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theses

Lanthanum Gallium Silicate (La3Ga5SiO14, Langasite, LGS) and its isomorphs are gaining in popularity due to their superior piezoelectric material properties. These materials have similar crystal properties as the quartz crystal, which is widely used in BAW applications such as resonators and piezoelectric vibratory gyroscopes. The langasite and langatate have better stability at high temperatures that have no phase transition up to the melting point at 1475°C and 1450°C, respectively. Additionally, quartz, langasite, and langatate crystals are trigonal class crystals that belonging to the same point group 32, for which well-known methods of trapping energy of piezoelectric resonator can be easily and accurately applied. Quartz, langasite and langatate crystals are used for studying and designing piezoelectric vibratory gyroscopes. The three-dimensional finite element models are developed to simulate the characteristic of the vibratory gyroscopes. The piezoelectric double-ended tuning fork gyroscope is used to verify and validate the finite element analysis. The geometric and gyroscopic sensitivity of the finite element models of the quartz doubled-ended tuning fork gyroscope showed the excellent agreement with the experimental data. The sensitivity of the quartz, langasite and langatate gyroscope are found to be 0.191 mV/(deg./s), 0.469 mV/(deg./s) and 0.784 mV/(deg./s), respectively. The results show that langasite and langatate crystal are more effective than quartz crystal for high precision piezoelectric gyroscopes. A length-extension vibratory gyroscope is our newly designed gyroscope, which utilizes a length extension mode as a driving mode and a flexure mode as a sensing mode to detect the Coriolis force generated by the rotation of the system. The singly rotated quartz, langasite and langatate crystals are used and their calculated optimum cut angles are ϕ=0̊, θ=-9̊ , ϕ=0̊ , θ =24̊ and ϕ=0̊ , θ =24̊, respectively. The sizes of the gyroscopes vary due to the material properties and length of the driving arms. The langasite and langatate gyroscopes are nearly the same size and are smaller than the quartz gyroscope. The gyro-sensitivity rotations about the z-axis of quartz, langasite and langatate gyroscopes were 2.78e-4 V/(deg/s), -1.60e-2 V/(deg/s) and -1.6e-2 V/(deg/s), respectively. The results show that the newly designed length-extension gyroscope can be used as a gyro-sensor, and that langasite and langatate gyroscopes provide the stronger sensitivity to angular velocity than the quartz gyroscope. The length extension gyroscope is also able to detect the angular velocities about the other two axes(x- and y-axes). The temperature behaviors of the langasite and langatate crystals have not been established unlike the quartz crystal. The three-dimensional Langrangian formulations with second kinds of Piola-kirchoff tensor that uses the coordinates of a material point in the reference point as independent variables are used to calculate the frequency-temperature behaviors of the langasite. Normally, the piezoelectric effect is ignored in analysis of the quartz crystal due to their weak piezoelectric coupling. The piezoelectric coupling factor of the langasite crystal is much larger than that of the quartz crystal, which cannot be ignored. However, the analysis shows that the piezoelectric effect on the frequency-temperature behavior of langasite is negligible. The study on the temperature behaviors of the langatate cannot be completed, since the third-order non-linear elastic constants have not been published. The results show that no zero-temperature compensated cuts for A- and B- mode exist, while a more than sufficient number of the zero-temperature compensated orientations of langasite for C-mode have been identified. The temperature compensated cuts of langasite for any order higher than the first were not found.

ETD_7002

Ph.D.

Includes bibliographical references

by Gobong Choi

doi:10.7282/T35B04KC

ETD doctoral

The author owns the copyright to this work.