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 ␣-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 piezoelectric͒ 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

Residual stress preserved in quartz from the San Andreas Fault Observatory at Depth

“…The stress tensor (s ij ) is calculated from the strain tensor and the elastic stiffness constants (C ijkl ) (i,j,k,l = 1,3) for trigonal quartz (Ogi et al, 2006), by applying Hooke's law, s ij = C ijkl e kl . Calculating orientation and strain tensor for each measured image allows preparation of maps that display their variations as a function of position.…”

Evidence for residual elastic strain in deformed natural quartz

“…From the measured deviatoric strain tensor ε'kl one can deduce the deviatoric stress field σ'ij experienced by the quartz grain within its setting, applying Hooke's Law σ'ij = cijkl · ε'kl. Using the elastic stiffness tensor by Ogi et al (2006) for α-quartz, combined with the measured strain tensor, we derive a residual stress tensor corresponding to an equivalent stress of approximately 50 MPa. This is a first documentation of high residual lattice strains in natural minerals.…”

Resonant-ultrasound spectroscopy for studying annealing effect on elastic constant of thin film

“…RUS has been developed and advanced by Anderson et al [23], Ohno [24], Miglioiri et al [25], Ledbetter et al [26], and Maynard [27], and elastic properties of single crystal [28,29], piezoelectric material [30,31], composite [32], and thin films [33] have been studied. RUS is superior to other techniques because it is capable of determining anisotropic elastic constant and being unnecessary to grip the specimen.…”