A new method for continuous monitoring of series resonance frequency and simple determination of motional impedance parameters for loaded quartz-crystal resonators

A new electronic design for continuous motional series resonant frequency monitoring of loaded quartz crystal resonators is presented. Using this circuit, a low-cost method for a simple determination of equivalent circuit parameters of quartz crystal resonators is described. Measurements made with the proposed system on typical AT cut quartz crystals are in good agreement with those of an Impedance Analyzer.     

Bulk wave membrane quartz resonators fabricated by a hollow cathode RF plasma etching technique

A hollow cathode maskless plasma etching method for fabrication of thin quartz membranes is presented. A special geometric arrangement of electrodes and substrates allows the complete plasma structure (plasma sheath, bulk plasma) to be transferred to the substrate area during the etching process. The process has successfully been used in preparing thin quartz membranes with plane-convex and plane-parallel shape, and thicknesses of less than 5 mum. Vibration modes in these thin quartz membranes are calculated using the method of equivalent resonant radius. The membranes are used for realization of bulk acoustic wave resonators at fundamental frequencies above 60 MHz. Good agreement between theoretical and experimental characteristics is achieved.     

Modeling of a short-term stability measuring system of quartz crystal resonators

A new numerical model of a short-term stability measuring system of quartz crystal resonators is presented. It is based on the phase bridge method using a pair of resonators driven by a low-noise source. The output signal, obtained with a phase detector, is proportional to the phase difference introduced by the resonators. The numerical transfer function of each bridge path is given by the model. The output spectral density of the phase fluctuations is computed from these transfer functions and the numerical approximation of the low-noise source. The model was applied to third overtone, SC-cut, 10 MHz BVA quartz crystal resonators. It enables the rejection of the source noise versus the resonant frequency of quartz crystal resonators to be quantified.     

Precise optical activity measurement of quartz plate by using a true phase-sensitive technique

A method of considering the circular and linear birefringent properties of a material on the basis of circular and linear polarization eigenstates is presented theoretically and experimentally. A polarized common-path optical heterodyne interferometer with respect to both right-hand and left-hand circularly polarized light was set up. It was used in conjunction with a phase lock-in technique to measure the optical activity of quartz crystal in real time. The signal-to-noise ratio of the measured phase change caused by the lateral displacement of quartz cornus was 75, which corresponded to a measuring accuracy of 10(-7). This novel method, in which a true-phase-sensitive optical heterodyne interferometer is used, has higher detection sensitivity and higher immunity to environmental disturbances.     

Thickness-shear mode shapes and mass-frequency influence surface of a circular and electroded AT-cut quartz resonator

Finite-element solutions for the fundamental thickness shear mode and the second-anharmonic overtone of a circular, 1.87-MHz AT-cut quartz plate with no electrodes are presented and compared with previously obtained results for a rectangular plate of similar properties. The edge flexural mode in circular plates, a vibration mode not seen in the rectangular plate is also presented. A 5-MHz circular and electroded AT-cut quartz plate is studied. A portion of the frequency spectrum is constructed in the neighborhood of the fundamental thickness-shear mode. A convergence study is also presented for the electroded 5-MHz plate. A new two-dimensional (2-D) technique for visualizing the vibration mode solutions is presented. This method departs substantially from the three-dimensional (3-D) ;wire-frame' plots presented in the previous analysis. The 2-D images can be manipulated to produce nodal line diagrams and can be color coded to illustrate mode shapes and energy trapping phenomenon. A contour plot of the mass-frequency influence surface for the plated 5-MHz resonator is presented. The mass-frequency influence surface is defined as a surface giving the frequency change due to a small localized mass applied to the resonator surface.     

Estimation of quartz resonator Q and other figures of merit by an energy sink method

An important determinant of the quality factor Q of a quartz resonator is the loss of energy from the electrode area to the base via the mountings. The acoustical characteristics of the plate resonator are changed when the plate is mounted onto a base substrate. The base substrate affects the frequency spectra of the plate resonator. A resonator with a high Q may not have a similarly high Q when mounted on a base. Hence, the base is an energy sink and the Q will be affected by the shape and size of this base. A lower bound Q will be obtained if the base is a semi-infinite base since it will absorb all acoustical energies radiated from the resonator. A scaled boundary finite element method is employed to model a semi-infinite base. The frequency spectra of the quartz resonator with and without the base are presented. In addition to the loss of energy via the base, there are other factors which affect the resonator Q, such as, for example, material dissipation, and damping at the interfaces of quartz and electrodes. The energy dissipation due to material damping increases with the resonant frequency and the reduction of resonator size; hence material damping becomes important in the current and future miniaturized resonators operating at very high frequencies. An energy sink model along with material dissipation would provide realistic Q, motional capacitance, motional resistance, and other figures of merit useful for designing resonators. The model could be used for evaluating resonator and mountings designs of microelectromechanical systems and miniaturized devices. The effect of the mountings, and plate and electrode geometries on the resonator Q and other electrical parameters are presented for AT-cut quartz resonators. Model results from the energy sink method were compared with experimental results and were found to be good.     

An analysis of nonlinear thickness-shear vibrations of quartz crystal plates using the two-dimensional finite element method

A nonlinear analysis of high-frequency thickness-shear vibrations of AT-cut quartz crystal plates is presented with the two-dimensional finite element method. The Mindlin plate equations are truncated to the first-order ones as an approximation, and then they are used for the formulation of nonlinear finite element analysis with all zero- and first-order displacements. The matrix equation of motion is established with the first-order harmonic approximation, and the generalized nonlinear eigensystem is solved by a direct iterative procedure. A displacement amplitude versus frequency curve and corresponding mode shapes are obtained and examined. The nonlinear finite element program is developed based on the earlier linear edition and can be utilized to predict nonlinear characteristics of miniaturized quartz crystal resonators in the design process.     

Two-dimensional analysis using one-dimensional FEM forstraight-crested waves in arbitrary anisotropic crystal plates andaxisymmetric piezoelectric vibrations in ceramic disks

We have developed a hybrid method applicable to straight-crested waves in arbitrary anisotropic crystal plates and to axisymmetric piezoelectric vibrations in ceramic disks. The solutions to two-dimensional (2-D) equations of motion are described with a linear combination of eigenmodes guided by a pair of parallel edges. The guided eigenmodes and their amplitudes are determined by using one-dimensional (1-D) finite element method (FEM). The method developed here provides rapid convergence with small matrix size compared with 2-D FEM. Computer programs have been developed for three examples, SC- and AT-cut quartz plates and barium titanate (BaTiO₃) disks, for which the frequency spectra and the corresponding mode shapes were calculated. The frequency spectra of AT-cut quartz plates are compared with those obtained from Mindlin's plate equations, with the aim of examining the accuracy of the straight-crested wave solutions for Mindlin's plate equations. A convergence study is also presented for BaTiO₃ disks     

Simulation of the experimental pre-dose technique for retrospective dosimetry in quartz

The pre-dose technique of thermoluminescence for quartz has been used extensively for retrospective dosimetry of quartz and other natural materials. A recently published model that is a modification of the well-known Zimmerman theory is used here to simulate the complete sequence of experimental steps taken during the additive dose version of the pre-dose technique. The results of simulation show how the method can reproduce accurately the accumulated dose or paleodose received by the sample. The solution of the kinetic differential equations elucidates the various electron and hole processes taking place during the experimental pre-dose procedure and shows clearly the mechanism of hole transfer from the reservoir to the luminescence centre caused by heating to the activation temperature. The numerical results show that the pre-dose technique can reproduce the paleodose with an accuracy of +/- 1-5%, even when the paleodose is varied over more than an order of magnitude. New quantitative results are presented for the effect of the test dose and of the calibration beta dose, beta, on the accuracy of the pre-dose technique. The conclusions drawn from the simple model for quartz can be used to make improvements to more general quartz models.     

剔除硅石矿中气液包裹体方法的研究

高纯石英玻璃具有良好的物理化学性能,被广泛应用于各种高科技行业,然而天然水晶矿产资源日渐枯竭,采用硅石矿替代天然水晶生产高纯石英玻璃是行之有效的方法。由于硅石矿中原子的排列方式和受地质因素影响其内部存在气液包裹体,这是硅石矿制备高纯石英玻璃产生气泡的主要原因,它的存在直接影响着石英玻璃的纯度及应用性能。气液包裹体的剔除是硅石矿替代天然水晶生产高纯石英玻璃的关键。综合阐述了国内外常用气液包裹体的剔除方法:机械破碎法、热爆裂法、酸蚀法、高温氯化脱气法以及微波法,这些方法能够对气液包裹体起到较好的剔除效果,但存在一定的局限性。最后,对气液包裹体剔除法的发展方向进行了展望。     

Method and certain results of a semiempirical description of the heat conductivity of composite materials

A semiempirical method of describing the heat conductivity of composite materials is described. Examples are presented of its application to determine the heat conductivity of gas mixtures, solid-porous quartz materials, and aluminosilicate refractories.     

A perturbation method for finite element modeling of piezoelectric vibrations in quartz plate resonators

When the piezoelectric stiffening matrix is added to the mechanical stiffness matrix of a finite element model, its sparse matrix structure is destroyed. A direct consequence of this loss in sparseness is a significant rise in memory and computational time requirements for the model. For weakly coupled piezoelectric materials, the matrix sparseness can be retained by a perturbation method which separates the mechanical eigenvalue solution from its piezoelectric effects. Using this approach, a perturbation and finite element scheme for weakly coupled piezoelectric vibrations in quartz plate resonators has been developed. Finite-element matrix equations were derived specifically for third-overtone thickness-shear, SC-cut quartz plate resonators with electrode platings. High-frequency piezoelectric plate equations were employed in the formulation of the finite element matrix equation. Results from the perturbation method compared well with the direct solution of the piezoelectric finite element equations. This method will result in significant savings in the computer memory and computational time. Resonance and antiresonance frequencies of a certain mode could be calculated easily by using the same eigenpair from the purely mechanical stiffness matrix. Numerical results for straight crested waves in a third overtone SC-cut quartz strip with and without electrodes are presented. The steady-state response to an electrical excitation is calculated.     

Resonant spectrum method to characterize piezoelectric films in composite resonators

In this paper, we present a direct method to characterize a piezoelectric film that is sandwiched with two electrodes and deposited on a substrate to form a four-layer thickness extension mode composite resonator (also known as over-moded resonator). Based on the parallel and series resonant frequency spectra of a composite resonator, the electromechanical coupling factor, the density and the elastic constant of the piezoelectric film can be evaluated directly. Experimental results on samples consisting of ZnO films on fused quartz substrates with different thickness are presented. They show good agreement with theoretical prediction. The mechanical effect of the electrode on the method is investigated, and numerical simulation shows that the effect of the electrodes can be properly corrected by the modified formulae presented in this paper. The effect of mechanical loss in piezoelectric film and in substrate on this method also has been investigated. It is proven that the method is insensitive to the losses.     

Quartz crystal oscillator at very low temperature

The most significant results concerning quartz crystal resonators and semiconductors properties at liquid helium temperature are presented. A cryogenic quartz oscillator is realized with these elements and some values of its frequency stability are given.     

Sensitivity of quartz oscillators to the environment: characterization methods and pitfalls

The advantages and disadvantages of characterizing a complete quartz crystal oscillator or characterizing only the quartz resonator by using a passive phase bridge are discussed. Measurements of temperature sensitivities, including quasistatic or dynamic thermal conditions, are presented. One important point is how to measure the real temperature of the device under test (quartz crystal, for instance) rather than the temperature of the probe. Methods for measuring acceleration and pressure sensitivities are presented, and spurious effects of temperature changes are considered. Problems are discussed in connection with the measurement of the sensitivity to magnetic fields, and to electric fields. Methods used for measuring these sensitivities and the many pitfalls that can be encountered are the focus of the investigation.     

Experimental study of the plasmochemical method for the direct production of silicon from quartz

The results of experimental studies of the nonequilibrium plasmochemical method for production of polycrystalline silicon from quartz are presented. It is shown that polycrystalline silicon in the form of spherelike particles with an average size of 100–200 μm and purity of 99.8–99.9% can be obtained with a yield of up to 60% using the electric arc installation developed.     

Implementation of pseudo-nondiffracting beams by use of diffractive phase elements

We report the experimental implementation of pseudo-nondiffracting beams by use of diffractive phase elements (DPE's). Based on the conjugate-gradient method presented in J. Opt. Soc. Am. A 15, 144-151 (1998), these DPE's are designed and fabricated on a flat quartz substrate. The experimental results show that the performance of the fabricated DPE's is in good agreement with the theoretical prediction.     

Electrically driven flexural resonant modes in symmetrically electroded X-cut and Z-cut quartz discs

While it is well known that flexural mechanical resonant modes can be electrically driven in specimens of quartz and other piezoelectric materials by the judicious choice of electrode patterns, specific experimental data, based on simultaneous interferometric observations of opposite surface points, are presented to show that symmetrically electroded X-cut and Z-cut quartz discs exhibit flexural resonant modes of quite large amplitudes. These resonances are not accompanied by detectable electrical disturbances in the AC-drive circuits. The existence of these modes is demonstrated for an X-cut quartz disc, and specific resonant modes of a Z-cut quartz disc are characterized in detail.     

Determination of physicomechanical properties of soft soils from medium to high strain rates

A method is presented for obtaining materials parameters, for quartz sand, over a wide range of strain rates. This involves the use of a modified Kolsky bar and plate impact experiments. Data were analysed based on the determination of longitudinal and lateral stresses in the Kolsky method. These values were combined with the longitudinal stress data from shock experiments to provide a stress–compression curve. From this curve, other parameters can be determined.     

Upgraded sublimation energy determination procedure for icy films

A method to determine the sublimation energy of a bulk ice in high vacuum systems, allowing other simultaneous analysis techniques, is presented. Variation in frequency of a quartz crystal microbalance, due to sublimating material, during a zeroth-order desorption consents to obtain this energy. CO₂ sublimation energy is obtained to check this method, its value is coherent with that reported in the literature. Our method permits to simplify the setup used so far by other authors, and to obtain relevant parameters for ices simultaneously. The procedure explained here corrects the temperature frequency dependence of the microbalance and the effect of contaminants by using a unique microbalance.