Elastic Moduli of Quartz versus Hydrostatic Pressure at 25° and − 195.8°C

TLDR

The study derives adjusted ultrasonic velocities and pressure derivatives that satisfy cross‑checks and minimize adjustment errors. Ultrasonic wave velocities in single‑crystal quartz were measured across temperature and pressure using a pulse‑superposition method, then adjusted and used to compute elastic moduli. The resulting zero‑field elastic moduli at 0 MPa and their initial pressure derivatives for quartz at 25 °C and –195.8 °C are reported. Soc.

Abstract

Ultrasonic wave velocities in single-crystal quartz have been measured as a function of temperature and pressure by means of a pulse superposition method described in J. Acoust. Soc. Am. 33, 12 (1961). In order to make good use of all the experimental data, a set of ``adjusted'' velocities and initial pressure derivatives was obtained which satisfies all the cross-checks exactly, while minimizing a weighted sum of the squares of the adjustments from the measured values. These adjusted values were then used to calculate the elastic moduli as functions of temperature and pressure. Values of ``zero-field'' moduli at zero pressure and the initial pressure derivatives determined in this way are shown below. T=25∘CT=−195.8∘CValue at p=0PressureValue at p=0PressureModulus(1011 dyn/cm2)derivative(1011 dyn/cm2)derivativec118.6803.288.7263.40c12=c11−2c660.7048.660.9907.40c131.1915.971.3025.41c14−1.8041.93−1.7732.00c3310.57510.8410.91910.26c445.8202.665.9721.77c663.988−2.693.868−2.00