Abstract
We calculated the turnover temperatures Tto of crystallographically doubly rotated quartz plates vibrating in the thickness mode. In addition to the known cuts situated along the loci of zero value of the first-order temperature coefficient of frequency, there is another family of orientations, with Tto≥75 °C, which, compared to other singly or doubly rotated cuts, are relatively insensitive to crystallographic orientations. We designate these orientations as the AK cut. We report experimental static frequency as a function of temperature characteristics f(T) for 14 AK-cut orientations, with angular combinations 30°≤φ≤46.1° and 21° ≤θ≤28.44°. Tto values are between 80 and 150 °C, in good agreement with computations. The f(T) curves have been fitted with third-order polynomials. Compared to the fundamental mode of vibrations, the 3rd overtone shows a larger number of modes, and resonance amplitudes are weaker. The frequencies of the harmonic and anharmonic modes are in fairly good agreement with calculations based on a trapped energy resonator model, including effects of coupled thickness shear and thickness twist.
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