The various relations for bulk acoustic wave (BAW) propagation in materials of arbitrary anisotropy and piezoelectricity have been expressed in forms suitable for an interactive graphics presentation of the wave properties. The resulting menu-type program a1 lows the simultaneous display of curves in polar or Cartesian coordinates of slowness or velocity, power-flow angle, and electromechanical coupling constant for propagation in an arbitrary plane. Numerical data for propagation in a particular direction in such a plane is displayed when a line cursor is moved to the desired direction. The computational part of the program generates a numerical data file containing all the calculated BAW properties for an arbitrarily selected crystal plane. The interactive part of the program allows the user a variety of choices for displaying simultaneously up to four seperate panels for data and curves pertaining to the selected plane.
I . INTRODUCTIONIn the analysis, design and application of bulk acoustic waves (BAW) transducers and delay lines 11-31. surface skimning bulk waves [41, surface acoustic waves [SI, reflective BAW devices using interdigital transducers [61, in acoustooptics research [71, and in the study of reflection and refraction phenomena in anisotropic media [31, one often needs rather detailed information on BAW properties for various directions of propagation in media of arbitrary anisotropy and piezoelectricity. Since BAW properties are not normally catalogued, it is extremely useful to be able to display on a video terminal (VDT) graphs showing how these bulk wave properties vary with the BAW propagation direction.In this paper, section I1 briefly sumnarizes the theortical approach of the BAW calculation, section I11 illustrates the computer program structure and the diversities of the various menus, and explains the reasons for choosing an IBM personal computer and some of the peripheral hardware and software. Some examples are givev in section I V to demonstrate the usefulness of this interactive menu-type computer program. Section V constitutes a summary of the main results and identifies some potentially useful applications not specifically addressed in the paper.
CALCULATION OF BAW PROPERTIESChoosing an orthogonal coordinate system X I , X2, X3 with X1 as the propagation direction, the material stiffness [ C], piezoelectric [el, and permittivity [ E I constants with respect to this coordinate system are obtained from those with respect to the crystalline X, Y, Z axes [el,, and I E loby the simple matrix operations:a ][e lo[M1, t L E I = [a ][E Io[a 1 , and where the transformation matrices [a 1 and [M 1 are given in [3, ch.3D 1, and the superscript t means transpose. Efficient and simple computer programs for carrying out these transformations I 8 1 are usually expressed in terms of the Euler angles S I e, Y .In this rotated X1, X2, X3 coordinate the Christoffel equation for propagation X 1 direction is written as I3, Eq. 8.1471 vector-matrix equation -ClJ = P V 2 L , system in the he 3x3 (2) where...
