Circular Quartz Plates Research Articles

Multichannel quartz crystal microbalance array: Fabrication, evaluation, application in biomarker detection

A multichannel quartz crystal microbalance array (MQCM) with three pairs of gold electrodes was fabricated for detection of two biomarkers: acetone and nitric oxide (NO). The gold electrodes were deposited symmetrically on an AT-cut 10 MHz circular quartz plate using photolithography, sputtering, and lift-off technologies. The effect of gold layer thickness on MQCM performance was investigated and the optimized thickness was 101 nm. The simulation values of the electric parameters C0, Cq, Lq, and Rq in the Butterworth–Van Dike equivalent circuit for the MQCM device were 97 pF, 1.3 pF, 1.05 mH, and 9.8 Ω, respectively. Simulation values were in the theoretical range, which indicated that the fabricated MQCM device had good resonance performance. Two types of nanocomposites, titanium dioxide–multiwalled carbon nanotubes and cobalt (II)phthalocyanine–silica, were synthesized as sensing materials. The sensing mechanism is based on coordination adsorption of target molecules onto the sensing material, resulting in a resonant frequency shift of modified QCM sensor. A linear range from 4.33 to 129.75 ppmv for acetone was obtained and one from 5.75 to 103.45 ppbv for NO.

Thickness-shear vibration analysis of circular quartz crystal plates by a differential quadrature hierarchical finite element method

Piezoelectric crystals are widely used to make acoustic wave resonators. A large portion of quartz crystal resonators are operated with the so-called thickness-shear (TS) modes of a plate, which is characterized by high frequency vibration that needs both huge computational cost and high accuracy. The situation is even more difficult for circular resonators because the scalar differential equation is not separable in polar coordinates due to material anisotropy. In this paper, TS vibration analysis of circular quartz plates was carried out by a differential quadrature hierarchical finite element method (DQHFEM). The DQHFEM adopts the formulations of the DQFEM that are compact and highly accurate. The numerical stability problem of the high-order or very high-order hierarchical basis is overcome by using the recursion formula of Legendre polynomials and more than 2000th order can be reached. The high frequency thickness-shear vibration of a circular quartz plate can be modeled by using only one or several DQHFEM elements, which greatly simplifies pre- and post-processing. Numerical comparison of the DQHFEM results with the results in literatures validated the high accuracy of the DQHFEM.

On the acceleration sensitivity and its active reduction by edge electrodes in AT-cut quartz resonators.

Incremental piezoelectric equations for small vibrations superposed on initial deformations are presented. The equations are implemented in COMSOL finite element models (FEA). Equations are validated by comparing the results for the force sensitivity coefficient Kf of a circular quartz plate subjected to a pair of diametrical forces with measured data. The model results show a consistent trend with the experimental results, and the relative difference between our FEA results and Ballato's measured result is about 13%. A detailed study of the acceleration sensitivity of a rectangular AT-cut quartz plate is presented. The plate resonator is fixed along one edge as a cantilever. For AT-cut quartz resonators with the crystal digonal X-axis perpendicular to plate X-axis, the in-plane acceleration sensitivity is found to be negligible compared with the out-of-plane (Y-axis) acceleration sensitivity. For AT-cut quartz resonators with the crystal digonal X-axis parallel to plate X-axis, the Y-axis acceleration sensitivity is found to be rectified, that is the fractional change in frequency is positive with respect to both positive and negative Y-axis accelerations. The Y-axis acceleration sensitivity is small in comparison with the in-plane acceleration sensitivity for small body forces. However, for large body forces, the Y-axis acceleration sensitivity dominates because it increases nonlinearly with the Y-axis acceleration. The resonator rectified acceleration sensitivity is confirmed by phase noise measurements. For reduced acceleration sensitivity, two pairs of electrodes along the plate edges reduce the bending of the plate resonator and subsequently reduce acceleration sensitivity. We present a new method using these edge electrodes in which a dc bias field is employed to control the resonant frequency of resonator subjected to g body forces. A dc bias field with an appropriate dc bias voltage could potentially yield a reduction of acceleration sensitivity in Y-axis direction of about two orders of magnitude.

Stress Distribution of Thin Circular Quartz Plate with the Radial Force

Based on the analysis of stress distribution in the medium of semi-infinite anisotropic thin medium plates with centralized forces, in the method of protracting and adding additional stress, the relation of relative frequency variation and adding force azimuth and strength of the plates with the diameter centralized forces can be gained. And it is compared with relative frequency variation of resonation with central electrode. Meanwhile by using finite element method to analyze stress variation in different places when the quartz plate is with the diameter centralized forces, and the frequency variation characteristic of resonator in different places is also be measured in the actual evaporated electrode way.

Appearance of target pattern and spiral flames in radial microchannels with CH4-air mixtures

This paper presents the experimental evidence of the formation of rotating spiral flames with premixed methane-air mixtures introduced at the center of the two parallel circular quartz plates which are separated by a millimeter scale distance (≤5mm). Both plates are externally heated to create a positive wall temperature gradient in the flow direction to resemble heat recirculation through solid walls, which is a requisite to obtain stabilized combustion in microburners. Contrary to the general perception of a stable premixed flame front at a radial location, a variety of nonstationary flame propagation modes are observed. For lower mixture flow rates and a range of mixture equivalence ratios, a radial flame propagation mode is observed with simultaneous presence of two circular flames at different radial locations. For higher flow rates, a rotating spiral flame propagation mode is observed. In addition to radial and spiral flame propagation modes, random and unsymmetrical flame oscillations are also observed. The rotational rates of the spiral flame fronts were observed to vary from 28 to 83Hz. A simple analysis is carried out to describe the formation of spiral flames from a steady circular flame.

Regime diagrams and characteristics of flame patterns in radial microchannels with temperature gradients

Comprehensive regime diagrams of flame pattern formation in radial microchannels with temperature gradients were drawn based on experimental findings. A premixed methane–air mixture was introduced at the center of microchannels formed by two parallel circular quartz plates that were heated with an external porous burner to create a positive temperature gradient condition in the direction of flow. Combustion behavior in those microchannels at channel widths of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 mm were experimentally investigated. Regime diagrams of various stable and unstable flame patterns were obtained, confirming that the flame pattern is a strong function of mixture equivalence ratio, inlet mixture velocity, and channel width. Furthermore, some combustion characteristics, such as the rotating frequency of the single pelton-like flame and the triple flame, the radius of the stable circular flame front, and comparison between the major combustion products of the single and double pelton-like flames, were also investigated.

Experimental investigations on the combustion behavior of methane–air mixtures in a micro-scale radial combustor configuration

Experimental investigations on combustion stability limits for methane–air mixtures in a radial micro-scale combustor configuration are herein reported. To study the flame stability characteristics in this radial combustor configuration, two circular quartz plates were arranged parallel to each other and a fuel–air mixture was supplied at the center of the plates. The plates were externally heated to create a positive temperature gradient condition in the flow direction to simplify the heat recirculation process through the solid walls. The fuel–air mixture emanating from the center was subjected to a positive wall temperature gradient and a negative velocity gradient in the radial combustor configuration. Various stable and unstable flame propagation modes were observed during the experimental investigations. The appearance of these modes was a strong function of mixture flow rate, channel width, temperature distribution and mixture equivalence ratio. The effects of wall temperature and mixture equivalence ratios were investigated for a range of mixture flow rates. These investigations showed that the combustion zone moved linearly outward with the increase in the mixture flow rate. At intermediate channel widths (∼2.5 mm), an unstable combustion mode appeared. In this combustion mode, large-scale random fluctuations in flame radius were observed along with the leakage of large amounts of unburnt fuel. Exhaust gas analysis was carried out to compare the combustion performance in stable and unstable combustion modes. Based on the experimental investigations, recommendations are made to facilitate the efficient design of a combustor for micro gas turbine applications.

Pattern formation of flames in radial microchannels with lean methane-air mixtures

Premixed methane-air mixture is introduced at the center of two parallel circular quartz plates separated by a millimeter scale distance (<or= 5mm). Two plates are heated with an external heater to create a positive temperature gradient condition along the flow direction. The combustion characteristics of lean methane-air mixtures are investigated at phi=0.67 and phi=0.85 in the laminar flow regime (Re approximately 500-1800). Contrary to the general perception of a stable premixed flame front at a radial location, a large variety of unstable and dynamic flame front patterns are observed at phi=0.67. At phi=0.85, stable flame propagation mode dominated the regime diagram and unstable flame propagation modes are observed under limited conditions. In these unstable flame propagation modes, single and multiple flame fronts rotate around the center at a rate of 15-50 Hz.

On the formation of multiple rotating Pelton-like flame structures in radial microchannels with lean methane–air mixtures

This paper reports the experimental observation of multiple Pelton-like rotating flame structures in radial microchannels with lean methane-air mixtures supplied at the center of the two closely placed circular quartz plates. The bottom quartz plate was heated with a porous burner to create a positive temperature gradient distribution along the flow direction. Stable flames were observed at a radial location for stoichiometric and rich mixtures over a wide range of operating conditions. On the other hand, for lean methane-air mixtures at ϕ = 0.67 and channel gap of ∼1–2 mm, distinct and single/multiple Pelton-like rotating flame structures were observed experimentally. These rotating flames were semi-circular in shape with a rotational speed varying from 15 to 50 Hz. Due to continuous rotation and a semi-circular flame shape; the rotating flames resemble a classical Pelton wheel. These flame structures were observed to appear over a range of velocities varying from 1.5 to 6 m/s. One, two and three rotating flames fronts appear in the domain at similar operating conditions. The effects of change in the temperature gradient and temperature profile were examined by employing a different porous burner and these modes were observed to be present for an asymmetric temperature profile. The appearance of these multiple rotating flame fronts was a function of peak temperature of the plates.

Potential of the thickness shear mode acoustic immunosensors for biological analysis

This paper describes the principles underlying the most widely used mass-detecting immunosensor, the so-called quartz crystal microbalance or thickness shear mode resonator. The transducer consists in a circular quartz plate which is piezoelectrically excited in the thickness shear mode by means of a pair of planar electrodes. One of the transducer electrode is functionalized with antibodies that are covalently immobilized. The authors stress a very important aspect which has been neglected so far and deserves special attention for biosensors applications: The necessity is not only to consider mass effects, but also boundary viscoelastic properties, with respect to changes of the shear acoustic impedance when antibody binding reactions take place at the surface of a thickness shear mode acoustic sensor. Two representative examples are given for cases when 1. (1) changes of boundary liquid viscosity dominate (selective binding of erythrocytes by IgM), or 2. (2) mass effects dominate (binding of IgG by anti-IgG antibodies).

Surface-acoustic-wave devices with low sensitivity to mechanical and thermoelastic stresses.

Surface-acoustic-wave (SAW) devices with a low sensitivity to both temperature and stresses effects are presented and experimentally tested. Devices are built on SAW quartz cuts with zero first-order temperature coefficient and zero sensitivity to planar isotropic stresses. In comparison with similar devices built on conventional (ST, X) cuts, two kinds of experiments are reported. First, devices built on circular quartz plates are submitted to in-plane diametrical compressions. The force-frequency effect is measured and results are compared to theoretical predictions either by analytical models or using finite element analysis. In a second experiment, the same devices are submitted to in-plane thermoelastic stresses in a dynamical thermal regime. It is shown that the sensitivity of the new cuts to dynamical thermal effects is one order of magnitude lower than the conventional (ST, X) cut, an attractive potentiality for fast-warm-up high-stability SAW oscillators in severe environmental conditions.

ChemInform Abstract: Reactive Ion Etching in SF6 Gas Mixtures

Abstractcontaining varying amounts of O2, N2, H2, and Ar has been studied for crystalline and polysilicon, SiO2, and S3N4 using RF cathodes covered with Al disk or with a 0.5 cm thick circular quartz plate.

Reactive Ion Etching in SF 6 Gas Mixtures

Reactive ion etching of crystalline silicon, polysilicon, , and has been studied in a parallel plate electrode configuration, with and without magnetic confinement, in gas diluted with varying proportions of , , , and Ar. In order to investigate the contamination from the RF cathode, RIE studies were done with RF cathode covered with aluminum disk as well as with 0.5 cm thick circular quartz plate. The RF frequency used is 13.56 MHz and RF power density varied from 0.1 to 0.4 Wcm−2. Experimental results indicate the following: (i) significant contamination occurs on the etched surface with the aluminum covered cathode, but no detectable contamination occurs with the quartz plate covered cathode, (ii) there are etch rate maxima both for silicon and polysilicon with dilution in the range 10–20 volume percent for aluminum covered cathode; these maxima are more pronounced at higher power levels, (iii) etch rates of silicon and polysilicon are much reduced with , , and especially dilution in volume proportions >30% at all power levels and irrespective of cathode covers; argon dilution has the least effect on the etch rates; (iv) due to loading effect the etch rates of silicon and polysilicon are reduced significantly if the aluminum cover on the cathode is substituted by a quartz plate. Moreover, scanning electron microscopic studies of silicon and polysilicon etch profiles have shown that in gas mixtures, the RIE process is physical‐chemical and not purely chemical. The degree of etch anisotropy has been found to vary from 0.5 to 0.3 depending upon argon dilution in and operating pressure. Magnetic confinement has been found to reduce anisotropy, and RF power density levels above 0.1 Wcm−2 have not been found to affect anisotropy. The highest selectivity obtained with quartz cathode is 18:1 for 100% at 0.1 Wcm−2 power density level with magnetic confinement. At higher power density levels, the selectivity has been found to decrease.

Generalized Equation for the Force-Frequency Characteristics of Circular Quartz Plates

A generalized equation which expresses the force-fre- quency characteristics of a circular disk plate supported by three un- symmetrical points is derived from the concept of balance of applied forces and the superposition of virtual force pairs. Optimum support- ing angles of an SC-cut plate, which is less immune to radially applied forces, are computed and the validity of the equation is confirmed with experiment. It is proposed that the most probable expansion coefficients of the force-frequency characteristics should be compiled from exten- sive experimental results.

The influence of support-configuration on the acceleration sensitivity of quartz resonator plates

The changes in the thickness-shear resonance frequencies of a circular, rotated Y-cut of quartz plate subject to in-plane steady accelerations was found to be a function of the direction and magnitude of the acceleration, the orientation of the crystal cut, the diameter-to-thickness ratio of the plate, and the numbers and positions of the metal ribbon supports at the edge of the crystal. The purpose of the present study is to investigate how the support configuration will influence the acceleration sensitivity of a resonator. An AT-cut circular quartz plate with four metal ribbon supports is chosen for a systematic parametric study. In order to examine the influence of the supportconfigurations on the frequency changes, the support configuration is changed from a reference configuration by displacing, for instance, one support in increments of 15° counterclockwise while holding the other supports fixed. For each displaced configuration, the frequency changes due to acceleration are computed as a function of the acceleration direction. In the same manner, computations are performed for a total of seven series of configuration variations. Then in each series, the particular support configurations and acceleration directions are identified as giving maximum and zero acceleration effects.

The Vibrations of Quartz Plates

By vibrating quartz crystals in an electric circuit Wright and Stuart have shown that the crystals break up into different parts while oscillating. The nodal lines thus formed are made visible to the eye by lycopodium powder. In the present paper it is pointed out that the mathematical theory of Chladni plates gives a general equation, A cos-cos -+ Bcos --cos = 0, for the nodal lines of square plates. This equation is also applicable to quartz plates in so far as the forms of the nodal lines are concerned. It gives no information regarding the manner of vibration of the quartz. Chladni plates both square and round have been vibrated by mechanical impact from a vacuum tube oscillator circuit. A few of the figures thus obtained are shown and may be compared with those of Wright and Stuart. The nodal lines for circular quartz plates do not in general resemble those of circular Chladni plates.

Quartz Plate Mountings and Temperature Control for Piezo Oscillators

In this paper are described a number of representative types of mountings for rectangular and circular quartz plates to be used as frequency standards. Unless the movement of the quartz plate in the holder is restricted, the frequency will change with each slight jar. A satisfactory holder for mounting a long rectangular quartz plate to vibrate at its extensional mode may be made by clamping the plate along a central line perpendicular to its length between two keys, one in the face of each electrode. The electrodes are spaced by quartz washers. A plate mounted in such a holder will be constant in frequency to 1 part in 300,000. Such a mounting has not been found satisfactory for frequencies above 100 kc as the damping caused by the pressure of the keys is too great. A very satisfactory holder for mounting a cylindrical quartz plate for "thickness oscillation" may be made by clamping the plate between three screws, mounted radially 120 degrees apart in a ring so that they press into a V-shaped groove cut around the cylindrical surface of the quartz plate midway between the faces. The electrodes are spaced on either side of the quartz plate by pyrex washers. Mounted in such a way, the plate has been found to be constant in frequency to 1 part in 1,000,000 in a portable frequency standard with the addition of temperature control to the oscillating circuit. Some discussion is given to the subject of temperature control of the piezo oscillator.