Ultrasonic Attenuation in Dirty Dielectric Crystals

The attenuation of a sound wave by anharmonic interaction with the thermal phonons in a dielectric crystal has been calculated using the Boltzmann-equation approach of Woodruff and Ehrenreich. Contributions to the thermal-phonon collision rate due to elastic scattering of phonons by crystal defects (relaxation time τₑ) and due to intrinsic inelastic anharmonic processes (relaxation time τᵢ) are considered separately. In the case of longitudinal waves the attenuation remains finite as τₑ→0, whereas for transverse waves propagating in high-symmetry directions the attenuation tends to zero in this limit. For Ωτᵢ1, an estimate is made of the ratio of the longitudinal-wave attenuation in a dirty crystal (Ωτₑ→∞) to that in a clean crystal (Ωτₑ→0). This ratio is found to be a sensitive function of the Gr\"uneisen constants of the crystal and of the temperature.