Acoustic losses in a thick quartz plate at low temperatures

We have shown that thermoelastic losses give the significant contribution to the total mechanical damping in the low loss quartz even for the bulk samples if the thickness of the sample is smaller than other dimensions. We have developed a model that describes experimental data of mechanical losses in a round quartz plate with the diameter 7.48 cm and the thickness 1.2 cm at temperatures 5-25 K in the range of eigenfrequencies 11-300 kHz. The model takes into account both the contribution of thermoelastic losses and the contribution due to the interaction of the acoustic wave with thermal phonons (Akhieser damping). Thermoelastic processes determine losses below 120 kHz. At larger eigenfrequencies, the Akhieser damping dominates.