Theory of Plane Elastic Waves in a Piezoelectric Crystalline Medium and Determination of Elastic and Piezoelectric Constants of Quartz
Atanasoff and Hart made a series of elaborate experiments in order to determine dynamically the elastic constants of quartz. However, they reported that in the evaluation of the elastic constants from the experimental data, there was a small but not easily explained discrepancy between theory and experiment. Lawson pointed out later that the piezoelectric effect could not be neglected in the dynamic determination of elastic constants. The present writers became aware that in the case of a plane elastic wave in a piezoelectric crystalline medium, only the component of piezoelectric polarization in the direction of wave propagation produces a restoring force against mechanical strain, as far as the piezoelectric effect is concerned. Thus the writers could derive the equation of a plane wave in a piezoelectric crystalline medium in general and could further determine the elastic and piezoelectric constants, together with their temperature coefficients, from experimental data. Various experimental results reported by the foregoing authors, including Atanasoff and Hart, can now be adequately explained, even at high temperatures, so that there is no longer any discrepancy between theory and experiments.