Interface Effects on Phonon Focusing in Rutile

Abstract

The phenomenon of phonon focusing, i.e., the influence of elastic anisotropy on the propagation of heat pulses through solids, was initially studied by Taylor et al. (1). The framework of elastic continuum theory appears to be an appropriate starting point for calculations, but agreement is mostly qualitative. One way to improve upon the situation is to include the effects of reflection and refraction at the heater-crystal and the crystal-detector interfaces, again by using classical elastic theory. Another motivation for such calculations and their experimental verification is that these ideas are also applied in the more basic theories of the Kapitza resistance (see e.g. Little (2)). We have chosen to study the angular dependence of the focusing of the longitudinal wave around the [110]-direction in tetragonal rutile (TiO₂), because in this case the focusing is of almost two-dimensional nature, making it more amenable to calculation.