On the ultrasonic attenuation of transverse modes in cubic crystals

Interaction of collinear and noncollinear phonons in anharmonic scattering processes and their role in ultrasound absorption of fast quasi-transverse modes in cubic crystals

The absorption of fast quasi-transverse modes during anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond and InSb) or negative (KCl and CaF(2)) anisotropies of the second-order elastic moduli is studied. Mechanisms underlying the relaxation of the fast quasi-transverse mode by two fast (the FFF mechanism) or two slow (the FSS) modes are discussed in the long-wavelength approximation. Angular dependences of the ultrasound absorption for the FFF, FSS and Landau-Rumer relaxation mechanisms are analyzed in terms of the anisotropic continuum model. The full absorption of the fast quasi-transverse mode is determined. The problem of the scattering of collinear and noncollinear phonons in cubic crystals and their role in the ultrasound absorption of the fast quasi-transverse modes is considered. It is shown that the FFF and FSS relaxation mechanisms are due to the cubic anisotropy of the crystals, leading to the interaction between noncollinear phonons. In crystals with a considerable anisotropy of the elastic energy (InSb and KCl), the total contribution of the FFF and FSS relaxation mechanisms to the full absorption is 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. The role of the Landau-Rumer mechanism in ultrasound absorption may be considerable in cubic crystals with a smaller anisotropy of the elastic energy. It is demonstrated that when anharmonic scattering processes play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the FFF or FSS mechanisms of relaxation) is insufficient for the quantitative description of the anisotropy of the full absorption of the fast quasi-transverse modes in cubic crystals.

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.

Quasi-transverse ultrasound absorption due to point defects and anharmonic scattering processes in cubic crystals with positive and negative anisotropies of the second-order elastic moduli

The quasi-transverse ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli is analyzed. The scattering of the ultrasound by point defects and during anharmonic scattering processes is considered. The quasi-transverse ultrasound absorption is analyzed as a function of the wavevector direction in terms of the anisotropic continuum model. The Landau-Rumer mechanism is considered for anharmonic scattering processes. Known values of the second- and third-order elastic moduli are used to calculate parameters determining the ultrasound absorption. It is shown that the angular dependences of the quasi-transverse ultrasound absorption differ qualitatively if the anharmonic scattering processes dominate in cubic crystals with positive and negative anisotropies of the second-order elastic moduli. For the scattering by point defects and the anharmonic scattering processes, the angular dependences of the quasi-transverse ultrasound absorption exhibit the inverse behavior, making it possible to determine the dominating mechanism of the ultrasound relaxation in the crystals under study.