Elastic, anelastic, and piezoelectric coefficients of α-quartz determined by resonance ultrasound spectroscopy

Abstract

All independent components of the elastic constants, internal friction, and piezoelectric coefficients of synthetic α-quartz have been simultaneously determined by resonance ultrasound spectroscopy coupled with laser-Doppler interferometry. Seventeen crystals obtained from Z and X regions with various infrared-absorption values were used; for each crystal, a complete set of the coefficients was determined using 72 resonance frequencies, which were measured by a needle-transducer tripod in a vacuum at a constant temperature with frequency-error limit of 0.001%. The infrared-absorption value and grown region did not strongly affect the material coefficients. Among the eight (elastic plus piezoelectric) coefficients, piezoelectric coefficients were significantly different from previously reported values. The six independent internal-friction components showed a positive correlation with the temperature derivatives of the corresponding elastic constants, indicating that the dominant damping mechanism was the phonon-phonon scattering. Our values at 30°C are C11=86.76GPa, C12=6.868GPa, C13=11.85GPa, C14=−18.02GPa, C33=105.5GPa, C44=58.14GPa, and e11=0.151C∕m2, and e14=−0.061C∕m2.