Anharmonic Processes of Scattering and Relaxation
of Slow Quasi-Transverse Phonons in Cubic Crystals

I. G. Kuleyev*, I. I. Kuleyev, and I. Yu. Arapova

Institute of Metal Physics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevsko 18, Yekaterinburg, 620219 Russia

*e-mail: kuleev@imp.uran.ru

Received June 30, 2008

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 scat-
tering 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.

PACS numbers: 62.20.D-, 62.80.+f, 63.20.-e, 63.20.K-, 63.20.D-

DOI: 10.1134/S1063783409050035

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