A Method for Determining the Elastic Constants of a Cubic Crystal from Velocity Measurements in a Single Arbitrary...

Three independent velocities of sound can be measured along any direction of propagation in a cubic crystal except the [100] and [111] directions. These three velocities suffice to determine the three elastic constants and for the [110] direction, the calculation of these constants is easy. For all other directions, the calculation is more difficult; the only existing method appears to be a perturbation technique developed by Neighbours. The present paper presents a method using exact equations and an iterative procedure to solve these equations and to calculate both the elastic constants and their standard deviations from the sound velocities and their standard deviations. The method is illustrated with new data on SrTiO₃ which give c₁₁=3.156±0.027, c₁₂=1.027±0.027, c₄₄= 1.215±0.006×10¹² dynes/cm² at 25 °C. The importance of including covariance terms in calculations of the standard deviations is emphasized.