The influence of the radius of the contour on the orientation of the zero-temperature contoured SC-cut quartz resonator

On account of small inaccuracies in the measured temperature derivatives of the elastic constants of quartz, only the nominal phi and theta angles of zero-temperature cut quartz resonators can be calculated. In previous work, the correction to the nominal phi angle was obtained from measurements on the third overtone of a contoured SC-cut quartz resonator at 25 degrees C. The correction reported for the phi angle was 48.3'. The errors are corrected, and the revised calculation shows that not only do the magnitudes of the angles change, but also the signs. This is in conformity with measurement. Similarly, both the magnitude and sign of the temperature derivative of the effective piezoelectric constant for the C-mode differ from the earlier incorrect value. The calculations also show that the change in orientation with the radius of the contour for the third and fifth harmonic is significant in the SC cut as well as the fundamental.<
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