Influence of a magnetic field on quartz crystal resonators

The magnetic sensitivity of quartz crystal resonators is a consequence of the ferromagnetic properties of the metal used as support for the vibrating plate. Various magneto-mechanic interactions can contribute to the overall sensitivity, the most important of which is shown to be the change in Young's modulus of the spring material submitted to a magnetic field, which in turn modifies the stress in the quartz plate and then induces a change in the crystal resonant frequency. The experimental setup and procedure are described and a large number of experimental results obtained with resonators of different technologies are presented and discussed. A comparison between the magnetic behavior of identical resonators mounted with different materials definitely proves the responsibility of the supports in the magnetic sensitivity of resonators and gives interesting information on its reduction     

An X-ray double crystal topographic assessment of defects in quartz resonators

This paper describes an X-ray double crystal topographic study of defects in eighteen quartz resonators designed to operate at 1.4 MHz. The types of defects found in quartz are described, together with their reported effects on resonator performance. The mode of operation of the bulk resonator and the technique of X-ray double crystal reflection topography are outlined. Topographs reveal the electrode structures and surface features of the resonators together with the presence of growth defects such as dislocation cells, sub-boundaries, growth striations and growth sector boundaries. Spurious flexure modes in two resonators are also shown. It is demonstrated that a correlation exists between the presence of growth striations (and probably sub-boundaries) and a higher equivalent series resistance of the resonators. It is shown that such defects change the contributions to the losses, possibly by changing the nature of the vibration pattern of the resonator.     

Phase noise measurements of 10-MHz BVA quartz crystal resonators

In this paper, we review a new piece of equipment that allows one to characterize the phase noise of crystal resonators using a phase bridge system with carrier suppression. This equipment allows one to measure the inherent phase stability of quartz crystal resonators in a passive circuit without the noise usually associated with an active oscillator. We achieved a system noise floor of approximately -150 dBc/Hz at 1 Hz and -160 dBc/Hz, at 10 Hz. A SPICE characterization of the carrier suppression system is given. An investigation of the phase modulation (PM) noise in 10 MHz BVA, SC-cut quartz crystal resonator pairs is presented.     

Inverted mesa-type quartz crystal resonators fabricated by deep-reactive ion etching

In this letter, we present experimental data showing Q change versus thickness for a quartz-crystal resonator fabricated with deep-reactive ion etching. Measurements show that Q increases as etch depth increases, and further that Q can be optimized as a function of etch depth and diameter of the resonator.     

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.     

Temperature coefficient of sensitivity dependence of themeasurement error of quartz crystal resonators

This paper discusses the measurement error of quartz crystal resonators (QXRs) vs. the temperature coefficient of force sensitivity. Based on the analysis of the difference between the temperature coefficient of frequency and the temperature coefficient of force sensitivity, the measurement error formula is deduced. According to the error formula, the physical significance of the temperature coefficient of force sensitivity is explained, and the method of selecting a scale temperature is given. The measurement error formula has been verified recently by experimental results. To expand the selectable range of cut modes and to compare the performances of QXRs, the selecting principle of the best group of the angles of cut of quartz crystal plate, &thetas;, ϑ, and azimuth angle of applied force, ψ is given simultaneously. According to the measurement error formula and the selecting principle of the best group of the angles, the best azimuth angle of AT-cut used as force sensitive resonators is found through the analysis of the measurement error. This paper provides a theoretical basis on which the measurement accuracy of QXR force sensors can be improved     

Organic vapor sensing with ionic liquids entrapped in alumina nanopores on quartz crystal resonators

We report on a concept for vapor sensing with the quartz crystal microbalance where the vapor phase is absorbed into small droplets of an ionic liquid. The liquid is contained in the pores of a nanoporous alumina layer, created on the front electrode of the quartz crystal by anodization. Ionic liquids are attractive for vapor sensing because--being liquids--they equilibrate very fast, while at the same time having negligible vapor pressure. Containing the ionic liquids inside cylindrical cavities of a solid matrix removes all problems related to the liquid's softness as well as the possibility of dewetting and flow. The absence of viscoelastic effects is evidenced by the fact that the bandwidth of the resonance remains unchanged during the uptake of solvent vapor. The Henry constants for a number of solvents have been measured.     

Application of the photo-elastic method to measurement of dynamicstress distribution for NS-GT cut quartz crystal resonators

NS-GT cut quartz crystal resonators are widely used as a frequency standard element in consumer products and communication equipment. The vibration mode of the resonators was analyzed by the finite element method (FEM) because they have a complicated shape. As a result, an asymmetrical vibration mode at the main resonant frequency has been obtained by the FEM simulation. But, it is necessary to confirm the asymmetrical vibration mode experimentally because it is just a simulation. In this paper, stress distributions of the NS-GT cut quartz crystal resonators are measured experimentally by using a dynamic photo-elastic method when the resonators are vibrating in the resonant frequency; thereafter, vibration modes of the NS-GT cut resonators are estimated with the experimental data of the stress distributions. This experiment for the NS-GT cut quartz crystal resonators exposes the existence of a twisted asymmetrical vibration mode at the main resonant frequency, with the magnitude of the twisted vibration in proportion to thickness of the resonators     

Study of the bending modes in circular quartz resonators

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.     

Flicker noise measurement of HF quartz resonators

Frequency flicker of quartz resonators can be derived from the measurement of S(phi) (f), i.e., the power spectrum density of phase fluctuations phi. The interferometric method appears to be the best choice to measure the phase fluctuations of the quartz resonators because of its high sensitivity in the low power conditions, which is required for this type of resonator. Combining these two ideas, we built an instrument suitable to measure the frequency flicker floor of the quartz resonators, and we measured the stability of some 10-MHB high performance resonators as a function of the dissipated power. The stability limit of our instrument, described in terms of Allan deviation sigma(y)(tau), is of some 10(-14).     

Thermal behavior simulation of quartz resonators in an ovenenvironment

The fine performance of an ovenized oscillator is dependent on the thermal behavior of the quartz resonator, especially when there are thermal transients. In this paper, the thermal behavior of the quartz is simulated by a finite difference technique including nonlinearity as an effect of radiation. This method, based on the electrical analogs of the thermal parameters, provides an easy interaction with the electrical parameters of the oven control. A model fitting various resonator configurations, like a flat pack or a BVA resonator, is proposed. The temperature of the direct quartz environment is compared with a reference. It acts on the heating elements that are electronically driven into a closed loop. The simulation results obtained in practical situations are compared for various types of resonator assembly, in relation to heating and thermal loss parameters     

Piezoelectric quartz crystal microbalance sensor for trace aqueous cyanide ion determination

Using selective reaction chemistry, our present research has developed an online, real-time sensor capable of monitoring toxic cyanide at both drinking water standard and environmental regulatory concentrations. Through the use of a flow cell, aqueous samples containing cyanide are reacted with a gold electrode of a piezoelectric crystal to indirectly sense cyanide concentration by the dissolution of metallic gold. The quartz crystal is an AT-cut wafer sandwiched between two neoprene O-rings within the liquid flow cell. The presence of cyanide in solution results in the selective formation of a soluble dicyano-gold complex according to the Elsner reaction: 4Au + 8CN- + 2H2O + O2 <=> 4Au(CN)2- + 4OH-. The resulting loss of gold from the electrode is detected by the piezoelectric crystal as a resonant frequency change. Since free cyanide is a weak acid (pKa = 9.3), available protons compete for cyanide ligands. Therefore, increased sample pH provides higher sensitivity. The detection limits at pH 12 are 16.1 and 2.7 ppb for analysis times of 10 min and 1 h, respectively. The incorporation of the flow cell improves both analyte sensitivity and instrument precision, with an average signal intensity drift of only 5% over a 2-h analysis. The calibrations show excellent linearity over a variety of cyanide concentrations ranging from low ppb to hundreds of ppm. This detection method offers the advantage of selectively detecting cyanides posing a biohazard while avoiding detection of stable metal cyanides. This aspect of the system is based on competitive exchange of available metals and gold with cyanide ligands. Stable metal cyanide complexes possess a higher formation constant than cyanoaurate. This detection system has been configured into a flow injection analysis array for simple adaptation to automation. Anions commonly found in natural waters have been examined for interference effects. Additionally, the sensor is free from interference by aqueous cyanide analogues including thiocyanate. The developed detection system provides rapid cyanide determinations with little sample preparation or instrument supervision.     

A study of quartz tuning fork resonators in the second flexuralmode

Quartz tuning fork resonators in the second flexural mode have been studied in less detail than those in the fundamental mode. It is necessary for quartz tuning fork resonators in the second flexural mode to be carefully designed from the viewpoint of total vibrational system design including the mounting leads and capsules, since vibration in the base portion of quartz tuning forks is more readily transmitted to the mounting leads and the capsules as a result of the larger amplitude in the base portion in the second flexural mode than in the fundamental mode. We will discuss here the characteristics in detail on the basis of experimental data and theoretical analysis. Considerations are presented in order to achieve optimal design     

Effects of electromagnetic radiation on the Q of quartz resonators

The quartz resonator Q with aluminum electrodes was studied with respect to its fundamental thickness shear mode frequency and its viscoelastic, viscopiezoelectric, and viscopiezoelectromagnetic behaviors. The governing equations for viscoelasticity, viscopiezoelectricity, and viscopiezoelectromagnetism were implemented for an AT-cut quartz resonator. To simulate the radiation conditions at infinity for the viscopiezoelectromagnetic model, perfectly matched layers over a surface enclosing the resonator were implemented to absorb all incident electromagnetic radiation. The shape of the radiation spectrum of a 5.6 MHz AT-cut quartz resonator was found to compare relatively well the measured results by Campbell and Weber. The mesa-plate resonator was studied for a frequency range of 1.4 GHz to 3.4 GHz. The resonator Q was determined to be influenced predominantly by the quartz viscoelasticity; however at frequencies greater than 2.3 GHz, the quartz electromagnetic radiation had an increasingly significant effect on the resonator Q. At 3.4 GHz, the electromagnetic radiation accounted for about 14% of the loss in resonator Q. At frequencies less than 2 GHz, the calculated resonator Q compared well with the intrinsic Q_x provided by the formula Q_x = 16 times 10⁶/f where f was in MHz. At frequencies higher than 2.3 GHz, the aluminum electrodes had significant effects on the resonator Q. At 3.4 GHz, the electromagnetic radiation loss in the electrodes was an order of magnitude greater than their viscoelastic loss; hence, the vibrating aluminum electrodes became an efficient emitter of electromagnetic waves. The effects of electrical resistance in both the electrodes and quartz were determined to be negligible.