Resonant ultrasound spectroscopy applied to misoriented crystals of low symmetry: Corundum

Abstract

The vibrational resonance spectrum of a single crystal depends on the mass density, geometry, and elastic tensor of the material. Resonant ultrasound spectroscopy (RUS) derives the elastic tensor from a measured set of sample resonances. Any tensor quantity must be defined relative to some coordinate system which, for single crystals, is often coordinated with the crystal lattice vectors. If the elastic tensor coordinate system does not coincide with the principal axes of the sample, the tensor must be transformed via a rotation matrix creating an effective elastic tensor for the sample. Misorientation may occur by design, sample preparation constraints, or errors. This problem becomes particularly important for crystals of low symmetry, such as corundum, a trigonal crystal with six independent elastic constants, or when highly accurate results for derived elastic constants are desired. In this talk, techniques for analyzing such misoriented samples with RUS will be presented along with experimental data for corundum and a correction for the sign of C14.