The electromechanical coupling in ferroelectric materials is controlled by several coexisting structural phenomena which can include piezoelectric lattice strain, 180° and non‐180° domain wall motion, and interphase boundary motion. The structural mechanisms that contribute to electromechanical coupling have not been readily measured in the past, particularly under the low‐to‐medium driving electric field amplitudes at which many piezoelectric materials are used. In this feature, results from in situ, high‐energy, and time‐resolved X‐ray diffraction experiments are interpreted together with macroscopic piezoelectric coefficient measurements in order to better understand the contribution of these mechanisms to the electromechanical coupling of polycrystalline ferroelectric materials. The compositions investigated include 2 mol% La‐doped PbZr0.60Ti0.40O3, 2 mol% La‐doped PbZr0.52Ti0.48O3, 2 mol% La‐doped PbZr0.40Ti0.60O3, undoped PbZr0.52Ti0.48O3, and 2 mol% Fe‐doped PbZr0.47Ti0.53O3. In all compositions, a strong correlation is found between the field‐amplitude‐dependence of the macroscopic piezoelectric coefficient and the contribution of non‐180° domain wall motion determined from the diffraction data. The results show directly that the Rayleigh‐like behavior of d33 piezoelectric coefficient is predominantly due to a Rayleigh‐like behavior of non‐180° domain wall motion. Furthermore, after separating contributions from lattice (atomic level) and domain wall motion (nanoscale level) to the measured macroscopic piezoelectric properties, we show that previously ignored intergranular interactions (microscopic level) account for a surprisingly large portion of the electromechanical coupling. These results demonstrate that electromechanical coupling in polycrystalline aggregates is substantially different from that observed in single crystalline materials. The construct of emergence is used to describe how averaged macrolevel phenomena are different from the material response observed in an isolated subcomponent of the material. Consequently, and due to its size‐scale complexity, the description of grain‐to‐grain interactions is presently inaccessible in most ab initio and phenomenological approaches. Results presented here demonstrate the need to account for these interactions in order to completely describe macroscopic electromechanical properties of polycrystalline materials.
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.
Structural changes such as non‐180° domain wall motion and lattice strains in Pb(Zr,Ti)O3 ceramics are measured during the application of subcoercive cyclic electric fields using time‐resolved high‐energy X‐ray diffraction with a stroboscopic data collection technique. The contributions to the electric‐field‐induced strains from non‐180° domain wall motion and lattice distortions are determined as a function of material composition and type of dopant. For the different compositions studied, the largest strains due to non‐180° domain wall motion are measured for La‐doped tetragonal ceramics with a composition close to the morphotropic phase boundary. It is further observed that strain contributions from both non‐180° domain wall motion and lattice distortions can be nonlinear with respect to the applied electric field. The correlation between the electric‐field‐induced structural changes and the macroscopic piezoelectric properties is discussed.
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