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This document is a correction to an article titled "Acoustic properties of piezoelectric cubic crystals." It addresses errors and provides corrections for symbols, subscripts, and captions in the original article. The purpose of this correction is to ensure the accuracy of the information presented. The document includes corrections for equations involving variables e12 and e13, coefficients involving variables c26 and c44, coefficients involving variables c46 and c14, and the labeling of a path in Figure E.1. The corrected figure can be found in Figure 1 of the document. [Extracted from the article]

The studies of the quartz resonator Q with aluminum electrodes with respect to its fundamental thickness shear mode frequency and its viscoelastic, viscopiezoelectric, and viscopiezoelectromagnetic behaviors are presented. The data obtained provide insight into the effects of electrical resistance in both the electrodes and quartz that are found to be negligible.

The measurements of the series resonant frequency and the motional arm resistance of doubly rotated quartz resonators (theta approximately equal 35 degree and phi = 7degree) in liquids to compare with singly rotated AT-cut resonators (theta approximately equal 35 degree and phi= 0 degree). A modified Butterworth-Van Dyke equivalent circuit model is suggested to analyze doubly rotated cut resonators under liquid loading.

The linear theory of using piezoelectricity with quasi-electrostatic approximation in which the medium is assumed to be perfectly elastic is used since long and it is useful in analyzing high quality (Q) resonators like quartz crystal. Three-dimensional (3-D) equations of linear piezoelectricity with quasi-electrostatic approximation were studied to investigate effects of dissipation on propagation of plane waves in an infinite solid.

Force frequency coefficients of a Y-cut langanite (LGN) resonator and a Y-cut langatate (LGT) resonator as a function of the azimuthal angle is measured. The maximum magnitudes of the coefficients of the LGN and the LGT are five and seven times smaller than that of stress compensated cut (SC-cut) quartz.

Force frequency coefficients of a Y-cut langanite (LGN) resonator and a Y-cut langatate (LGT) resonator as a function of the azimuthal angle is measured. The maximum magnitudes of the coefficients of the LGN and the LGT are five and seven times smaller than that of stress compensated cut (SC-cut) quartz.

Bulk acoustic wave (BAW) thin film devices are described and discussed.

Piezoelectric coupling factors for thickness-vibration modes driven by lateral-field excitation are calculated using the Christoffel-Bechmann method. Results are presented and discussed.

This paper surveys applications of acoustic waves in microwave devices. After a general and historical introduction to bulk acoustic waves (BAWs), surface acoustic waves (SAWs), practical wave types, and acoustoelectric transducers, a review is given of technologically important materials for microwave acoustic applications. Following this, we discuss BAW and SAW microwave devices and their technologies. Specifically reviewed are thin-film resonators and filters, transversal filters, and filters for correlative analog signal processing. Finally, an overview of the most important microwave applications is given, along with manufacturing and packaging issues. Index Terms--BAW, bulk acoustic-wave devices, communications and sensor applications, SAW, signal processing, surface acoustic-wave devices.

A historical review of equivalent circuit modeling of acoustic structures is provided. PE (piezoelectric) and PM (piezomagnetic) crystal plates, of arbitrary anistropy, executing simple thickness motion, are discussed.

Micromachined piezoelectric heterogeneous bimorphs are produced using integrated circuit fabrication techniques. The deflections of the bimorphs are measured as a function of frequency and applied voltage. A significantly large quadratic deflection superimposed on the linear piezoelectric behavior is observed. Resonance and deflection antiresonance identified from experimental data are in good agreement with theory.

An enhancement of the resonator method provided by the IEEE Standard on Piezoelectricity in calculating the piezoelectric material constants is presented. The IEEE Standard equations obtain the vibrator response and material constants by using a 1-D approximation of an infinite flat plate with a uniform distribution of vibration thereby limiting their capacity to compute the 'intrinsic' material constants. The enhanced technique is based on measurands unaffected by the vibrational amplitude distribution.

General equations for Poisson's ratio (nu) are derived for arbitrary orientations of crystals in the tetragonal, hexagonal and cubic systems. For the tetragonal with longitudinal extension along x1 and x3 along the fourfold symmetry axis, nu21 = -s12/s11 and nu31 = -s13/s11. For the hexagonal with a longitudinal extension along the sixfold axis, nu21 = nu31 = -s13/s33. For cubes with a longitudinal extension along the cube axis, nu21 = n31 = -s12/s11.

A brief discussion of the piezoelectric effect is presented in the context of its history, traditional uses, and relation to crystal symmetry. Future applications, particularly in the area of microelectromechanical systems/structures (MEMS) are also discussed. Sample material coefficients are provided, with ample references to the present literature.

Application of an intrinsic parameter, motional time constant tau, for a specific mode m, helps the comparative study of piezoelectric devices and materials. Determination of material coefficients and inclusion of acoustic loss in elastic compliance/stiffness enables the application of tau1(m). Tau1(m) is variable for the various cuts and modes of quartz and indicates that mounting loss and losses due to crystal inhomogeneties account for losses in the devices. Derivation of a physical parameter that includes tau, piezoelectric coupling and acoustic velocity enables the interpretation of maximum frequency bounds of plate resonators.

The matrix that relates the harmonically varying driving parameters: a moment M at the tip, a force F at the tip, a uniformly applied body force p and voltage V to their response parameters: the tip rotation [Alpha], the tip deflection [Delta], the volumetric displacement [Nu] and the electrode charge Q, have been determined. The electrical element of this matrix is the (4,4) element, which is the electrical capacitance, hence we call this the dynamic admittance matrix. It is a four by four symmetric matrix having a purely electrical part, a purely elastic part and a mixed (piezoelectric) part. A common factor in nearly all elements describes the resonance frequencies that are to be expected.

Doubly rotated plate resonators help measure the elastic, piezoelectric and dielectric constants of dilithium tetraborate at room temperature. Available lattice constants enable the determination of theoretical density. This new set of constants is used to calculate dilithium tetraborate device characteristics. Frequency domain measurements of thin, flat plates are the basis of this technique.

A study of several material constants for surface acoustic wave devices are considered for langasite, lithium niobate/lithium tantalate and dilithium tetraborate. The materials include piezoelectric glass-ceramics with symmetry classes mm2, 32, 3m, 4mm, 6mm and 43mm. The material constants include mass density, elastic stiffness, piezoelectric stress, dielectric permittivity and thermal expansion coefficient.

Advances in low acceleration sensitivity measurements in piezoelectric devices illustrate their effect on future design and modelling for low acceleration sensitivity. The crystal resonator functions as a mechanical vibrator and the need for eigenfrequency changes in the resonator due to acceleration in both surface acoustic waves and bulk acoustic waves is discussed. The crystal oscillator acts as an electronic circuit, and resonator transimpedance minimization ion is dismissed.

Preceding investigations of pure-mode Loci have not focussed on the necessity for an engineering technique for pure-mode sample set selections for materials evaluation. An alternative approach for identifying the pure-mode Loci in piezoelectric crystals focussed on the theory of simple thickness modes in piezoelectric plate vibrators and its application to pure-mode sample selection for identifying the important material properties of dilithium tetraborate using the resonator method. The sample set includes 17 samples modelled on seven doubly-rotated plate orientations.

Experimental data on the properties of doubly rotated dilithium tetraborate resonators are compared to recently published numerical results. The measurements cover wave velocities, piezoelectric coupling, equivalent circuit parameters, temperature coefficients and energy trapping. Except for the second-order temperature coefficients, the measured data show a good fit with the computed results to highlight the viability of dilithium tetraborate as a piezoelectric medium.

The Sauerbrey equation describes the link between mass loading and frequency of a quartz crystal microbalance (QCM). In such expressions, mass is often assumed to be attached rigidly to the QCM surfaces, although this is not always a good approximation. Deviations from the Sauerbrey equation can occur when the mass is not rigidly coupled to the QCM, and the relationship between mass added and frequency change can be complicated by variations in the mechanical displacement.