A. Zarka

Optimisation of the design of the resonators using the new materials: application to gallium phosphate and langasite

The coupling coefficient, the frequency constants and the temperature coefficients of the resonance frequencies of gallium phosphate and langasite thickness mode resonators were determined for all the crystalline orientations using a one dimensional model. It appears that both materials possess compensated orientations leading to a coupling coefficient (k/sup 2/) nearly four times that of AT quartz. For these orientations the properties of energy trapping resonators were determined for two electrode geometries as a function of the mass loading and of the electrode dimensions. Designs optimising the capacitance ratio, the size of the plates and the unwanted responses were found. A comparison is made between computed and experimental results. It is concluded that nearly all the theoretical potential of these materials can be attained by well designed resonators.

New results on high perfection langasite crystals: studies of crystalline defects and mode shapes

Langasite (LGS: La/sub 3/Ga/sub 5/SiO/sub 14/) is a new piezoelectric material obtained by the Czochralski method. In this paper we present results obtained on new samples which are more representative of the crystalline quality achieved with this material. Observations using X-ray transmission topography have permitted verification of the quality of samples of different origins and to analyse the nature of their crystalline defects. Vibration modes of different types of devices made with LGS have been studied by X-ray transmission topography. This study was essentially concerned with plane or plano-convex resonators. This material has interesting properties and among them compensated cuts with a large coupling coefficient and a very reduced angular sensitivity.

Whispering gallery like modes in quartz energy trapping resonators

The modes of the resonators with geometries conforming to the lateral anisotropy of the plates have many very interesting properties that result from a higher symmetry in a particular axis system. When they are excited by sectored elliptical electrodes they can a have a very reduced displacement in their central region. The modes with m-fold symmetry can be efficiently excited by the choice of the electrode parameters. In plane resonators, they can be selectively excited, in the resonators with the non-spherical contour less modes are excited than in usual plano-convex resonators. The resonators using the unspherical contours related to the lateral anisotropy can now be easily obtained using the recent technology. Both types have the potential to constitute very efficient new approaches towards resonators with reduced acoustic dissipation since their mode shapes can minimise the influence of the acoustic losses due to the energy transfer to the fixations. The bevelled resonators using such contours should also present a great interest.

A new model for the thickness shear resonators with spherical contours: application to bevelled devices

Contoured resonators are mostly employed to obtain very low loss devices employed to generate very stable frequencies. The partially contoured (bevelled) resonators are also used for filtering. Their design remains still somewhat empirical, so that a better theoretical understanding of such devices is very desirable. In a preliminary study, experimental determinations of the mode shapes were performed using an important set of bevelled resonators, with designs ranging from nearly biconvex ones to nearly plane ones having only a very small bevel at their edge. Several conclusions were drawn from these experiments. The present model of the contoured and the partially contoured resonators is based upon the Tiersten theory of the transversely varying essentially thickness modes. We propose a new method of resolution of the Tiersten partial derivative equations based upon the algebraical solutions obtained for the same problem in the case of a very close geometry (non spherical contour respecting the lateral anisotropy of the plate). These simple solutions are of a very large generality since they contain nearly all the previously known ones. They bring a better understanding of the different kinds of thickness shear contoured resonators. In this model, for the plane electroded regions (bevelled resonators) we use solutions of the Tiersten equations which are basically series expansions in the exact solutions for a case where the electrodes and the plate have elliptical geometries respecting the lateral anisotropy. For the contoured regions, we use similarly a representation of the shear displacement consisting in an expansion in the eigen solutions obtained for the above mentioned non-spherical contours. The continuity conditions between the different regions and the boundary conditions at the edge are expressed at a discrete number of points to fit nearly or more exactly, the actual geometry of the resonators presenting a spherical contour and a circular geometry. The set of linear equations so obtained constitute an homogeneous linear system whose determinant must vanish to have a solution. This condition is a frequency equation which is solved to find the eigen frequencies and the eigen modes. The numerical implementation of this model makes use, for the contoured regions, of the confluent hypergeometric (Whittaker) functions [M/sub k,m/(r/sup 2//2) or W/sub k,m/(r/sup 2//2)] which are bounded at zero or at infinity, and of the Jn(r) Bessel functions for the flat region. The convergence of the solution with the discretization appears to be extremely fast, and a very high accuracy seems to be obtained. The comparison with the experimental results indicates a very good agreement. Several important features observed during the experimental study were confirmed and explained by the calculations.

X ray topography study of gallium phosphate crystals and resonators

Using the synchrotron radiation delivered by the DCI storage ring at LURE (Orsay, France), the X-ray topography technique was used to study the crystalline perfection of GaPO/sub 4/ samples grown under different conditions. The growth of gallium phosphate on a berlinite seed is analyzed by X-ray section topography. The results obtained demonstrate the feasibility of gallium phosphate epitaxy on large berlinite seeds in a sulphuric acid medium. These first characterizations indicate the good quality of gallium phosphate epitaxy on berlinite seeds. This method is a good solution for obtaining gallium phosphate crystals of good quality and large sizes. Different vibration modes of approximately rhombohedral face cut and near AT cut thickness shear resonators were observed.<<ETX>>

New contrasts in the topographs of quartz obtained with the third generation synchrotron

The synchrotron radiation delivered by the topography beam line of the European Synchrotron Radiation Facility (ESRF) was used to study quartz crystals and resonators. Several experimental set-ups taking advantage of the unique properties of the beam (very small divergence, extended spectra, time structure, etc.) were used to enhance the sensibility of detection of strain gradients due either to defects or to vibration modes. New contrasts were observed at the limits of the Z growth sectors (and also in the X or 8 sectors) in the most perfect crystals obtained by the crossed growth technique. In several samples of synthetic quartz, we have observed in the Z growth region, contrasts normal to the growth direction and resembling those of stacking faults. The increase of the sensibility of the stroboscopic technique has allowed to observe an important feature concerning the interaction of the vibration mode with the mounting clips (3rd overtone plano-convex resonator). The experiments and the results obtained are, in their principles, similar to those previously reported (1989) but the new experimental diffraction conditions bring an important increase of the sensibility of detection.

Observations of the crystal perfection and of surface acoustic waves in lithium niobate

The extended defects in lithium niobate have been studied by X-ray topography using the white radiation delivered by the DCI synchrotron at LURE (Orsay, France). Very few low angle subgrains were observed in slices cut perpendicularly to the X, Y, and Y-45/spl deg/ direction. The high intensity of the synchrotron source has permitted an experimental study of the surface acoustic waves (SAWs) in different filters. Using the time structure of the radiation of the synchrotron and a synchronous excitation, stroboscopic observations were made. It was thus possible to investigate the interactions of the SAWs with the crystal defects, the plate edge, and an acoustic absorbent. The observation of the displacement fields in high-performance filters has revealed interesting properties of apodized transducers and multistrip couplers. It is shown that stroboscopic topography is a good technique for observing and analyzing the wave fields in surface wave devices.<<ETX>>