Ultrasonic Attenuation in Quartz at Low Temperatures

Abstract

The attenuation of longitudinal ultrasound in $X$-cut quartz is explained in terms of three-phonon interactions involving slow transverse thermal phonons. The approximately ${\mathrm{T}}^{6}$ temperature dependence of the attenuation is understood when the dispersion of the slow transverse branch is properly considered. This mechanism can also account for the measured attenuation of four additional acoustic modes.