Determination of the elastic constants of anisotropic solids from acoustic-wave group-velocity measurements

Abstract

A method is proposed for determining the elastic constants of an anisotropic solid from acoustic-wave group velocities measured in off-symmetry directions in a specimen. The method corresponds to a two-stage optimization procedure in which the elastic constants are varied so as to obtain a least-squares fit of measured to calculated group velocities. At each iterative step a numerical minimization process is employed to find the wave normals and velocities of waves having the required ray directions. The method is demonstrated with synthetic data generated for a number of cubic crystals, and to experimental data obtained on single crystals of silicon using the ultrasonic point-source/enpoint-receiver technique. When provided with longitudinal- and transverse-mode velocity data, the method is able to accurately recover all three independent elastic constants. When only longitudinal mode data are provided, ${\mathit{C}}_{11}$ and the combination ${\mathit{C}}_{12}$+2${\mathit{C}}_{44}$ can be accurately recovered, but not ${\mathit{C}}_{12}$ and ${\mathit{C}}_{44}$ individually.