SC Cuts Research Articles

Effect of Tilted Edges on Coupled Vibrations of Doubly Rotated Quartz Plates

We numerically analyze the two-dimensional (2-D) coupled vibrations of a doubly rotated quartz plate with tilted edges. An efficient technique that uses a combination of 1-D and 2-D finite element methods is developed to solve coupled vibrations in the Y'-Z' cross section of a parallelogram shape. When the orientation of a quartz plate is described using the IEEE notation, as (YXwlt)φ/θ/ψ, the third rotation ψ about the plate normal is selected such that the Z'-width faces are parallel to the particle motion of a slow-shear wave propagating in the Y'-thickness direction. For SC-cut plates operating in the fundamental slow thickness-shear mode, we evaluate the effect of tilted edges on the frequency spectra and the first frequency-temperature coefficients, and verify the strong decoupling effect on the thickness-shear and face-shear modes. The optimal inclination angle of tilted edges for SC and FC cuts is appropriately defined as the equiphase plane of the main displacement of the face-shear traveling wave.

Surface state improvement of ground AT and SC quartz cuts by controlled dissolution in NaOH, KOH, LiOH

After the studies which allowed us to perfect the chemical thinning down, or controlled dissolution, of both AT and SC quartz plates in NaOH and KOH media, respectively, we have investigated mixtures of these with another basic compound (LiOH) in order to discover a common solvent for both AT and SC cuts. The results show that crystallographic orientation and solvent nature have a great influence on controlled dissolution especially on the surface texture. It appears that the basic compound which has the smallest cation imposes its properties and consequently, the chemical polishing of both AT and SC cuts cannot be made in good conditions with the same solvent.

Solvent Influence on Kinetics and Dissolution Mechanism of Quartz in Concentrated Basic Media (NaOH, KOH, LiOH)

Quartz chemical lapping of AT and SC cuts in concentrated basic solvents and mixtures (NaOH, KOH, LiOH) has led us to study the dissolution mechanism of quartz in order to explain the experimental results in terms of kinetic evolutions. Using X-ray diffraction and 29Si NMR analysis of the species in solution, we propose a dissolution mechanism of quartz in concentrated basic solutions. According to the dissolution process, and taking into account the nature and the size of the alkali cation of the solvent, we explain the kinetic curve evolution.

Controlled dissolution of quartz material.Part I. Controlled dissolution of quartz plates in potassium and sodium hydroxides : chemical thinning down of SC cuts

From previous studies suggesting that controlled crystal growth and crystal dissolution are governed by the same laws, we have previously finalized the chemical lapping or controlled dissolution of AT quartz plates in NaOH,H 2 O. The quality of chemical polishing changes with the crystallographic orientation of plates. Consequently, we have investigated similar basic solvents other than NaOH medium to obtain a good chemical polishing of SC cuts. Surface roughness evolution was checked and shows that controlled dissolution of SC cuts has to take place in KOH medium. As shown in NaOH medium, initial surface state has a great influence on thinning down. Dissolution rates measured against temperature in different media and activation energies are compared

Controlled crystal dissolution applied to quartz

Quartz chemical lapping of AT and SC cuts was performed in NaOH·xH2O medium and this controlled dissolution resulted in reasonable quality of surface texture. Activation energy was calculated from dissolution rates measured against temperature. The initial surface texture of the samples influenced roughness parameter evolution but not the final roughness value. The electrical response of piezoelectric devices made by chemical lapping has been compared against others obtained by the IBE process. The comparison has shown that the controlled dissolution process is at least as good as IBE for producing piezoelectric devices.

Static and Dynamic Behavior of Quartz Resonators

Abstract : The frequency-temperature (f-T) behavior of a crystal resonator depends upon temperature, and its spatial and temporal gradients. For quasi-isothermal changes the static f-T curve can be used to determine frequency shifts that occur, e.g., in oven-controlled units. The frequency then depends upon the parameters of the static f-T curve, the temperature range over which the oven cycles, and upon the oven setting point. The maximum frequency excursion has been computed for the AT and SC cuts of quartz in terms of these parameters as a function of the orientation angle. When thermal-transient-compensated cuts are not utilized, oven cyclings or other temperature perturbations introduce an additional nonnegligible component of the frequency shift. This effect is quantified by means of a simple mathematical model. The model is capable of predicting the thermal transient effects for AT cuts appearing in the literature. Simulations, using the model, disclose that sinusoidal temperature variations with periods of hours can readily lead to frequency instabilities much larger than would be expected using the static f-T curve for the AT cut. This effect should be greatly diminished in the vicinity of the SC cut.