Subcoercive cyclic electrical loading of lead zirconate titanate ceramics I: nonlinearities and losses in the converse piezoelectric effect
The converse piezoelectric response of Pb(ZrxTi1−x)O3 ceramics is investigated as a function of material composition. The effects of the crystallographic phase and different dopants on piezoelectric nonlinearity are separately examined. For a linear dependence of d33 on E0, the Rayleigh law is applied to describe the material behavior. The observed piezoelectric nonlinearities are described in terms of contributions from extrinsic mechanisms. It is observed that the fractional contribution to d33 from irreversible extrinsic mechanisms in the rhombohedral phase is greater than in tetragonal phases for all amplitudes of applied electric fields, which is attributed to a greater degree of possible non-180° domain wall motion for the rhombohedral phase. The fractional contribution to d33 from irreversible extrinsic mechanisms is also observed to be greatly enhanced with La-doped ceramics in comparison with undoped and Fe-doped ceramics (for compositions near morphotropic phase boundary, the irreversible extrinsic contribution is ∼45% for La-doped ceramics as compared with ∼25% for undoped-ceramics and ∼2% for Fe-doped ceramics, under an applied sinusoidal electric field of amplitude ±750 V/mm). This can be explained due to the promotion of domain wall displacement in the material with La doping, while doping with Fe restricts the motion of the domain walls. The effect of piezoelectric nonlinearities on strain–electric field hysteresis is subsequently examined. It is observed that Rayleigh-type nonlinearity has the dominant contribution to the total strain–electric field hysteresis, although a small contribution can originate from the linear viscoelastic nature of domain wall motion in the material. In order to calculate the complex piezoelectric coefficients, a method based on Fourier expansion of the Rayleigh relations is adopted. Finally, a description of first and higher order harmonics is used to show that the Rayleigh component is dominant in the overall piezoelectric strain of the material.