer mechanism is explained by second-order elastic moduli.