M. A. Breazeale
Natl. Ctr. for Physical Acoustics, University of Mississippi, University, MS 38677
With single crystals, an acceptable approximation is achieved with only the first nonlinear term in the wave equation. With such crystals and weakly nonlinear solids, one can define a nonlinearity parameter (beta) as the negative ratio of the coefficients of the nonlinear and the linear terms. Values of (beta) between three and 15 have been observed for single crystals. It appears that the approximation no longer is adequate when (beta) becomes larger. Values of (beta) between 80 and 1000 have been observed for rocks. A value of (beta)=1500 has been observed for PZT at the Curie temperature. In addition, frequency dispersion of the nonlinearity has been observed in PZT, and the third harmonic is much larger than expected from an extrapolation of second harmonic data. Since the approximate theory no longer is adequate, terms have been added to the nonlinear equation. The nonlinear equation required to fit data on PZT has been determined. The next step is to explain this mathematical success in physical terms. This will involve the effect of grain boundaries. Then the results can be applied to rocks, which are more complicated.