Harmonic generation of 30-MHz ultrasonic waves in small solid samples is analyzed to establish a technique for evaluating combinations of third-order elastic constants of samples which cannot be grown large enough to allow one to make the infinite plane-wave approximation. Results are reported for CsCdF3 and KZnF3.

The radiation pattern of transducers excited by a strip electrode and a ground plane closely approximates a Gaussian function, and hence is a single beam if the ratio of the electrode width to the transducer thickness is between 2 and 4. We calculate the electric fringing at the surface of the transducer and show the extent to which electric fringing accounts for the radiation pattern.

In order to use the harmonic generation technique to measure the nonlinearity parameters of solids, one must determine the amplitudes of both the fundamental and the second harmonic of an initially sinusoidal ultrasonic wave. In our experiment performed at 30 MHz, a typical value of the fundamental amplitude is 1 Å with a second harmonic amplitude of 0.001 Å. Since interesting samples often are smaller than those in which the infinite plane-wave model is sufficiently accurate, we consider the effect of diffraction on the measurements. Ten transducers having diameters between 1.9 mm and 12.7 mm (∼10λ and ∼90λ) were used with the same [100] copper sample. The resulting data show that diffraction does influence the calculated amplitude with the smaller transducers. Interpretation of the data in terms of a nonlinear diffraction model is attempted. Theoretical considerations are discussed. [Research supported by the Office of Naval Research.]