Third-order Piezoelectric Constants Research Articles

Nonlinear, elastic, piezoelectric, electrostrictive, and dielectric constants of lithium tantalate

Three third-order dielectric constants, 8 electrostrictive constants, 13 third-order piezoelectric constants, and 14 third-order elastic constants for lithium tantalate (LiTaO3) single crystals, which are mainly used in surface acoustic wave (SAW) devices, were determined as part of basic research to realize SAW devices with a low degree of nonlinearity. The third-order dielectric constants were determined by measuring the change in capacitance along selected directions when an alternating electric field was applied to the crystal. The electrostrictive constants were determined by measuring the change in capacitance when static stress was applied. Some of the piezoelectric constants were determined directly from the change in sound velocity due to the application of an alternating electric field, whereas others were obtained from the measured dielectric constants, electrostrictive constants, and the change in sound velocity due to an alternating electric field. In addition, the elastic constants (compliance) were determined using the three aforementioned determined nonlinear constants and the measured small-amplitude ultrasonic velocity change as a function of applied static stress. The measurements performed in the present study are more advanced than those reported for LiNbO3 single crystals in 1987 due to the adoption of the d-form nonlinear piezoelectric equation (instead of the e-form) and a higher degree of precision using dynamic measurement methods. The use of the d-form of the nonlinear piezoelectric equation allows many nonlinear constants to be determined independently from other nonlinear constants, eliminating measurement errors associated with these other constants. The d-form nonlinear constants obtained in the present study were converted to e-form constants to make them applicable to the analysis of nonlinear phenomena in piezoelectric devices.

Third-order elastic, piezoelectric, and dielectric constants

The definitions of the third-order elastic, piezoelectric, and dielectric constants and the properties of the associated tensors are discussed. Based on the energy conservation and coordinate transformation, the relations among the third-order constants are obtained. Furthermore, the relations among the third-order elastic, piezoelectric, and dielectric constants of the seven crystal systems and isotropic materials are listed in detail. These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials. It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups, while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material. The reason is that some of the point groups are centrally symmetric, and the other point groups are high symmetry. These results provide the foundation to measure these constants, to choose material, and to research nonlinear problems. Moreover, these results are helpful not only for the study of nonlinear elastic and piezoelectric problems, but also for the research on flexoelectric effects and size effects.

Analysis of contributions of nonlinear material constants to temperature-induced velocity shifts of quartz surface acoustic wave resonators

In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.

Optimal cuts to extract the third-order piezoelectric constants and electrostictive constants of langasite single crystals through the electroelastic effect.

Optimal cuts to determine the third-order piezoelectric constants and electrostrictive constants of langasite single crystals by the resonator method are proposed. By selecting several langasite resonators with optimal cut angles and measuring their electroelastic effects, third-order piezoelectric constants and electrostrictive constants of langasite single crystals may be extracted. The numerical method to search these optimal cut angles is presented. The methodology has been validated by finite element analysis. This method will simplify traditional methods used to determine the third-order piezoelectric and electrostrictive constants for langasite single crystals and could potentially produce more accurate results. The method could also be used to determine the third-order piezoelectric and electrostrictive constants for other crystals with trigonal 32 symmetry.

Experimental measurement of the electroelastic effect in thickness-mode langasite resonators

The electroelastic effect describes the shift in resonant frequency that a resonator experiences as a result of the application of a dc electrical field. We report on experimental measurements of the electroelastic effect observed in fourteen plano-plano configuration thickness-mode langasite (La3Ga5SiO14) resonators. The orientations of the fourteen samples provide a sufficient data set to extract all eight of the third-order piezoelectric constants of this material. The role of this type of measurement in determining third-order piezoelectric constants is discussed. We compare the experimentally observed behavior to that predicted when using the langasite material constants currently available in the literature.

Analysis of contributions of nonlinear material constants to stress-induced velocity shifts of quartz and langasite surface acoustic wave resonators

Stress-induced surface acoustic wave velocity shifts are analyzed for langasite (LGS) SAW resonators. The analytical methodology has been verified by comparing experimental results and analytical results for quartz resonators. LGS SAW resonators with Euler angles which are most sensitive and least sensitive to diametrical forces are determined and their applications in force sensors and resonators with minimum acceleration sensitivity are discussed. Sensitivity of the analytical results to different groups of nonlinear material constants is discussed; it was found that for specific configurations, failure to include the third-order piezoelectric constants, dielectric constants and electrostrictive constants may lead to a significant calculation error. Surface acoustic waves propagating on an LGS square plate subject to bending moment along the propagation direction and normal to the propagation direction are analyzed; it was found that the average momentinduced velocity shift of LGS resonators are comparable to quartz resonators. Analyses of the sensitivity of the results to different groups of nonlinear material constants shows that for some specific wave propagation directions, failure to include the third-order piezoelectric constants, dielectric constants, and electrostrictive constants may lead to large errors.

Quantitative study on the nonlinear piezoelectric effect in KNbO3 single crystals for a highly efficient surface acoustic wave elastic convolver

In this article we describe quantitative studies on the nonlinear piezoelectric effect in KNbO3 single crystals for a highly efficient surface acoustic wave elastic convolver. First, we demonstrate that a simple measurement of the nonlinear piezoelectric constant of e355 is very effective for quantitative estimation of the efficiency of an elastic convolver. Next, the third-order piezoelectric constants, e355, e333, and e344, in rotated Y-cut KNbO3 substrates are measured by varying the velocity under an applied electric field. Using the third-order piezoelectric constants measured, quantitative estimations of the convolution efficiency are discussed.

Linear combinations of the third-order elastic and piezoelectric constants of quartz

The DC-field-induced change in the resonant frequency of the extentional mode of quartz rods is related to the third-order elastic and the third-order piezoelectric constants. Five linear combinations of these constants are determined by least-squares fit to data obtained from 50 different rods. The results are notable for their small standard errors of about two percent on average. They also agree very well with the values obtained independently by the transit-time method.

Determination of the third-order piezoelectric constants of quartz using the extentional mode of rods

The dc field-induced change in the frequency of the extentional mode of rods is used to determine the fundamental nonlinear third-order piezoelectric constants of quartz. Five combinations of the total number of eight third-order piezoelectric constants are determined by least-squares fit to data obtained from 50 different rods. The results are notable for their small standard errors of less than 2% on average. They also agree very well with the values obtained independently by the transit-time method.

Application of ultrasonic standing waves to optical-beam scanning: Journal of the acoustical society of America, 36, No. 10, 1706 (1964)

In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.

Ultrasonic atomization-some recent developments: Fuel efficiency, 12, No. 12, 16 (1964)

In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.