Classification of the phonon-focusing patterns of tetragonal crystals

A classification scheme for the long-wavelength phonon-focusing patterns of nonpiezoelectric tetragonal crystals is proposed. On the basis of their overall appearance and the most prominent features they contain, these patterns can be grouped into 11 categories labeled A,B,C,...,K. In most cases the focusing patterns of tetragonal crystals can be traced to the much simpler and more symmetric focusing patterns of transversely isotropic media. In such cases two parameters $R_2$ and Δ are a good indicator of the type of focusing pattern. Δ is a measure of the deviation of the elastic constants from transverse isotropy, and $R_2$ is a measure of their polar anisotropy. Category-K crystals approximate the condition where the acoustic slowness surface takes the form of three intersecting ellipsoids.