VELOCITIES AND DISPLACEMENTS OF ELASTIC-WAVES IN CUBIC-CRYSTALS

Approximate general equations for the phase velocities and displacements of quasilongitudinal and quasitransverse elastic waves in any nonpiezoelectric cubic crystal with an arbitrary direction of the wave normal are derived in explicit form. These equations differ from the Cardan solution in that they do not contain any square or cube roots, i.e., the velocities and displacements of all three isonormal waves are rational functions of the components of the wave normal vector and the elastic constants of the crystal. The equations are subjected to a detailed error analysis by comparing the results the results of calculations according to the derived approximate equations with an exact numerical solution. The comparison is made for three crystals: sodium, which is the most anisotropic; moderately anisotropic copper; and slightly anisotropic aluminum. It is shown that the worst-case error of the approximate calculation does not exceed the error in the experimental values of the elastic constants. In addition, it is proved that the polarizations of all waves in nonpiezoelectric cubic crystals are determined entirely by a single parameter, which is a linear fractional function of the elastic constants.