Third overtone frequency turn-over temperature characteristics vs. orientations for quartz resonators vibrating in thickness-shear B-mode

To conduct a theoretical analysis regarding precise prediction of frequency turn-over temperature (FTT) of the third overtone mode vibrating in thickness-shear B mode, in the vicinity of BT-cut resonator, measurements were conducted by the oscillation method, over a wide temperature range from -196 to 100°C and compared with the fundamental FTT. The precise quadric relationships between the FTT and the crystallo-graphic orientation were obtained theoretically for the fundamental- and the third-overtone thickness-shear B-modes, respectively, and the coefficients of quadrics were determined experimentally by the least squares method. It was found that there were the new resonators having a small temperature dependence of cubic curve in the vicinity of -100°C, in the region of the angels of cuts -51.5 to -53°. The important relationships between the quadric coefficients and the first-, second- and third-order frequency temperature coefficients for the third overtone mode were also obtained and compared with those for the fundamental waves vibrating in thickness-shear B-mode