Second-order phenomena in α-quartz and the polarizing effect with plates of orientation (xzl)Ψ

Abstract

The change in series resonance frequency of piezoelectric resonators caused by a superposed dc electric field, known as the polarizing effect, is studied on the three thickness modes of thin plates made of α-Quartz. For cuts of orientation (xzl)Ψ, which operate in the fundamental frequency range between 2.7 and 5.0 MHzand at dc electric field intensities between ±106 V_m^-1, the change in frequency is proportional to the intensity of the applied dc electric field and depends on the cut angle Ψ and on the mode of vibration. At the dc field of 106 V_m^-1, the maximum change in frequency is found to be 16 parts per million. Quasilinear interpretation of the polarizing effect and the subsequent formula for its magnitude lead to determination of several components of the tensors of electroelasticity, second-order piezoelectricity, and second-order permittivity of α-quartz. The order of magnitude of these components is found to be 10⁰ NV^-1m^-1, 10^-10 NV^-2, and 10^-20 FV^-1, respectively; the mean probable errors in the determined values are less than 4%, 30% and 30% in the same order. While an allowance must be made for the cumulative character of the determined values of the second-order constants, the available evidence indicates that the polarizing effect is caused mainly by the change in values of the elastic constants; with the polarizing effect exceeding 10^-11 V^-1m^-1, the converse piezoelectric effect accounts only for multiples 10^-12 V^-1m^-1, and typical contributions of the second-order piezoelectricity and the second-order permittivity are of the order of 10-13 V-1m. Based on these results, our experimental data are reproduced with an accuracy of better than 3% on the average. The potential of the polarizing effect for investigation of the second-order phenomena becomes evident and should be recognized.