Ultrasonic Determination of Combinations of Third - Elastic Constants of Small Cubic Single Crystals.

The ultrasonic harmonic generation technique for measuring. combinations of third-order elastic constants of cubic single crystals. previously has been limited by the plane wave approximation to. measurement of samples whose cross sectional dimensions are > 1.5 cm.(, ). By obtaining data with small transducers and considering the effects of diffraction, the range of samples measurable with the technique has been extended to samples of (TURN) 5 mm on a side. This development has made possible measurement of single crystals unavailable in larger dimensions. The minimum length required for measurement depends on the material and on the cross sectional dimensions; the current estimate of the minimum length is (TURN) 4 mm. Diffraction corrections based on the Kirchhoff diffraction theory are presented and analyzed for both the fundamental frequency component and the second harmonic component of the ultrasonic wave. The technique was used to measure combinations of third-order elastic constants of small samples of CsCdF(,3) and KZnF(,3). The measured combinations, in units of 10('12) dyn/cm('2), obtained by correcting only the fundamental frequency component for diffraction, are as follows. Sample C(,111) (C(,112) + 4C(,166)) (6C(,144) + C(,123) + 8C(,456)). CsCdF(,3) -13.4 - 7.24 -46.6. KZnF(,3) -16.8(, )-11.3(, ).