A Determination of the Elastic Constants of Beta-Quartz

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Abstract
A new technique is described for quickly locating and measuring weak resonance points of a plate of piezoelectric material. The method involves driving the resonator with a frequency modulated carrier and demodulating and amplifying a voltage related to the motion of the resonator. The output of the amplifier is placed on one set of plates of an oscilloscope and the other plates are charged with the modulating voltage. The resulting pattern on the oscilloscope screen permits easy location and measurement of resonant frequencies. This arrangement was employed with a dynamical method to determine all elastic constants of beta-quartz. Edge effects were eliminated by the use of high harmonics as described by Atanasoff and Hart. Several hundred frequencies related to six modes of four cuts were measured, this number of modes being sufficient to permit the simultaneous solution of the resulting secular equations with an over determination of the five elastic constants. Table III gives the values obtained for these constants and also contains all the known results of other experimenters.

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