The Temperature Sensitivity of the Piezoelectric Thickness Shear Mode of α-GeO2 Single Crystals
Abstract
1. Introduction
2. Methodology
- −
- Determining, based on experimental measurements, the curves of the evolution of elastic constants as a function of the temperature, as well as the first- and second-order temperature coefficients.
- −
- Researching and calculating the temperature-compensated cut angles of Y-plates in single and double rotations within a temperature range of 25–900 °C.
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- Examining the effect of rotation on Y-plates on the emergence of parasitic vibration modes.
2.1. First- and Second-Order Temperature Coefficients of the Resonant Frequency
2.2. Rotated Y-Cut Plates
2.3. Elastic Constants of Rotated Y-Cut Plates
2.3.1. Elastic Constants of a Singly Rotated Y-Cut Plate
2.3.2. Elastic Constants of a Doubly Rotated Y-Cut Plate
3. Results and Discussion
3.1. Temperature-Dependent Elastic Constants of α-GeO2
3.2. Cuts with Zero Temperature Coefficients
3.2.1. Singly Rotated Y-Cut Plate
3.2.2. Doubly Rotated Y-Cut Plate
3.3. Second-Order Resonance Frequency Temperature Coefficients for Rotated Y-Plates
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Elastic Stiffness (Gpa) | First-Order Temperature Coefficients of Cij (ppm°C−1) | Second-Order Temperature Coefficients of Cij (ppm°C−2) | |||||||
---|---|---|---|---|---|---|---|---|---|
T = 25 °C | T = 500 °C | T = 900 °C | T = 25 °C | T = 500 °C | T = 900 °C | T = 25 °C | T = 500 °C | T = 900 °C | |
69.51 | 69.38 | 68.55 | +3.27 | −14.82 | −48.69 | −0.007 | −0.003 | −0.053 | |
27.34 | 27.50 | 27.01 | +60.21 | −26.86 | −54.42 | −0.124 | −0.060 | −0.007 | |
0 | 0.91 | 2.04 | +50,266.70 | +2680.22 | +1578.92 | −32.06 | +1.108 | +0.490 | |
119.98 | 114.90 | 109.99 | −81.93 | −100.63 | −118.45 | −0.015 | −0.016 | −0.017 | |
38.77 | 39.71 | 40.33 | +39.59 | +51.73 | +19.11 | +0.044 | −0.015 | −0.064 | |
22.98 | 23.85 | 24.56 | +81.98 | +73.34 | +70.19 | −0.004 | −0.004 | −0.004 |
Elastic Stiffness at 25 °C (Gpa) | First-Order Temperature Coefficients of Cij at 25 °C (In Units of ppm°C−1) | Second-Order Temperature Coefficients of Cij at 25 °C (In Units of ppm°C−2) | ||||
---|---|---|---|---|---|---|
α-SiO2 [17] | α-GeO2 | α-SiO2 [17] | α-GeO2 | α-SiO2 [17] | α-GeO2 | |
86.74 | 69.51 | −48.50 | +3.27 | −0.107 | −0.007 | |
11.90 | 27.34 | −550.00 | +60.21 | −1.150 | −0.124 | |
17.91 | 0.01 | +101.00 | +50,266.70 | −0.048 | −32.06 | |
107.20 | 119.98 | −160.00 | −81.93 | −0.275 | −0.015 | |
57.93 | 38.77 | −177.00 | +39.59 | −0.216 | +0.044 | |
39.89 | 22.98 | +178.00 | +81.98 | 0.118 | −0.004 |
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Papet, P.; Armand, P. The Temperature Sensitivity of the Piezoelectric Thickness Shear Mode of α-GeO2 Single Crystals. Crystals 2025, 15, 613. https://doi.org/10.3390/cryst15070613
Papet P, Armand P. The Temperature Sensitivity of the Piezoelectric Thickness Shear Mode of α-GeO2 Single Crystals. Crystals. 2025; 15(7):613. https://doi.org/10.3390/cryst15070613
Chicago/Turabian StylePapet, Philippe, and Pascale Armand. 2025. "The Temperature Sensitivity of the Piezoelectric Thickness Shear Mode of α-GeO2 Single Crystals" Crystals 15, no. 7: 613. https://doi.org/10.3390/cryst15070613
APA StylePapet, P., & Armand, P. (2025). The Temperature Sensitivity of the Piezoelectric Thickness Shear Mode of α-GeO2 Single Crystals. Crystals, 15(7), 613. https://doi.org/10.3390/cryst15070613