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At least 811 records · Page 45Linked to original sources
PubMed2006

Capillary aging of the contacts between glass spheres and a quartz resonator surface.

The strength of the contacts between small glass spheres and the surface of a quartz crystal resonator has been probed based on the increase of resonance frequency induced upon sphere contact. The acoustic interaction between the sphere and the plate is modeled as a low-frequency coupled resonance; the dependence of the resonant parameters on overtone order lends support to this model. After exposing the sample to humid air and drying it again, the contact strength increases at least tenfold due to capillary forces--we observe a hysteretic form of the sand-castle effect. Repeated wet-dry cycles reveal logarithmic capillary aging with time. The experiments suggest that the drying of the liquid bridges leads to a contraction of small voids in the contact zone, subsequently increasing cohesion.

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PubMed2000

Elucidation of simple pathways for reconstructive phase transitions using periodic equi-surface (PES) descriptors. The silica phase system. I. Quartz-tridymite

A method of estimating short topological pathways for solid-solid reconstructive phase transitions is proposed. To screen the simplest pathways out of the infinite manifold in configurational space, a Fourier function approach is used, based on periodic nodal (PNS) and periodic equi-surface (PES) descriptors. The simplicity of the chosen functions representing the structures in question and the linear transition approach provide for most simple relevant transition models. Here it is shown that the tetrahedral networks of quartz and tridymite are represented topologically and transformed into each other by this approach. A trigonal network related to alpha-ThSi2 and B2O3 appears as intermediate during the transition model of the periodic functions. The transition path found in this way seems to be of exciting directness and of fundamental topological interest. The presented approach is not restricted to this specific case and is expected to be applicable to a wide variety of reconstructive phase transitions of solids.

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PubMed2002

Group-theoretical and geometrical considerations of the phase transition between the high-temperature polymorphs of quartz and tridymite.

A model was derived for the temperature-dependent phase transition between the high-temperature polymorphs of quartz (P6(4)22) and tridymite (P6(3)/mmc). Only the Si framework is considered, and the transformation can be described as a deformation of a homogeneous sphere packing with three contacts per sphere (type 3/10/h1) in the common subgroup P6(1)22 of P6(4)22 and P6(3)/mmc. The proposed model guarantees the three-dimensional connection of the crystal structure during the whole transformation process.

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PubMed2001

Analysis of 3-D vibrations of rectangular AT-cut quartz plates with a bi-mesa structure.

A method to analyze 3-D vibrations of rectangular AT-cut quartz bi-mesa-shaped plates is developed. The method is based on a classical approach. As in 2-D analysis, the half structure of a plate is separated into a thick bi-mesa and a thin-side portion, and the displacement field of each region is represented by a linear combination of guided waves. In the 3-D analysis, we apply the 2-D finite element method (FEM) to obtain the waves guided by two pairs of parallel surfaces. The orthogonal property of guided modes is incorporated to approximately fulfill the continuity conditions at the interface between the thick and thin portions. The stress-free conditions on the plate edges are satisfied by employing the method of weighted residuals (MWR). The computational advantage of this method is that it can greatly reduce the matrix size compared with the 3-D FEM. As a numerical example, the frequency spectra are calculated for X-elongated plates of bi-mesa shape, and the strong energy-trapping effect on the fundamental thickness-shear (TS) resonance is verified.

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PubMed2001

Analysis of thickness modes of contoured doubly rotated, quartz resonators.

It is the intent of this work to provide a working resource for calculating all three mode families of a doubly rotated, contoured quartz resonator. It is shown that the theoretical development of Stevens and Tiersten [1] can be used for this purpose. Their approach uses a transformation of the mechanical displacement vector to the eigenvector triad of the pure thickness solution. The solution methodology here reorganizes the transformation matrix Q in their formulation to calculate the other two mode families. Calculations compare well with experimental results for the three mode families of an SC-cut crystal and an FC-cut crystal and with published calculations for the SBTC-cut mode family with major displacement along the x3 blank axis. The key constants for the SC-cut are presented for workers to use in the future. In addition, the equations of motion and boundary conditions are derived for the two additional mode families using assumptions parallel to those used by Stevens and Tiersten [1]. Calculations with these equations are presented for completeness to support the present conclusions by showing the equivalence of either simply reorganizing the Q matrix or using separate equations for each of the three mode families.

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PubMed2001

Force-frequency coefficient of symmetrical incomplete circular quartz crystal resonator.

The changes in the resonance frequencies of the thickness-shear vibration of symmetrical incomplete circular AT-cut quartz crystal resonators (QXRs), which are used as sensing elements in digital force sensors or pressure transducers, by the application of diametrical forces are discussed by considering the piezoelectric effect and the anistropic characteristics of crystal plates. Two-dimensional motion equations for predicting the frequency changes are derived from three-dimensional piezoelectricity equations, and equations deduced by Janiaud for solving the stress distribution in crystal plates are used to calculate the force-frequency coefficients of incomplete circular resonators. The results show that the piezoelectric effect of crystal plates decreases the force-frequency coefficient of the azimuth angle 0 degrees by 7% as compared with no piezoelectricity assumption. The incomplete circular shape can be applied to a larger load than the circular disc because the flat regions of the incomplete shape provide a distributed load application without the problems of stress concentration of a point force inherent to a circular disc. The incomplete shape gives an increased force sensitivity when compared with the complete disc near azimuth angle 0 degrees. The theoretical curves agree well with Ratajski's experimental results.

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PubMed2001

Doubly rotated quartz resonators with a low amplitude-frequency effect: the LD-cut.

This article deals with a crystal quartz cut with virtually no amplitude-frequency effect (also called "isochronism defect" or "anisochronism"). The cut, called LD-cut (Low isochronism Defect), is set in a BVA-type structure for later use in an Ultra-Stable Oscillator (USO). Various design parameters are presented, along with the properties of the resonator. The resonance frequencies of various modes, the temperature dependence, the motional parameters and the phase noise in relation to the power supplied to the resonator are mainly studied. These properties are compared to those of the SC-cut resonators.

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PubMed2002

Accurate measurements of the acoustical physical constants of synthetic alpha-quartz for SAW devices.

Accurate measurements of the acoustical physical constants (elastic constants, piezoelectric constants, dielectric constants, and density) of commercially available and widely used surface acoustic wave (SAW)-grade synthetic a-quartz are reported. The propagation directions and modes of bulk waves optimal for accurately determining the constants were selected through numerical calculations, and three principal X-, Y-, and Z-cut specimens and several rotated Y-cut specimens were prepared from a single crystal ingot to determine the constants and to confirm their accuracy. All of the constants were determined through highly accurate measurements of the longitudinal velocities, shear velocities, dielectric constants, and density. The velocity values measured for the specimens that were not used to determine the constants agreed well with those calculated from the determined constants, within a difference of +/- 0.20 m/s (+/- 0.004%).

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PubMed2003

A "space experiment" examining the response of a geosynchronous quartz crystal oscillator to various levels of solar activity.

Viewing the frequency history of the high-quality quartz crystal oscillator onboard Milstar FLT-1 as a "space experiment," we have examined the response of the crystal to various solar flares that have occurred over the past 4 years. Our results show that, even for the largest solar flares that can be expected, timekeeping onboard a geosynchronous communications satellite need not be unduly perturbed by the enhanced space-radiation environment of a solar flare, so long as the ground station can take mitigating action within a few hours of the flare's onset.

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PubMed2003

Thickness-shear vibrations of a quartz plate under time-dependent biasing deformations.

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.

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PubMed2005

Multistage chemical etching for high-precision frequency adjustment in ultrahigh-frequency fundamental quartz resonators.

Chemical etching to precisely adjust and to make uniform the thicknesses of vibrating areas of multiple resonators in a single wafer was applied to inverted-mesa quartz resonators exciting an ultrahigh-frequency fundamental thickness vibration. The process consisted of five stages, combining high-rate etching for high productivity and low-rate etching for high-precision adjustment. By using this process, the resonance frequencies of 41 resonators in the single wafer were adjusted to 620 +/- 1.5 MHz, which corresponds to vibrating area thicknesses of 2.2 microm +/- 6 nm. In the temperature-frequency characteristics of these resonators in the single wafer, the difference between the maximum first-order temperature coefficient and the minimum first-order temperature coefficient was equivalent to a cut angle change of two arcminutes. In addition, vibrating areas with an arithmetic mean surface roughness of 0.17 nm on the concave side were produced by this multistage etching.

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PubMed2006

Frequency-temperature behavior of flexural quartz resonators by means of Timoshenko's model.

The frequency of a flexural resonator and its frequency-temperature behavior usually are computed by Bernoulli's classical approximation. This approach is valid for beams with a large length-over-thickness-ratio. For shorter beams, the effects of shear stress and rotary inertia may play a significant role for temperature-compensated resonators. These effects have been taken into account for isotropic beams. The aim of this paper is to discuss the extension of the shear coefficient in the case of an anisotropic material and to compute the frequency-temperature characteristic of an (XYt)theta cut resonator when the shear stress and the rotary inertia have been taken into account. Comparisons between the classical approximation and this treatment are given for quartz. Furthermore, the numerical predictions obtained by means of different sets of data available for thermal sensitivities of elastic coefficients are compared.

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PubMed2006

Design and fabrication of a length-extensional mode rectangular X-cut quartz resonator with zero temperature coefficient.

Rectangular X-cut quartz crystal resonators with cut angles theta > 5.0 degrees and aspect ratios Rzy (= width 2z0/length 2y0) from 0.3 to 0.5 are investigated. The resonators oscillate mode is a length-extensional mode. A semiempirical frequency equation was derived from the stress expressed in terms of the trigonometric and the hyperbolic transcendental functions with constants estimated by the regression curve fit to the stress simulated by the finite-element method (FEM). Contours on which a point satisfies a zero first order temperature coefficient condition are shown in a cut angle theta and Rzy diagram. We proved that a fabricated resonator with Rzy = 0.400 and theta = 16.0 degrees, whose design parameter is located in the area of the contour, had a zero temperature coefficient.

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PubMed2006

Analysis of capacitance ratio of a rectangular X-cut length-extensional mode quartz crystal resonator by stresses.

The electrical properties of an X-cut, length-extensional mode quartz crystal resonator of a cut angle theta around the X-axis were calculated by a variational method using stresses as trial functions. Analytical expressions of stresses were estimated by a linear regression on a cut angle best-fit to the results of finite-element method. The calculated dependence of the capacitance ratio on the cut angle was consistent with the measured results.

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