Temperature Dependence of Piezoelectric Coefficients

Temperature dependence of the piezoelectric du and du coefficients is displayed in Fig. 7.4. The piezoelectric coefficient of X-cut and XY-cut (it is d 2 = —du for quartz) for transversal effect is changing significantly (decreasing) with increasing temperature. Second independent piezoelectric coefficient du contributes in an opposite sense (see Fig. 7.4). It makes possible to find special quartz cut orientation with compensated temperature dependence in transversal mode. Piezoelectric coefficient is independent on the temperature for such cut practically in certain limited temperature range. 

Calculation of the desired crystal cut orientation is simple. Let us suppose quartz cut (XYa)f (working in transversal mode) with the lengthy-axis rotated by an angle I about the crystallographic x-axis. The rotated components of the piezoelectric tensor can be calculated using Eqs. (5.10) and (5.15) 

Zero temperature coefficient i S zero temperature derivative of 7 2, sets the condition for the cut orientation 

The temperature coefficients Td and Tdu might depend also on the temperature themselves. Temperature compensated cut orientation (condition = 0) is exact for certain temperature only. The cut orientation f 155 is calculated from the average temperature coefficients Td and Tdu over the temperature range from 0 to 400°C. Corresponding piezoelectric coefficient for such cut reaches Jj2 = —2.15 x 10 CN (for left-handed quartz) which is about 93% of d value. 

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