General, Closed-Form Expressions for Acoustic Waves in Cubic Crystals

Abstract

The Christoffel elastic equations are solved for long-wavelength elastic waves of arbitrary direction in cubic crystals, and exact explicit closed expressions are obtained for the phase and group velocities and displacement amplitudes. The velocity expressions that hold in the special directions are shown to follow from the general result. The problem of determining the elastic constants from the phase velocities in a general crystallographic direction is discussed with particular reference to Brillouin scattering.