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Relaxation of quasi-transverse phonons in the Herring mechanism and ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli

“…In accordance with the prevailing concepts [1][2][3][4][5][6][8][9][10][11], the main mechanism of the transverse phonon relaxation in normal three-phonon scattering processes is the Landau-Rumer mechanism [14] when the merging of the transverse and the longitudinal phonon produces a longitudinal phonon (T+L→L). The expression for the relaxation rate of phonons moving in an arbitrary direction relative to the crystallographic axes of crystals was obtained for this mechanism in terms of the anisotropic continuum model in [18]. Unlike earlier calculations, this expression exactly allows for the effect of the cubic anisotropy both on the spectrum of the vibrational branches involved in the energy conservation law and on the phonon polarization vectors.…”

“…Using experimentally determined elasticity moduli of the second and third orders, the researchers [12] derived an equation for the elastic energy associated with the lattice anharmonicity in cubic crystals and calculated phonon relaxation rates for some anharmonic scattering processes. The transverse ultrasound absorption in cubic Ge, Si and diamond crystals was discussed in [13].…”

“…If the cubic anisotropy in the matrix element describing threephonon scattering processes was taken into account, the dependences of the relaxation rates on the wave-vector of transverse phonons were shown to be qualitatively different from the classical linear Landau-Rumer dependence [14]. However, the analysis [12,13] was performed in the isotropic approximation for the spectrum and the polarization of phonons: the effect of the cubic anisotropy on the phonon spectrum was disregarded in the energy conservation law. Moreover, the vibrational modes were assumed to be pure (purely longitudinal or purely transverse) modes.…”

“…Such analysis was performed [18] for the relaxation rates of transverse phonons in terms of the Landau-Rumer mechanism. Unlike earlier calculations, the analysis took into account exactly the effect of the cubic anisotropy on both the spectrum of the vibrational branches involved in the energy conservation law and the phonon polarization vectors.…”

“…In the case of quasi-transverse phonons moving in directions other than symmetric ones, the maximum contribution of the longitudinal component to the transverse-longitudinal vibrations is 27% in KCl, 16.5% in Ge, 10% in Si, and 8% in diamond [17]. Therefore, our calculations of the ultrasound absorption in an arbitrary direction of the wave vector will allow for the contribution of the longitudinal component to the transverse-longitudinal vibrations similarly to [18]. It will be shown that the angular dependences of the absorption of quasi-transverse vibrational modes are qualitatively different in cubic crystals with the positive and the negative anisotropy of the second-order elasticity moduli.…”