Face-shear Vibrations Research Articles

Electro-elastic features of YBa3(PO4)3 and YbBa3(PO4)3 crystals with pure face-shear mode for acoustic wave sensor applications

The fundamental shear horizontal (SH0) waves have been proved to be a very useful method for non-destructive testing due to their non-dispersive characteristics. Currently, although several methods have been proposed to generate SH0 waves, it is still a challenge to obtain pure SH0 wave mode efficiently. Herein, in this study, non-centrosymmetric YBa3(PO4)3 (YBP) and YbBa3(PO4)3 (YbBP) crystals with pure face-shear mode were grown via the traditional Czochralski pulling method at temperatures above 1800 °C. High resolution X-ray diffraction was carried out to evaluate the crystalline quality. Results showed that the YBP and YbBP crystals were of good quality, with the full width at half-maxima being on the order of 42.5″ and 52.3″, respectively. Moreover, the full set of electro-elastic constants for the YBP and YbBP crystals were determined and collated using a combination of impedance and pulse-echo methods. The piezoelectric coefficient (d14) of the YBP and YbBP crystals were determined to be 10.6 pC/N and 11.4 pC/N, respectively, corresponding to the electromechanical coupling coefficient (k14) equal to 15.4% and 15.9%, exhibiting large and pure face-shear vibration mode. Collectively, these results indicate that the YBP and YbBP crystals are promising for acoustic wave sensing application.

Bismuth-Based Oxyborate Piezoelectric Crystals: Growth and Electro-Elastic Properties

The non-centrosymmetric bismuth-based oxyborate crystals have been extensively studied for non-linear optical, opto-electric and piezoelectric applications. In this work, single crystal growth and electro-elastic properties of α-BiB3O6 (α-BIBO) and Bi2ZnB2O7 (BZBO) crystals are reported. Centimeter-sized α-BIBO and BZBO crystals were grown by using the Kyropoulos method. High resolution X-ray diffraction tests were performed to assess the crystal quality. The full-width at half-maximum values (FWHM) of the rocking curves were evaluated to be 35.35 arcsec and 47.85 arcsec for α-BIBO and BZBO samples, respectively. Moreover, the electro-elastic properties of α-BIBO and BZBO crystals are discussed and summarized, based on which the radial extensional and the face shear vibration modes were studied for potential acoustic device applications. The radial extensional mode electro-mechanical coupling factors kp were evaluated and found to be 32.0% and 5.5% for α-BIBO and BZBO crystals, respectively. The optimal crystal cuts with face shear mode were designed and found to be (YZt)/−53° (or (YZt)/37° cut) for α-BIBO crystal, and (ZXt)/±45° cut for BZBO crystal, with the largest effective piezoelectric coefficients being in the order of 14.8 pC/N and 8.9 pC/N, respectively.

Frequency interferences of two-unit quartz resonator arrays excited by lateral electric fields.

The coupled thickness-twist and face-shear vibrations of the lateral-field-excitation (LFE) two-unit resonator array are analyzed, and the frequency interference and shift of LFE resonator arrays are both studied. Different from most of the quartz resonator arrays based on thickness-field-excitation, the resonator array in this study operates with LFE generated by a pair of electrodes on the top surface of the resonator. By using Mindlin's first-order theory of piezoelectric plates, the electrically forced vibrations are analyzed. The effects of various structural parameters on the frequency interference and shift are examined; furthermore, the corresponding mechanisms are discussed. Varying trends of the frequency interference and shift with various structural parameters are verified by the finite element method. The results are crucial for avoiding frequency interferences between two adjacent units in parameter design of the resonator array operating on LFE.

High-order face-shear modes of relaxor-PbTiO3 crystals for piezoelectric motor applications

The face-shear vibration modes of [011] poled Zt ± 45° cut relaxor-PT crystals and their applications for linear piezoelectric motors were investigated. Unlike piezoelectric ceramics, the rotated crystal was found to exhibit asymmetric face-shear deformations, and its two high-order face-shear modes degraded into two non-isomorphic modes. As an application example, a standing wave ultrasonic linear motor (10 × 10 × 2 mm3) operating in high-order face-shear vibration modes was developed. The motor exhibits a large driving force (1.5 N) under a low driving voltage (22 Vpp). These findings could provide guidance for design of crystal resonance devices.

Measurements of face shear properties in relaxor-PbTiO3 single crystals

The face (contour) shear piezoelectric properties of Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMNT) single crystals were experimentally determined by the impedance method. Zt ± 45° cut samples with various aspect ratios were investigated based on Bechmann’s zero-order approximate solution. Square plates were found to exhibit a clean face shear vibration mode and the experimental data were in good agreement with the rotated matrix calculations and finite element method simulations. The piezoelectric coefficients d36 were determined to be in the range of 1600-2800 pC/N, depending on the compositional variations, with an ultralow frequency constant N36, in the range of 490–630 Hz.m. In contrast to conventional thickness shear modes, the mechanical quality factors of face shear vibrations are relatively high, with Q values being on the order of ∼100-450, demonstrate promising for low frequency transducer applications.

Evaluation of material constants in NdCa4O(BO3)3 piezoelectric single crystal

A neodymium calcium oxoborate NdCa4O(BO3)3 piezoelectric single crystal that belongs to the monoclinic system with point group m was grown by the Czochralski technique. A practical evaluation method was developed to determine the 27 independent material constants for acoustic wave device applications. A longitudinal effect face–shear vibration was analyzed and used in the resonance–antiresonance measurement. This method avoided measuring d 11 and d 33 directly by use of X-bar and Z-bar, in which leak of electric field would cause large errors because of the very small dielectric constants. At room temperature, dielectric constants were $${{\varepsilon _{11}^{\text{T}} } \mathord{\left/{\vphantom {{\varepsilon _{11}^{\text{T}} } {\varepsilon _0 }}} \right.\kern-\nulldelimiterspace} {\varepsilon _0 }} = 9.9$$ , $${{\varepsilon _{22}^{\text{T}} } \mathord{\left/{\vphantom {{\varepsilon _{22}^{\text{T}} } {\varepsilon _0 }}} \right.\kern-\nulldelimiterspace} {\varepsilon _0 }} = 15$$ , $${{\varepsilon _{33}^{\text{T}} } \mathord{\left/{\vphantom {{\varepsilon _{33}^{\text{T}} } {\varepsilon _0 }}} \right.\kern-\nulldelimiterspace} {\varepsilon _0 }} = 10$$ and $${{\varepsilon _{13}^{\text{T}} } \mathord{\left/{\vphantom {{\varepsilon _{13}^{\text{T}} } {\varepsilon _0 }}} \right.\kern-\nulldelimiterspace} {\varepsilon _0 }} = - 0.8$$ , respectively. All the independent dielectric and elastic constants were determined in this work. The simulation of surface acoustic wave velocity showed a good agreement with the measured value.

Two-dimensional equations for electroelastic plates with relatively large in-plane shear deformation and nonlinear mode coupling in resonant piezoelectric devices

A set of two-dimensional equations for electroelastic plates in nonlinear face-shear motion are derived from the three-dimensional equations of nonlinear electroelasticity. The equations can describe the nonlinearity due to moderately large in-plane shear deformation associated with face-shear modes. The equations are used to study nonlinear face-shear vibration of a plate of 6mm crystals.

The influence of electrodes on frequency of piezoelectric crystal resonators

On the basis of Mindlin's two-dimensional approximation theory, relationships for elastic stresses, electric displacements, stress equations of motion and charge equations of electrostatics for zero and first order approximation are given here for cases of unplated crystals, plated crystals with shorted electrodes and plated crystals with open electrodes. In all these cases, dispersion equations for length-extensional and face-shear vibrations of a crystal plate with XYt α orientation made from α-quartz are obtained. From boundary conditions of mechanically free resonators, frequency equations of these vibrations for partially plated resonator of that orientation are derived. Comparisons of measured and calculated dependences of electrode effect on length-extensional vibrations frequency give very good agreement, if the elastic constant values of thin film electrode materials are the same as those in the bulk.

Thickness-twist and face-shear vibrations of a contoured crystal plate

Solutions are obtained for the thickness-twist and face-shear vibrations in a crystal plate with a linearly varying thickness. The results are compared to those obtained for a plate of constant thickness. It is found that the frequency of the lowest thickness-twist mode of a linearly tapered plate is only slightly higher than the frequency of the lowest thickness-twist mode of a uniform plate of the same maximum thickness. It is also found that the frequencies of the face-shear modes in a tapered plate differ very little from those in a uniform plate.

Study of the Admittance Spectra of Piezoelectric Plates in Thickness-Shear Vibration

A thin square plate vibrating in thickness shear has an infinite number of possible modes of vibration characterized by different standing-wave formation along the three major axes of the plate. When the plate is piezoelectric and connected into an electric circuit, the observed admittance spectrum may be further complicated by coupling between the thickness-shear modes and modes of other types of vibration, such as flexure or face-shear vibration. This paper describes observations made with a spectrum analyzer specially designed for the purpose. Two kinds of observations are made: (a) with the plate resing on a flat electrode, while the upper electrode is a small steel ball, which can be moved to any point of the surface of the plate, (b) with the plate mounted between electrodes of standard type. The first kind makes it possible to identify the modes and to determine their frequencies and their amplitude distribution over the surface. The second kind indicates to what extent the various modes are coupled to the electrical circuit in conventional operation. Some results are reported as to the effect of variation in thickness contour, ratio of width to thickness, and clamping conditions of the plate. The work is being done under a contract with U. S. Signal Corps.