Effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in germanium crystals

A method has been proposed for approximating a phonon spectrum of cubic crystals, which has been obtained from data on inelastic neutron scattering for symmetric directions, over the entire Brillouin zone in the form appropriate for studying relaxation characteristics of phonon systems. The effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in anharmonic processes of scattering with the participation of three longitudinal phonons has been investigated for germanium crystals. It has been shown that the inclusion of the dispersion leads to a decrease in the anisotropy of ultrasonic absorption in the LLL relaxation mechanism and makes it possible to fit the results obtained from calculations of the ultrasonic absorption coefficients to the experimental data in the low-temperature range. The temperature dependence and anisotropy of the relaxation rate of longitudinal thermal phonons in germanium crystals have been determined from experimental data on ultrasonic absorption. The performed analysis has refined values of the relaxation parameters obtained from the interpretation of the data on thermal conductivity of germanium crystals with different isotopic compositions in the isotropic-medium model.