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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.

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.

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 viscopiezoelectromagnetism 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; however 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 Q(x) provided by the formula Q(x) = 16 x 10(6)/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.

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 (theta approximately 35 degrees and phi = 7 degrees) in liquids to compare with singly rotated AT-cut resonators (theta approximately 35 degrees and phi = 0 degrees). A modified Butterworth-Van Dyke (BVD) equivalent circuit model is suggested to analyze doubly rotated cut resonators under liquid loading.

The three-dimensional (3-D) equations of linear piezoelectricity with quasi-electrostatic approximation are extended to include losses attributed to the acoustic viscosity and electrical conductivity. These equations are used to investigate effects of dissipation on the propagation of plane waves in an infinite solid and forced thickness vibrations in an infinite piezoelectric plate with general symmetry. For a harmonic plane wave propagating in an arbitrary direction in an unbounded solid, the complex eigenvalue problem is solved from which the effective elastic stiffness, viscosity, and conductivity are computed. For the forced thickness vibrations of an infinite plate, the complex coupling factor K*, input admittance Y are derived and an explicit, approximate expression for K* is obtained in terms of material properties. Effects of the viscosity and conductivity on the resonance frequency, modes, admittance, attenuation coefficient, dynamic time constant, coupling factor, and quality factor are calculated and examined for quartz and ceramic barium titanate plates.

Most recently, langasite and its isomorphs (LGX) have been advanced as potential substitutes for quartz, owing to their extremely high-quality (Q) factors. At least twice higher Q value of LGX than that of quartz has been reported. High Q translates into potentially greater stability. In order to make such materials practical, the environmental sensitivities must be addressed. One of such sensitivities is the force-frequency effect, which relates the sensitiveness of a resonator to shock and vibration via the third-order (non-Hookean) elastic constants. In this paper, we report 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, which is the angle between the crystalline x-axis of a resonator plate and the direction of in-plane diametric force applied to the periphery of the resonator. It was found that the LGN and the LGT behave like AT-cut quartz in the polarity of the frequency changes and the existence of zero-coefficient angle. 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, respectively (or, 7 and 10 times smaller comparing to AT-cut quartz). The coefficients of planar-stress, which represent the superposition of a continuous distribution of periphery stresses, also were obtained as 0.52 X 10(-15) m x s/N and 0.38 X 10(-15) m x s/N for the LGN and the LGT, respectively.

Piezoelectric thin film zinc oxide (ZnO) and its ternary alloy magnesium zinc oxide (MgxZn1-xO) have broad applications in transducers, resonators, and filters. In this work, we present a new bulk acoustic wave (BAW) structure consisting of Al/MgxZn1-xO/n(+)-ZnO/r-sapphire, where Al and n+ type ZnO serve as the top and bottom electrode, respectively. The epitaxial MgxZn1-xO films have the same epitaxial relationships with the substrate as ZnO on r-Al2O3, resulting in the c-axis of the MgxZn1-xO being in the growth plane. This relationship promotes shear bulk wave propagation that affords sensing in liquid phase media without the dampening effects found in longitudinal wave mode BAW devices. The BAW velocity and electromechanical coupling coefficient of MgxZn1-xO can be tailored by varying the Mg composition, which provides an alternative and complementary method to adjust the BAW characteristics by changing the piezoelectric film thickness. This provides flexibility to design the operating frequencies of thin film bulk acoustic wave devices. Frequency responses of devices with two acoustic wave modes propagating in the specified structure are analyzed using a transmission line model. Measured results show good agreement with simulation.

Piezoelectric coupling factors for langatate (La3Ga5.5Ta0.5O14) single-crystals driven by lateral-field-excitation have been calculated using the extended Christoffel-Bechmann method. Calculations were made using published materials constants. The results are presented in terms of the lateral piezoelectric coupling factor as functions of in-plane (azimuthal) rotation angle for the three simple thickness vibration modes of some non-rotated, singly-rotated, and doubly-rotated orientations. It is shown that lateral-field-excitation offers the potential to eliminate unwanted vibration modes and to achieve considerably greater piezoelectric coupling versus thickness-field-excitation for the rotated cuts considered and for a doubly-rotated cut that is of potential technological interest.