Institute of Metal Physics, Ural Division, Russian Academy of Sciences, 620219 Ekaterinburg, Russia.
J Phys Condens Matter. 2010 Mar 10;22(9):095403. doi: 10.1088/0953-8984/22/9/095403. Epub 2010 Feb 17.
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.
在具有正各向异性（Ge、Si、金刚石和 InSb）或负各向异性（KCl 和 CaF2）二阶弹性模量的立方晶体中，研究了非谐散射过程中快横向准模态的吸收。在长波长近似下，讨论了由两个快（FFF 机制）或两个慢（FSS 机制）模式弛豫快横向准模式的机制。在各向异性连续体模型的基础上，分析了 FFF、FSS 和 Landau-Rumer 弛豫机制的超声吸收角依赖性。确定了快横向准模态的完全吸收。考虑了立方晶体中共线和非共线声子的散射及其在快横向准模态超声吸收中的作用。结果表明，FFF 和 FSS 弛豫机制是由于晶体的各向异性，导致非共线声子相互作用。在弹性能量各向异性相当大的晶体（InSb 和 KCl）中，FFF 和 FSS 弛豫机制对完全吸收的总贡献比 Landau-Rumer 机制的贡献大一个到两个数量级，这取决于方向。前两种弛豫机制比 Landau-Rumer 机制更为优势的原因很大程度上可以用二阶弹性系数来解释。在弹性能量各向异性较小的立方晶体中， Landau-Rumer 机制在超声吸收中可能具有相当大的作用。结果表明，当非谐散射过程起主导作用时，包含一种弛豫机制（Landau-Rumer 机制或 FFF 或 FSS 弛豫机制）不足以定量描述立方晶体中快横向准模态完全吸收的各向异性。
