Shear response of lead zirconate titanate piezoceramics

The piezoelectric shear strain $S_5$ of several commercial lead zirconate titanate (PZT) piezoceramics was evaluated under the nonresonant condition in a sinusoidal ac-field $E_1\mathrm{(t)}$ applied perpendicular to the poling direction. Results obtained on donor doped (soft PZT) and acceptor doped (hard PZT) ceramics are compared. At fields sufficiently below the limiting field $E_{\lim }$ necessary to electrically depole the sample, we find a linear, nonhysteretic relationship between $S_5$ and the polarization $P_1.$ In soft PZT ceramics, the effective piezoelectric shear coefficient $d_{15}{\mathrm{=S}}_5{\mathrm{/E}}_1$ shows a pronounced ac-field dependence which was fitted according to $d_{15}{\mathrm{(E}}_1{\mathrm{)=d}}_{\mathrm{lin}}{\text{[1+(d}}_{\mathrm{nl}}{E}_1{)}^{\alpha }]$ with $\text{α≈1.2.}$ The results indicate that irreversible motion of non-180° walls causes the nonlinearity of PZT and the contribution of 180° walls to the linear and nonlinear coefficients is negligible. The analysis of the relationship between linear and nonlinear coefficients obtained at different ceramic systems suggests that there exists another extrinsic contribution to the permittivity in PZT which may not be attributed to domain wall motion but may be responsible to the dielectric dispersion at microwave frequencies.