Ultrasonic orientation and elastic constant determination of single cubic crystals by minimization of functions

A method is presented for determining the elastic constants and the orientation of cubic single crystals by the simultaneous iterative solution of equations. To construct a system of equations for a crystal specimen, one must know, in addition to the fact that the crystal is cubic, the density of the specimen and at least six distinct velocities of wave propagation in the crystal. Systems of equations, which utilize either characteristic equations of the linear acoustic tensor or equations expressing the invariants of that tensor, have been solved for the elastic properties and the orientation of cubic crystals. For systems based on characteristic equations, a detailed study has been made to determine the errors produced in the elastic constants and orientation parameters by errors in the velocity data.