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

“…Notice that in an arbitrary direction of the wavevector q 1 the matrix element ( 16) includes a term proportional to the third-order elastic modulus c111 . This modulus is one order of magnitude larger than the other third-order moduli in the majority of cubic crystals, but its sign is opposite to the sign of the initial modulus c 111 (see [22], table 1). It is responsible for the small deviation of the relaxation characteristics in cubic crystals from those calculated in the context of the isotropic medium model [12].…”

“…The exact expression for the matrix element of the threephonon scattering processes [2,22] will only include the terms that are linear in longitudinal components of quasitransverse vibrations, while the terms proportional to quadratic combinations of (e 1 n 1 ), (e 2 n 2 ), (e 3 n 3 ) will be neglected. The error of this approximation is about 1% in Ge, InSb, GaSb and GaAs, and less than 1% in Si and diamond.…”

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

“…Therefore, the phonon relaxation rates calculated in the framework of this model provide a reliable basis for the interpretation of experimental data on the ultrasonic absorption and phonon transport in cubic crystals. It should be noted that the anisotropy of the spectrum and the presence of degeneracy points in vibrational modes of transverse phonons lead to a new relaxation mechanism of the phonons in some anharmonic processes of scattering in cubic crystals as compared to isotropic media [19][20][21]. For example, the Herring mechanism [19], in which the fusion of a longitudinal phonon with a slow (ST) transverse phonon generates a fast (FT) transverse phonon, becomes possible.…”

“…For example, the Herring mechanism [19], in which the fusion of a longitudinal phonon with a slow (ST) transverse phonon generates a fast (FT) transverse phonon, becomes possible. A new mechanism of transverse phonon relaxation in cubic crystals, according to which the fusion of a transverse phonon (slow or fast) with a slow transverse phonon generates a fast transverse phonon, has been investigated in [21]. This mechanism is similar to the Herring relaxation mechanism for longitudinal phonons [19] and can be referred to as the Herring mechanism for transverse phonons.…”

“…These mechanisms are absent in isotropic media, because the transverse modes in them are degenerate. A new relaxation mechanism of transverse phonons [21], like the Herring mechanism for longitudinal phonons [19], leads to a dependence of the longwavelength ultrasound absorption on the wavevector q and temperature T in the form α TTT ∼ α LTT ∼ q 2 T 3 . As a rule, this dependence appears to be less effective in the long-wavelength limit than dependences of the Landau-Rumer type: α λ TTT ∼ qT 4 .…”