Acoustic axes for elastic waves in crystals: theory and applications

The purpose of this paper is to present a simple and direct way of finding the number of acoustic axes and their locations for all crystals of orthorhombic, tetragonal, hexagonal or cubic symmetry (‘RTHC crystals’). The procedure is based upon a decomposition of the acoustical tensor due to Fedorov and Fedorov. Excepting cases for which there may be an infinity of acoustic axes (for instance, the case of hexagonal crystals), it is shown that RTHC crystals may have at most sixteen acoustic axes, four in each coordinate plane, and four out of coordinate planes. Very simple equations are presented for the explicit determination of these acoustic axes.Then, these results are applied in turn to each of the RTHC crystal systems. In each case the possible numbers of acoustic axes are easily obtained. Explicit numerical examples are presented for several specific crystals.