Ballistic phonon imaging in sapphire: Bulk focusing and critical-cone channeling effects

Abstract

Phonon imaging has been used to study the anisotropy of ballistic phonon flux in single crystals of sapphire cut in several different crystallographic orientations. Three types of intense local maxima in phonon flux are observed in these images. The most prominent of these structure types corresponds to mathematical singularities in bulk phonon focusing. The second type of structure, which has not been noted in previous phonon-imaging experiments, is a nonsingular local maximum in flux which can be quite sharp, and would evolve into a genuine singularity if the elastic constants were appropriately changed. These "precursors" and the singularity structures are well predicted in sapphire by Monte Carlo simulations based on the low-temperature elastic constants. The third type of structure is intrinsic to the surfaces of the sapphire and is sensitive to the crystallographic orientation and the quality of these surfaces. It corresponds to a concentration of transverse phonons close to the critical cone for mode conversion between transverse and longitudinal waves at the surface. We interpret this wave-vector channeling effect in terms of a longitudinal pseudo-surface-wave that exists at the sapphire surface when it is either free or only weakly perturbed by an adjoining medium. In our experiments the adjoining medium is a metal film. A model for treating weak mechanical bonding between two adjacent media is developed which is able to account qualitatively for the width and intensities of the observed critical-cone structures. The existence of these new surface-related structures signifies the potential usefulness of phonon imaging for characterizing the scattering of thermal phonons at interfaces. In particular, our results provide a quantitative measure of the elastic coupling between crystal and metal film. The weak nature of this coupling helps to explain previously reported anomalous Kapitza resistance and phonon reflectivity of solid-solid interfaces.