LOCALIZATION AND PROPAGATION OF PHONONS IN CRYSTALS WITH HEAVY IMPURITIES

The energy spectrum of a harmonic lattice with heavy impurities is stu died within the framework of the scalar model approximation. A detaile d analysis of the dynamical properties of the system is made in the fr equency range close to the quasi-localized mode. It is shown that the dwell effect for the phonon diffusion coefficient occurs provided the lifetime of the quasi-localized mode becomes of the order of the phono n lifetime. The diffusion coefficient manifests a drastic reduction (t he dwell effect) under the same condition necessary for the peak in th e heat capacity to be observed. It is shown that the concentration of the impurities needed for observing this effect depends on the impurit y mass. For higher concentration of the impurities, the energy gap is shown to appear in the frequency range dose to the quasi-local mode. I n addition, localized modes are shown to exist in the frequency ranges adjoined to the energy gap.