SIMULATION OF SYNCHROTRON WHITE BEAM TOPOGRAPHS: APPLICATION TO THE STUDY OF PIEZOELECTRIC DEVICES . Y. Epelboin*, B. Capelle* & J. Détaint**, *LMCP, URA 009 CNRS, University P.M.Curie, Paris, France, **CNET, PAB, dept BAG/MCT/CMM, 92220 Bagneux, France

We present a new package which allows to simulate synchrotron white beam topographs for any kind of defect. It is split in two parts: a first program which computes the derivatives of the deformation and which must be written by the user for each model. A second general purpose simulation program takes these data and computes the image (Y. Epelboin, 1996, accepted in J. Appl. Cryst.). This program is valid for all studies. This allows to rapidly check new models for the defects without having to rewrite a whole simulation program.

A new algorithm for the integration of Takagi-Taupin equations has been written for massively parallel computers and multiple processors machines. It computes in parallel different lines of the image. The numerical method (C.A.M. Carvalho & Y. Epelboin (1993) Acta Cryst. A49, 460-467) has been modified to be able to vectorize the computation and to make it as efficient as possible. The simulation of an image needs from one up to three hours using one processor on a Cray C9x. It may be reduced by a factor equal to the number of available processors thus to less than one hour in all cases.

The study of the propagation of acoustic waves in piezoelectric devices is given as an example of the possibilities of this new program. The devices are circular plates from a quartz AT-cut crystal. The experimental topographs have been recorded by B. Capelle, J. Détaint & A. Zarka (1995). We consider an ideal case where the acoustic vibration mode is a pure thickness-shear mode. Two models have been investigated. describing the deformation inside the crystal either as exponentially decreasing cosine functions (Stevens & Tiersten, (1986) J. Acoust. Soc. Am. 79, 1811-1826) or as a development with Bessel functions (Détaint & al. (1991) Proc. 45th Annu. Frequency Control Symp., pp 166-180).

The agreement between the experiments and the simulation is good except in the center of the resonator, which may be explained by imperfections in the geometry of the devices.