Anharmonic character of the polarizing effect with the thickness modes of alpha -quartz plates

It is shown that for any thickness mode of vibrations the frequency change caused by a DC electric field applied to quartz plate resonators is only approximately proportional to the overtone frequency. It is shown that while this behavior can be predicted qualitatively, the deviations from proportionality are too irregular to claim a quantitative agreement. Concerning practical estimates of the magnitude of the frequency change for a chosen overtone, using the value known for the fundamental or another overtone, it appears that a field of 10/sup 6/ V/m the variation in Delta f/f among overtones will only rarely exceed 10/sup -6/. The highest value observed is 1.6*10/sup -6/.<
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