Curvature of acoustic slowness surface of anisotropic solids near symmetry axes

A detailed analysis is presented of the shape of the acoustic slowness surface of anisotropic elastic solids near axes of rotational symmetry. Particular emphasis is given to the consequences of phase-speed degeneracy along three- and fourfold symmetry axes, where the curvature of the slowness surface does not have a unique value but instead depends on the direction of approach. All the geometrically distinct patterns of curvature variation in the vicinity of three- and fourfold symmetry axes are identified, and the algebraic criteria for their occurrence are established. The results are of relevance to many problems concerned with acoustic-wave propagation and ballistic phonon transport in anisotropic solids. \textcopyright{} 1996 The American Physical Society.