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Quartz crystal resonators, including electric twins, are investigated. Electric twins are artificially formed in the usual AT-cut quartz crystal resonantor before the deposition of electrodes. We have directly observed that vibrations generated at electrodes propagate into the outside region isotropically, but cannot propagate into the region of electric twin.
Temperature is the main parameter that affects the stability of surface acoustic wave (SAW) devices such as the external and internal stress. The temperature sensitivity of the frequency as a function of quartz crystal anisotropy is presented by a perturbation equation because of a temperature change. The analytical result shows which cut is suitable for high temperature sensitivity of the quartz and which cut is associated with low temperature sensitivity. The theoretical sensitivity values are compared with experimental results. Both the experimental and theoretical results are in good agreement.
An extended Butterworth-Van Dyke (EBVD) model with frequency-independent parameters for the characterization of a resonant compound formed by a quartz crystal in contact with a finite viscoelastic layer contacting a semi-infinite viscoelastic medium is extracted by analysis of the lumped element model. The formulation of the EBVD model is compared with the complete expression of the electrical admittance of the loaded quartz derived from the transmission line model (TLM). Relative deviations between them do not exceed 3% around 1% bandwidth near resonance. An extended Martin & Granstaff's model and an explicit expression for the frequency shift that supposes an extension of Kanazawa's model for viscoelastic media are obtained. An analysis of the errors associated with the extraction of shear parameters of the coating for different materials prove that, to obtain an error less than 5% in the shear parameters determination, the viscoelastic contribution, defined as the relative error in the thickness computed from the frequency shift by Sauerbrey equation, must be greater than a limit that depends on Q, which is defined as the ratio of the shear storage modulus (G') to shear loss modulus (G"). In the materials studied, polymers in the transition range or in the rubbery state with Q = 1 and 10, the viscoelastic contribution must be higher than 15% and 50%, respectively, for a 5% limit error in the shear parameters extraction. A criterion for a practical determination of the appropriate viscoelastic regimes is indicated.
Commonly, the required short-term frequency stability of an ultra stable quartz crystal oscillator (USXO) is a few parts in 10(-13) for averaging times of a few seconds. Moreover, the USXO must typically achieve a relative frequency variation of a few parts in 10(-10) over a temperature range from -30 to +70 degrees C. Consequently, the USXO has to be ovenized. Basic data concerning the static and dynamic frequency versus temperature effects are first reviewed. These data allow one to evaluate how efficient the thermal regulator must be to achieve the aimed features in terms of temperature sensitivity. Usually the static thermal gain must reach at least 1000. A standard proportional-integral thermal controller, which can eliminate the static error, cannot afford doing this when fast thermal disturbances exist. Here, the thermal filtering must work in accordance with the cut-off frequency of the frequency-temperature transfer function of the quartz resonator. There exist various methods to control the oscillator temperature. The usual method consists of using more than one temperature-controlled oven. This is often a volume-consuming process. An alternative approach, which is much simpler, is to add a slight compensation upon the feedback control system. Finally, a third way to improve the temperature regulation is based on a distribution of the monitored power. Obviously, a combination of those solutions is possible. Advantages and drawbacks of each of them are discussed in the paper. Practical results are shown and illustrated with 10-MHz USXOs.
In this paper, the dissipation effects of an electroded AT-cut quartz resonator due to the intrinsic damping of the quartz plate and the surface damping of the coated electrodes are discussed. The results obtained provide a theoretical understanding of the energy losses by these effects.
A modal representation of the thickness vibrations of rotated Y-cut quartz plates, which was used in the treatment of driven transversely varying thickness modes, is shown to be defective in certain respects. The differential equations and edge conditions for transversely varying thickness modes have been used in the accurate treatment of trapped energy resonators, monolithic crystal filters, and contoured quartz resonators, even though those defects were present. In this work those defects in the thickness solution are corrected along with the influence on the differential equations and edge conditions in the transversely varying case. The corrected modal representation shows that, because in practical applications to the above mentioned devices, the driving frequency is always near a thickness resonant frequency, essentially the same results will be obtained with the corrected representation as were obtained with the defective one, which explains why the results obtained with the defective equations were so accurate.
Parametric oscillators have been well studied but currently are not used often. Nevertheless, they could be a low-phase noise solution, at least outside the frequency bandwidth of the resonant circuit. The theoretical aspect of parametric oscillations is briefly reviewed in this paper. Indeed, the basic theory of a simple resistance-inductor-capacitor (RLC) circuit working in parametric conditions easily can be extended toward a resonant loop that includes a quartz crystal resonator. Then, as an application, this study is transposed to a quartz crystal oscillator that has been modeled and tested as a first ptototype. Simulation results are compared with those actually obtained.
This paper discusses the effect of transverse force on the performance of quartz crystal resonator (QXR) force sensors that use symmetrical incomplete circular QXRs as sensing elements. Based on Lee's vibration theory and the transverse force-induced stress distribution, frequency changes are derived. This result and finite element method (FEM) are applied to investigate the performance of two metal-quartz combined sensors under the action of transverse force. Analytical and experimental results show that transverse force affects the sensitivity and linearity of QXR force sensors.
An experimental and theoretical study of bending modes in a partially electroded circular piezoelectric quartz (AT-cut) with free edge is presented. The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane displacements. The classical theory of bending of thin disks is used to describe the flexural modes at frequencies lower than the first thickness shear resonance (6 MHz). A fairly good agreement is found between experimental and theoretical results for the forced mode shapes and for the resonance frequencies. However, it appears that the two springs used to maintain the disk in position introduce extra clamping conditions. Several source shapes were studied, among which a collection of an arbitrary number of forces is particularly useful. The two-dimensional wavenumber representation shows the presence of anisotropy related to the crystallographic axes at higher frequencies, which is not predicted by the model. The experimental phase velocities are compared to those given by the classical theory of disks and to those of Lamb A(0) mode. This study confirms the correspondence at low frequencies between the A(0) mode and the bending eigenmodes of a disk with finite size.
Thermal and mechanical sensitivities of vibrating structures and wave guides are key parameters for the optimization of high stability resonant devices operating in the ultrasonic frequency range (from a few tenth of kilohertz to a few gigahertz). In this paper, the possibility to simulate and predict temperature coefficients of frequency (TCF) of quartz transducers of any shape as well as their stress sensitivity coefficients is addressed. The theoretical developments based on harmonic finite-element analysis coupled with a variational perturbation method are detailed, showing how to derive the regarded parameters. The proposed approach is validated using a two-dimensional (2-D) model of a plane face-bulk acoustic resonator for which an analytical model can give access to both TCF and stress sensitivity coefficients. It is then applied to a 2-D model of convex plane bulk acoustic resonator of singly rotated quartz and used to compute the first order TCF of a 3-D model of a tuning fork structure. In the latter case, the importance of considering the actual excitation of the device is demonstrated, allowing for the accurate definition of angular loci for which thermal compensation can be expected, in agreement with literature. Possible extensions and improvements of the proposed method is discussed in conclusion.
A solution is obtained from the three-dimensional equations of linear piezoelectricity for the pure thickness-shear vibration of rotated Y-cut quartz or langasite plates with imperfectly bonded surface mass layers. The solution includes a few results in the literature as special cases. It is shown that the mass layers lower the resonant frequencies when they are relatively perfectly bonded to the crystal surface, and that loosely bonded mass layers may raise the frequencies. The results are useful in the analysis of frequency stability of quartz resonators and acoustic wave sensors.
Phase retardation between two orthogonal circularly polarized light waves that propagate in an optical active medium is proportional to its optical activity. The measurement of optical activity of a quartz depolarizer in terms of the phase difference of two orthogonal circularly polarized waves is proposed. A circularly polarized optical heterodyne interferometer with a Zeeman laser to measure the optical activity of a quartz crystal is demonstrated experimentally. The accuracy of the measurement is discussed. In addition, the effect of elliptical polarization and nonorthogonality of linearly polarized light waves of a Zeeman laser on the optical activity measurement is analyzed.
We report experimental measurement of radiation characteristics of fused quartz containing bubbles over the spectral region from 1.67 to 3.5 microm. The radiation characteristics were retrieved by an inverse method that minimizes the quadratic difference between the measured and the calculated spectral bidirectional transmittance and reflectance for different sample thicknesses. The theoretical spectral transmittances and reflectances were computed by solving the one-dimensional radiative transfer equation by the discrete-ordinates method for a nonemitting, homogeneous, and scattering medium. The results of the inversion were shown to be independent of the sample thickness for samples thicker than 3 mm and clearly demonstrate that bubbles have an effect on the radiation characteristics of fused quartz.
We propose and experimentally demonstrate long-distance remote simultaneous measurement of strain and temperature based on a Raman fiber laser with a single fiber Bragg grating embedded on a quartz plate. A Raman fiber laser output with a high extinction ratio of more than approximately 50 dB is achieved by the fiber grating cavity. In the sensing probe, half of the fiber Bragg grating is fixed steadily on the quartz plate to respond to temperature only, while the other half of the grating is free to respond to both temperature and strain. Based on the proposed scheme, lasing wavelength shift and separation occur with temperature and strain change, respectively. Efficient simultaneous measurement of strain and temperature for long-distance sensing applications of more than 50 km is readily obtained.
A remote sensing method is presented that enables the determination of quartz concentration in mineral aerosols from simultaneously measured, high-spectral-resolution lidar and quartz Raman lidar signals.
An electrochemical quartz crystal impedance system (EQCIS) was used to study the resonance behavior of an AT-cut 9-MHz piezoelectric quartz crystal (PQC) with its Au electrode partially immersed in KCl, Na2SO4 and NaClO4 aqueous solutions, respectively. An in situ determination of the immersed area and the height of the electrode was achieved by simultaneous measurements of the PQC electroacoustic admittance and the electrochemical impedance. The rising of the solution meniscus for a gold electrode partially immersed in aqueous solutions was found at oxygen reduction potentials and evaluated versus the electrolyte, electrolyte concentration, solution pH and oxygen concentration. The solution meniscus rising was explained based on a lowering of the contact-angle hysteresis and a continued collection of the water product at the solid-gas-solution interface during oxygen reduction.
Silver(I) adsorbed selectively onto a quartz plate modified with N-(2-pyridylmethyl)chitosan in an ammonium chloride buffer solution containing EDTA, and the frequency of the quartz plate increased. It was supposed that the increasing frequency was caused by the desorption of adsorbed water on the chitosan derivative, which was induced from the reaction of silver(I) with the chitosan derivative. The concentration of the buffer, pH, temperature, conductivity and eluent affected the frequency shift resulting from the adsorption of silver(I). The frequency decreased at a conductivity lower than 2.2 mS/cm, and increased with increasing conductivity above this value. The frequency shifts caused by the adsorption of silver(I) were proportional to the concentration over the range 10-80 nM of silver(I), and the correlation coefficient was 0.9969. The detection limit and the relative standard deviation at 50 nM for five times were 6 nM and 3.4%, respectively. The proposed method was simple while showing higher sensitivity and selectivity.
An interconnecting technique, the "PDMS connection method", for quartz microchips in a high-pressure system is presented. The connection between quartz microchips is an essential technology for modular microfluidic devices, such as microchip-HPLC. PDMS was applied to the seal material, being spread on the seal side of the chips, and set into the metal housing. The characteristics of the PDMS connection method concerning pressure resistance and the extension of the peak were examined. The experimental results showed a good seal at 5 MPa, which seem to be sufficient for realizing microchip-HPLC utilizing a monolithic silica capillary column as a separation medium. The influence of the extra column effect on chromatographic separation was almost the same as in the case using a commercial union fitting. In addition, the PDMS connection enabled the detachability of chip-based modules with user-friendliness. Our experimental findings suggest that the novel PDMS connection method can possibly be applied as a generic technology in high-pressure microTAS.