By use of the pulse-echo technique, the hydrostatic pressure and uniaxial stress dependence of the ultrasonic wave velocities in single-crystal Al2O3 have been measured, and the values of the 14 independent third-order elastic stiffnesses were determined using a least-squares fit to 31 different experimental measurements. A generalized Gruneisen theory was used in the quasiharmonic approximation to calculate the high- and low-temperature limits for the two coefficients of linear thermal expansion. A numerical integration over 171 directions in the crystal was used for these calculations. The low-temperature limit does not compare well with the available thermal data; however, measurements of thermal expansion below 100°K, which are needed for a realistic comparison, are not presently available.
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Hankey et al. (1970) studied this question.