Determination of all elastic constants of transversely isotropic media with a cusp around the symmetric axis by use of elastic pulses propagating in two principal directions

This paper describes a method of determining all five elastic constants of a hexagonal or transversely isotropic medium of type II which has the cuspidal region of group velocity around the highest-symmetry axis [001] perpendicular to the transversely isotropic basal plane. The elastic constants are obtained from wave-speed data of broad-band ultrasonic signals propagating in two principal directions, namely the [001] and the other parallel to the basal plane. The method uses specific cuspidal features of the slow transverse (ST) mode propagating in the [001] direction with two distinct group velocities. An analytic formula that relates the slower group velocity of the ST mode with the elastic constant ${\mathit{C}}_{13}$ is derived. An example is provided with a single crystal of zinc exhibiting hexagonal symmetry. The advantages of this method lie in both its simplicity for implementation and its improved accuracy for determination of the elastic constant ${\mathit{C}}_{13}$.