Anelasticity of Quartz

Abstract

By means of the piezoelectric effect, measurements have been made of the variation with temperature of (1) the $Q$ of quartz bars executing free acoustical oscillations in torsion, and (2) the equivalent series electrical resistance of bars driven at their natural frequencies of longitudinal acoustical oscillations. For each of the bars studied, it was found that the internal dissipation had a maximum value at a temperature between room temperature and the quartz inversion temperature of 573°C. Measurements of resistance were made on one bar at several different frequencies. These data showed that part of the dissipation was due to a relaxation effect, whose decay time varied with temperature according to an Arrhenius equation. An activation energy of 22 kcal/mole and a relaxation-time constant of 2×${10}^{-14\mathrm{}}$ sec were deduced from the data, which showed also that the fraction of energy lost during each sinusoidal cycle of strain was independent of the frequency of vibration. Estimates of the activation energies and relaxation-time constants were deduced for the other bars measured. In one case, the dissipation was due to the migration of gold atoms from the electrodes into the quartz lattice.