The Ultrasonic Measurement of Elastic Constants of Cubic Crystals.
Interim technical rept.,
TENNESSEE UNIV KNOXVILLE DEPT OF PHYSICS
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To evaluate the combination of third order elastic constants K3 of cubic crystals, one needs very accurate values of the combination of second order elastic constants K2. Often one can obtain numerical values of second order elastic constants for the sample of interest from existing data. Due to the error propagation and the experimental uncertainties at the time of the original measurement, however, there may be uncertainties in the magnitude of K2. An alternative way to arrive at K2s would be to measure them at the time the K3 data are taken. This measurement is quite straightforward since K2s are directly related to the measureable sound velocities. The extra time and effort spent in doing the latter would be justified by an increase in accuracy. This thesis studies these alternatives and compare error propagation in an effort to arrive at the most accurate values of K2. The analysis shows that the question originally posed does not have a unique answer for all samples under all conditions. One cannot decide a priori whether the reference values of C sub ij should be used or whether one should measure the C sub ij each time one measures C sub ijk. The analysis given, however, suggests that one should use reference data rather than measuring each sample, if the reference data are as accurate as those of McSkimin. If such accurate data are not available, one has no choice. One must measure the K2 directly.