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

Abstract

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.

Коэффициенты Усиления Потока Фононов В Кристаллах С Различным Типом Анизотропии Упругой Энергии

“…1, а). Вектора q = qn, δq 1 = qn 1 и δq 2 = qn 2 образуют тройку взаимно орто-гональных векторов [19]. Тогда для изотропной среды имеем…”

“…В кристаллах второго типа (k − 1 < 0) для волновых векторов в плоскости грани куба фазовая скорость мед-ленной поперечной моды t 2 , принимает минимальные значения. Для нее спектр фононов при ϕ ≪ 1 определя-ется уравнением (18), и коэффициент усиления A t2 (θ, 0) совпадает с выражением (19). Поскольку во всех кри-сталлах второго типа параметр δ < 0, то коэффициент усиления для них оказывается меньше единицы (см.…”