Behavior of soft piezoelectric ceramics under high sinusoidal electric fields

The behavior of piezoelectric, dielectric, and elastic characteristics of soft piezoelectric lead zirconate titanate (PZT) ceramics was investigated under sinusoidal electric field E applied along the poling direction and under mechanical stress-free conditions for a frequency range 10 Hz-10 kHz. Electrical displacement D-3 along the poling direction, mechanical strain S-1 in the direction perpendicular to the poling direction, and the resonant frequency nu(r) of electromechanically uncoupled bending vibrations of polarized plates were measured. Commercial ceramics PZT5H, 3203HD, and PKI550 with chemical composition near the morphotropic phase boundary were used in the study. It was found that the amplitude and phase of the first harmonic of the relative strain S-1((1))/E-m and of the relative electrical displacement D-3((1)) / E-m increase similarly with increasing amplitude E-m of the electric field if the amplitude is less than coercive field. The corresponding increase in the square of the resonant frequency is more moderate. The dependencies are described well by linear functions except for low electric fields. The functions S-1m((1))/E-m and D-3m((1))/E-m demonstrate frequency dispersion as well. Relative amplitude of the second harmonic of the electrical displacement, D-3m((2))/D-3m((1)), which is polar, also increases almost linearly with increasing E-m. The relative third harmonic D-3m((3))/D-3m((1)) demonstrates saturationlike behavior. By means of the electric pulse technique, it was found that irreversible changes in the remnant polarization take place even at electric fields much smaller that the coercive field. A mathematical model of a hysteretic transducer, describing the electric field dependence of electromechanical properties of soft piezoelectric PZT ceramics, was suggested. According to this approach, the response depends not only on the instantaneous magnitude of the input signal (e.g., electric field) but also on its past extreme values. It was shown that the experimental Rayleigh law is a particular case of the suggested approach. The model relates directly electric field dependencies of complex piezoelectric coefficient d(31)(E-m) and S-1((1))/E-m, of complex dielectric permittivity epsilon(33)(T)(E-m) and D-3((1))/E-m, and of elastic compliance s(11)(E)(E-m) and v(r)(2). Application of the model to experimental data showed that the model describes well the first three complex harmonics of D3 and the irreversible change in the remnant polarization. Physical causes of the observed behavior were analyzed. As an alternative to the model based on the 90 degrees polarization reorientation and tetragonl/rhombohedral phase boundary motion, a new approach was suggested. In this model, the observed hysteretic changes in the electromechanical properties are assumed to be caused by the electric field dependency of the mechanical stress acting at interdomain boundaries in the partly constrained crystallites of these ceramics. (C) 1998 American Institute of Physics. [S0021-8979(98)08217-6]