Determination of Elastic Constants from Sound-Velocity Measurements in Crystals of General Symmetry

Abstract

The ``elastic constants'' of a crystal are referred to a Cartesian coordinate system which has a definite relation to the crystal axes. In determining these constants from sound‐velocity measurements at least as many measurements must be made as there are constants to be determined and in general more than one propagation direction will be used. Thus, in order to relate the measured velocities to the elastic properties of the crystal one needs to solve the equation of motion for the direction under consideration, and to know the transformation equations that relate the elastic properties along the propagation direction to the desired elastic constants. In this paper a perturbation solution to the equation of motion is presented as well as the transformation equations for triclinic and all higher symmetry crystal classes. Also presented are simplifications that will be of use in designing experiments and reducing the data. Several mistakes in previously published work are corrected.