Evaluation of the material parameters of piezoelectric materials by various methods

The elastic, dielectric and piezoelectric constants of four piezoelectric materials, including polyvinylidene fluoride, vinylidene fluoride-trifluoroethylene copolymer, PZT/epoxy 1-3 composite, and lead metaniobate ceramic, have been evaluated from the impedance data using five different methods. A method described in ANSI/IEEE Std. 176-1987, though based on formulae derived for loss-less materials, is found to be applicable to materials with moderate loss. However, for high-loss materials such as poly vinylidene fluoride, the electromechanical coupling constant (kt) obtained by the method of Std. 176 is substantially higher than the actual value. Calculations based on a piezoelectric resonance analysis program (PRAP) combine the best features of two earlier methods. In addition to the impedance at the parallel resonance frequency, impedances at two other frequencies are required for calculation. The PRAP method gives quite accurate material parameters regardless of the magnitude of the loss, but the parameters (including kt) vary by as much as 15% depending on the choice of data. In the nonlinear regression method described in the present work, all the impedance data points around the resonance are least-squares fitted to the theoretical expression for the impedance. Besides the advantage of requiring no arbitrary choice of data, the nonlinear regression method can readily take account of the frequency dependence of the dielectric constant