r-axis sound speed and elastic properties of sapphire single crystals

The sound speed was measured for plane wave propagation along the normal to the $\text{(11̄02)}$ plane of sapphire single crystals. The measured r-axis sound speed is significantly different (∼7%) from measured c- and a-axis sound speeds. These results contradict the previous assumption that the mechanical response of sapphire is nearly isotropic. Also, the r axis is not a pure mode direction for longitudinal acoustic wave propagation. The measured r-axis sound speed was not consistent with calculations using the elastic constants reported for sapphire. This discrepancy arises because the elastic constants determined previously used crystallographic conventions different from those in current use. By rotating the coordinate system used for describing the material properties of sapphire in earlier work, consistency is achieved with the current crystallographic conventions. The effect of this coordinate transformation on the second-order elastic constants, the third-order elastic constants, and the photoelastic constants of sapphire is discussed.