Localization of phonons in mixed crystals

The problem of phonon localization in mixed crystals is formulated using the self-consistent localization theory developed by Vollhardt and Wölfle. The coherent-potential approximation (CPA) is used to obtain the phonon density of states and CPA diffusion constant. Three-dimensional harmonic binary systems with random masses but constant isotropic force are studied in detail. With the use of the semielliptical band approximation, the phase diagrams, mean free path, correlation and localization lengths, and diffusion constant are calculated for various mass ratios and concentrations. The limit when the mass of one component is infinite is also studied.