A project was undertaken to measure the elastic and associated parameters of quartz to very high accuracy using a fully automated measurement system. Measurements were made of the properties of standard-grade synthetic quartz and of very-high-purity quartz. Significant differences between the two grades of quartz were found that are fully consistent with an anelastic relaxation of the known point defects in impure quartz. An automated pulse-echo phase detection system was used to gather an extreme large amount of transit time data which was then corrected for different effects and used to determine the parameters of the transducer bond accurately. Interferometry was used to eliminate length measurement error, and thus a highly accurate velocity measurement could be made. The dielectric moduli were measured using a capacitance technique and literature values for the piezoelectric moduli were used. A computer optimization routine was developed to fit the best set of independent elastic moduli to the entire set of experiment data. >

A new measurement of the basic elastic and dielectric constants of quartz

The Constants of Alpha Quartz

Three‐dimensional linear equations of motion for small vibrations superposed on thermal deformations induced by steady, uniform temperature change in quartz are obtained. The material properties of quartz, such as the elastic stiffnesses and thermal expansion coefficients, are assumed temperature dependent and expressible by third‐degree polynomials in temperature change. From the solutions of third‐order perturbations of these equations for the thickness resonances of infinite quartz plates, six values of the effective third temperature derivatives of elastic stiffnesses C(3)pq are calculated by the use of the measured temperature coefficients of frequency by Bechmann, Ballato, and Lukaszek [Proc. IRE 50, 1812 (1962)] for various doubly rotated cuts and the values of the first temperature derivatives C(1)pq and the effective second temperature derivatives C(2)pq obtained in a previous study. An infinite system of two‐dimensional equations of motion is derived by Mindlin’s method of power‐series expansi...

Frequency-Temperature Behavior of Thickness Vibrations of Doubly-Rotated Quartz Plates Affected by Plate Dimensions and Orientations

Stress Compensated Orientations for Thickness-Shear Quartz Resonators

The temperature coefficients of delay-time for Xpropagating acoustic surface-waves have been determined for rotated Y-cuts of alpha quartz ranging from 32' to 47.25\" and tested within an overall temperature range of -50\" to +lZO\"C. Substrates made from both natural and synthetic quartz were tested. The turnover temperatures, where the derivative of the delaytime with respect to temperature becomes zero, were determined. The range of cut angles yielded turnover temperatures from over 100°C to below 0°C. When matching inductors were used, the turnover temperature was shifted. In general, the effect of the tuning inductor is to lower the turnover temperature in proportion to the TC of the inductor, a fact which must be recognized when designing devices where the constancy of delay-time is a necessary requirement.

R.W. Ward

Papers

Selected Topics in Quartz Crystal Research

Analytical and Experimental Investigations of 32KHz Quartz Tuning Forks