South African Journal of Science
Print version ISSN 0038-2353
In the past, lattice dynamics models have been used in interpreting dispersive phonon focusing patterns of crystals. They have had mixed success in accounting for observed images and, moreover, different models applied to the same crystal tend to differ significantly in their predictions. In this paper we interpret observed phonon focusing images of two cubic crystals, germanium and silicon, through an extension of continuum elasticity theory that takes into account the first deviation from linearity of the phonon dispersion relation. This is done by incorporating fourth-order spatial derivatives of the displacement field in the wave equation. The coefficients of the higher-order derivatives are determined by fitting to phonon dispersion relations for the acoustic branches measured by neutron scattering in the ,  and  symmetry directions. With this model we simulate phonon images of Si and Ge projected onto the (100), (110) and (111) observation planes. These are able to account well for the observed phonon images.