General closed-form expressions for acoustic waves in elastically anisotropic solids

By solving the Christoffel equations, general closed-form expressions are obtained for the phase and group velocities and displacement eigenvectors of arbitrarily directed acoustic waves in elastically anisotropic solids. The relationship of these general results to expressions that hold in symmetry directions is shown, and applications to phonon focusing and the determination of acoustic axes and extrema of the phase velocity are discussed. Methods for extracting the elastic constants and orientation of a crystal from measured sound velocities are outlined.