Improved Extraction of Second-Order Material Constants for Current Generation Y-Grown La₃GaNbO₁₄ (LGN) Crystal.

With higher demand for sensor development, piezoelectric materials with advanced performance and wide availability draw more attention today. Accurate second-order material constants are necessary for modeling and mechanical design of sensors that make use of langanite (LaGaNbO, LGN) crystals. We report here on room temperature LGN bulk acoustic wave (BAW) velocities obtained with reduced uncertainties using ultrasound measurements and taking advantage of the cross correlation signal processing technique, and a full set of LGN material constants extracted from the BAW velocity results.

Measurement of the Second-Order Material Constants of Lanthanum-Gallium Tantalate (LGT) Through Ultrasound.

Lanthanum-gallium tantalate (LGT) is a member of the LGX crystal family (langasite, langanite, and langatate) known for high-quality factor and stability at higher temperatures. These characteristics enable filters and sensors for use in harsh environments. Accurate values for the second-order material constants are required for electromechanical modeling of such devices.

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.

An estimate of the second-order in-plane acceleration sensitivity of a Y-cut quartz thickness-shear resonator.

We perform a theoretical analysis of the secondorder in-plane acceleration sensitivity of a Y-cut quartz thickness- shear mode resonator. The second-order nonlinear theory of elasticity for anisotropic crystals is used to determine the biasing fields in the resonator under in-plane acceleration. The acceleration-induced frequency shift is determined from a perturbation analysis based on the plate equations for small-amplitude vibrations superposed on a finite bias.

Experimental measurement of the frequency shifts of degenerate thickness-shear modes in a rotated Y-cut quartz resonator subject to diametrical forces.

We report the first experimental measurement of the stress-induced frequency shifts of degenerate thickness-shear modes in a rotated Y-cut quartz resonator. Two distinct but nominally degenerate modes shifted toward higher frequencies at different rates and merged into a single mode as diametrical forces were applied gradually. The single mode split into the two distinctive modes progressively as the diametrical forces were released.

Experimental measurements of the force-frequency effect of thickness-mode langasite resonators.

Because of their excellent temperature behavior, high piezoelectric coupling, low acoustic loss, and high Q-factor, langasite resonators have been the subject of recent interest for use in a variety of applications. The force-frequency effect refers to the phenomenon of frequency changes resulting from the stress applied to the resonator. A clear understanding of this effect is essential for many design applications such as force sensors and stress-compensated resonators.

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.

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.

Drive-level dependence of doubly rotated langasite resonators with different configurations.

The miniaturization of crystal resonators and filters toward the micro electromechanical systems (MEMS) and nano-structured scales demands improvement of nonlinear piezoelectricity theory and a better understanding of the nonlinear behavior of new crystal materials. The nonlinearities affect the quality factor and acoustic behavior of MEMS and nano-structured resonators and filters. Among these nonlinear effects, drive-level dependence (DLD), which describes the instability of the resonator frequency resulting from voltage level and/or power density, is a potentially significant problem for miniaturized resonators.

Correspondence - Analysis of thickness vibrations of C-axis inclined zig-zag two-layered zinc oxide thin-film resonators.

The free vibrations of a two-layered C-axis inclined zig-zag ZnO thin-film bulk acoustic wave resonator (FBAR) connected to external impedance are analyzed. The frequency equation and mode shape for this resonator are derived based on the linear piezoelectric theory. The impedance characteristics of the FBAR are derived and compared with previous experimental results.

Shear-horizontal vibration modes of an oblate elliptical cylinder and energy trapping in contoured acoustic wave resonators.

We study shear-horizontal free vibrations of an elastic cylinder with an oblate elliptical cross section and a traction-free surface. Exact vibration modes and frequencies are obtained. The results show the existence of thickness-shear and thickness-twist modes.

Stress-induced frequency shifts of degenerate thickness-shear modes in rotated Y-cut quartz resonators.

We study stress-induced frequency shifts in a rotated Y-cut quartz resonator (theta = 23.7 degrees ) with degenerate fundamental thickness-shear modes when the biasing stress is not present. Using the recently derived perturbation procedure for degenerate frequencies in crystal resonators, we show that when a planar stress system is applied, the degenerate frequency splits into two.

Force-frequency effect of thickness mode langasite resonators.

Langasite resonators are of recent interest for a variety of applications because of their good temperature behavior, good piezoelectric coupling, low acoustic loss and high Q factor. The force-frequency effect describes the shift in resonant frequency a resonator experiences due to the application of a mechanical load. A clear understanding of this effect is essential for many design applications such as pressure sensors.

Stress-induced frequency shifts in langasite thickness-mode resonators.

In this paper, we report on our study of stress-induced effects on thickness vibrations of a langasite plate. The plate is assumed to be doubly rotated, specified by angles phi and theta. The stresses are assumed to be uniform and planar.

Electroelastic effect of thickness mode langasite resonators.

Langasite is a very promising material for resonators due to its good temperature behavior and high piezoelectric coupling, low acoustic loss, and high Q factor. The biasing effect for langasite resonators is crucial for resonator design. In this article, the resonant frequency shift of a thickness-mode langasite resonator is analyzed with respect to a direct current (DC) electric field applied in the thickness direction.

Perturbation analysis of frequency shifts in an electroelastic body under biasing fields.

We analyze the eigenvalue problem associated with small-amplitude vibrations superposed on finite-biasing fields in an electroelastic body. The widely used first-order perturbation integral by Tiersten is generalized in two different ways: a second-order perturbation analysis is given when the biasing fields are not infinitesimal and their second order effects need to be considered; a first-order perturbation analysis is given when an eigenvalue is associated with more than one eigenvector (a degenerate eigenvalue).

Thickness-shear vibrations of a quartz plate under time-dependent biasing deformations.

Incremental thickness-shear vibrations of a Y-cut quartz crystal plate under time-harmonic biasing extensional deformations are studied using the two-dimensional equations for small fields superposed on finite biasing fields in an electroelastic plate. It is shown that the incremental thickness-shear vibrations are governed by the well-known Mathieu's equation with a time-dependent coefficient. Both free and electrically forced vibrations are studied.

Two-dimensional equations for electroelastic plates with relatively large shear deformations.

A set of two-dimensional, nonlinear equations for electroelastic plates in moderately large thickness-shear deformations is obtained from the variational formulation of the three-dimensional equations of nonlinear electroelasticity by expanding the mechanical displacement vector and the electric potential into power series in the plate thickness coordinate. As an example, the equations are used to study nonlinear thickness-shear vibrations of a quartz plate driven by an electrical voltage. Nonlinear electrical current amplitude-frequency behavior near resonance is obtained.