Effects of radially applied angular sector stresses on the frequency of doubly rotated quartz crystal

Abstract

Summary. --A theoretical study is presented to determine the sensitivity of a doubly rotated crystal resonator, subject to radial compression along two diametrically opposed zones. The variation of frequency is calculated as a function of the stresses applied to the crystal, then a coefficient of sensitivity is deduced. Some solutions are put forward for obtaining the stability of frequency of a resonator in the particular case where a quartz crystal, stress compensated (SC), is used. Moreover, the particular conditions are described for limiting the influence of possible faults in the construction of such quartz resonators, which must be employed when a very high stability of frequency is needed.PACS. 77.60 -Piezoelectricity and electrostriction.