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The Sellmeier equation, ubiquitous in optics for characterizing an optical material's refractive index (n) as a function of wavelength (λ), is recast as an electrical immittance and realized in a circuit form. The circuit is shown to be identical to that widely used to portray piezoelectric resonators. This analogy further is shown to harmonize certain features common to both as well as to connect seemingly disparate applied physical phenomena including Lyddane–Sachs–Teller, Debye, Drude, plasma, and Lorentz–Zener effects. [ABSTRACT FROM AUTHOR]

This paper is offered as a complementary adjunct to the many treatments of the electronic and photonic properties of cubic III–V and II–VI compounds appearing in the literature. These crystals typically exhibit piezoelectricity, due to the molecular dissymmetry, thereby allowing the inclusion of classical mechanical/acoustic features along with the quantum. We discuss the history of this modality and then illustrate its use by applying it to an electro‐elastic problem that has the estimable virtues of having an exact solution, along with wide practical applicability: determination of the piezocoupling values governing the excitation of thickness vibrations in thin cubic films or plates of arbitrary crystallographic orientation by electric fields directed either along, or lateral to, the thickness. Explicit results are given for orientations along the great‐circle paths connecting the principal directions [100], [110], and [111]. The formalism is then applied to GaAs as an example; it is further demonstrated that various results, such as the orientational variations of piezocoupling factors, are generally applicable to other members of the III–V and II–VI families by scaling. Ancillary aspects, such as errors due to misorientations, nonlinearities, and equivalent circuit representations, are described and discussed. This work is dedicated to Gerald W. Farnell (1925–2015), Prof. Emeritus, McGill University, Montréal, Canada. [ABSTRACT FROM AUTHOR]

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.

Theoretical studies help derive quantized acoustic phonon modes for quantum- dot and quantum wire geometries that are useful in opto- and nanoelectronics. Derivation of the Hamiltonian values for deformation potential interactions along with the phonon modes enables the modeling of carrier-acoustic-phonon interactions in mesoscopic devices. The theoretical studies also indicate that selection rules govern the acoustic phonon-assisted mechanisms in spherical crystallites.

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.

Binary semiconductors are central to all modern electronic, optoelectronic, and electromechanical systems. Given such practical importance, there is value in finding routes to simplify the determination of physical properties, particularly with respect to nonlinearities. Fortunately, nearly all binary semiconductors crystallize into one of two structures: cubic zinc blende or hexagonal wurtzite. Correspondences between the linear rank 3 piezoelectric and rank 4 elastic tensors of zinc blende and wurtzite polytypes have been addressed. Nonlinear rank 6 elastic tensors have similarly been discussed. Provided herein are the analogous relations for the nonlinear rank 5 tensors that have not previously been treated and which complete this missing transformation gap and enable some nonlinear atomic-level phenomena to be investigated. [ABSTRACT FROM AUTHOR]

The piezoelectric performance of polyvinylidene fluoride (PVDF) is shown to double through the controlled incorporation of carbon nanomaterial. Specifically, PVDF composites containing carbon fullerenes (C60) and single-walled carbon nanotubes (SWNT) are fabricated over a range of compositions and optimized for their Young's modulus, dielectric constant, and d31 piezoelectric coefficient. Thermally stimulated current measurements show a large increase in internal charge and polarization in the composites over pure PVDF. The electromechanical coupling coefficients (k31) at optimal loading levels are found to be 1.84 and 2 times greater than pure PVDF for the PVDF-C60 and PVDF-SWNT composites, respectively. Such property-enhanced nanocomposites could have significant benefit to electromechanical systems employed for structural sensing, energy scavenging, sonar, and biomedical imaging. [ABSTRACT FROM AUTHOR]

Examines stress compensated quartz resonators having ultralinear frequency-temperature responses. Physical features of new linear and stress compensated cuts; Limitations existing in nonrotated Y-cut quartz plates; Resonance frequency equation for thickness-vibration modes in a thin ideal crystal plate.

Abstract: The purpose of this paper, Part IIB in the trilogy [Int J Appl Glass Sci. 2018 (not available); Int J Appl Glass Sci. 2018 (not available); Int J Appl Glass Sci. 2018 (not available)], is to describe the continuum models employed to deduce the effects of differential thermal expansion in the clad optical fiber in addition to the nonlinear optical behaviors at high intensities of light. In this continuation of Part IIA, more of the state‐of‐the‐art in W‐S‐based continuum material models are reviewed here with specific examples provided based on canonical material systems suggested from the findings of Part I and treated in detail in Part III. Part IIB pays particular attention to the optical fiber and its nonlinearities. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper, Part IIA in the trilogy (Int J Appl Glass Sci. 2018;9:263‐277; Int J Appl Glass Sci. 2018 (in press); Int J Appl Glass Sci. 2018 (in press)), is to describe the continuum models employed to deduce the physical, acoustic, and optical properties of optical fibers that exhibit intrinsically low optical nonlinearities. The continuum models described herein are based on the additivity approaches of Winklemann and Schott (W‐S). Initially developed over 120 years ago, W‐S additivity works well for predicting the basic properties of bulk silicate glasses. While high‐silica‐content glasses are still the gold‐standard for telecommunication and high energy laser fibers, the models have been systematically expanded to include deduction of the physical, thermophysical, and acoustic constants and coefficients that bear on parasitic nonlinearities. The state‐of‐the‐art in W‐S‐based continuum materials models is reviewed here with specific examples provided based on canonical material systems suggested from the findings of Part I and treated in detail in Part III. [ABSTRACT FROM AUTHOR]

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.

The companion paper (Part I; Dragic et al., this issue),1 resolved an anomaly involving the acoustical properties of high alumina content glass optical fibers. In Part II, some attributes of alumina and silica polymorphs are considered and used to infer approximate pertinent properties of amorphous Al2O3 'glass.' An efficient computational method is used, based on a simple, self-consistent version of the Voigt- Reuss- Hill procedure. Applied to SiO2 polymorphs, it provides insights into the short-range ordering in 'amorphous' silica. [ABSTRACT FROM AUTHOR]

The thermo-acoustic coefficient ( TAC, or the change of acoustic velocity with a change in temperature) of the alumina (Al2O3) component in aluminosilicate core silica clad glass optical fibers is anomalously large. It has been speculated previously that this anomaly is not due to a large alumina TAC, but instead due to the thermal expansion mismatch between the aluminosilicate core glass and the pure silica cladding glass. In this new work, it is shown that the acoustic velocity of the aluminosilicate core glass changes much differently than that for a bulk aluminosilicate glass. In the high alumina content compositional range, it is found that the larger core-region thermal expansion results in a net positive pressure imparted on the silica component in the core. As the acoustic velocity of silica has a strong negative dependence on any applied pressure, this offsets the bulk positive-valued thermal response of silica. Utilizing a modified form of the Winkelmann-Schott additivity model, the effect of the thermal expansion mismatch between the core and clad glasses is incorporated, and the resultant TAC determined for alumina is fully consistent with data found in the literature for bulk alumina. The consideration and incorporation of the thermal expansion of the core and clad glasses adds another degree of freedom to the design of specialty optical fibers for distributed sensor applications. Complementary to this article, Part II describes an efficient computational route for determining selected physical properties of an amorphous analog to a given crystalline form whose physical properties are known. [ABSTRACT FROM AUTHOR]

The author discusses the bulk acoustic wave analysis of crystalline zinc oxide (ZnO) films. Topics discussed include algebraic formulas for piezoelectric point group, extension of the Christoffel formulation to include piezoelectric excitation by a lateral field, and excitation of piezoelectric coupling coefficients by electric fields directed along phase progression.

Quartz shear resonators are employed widely as sensors to measure Newtonian viscosities of liquids. Perturbation of the electrical equivalent circuit parameters of the plate resonator by the fluid loading permits calculation of the mass density-shear viscosity product. Use of doubly rotated resonators does permit additional information to be obtained, but in no case can the viscosity and mass density values be separated. In these measurements, the resonator surface is exposed to a measurand bath whose extent greatly exceeds the penetration depth of the evanescent shear mode excited by the active element. Here we briefly review past techniques and current art, and sketch a proposal involving the interesting situation in which the separation between the resonator and a confining wall is less than the penetration depth of the fluid occupying the intervening region. To highlight the salient features of this novel case, the discussion is limited to the very idealized circumstance of a strictly 1-D problem, unencumbered by the vicissitudes inevitably encountered in practice. An appendix mentions some of these functional impedimenta and indicates how deviations from ideality might be approached in engineering embodiments. When the fluid confinement is of the order of the penetration depth, the resonator perturbation becomes a sensitive function of the separation, and it is found that viscosity and density may be separately and uniquely determined. Moreover, extreme miniaturization is a natural consequence because the penetration depth generally is on the order of micrometers for frequencies around 1 MHz at temperatures and pressures ordinarily encountered with gases and liquids. Micro-electro-mechanical (MEMS) versions of viscometers and associated types of fluid sensors are thereby enabled. [ABSTRACT FROM AUTHOR]

Poisson's ratio, the relation between lateral contraction of a thin, linearly elastic rod when subjected to a longitudinal extension, has a long and interesting history. For isotropic bodies, it can theoretically range from +1/2 to -1; the experimental gamut for anisotropics is even larger. The ratio is positive for all combinations of directions in most crystals. But as far back as the 1800s, Voigt and others found that negative values were encountered for some materials, a property now called auxeticity. Here we examine this property from the point of view of crystal stability and compute extrema of the ratio for various interesting and technologically important materials. Potential applications of the auxetic property are mentioned. [ABSTRACT FROM AUTHOR]

The quartz resonator Q with aluminum electrodes was studied with respect to its fundamental thickness shear mode frequency and its viscoelastic, viscopiezoelectric, and viscopiezoelectromagnetic behaviors. The governing equations for viscoelasticity, viscopiezoelectricity, and viscopiezo-electromagnetism were implemented for an AT-cut quartz resonator. To simulate the radiation conditions at infinity for the viscopiezoelectromagnetic model, perfectly matched layers over a surface enclosing the resonator were implemented to absorb all incident electromagnetic radiation. The shape of the radiation spectrum of a 5.6 MHz AT-cut quartz resonator was found to compare relatively well the measured results by Campbell and Weber. The mesa-plate resonator was studied for a frequency range of 1.4 GHz to 3.4 GHz. The resonator Q was determined to be influenced predominantly by the quartz viscoelasticity; how- ever at frequencies greater than 2.3 GHz, the quartz electromagnetic radiation had an increasingly significant effect on the resonator Q. At 3.4 GHz, the electromagnetic radiation accounted for about 14% of the loss in resonator Q. At frequencies less than 2 GHz, the calculated resonator Q compared well with the intrinsic Qx provided by the formula Qx = 16 x 106/f where f was in MHz. At frequencies higher than 2.3 GHz, the aluminum electrodes had significant effects on the resonator Q. At 3.4 GHz, the electromagnetic radiation loss in the electrodes was an order of magnitude greater than their viscoelastic loss; hence, the vibrating aluminum electrodes became an efficient emitter of electromagnetic waves. The effects of electrical resistance in both the electrodes and quartz were determined to be negligible. [ABSTRACT FROM AUTHOR]

The development of compact sensor and agile communications equipment together with electronically steerable antenna arrays for high mobility, on-the-move networking can be enhanced by use of nanoscale active thin film resonators, high stability frequency sources, integrated on-chip filters and complementary radiating structures supported by agile frequency selective surfaces. For mobile uses such as cell phones and highly mobile tactical communications, size and cost are severe additional constraints. Such systems also require miniaturized, high-Q passive components and interconnects which allow for high performance, including low noise, reduced coupling and reduced out-of-band interference, small volume and high-density. Active thin films can also be used to implement high quality resonators and tunable filters for use in high-density chip-based RFICs. Advanced filter technology using active thin films will enable a high level of integration. Such components would enable a system-on-a-chip architecture. Use of metamaterial frequency selective surfaces formed by fractal-space-filling-curve inclusions, together with non-linear thin-film elements or photonically-activated thin-film elements at a certain point(s) of each inclusion can be used to realize surface characteristics that can be potentially changed by an external field or an external optical signal. Finally, dense networks of carbon nanotube resonators offer the possibility of realizing CMOS-compatible reconfigurable systems and architectures. [ABSTRACT FROM AUTHOR]

Details a study which developed a modified Christoffel-Bechmann formalism to calculate acoustic wave velocities, displacements and piezoelectric coupling in plates and films. Overview of Christoffel-Bechmann elastic wave formalism; Application of Christoffel-Bechmann to wurtzite structure; Materials used.

When a doubly rotated resonator is operated in a liquid, the displacement of the surface is partly out of the plane of the plate of the resonator. The out-of-plane component of the displacement propagates a damped compressional wave into the liquid, and the in-plane component propagates a damped shear wave. In this paper, we report the measurements of the series resonant frequency and the motional arm resistance of doubly rotated quartz resonators (θ ≈ 35° and φ = 7°) in liquids to compare with singly rotated AT-cut resonators (θ ≈ 35° and 0 = 00). A modified Butterworth-Van Dyke (BVD) equivalent circuit model is suggested to analyze doubly rotated cut resonators under liquid loading. [ABSTRACT FROM AUTHOR]

Presents measured force-frequency coefficients of a Y-cut langanite (LGN) resonator and a Y-cut langatate (LGT) resonator as a function of the azimuthal angle. Force-frequency effect; Behavior of LGN and LGT in the polarity of the frequency changes; Maximum magnitudes of the coefficients of the LGN and the LGT; Stress-compensated cut; Contribution of the force-frequency effect to long-term aging.