Thickness shear mode quartz crystal resonators with optimized elliptical electrodes

Quartz crystal resonators （QCRs） with circular electrodes have been widely used for various liquid and gas sensing applications. In this work, quartz crystal resonators with elliptical electrodes were studied and tested for liquid property measurement. Mindlin＇s theory was used to optimize the dimension and geometry of the electrodes and a 5-MHz QCR with minimum series resistance and without any spurious modes was obtained. A series of AT-cut QCRs with elliptical electrodes of different sizes were fabricated and their sensing performances were compared to devices with circular electrodes. The experimental result shows that the device with elliptical electrodes can obtain lower resonance impedance and a higher Q factor, which results in a better loading capability. Even though the sensitivities of devices with elliptical and circular electrodes are found to be similar, the sensor with elliptical electrodes has much higher resolution due to a better frequency stability. The study indicates that the performance of QCRs with elliptical electrodes is superior to that of traditional QCRs with circular electrodes.

The Multi-field Coupled Vibration Analysis of AT-Cut Quartz Crystal Resonators with Parallelism Error

During the fabrication of quartz crystal resonators(QCRs),parallelism error is inevitably generated,which is rarely investigated.In order to reveal the influence of parallelism error on the working performance of QCRs,the coupled vibration of a non-parallel AT-cut quartz crystal plate with electrodes is systematically studied from the views of theoretical analysis and numerical simulations.The two-dimensional thermal incremental field equations are solved for the free vibration analysis via the coefficient-formed partial differential equation module of the COMSOL Multiphysics software,from which the frequency spectra,frequency–temperature curves,and mode shapes are discussed in detail.Additionally,the piezoelectric module is utilized to obtain the admittance response under different conditions.It is demonstrated that the parallelism error reduces the resonant frequency.Additionally,symmetry broken by the non-parallelism increases the probability of activity dip and is harmful to QCR’s thermal stability.However,if the top and bottom surfaces incline synchronously in the same direction,the influence of parallelism error is tiny.The conclusions achieved are helpful for the QCR design,and the methodology presented can also be applied to other wave devices.

Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid

The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.

Effect of strain-gradients of surface micro-beams on frequency-shift of a quartz crystal resonator under thickness-shear vibrations

With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator（QCR） system,consisting of a QCR and surface micro-beam arrays.The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained,which have important significance in resonator design and applications.

Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

We study the dynamic behavior of a quartz crystal resonator （QCR） in thickness-shear vibrations with the upper surface covered by an array of micro-beams （MBs） under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right （left） translation for increasing elastic modulus （length/radius ratio） of MBs. Moreover, the frequency right （left） translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one,

Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams

The electric admittance of a compound system composed of a thickness-shear mode （TSM） quartz crystal resonator （QCR） and an array of surface viscoelastic micro-beams （MBs） is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin （SU-8） MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak（s） and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.

ON THE INTERACTION BETWEEN A QUARTZ CRYSTAL RESONATOR AND AN ARRAY OF MICRO-BEAMS IN THICKNESS-SHEAR VIBRATIONS

We studied the coupled dynamic behavior of a quartz-crystal-resonator （QCR）/micro- beams system in the thickness-shear motions. Through taking into account the couple stress in the dynamic equations of the quartz plate, both continuous conditions of shear force and bending moment at the resonator/micro-beams interface are realized. Frequency shift of the compound QCR system induced by micro-beams is studied in detail. The obtained results are useful in device design and frequency-stability analysis of quartz crystal resonators.

Analyzing the response of a contactless conductivity detector in capillary electrophoresis by a resonant method

We report a resonant method to measure the wall capacitance（C_w） and solution resistance（R_S） in a capacitively coupled contactless conductivity detector（C^4D）.Under the typical operating conditions in capillary electrophoresis（I.D.50μm,O.D. 360μm,electrode length of 4 mm,electrode gap of 1 mm,frequency of 200 kHz）,the values of C_w measured in 1 and 20 mmol/L NaCl solutions are 2.8 and 32 fF,which are only 1.1%and 12%of prediction by the equation in references,respectively.The value of R_S is less than the prediction in solutions withκ〈0.02 S/m.The response current of C^4D is due to the change in C_w because the total impedance of a C^4D is composed mainly by the impedance from C_w.