Chapter 4 Influence of isotopic and substitutional atoms on the propagation of phonons in anisotropic media

Abstract

This chapter describes the properties of the Boltzmann kinetic equation (BKE) and its applications to the description of the propagation of long wavelength acoustic phonons in an anisotropic medium containing substitutional isotopic atoms. BKE is a natural tool for the study of the scattering of nonstationary phonon beams by substitutional and isotopic atoms (SIAs). This scattering mechanism the collision integral is a linear integral operator, which for some important classes of elastic media, can be spectrally decomposed. The basic principles of the phonon kinetics and the purely ballistic propagation of phonon beams are introduced in the chapter. The main concepts of phonon kinetics are discussed. The procedure for deriving the spectrum of the relaxation rates and the diffusion equation along with the diffusion coefficient is explained. It is shown that the diffusion constant determines the long-time asymptotics of a phonon pulse and can be measured experimentally. The suitable experimental data are presented. The general approach to the problem of thermalization of an initial state of a rarefied gas of dispersionless acoustic phonons based on the Fourier–Laplace transform (FLT) technique, valid also for elastic media of arbitrary symmetry, is presented.