ABSTRACT
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 (La3Ga5.5Nb0.5O14, 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. Our results compare favorably with prior results assessed as using a reliable measurement technique, and differ in expected fashion from other results based on techniques that do not address a known weakness in the measurement technique.
Subject(s)
Niobium , Ultrasonography/methodsABSTRACT
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. A sufficient set of bulk acoustic wave (BAW) propagation velocities have been measured in cube-shaped samples to obtain the full set of second-order elastic and piezoelectric material constants along with the experimental uncertainties. The cross correlation method was used to accurately measure the time-of-flight (TOF) values between the first two back-wall echoes under a constant room-temperature environment. The calculated BAW velocities and extracted material constants show good agreement with earlier work.
ABSTRACT
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.
ABSTRACT
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. We show that, whereas the first-order acceleration-induced frequency shift is zero for a structurally symmetric resonator under in-plane acceleration, the second-order frequency shift is nonzero and is quadratic in the acceleration. As the fourth-order nonlinear elastic constants of quartz have never been measured, we can only estimate the magnitude of the second-order frequency shift. For a particular case of interest, we find Δω/ω0 ~ 10(-18), 10(-16), and 10(-14) when the acceleration is 1, 10, and 100 g, respectively.
ABSTRACT
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. The experimental results are in excellent agreement with previous theoretical results and may provide an insight into mode-coupling phenomena as a possible cause of frequency jumps in quartz resonators.
ABSTRACT
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. In this article, we report on experimental measurements of the force- frequency effect of various doubly-rotated langasite resonator samples with plano-plano configurations. Comparisons with the available experimental data for the force-frequency effect of quartz resonators are made. The application of this effect for sensors and stress-compensated resonators is also discussed.
ABSTRACT
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.
ABSTRACT
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. The energy-trapping behavior of these modes is examined. Trapped modes are found wherein the vibration energy is largely confined to the central portion of the cross section and little vibration energy is found at the edges. It is also shown that face-shear modes are not allowed in such a cylinder. The results are useful for the understanding of the energy trapping phenomenon in contoured acoustic wave resonators.
ABSTRACT
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. This phenomenon is expected to be typical for degenerate frequencies in crystal resonators and may be responsible in part for the jump discontinuities in frequency temperature curves and other frequency jump phenomena.
ABSTRACT
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. In this article, the frequency shift is analyzed theoretically and numerically for thin, circular langasite plates subjected to a pair of diametrical forces. In addition, the sensitivity of the force-frequency effect is analyzed with respect to the nonlinear material constants. The results are anticipated to be valuable for experimental measurements of nonlinear material constants as well as for device design.
Subject(s)
Micro-Electrical-Mechanical Systems , Micro-Electrical-Mechanical Systems/instrumentation , Models, Theoretical , Sensitivity and SpecificityABSTRACT
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. The first-order perturbation integral as developed by Tiersten for frequency shifts in resonators is used. The dependence of frequency shifts on phi and theta is calculated and examined, and loci of stress-compensation are determined.
ABSTRACT
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. The vibration modes of a thin langasite plate fully coated with an electrode are analyzed. The analysis is based on the theory for small fields superposed on a bias in electroelastic bodies and the first-order perturbation integral theory. The electroelastic effect of the resonator is analyzed by both analytical and finite-element methods. The complete set of nonlinear elastic, piezoelectric, dielectric permeability, and electrostrictive constants of langasite is used in the theoretical and numerical analysis. The sensitivity of electroelastic effect to nonlinear material constants is analyzed.
ABSTRACT
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).
Subject(s)
Ceramics/chemistry , Ceramics/radiation effects , Computer-Aided Design , Electrochemistry/instrumentation , Electrochemistry/methods , Electromagnetic Fields , Models, Chemical , Computer Simulation , Electric ImpedanceABSTRACT
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. Approximate analytical solutions are obtained when the frequency of the biasing deformation is much lower than that of the incremental thickness-shear vibration. The incremental thickness-shear free vibration mode is shown to be both frequency and amplitude modulated, with the frequency modulation as a first-order effect and the amplitude modulation a second-order effect. The forced vibration solutions show that both the static and motional capacitances become time-dependent due to the time-harmonic biasing deformations.
ABSTRACT
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. The equations and results are useful in the study and design of pieszoelectric crystal resonators and the measurement of nonlinear material constants of electroelastic materials.
