Nonlinear elastic behavior of piezoelectric trigonal crystals : measurements on quartz and LiNbO₃₊

The ultrasonic harmonic generation technique previously used to measure third-order elastic (TOE) constants of crystals of cubic symmetry has been extended to measurement of crystals of trigonal symmetry. The theory for nonpiezoelectric trigonal crystals of J. Philip [Technical Report No. 22, Office of Naval Research, Contract No. N00014-81-K-0229 (to be published in 1983)] has been combined with the piezoelectric theory of McMahon [J. Acoust. Soc. Am. 44, 1007 (1968)] to determine the effective TOE constants in a piezoelectric solid, and a correction has been made in McMahon's expression.

Measurements in weakly piezoelectric quartz have produced values of C₁₁₁ and C₃₃₃ which agree within experimental uncertainty with values of R. N. Thurston, H. J. McSkimin and P. Andreatch, Jr. [J. Appl. Phys. 37, 267 (1966)] and R. Stern and R. T. Smith [J. Acoust. Soc. Am. 44, 640 (1968)] after corrections have been made for the effect of diffraction on the data. Measurements in strongly piezoelectric LiNbO₃ have resulted in values which agree reasonably well with those of J. Philip and M. A. Breazeale [Proc. IEEE Ultrasonics Symposium, Vol. 2 (1982)] but disagree with those of C. Y. Nakagawa, K. Yamanouchi and K. Shibayama [J. Appl. Phys. 44, 3969 (1973)]. There is indication of some sample dependence of the values of both the second-order elastic constants as well as the third-order elastic constants of LiNbO₃ samples currently available.

In the course of measurement of the TOE constants a negative nonlinearity parameter was observed for the piezoelectric [100] direction in quartz. This peculiarity is impossible for thermodynamic reasons in fluids, but has been observed once previously in fused silica [J. Bains and M. A, Breazeale, J. Acoust. Soc. Am. 57, 745 (1975)]. The nonlinearity parameter appears to be positive for the piezoelectric [001] direction in LiNbO₃.

The data presented are for the "piezoelectrically stiffened" TOE constants; however, there are preliminary indications that the harmonic generation technique may give access to the constant field TOE constants C_ijk^(E).