Tetragonal Lead Zirconate Titanate Research Articles

A phase-field approach to studying the temperature-dependent ferroelectric response of bulk polycrystalline PZT

Ferroelectric ceramics are of interest for engineering applications because of their electro-mechanical coupling and the unique ability to permanently alter their atomic-level dipole structure (i.e., their polarization) and to induce large-strain actuation through applied electric fields. Although the underlying multiscale coupling mechanisms have been investigated by modeling strategies reaching from the atomic level across the polycrystalline mesoscale to the macroscopic device level, most prior work has neglected the important influence of temperature on the ferroelectric behavior. Here, we present a phase-field (diffuse-interface) constitutive model for ferroelectric ceramics, which is extended to account for the effects of finite temperature by considering thermal lattice vibrations based on statistical mechanics and by modifying the underlying Landau-Devonshire potential to depend on temperature. Results indicate that the chosen interpolation of the Landau energy coefficients is a suitable approach for predicting the temperature-dependent spontaneous polarization accurately over a broad temperature range. Lowering the energy barrier at finite temperature by the aforementioned methods also leads to better agreement with measurements of the bipolar hysteresis. Based on a numerical implementation via FFT spectral homogenization, we present simulation results of single- and polycrystals, which highlight the effect of temperature on the ferroelectric switching kinetics. We observe that thermal fluctuations (at the phase-field level realized by a thermalized stochastic noise term in the Allen-Cahn evolution equation) promote the nucleation of needle-like domains in regions of high heterogeneity or stress concentration such as grain boundaries. This, in turn, leads to a faster polarization reversal at low electric fields and a simulated domain pattern evolution comparable to experimental observations, stemming from the competition between nucleation and growth of domains. We discuss the development, implementation, validation, and application of the temperature-dependent phase-field framework for ferroelectric ceramics with a focus on tetragonal lead zirconate titanate (PZT), which we demonstrate to admit reasonable model predictions and comparison with experiments.

Time-resolved X-ray diffraction study of the structural dynamics in an epitaxial ferroelectric thin Pb(Zr0.2Ti0.8)O3 film induced by sub-coercive fields

The electric field-dependence of structural dynamics in a tetragonal ferroelectric lead zirconate titanate thin film is investigated under subcoercive and above-coercive fields using time-resolved X-ray diffraction. The domain nucleation and growth are monitored in real time during the application of an external field to the prepoled thin film capacitor. We propose the observed broadening of the in-plane peak width of the symmetric 002 Bragg reflection as an indicator of the domain disorder and discuss the processes that change the measured peak intensity. Subcoercive field switching results in remnant disordered domain configurations.

Micromechanical simulation of ferroelectric domain processes at crack tips

The electromechanical loading situation at cracks in ferroelectric ceramics is essentially affected by domain switching. Under high electrical and/or mechanical external fields, the state of polarization and remanent strains is substantially changed at the crack tip. These irreversible dissipative processes influence the fracture toughness of the cracked ferroelectric material. In the present paper, the micromechanical domain switching processes at the crack tip are studied by numerical simulation and compared with the in situ experimental results obtained by Jones et al. (Acta Mater 55(16):5538–5548, 2007) using X-ray diffraction analyses in synchrotron. Main attention is payed to the spatial distribution of preferred domain orientation in a mechanically loaded compact tension specimen made of a soft tetragonal lead zirconate titanate ceramics. It is found that the mechanically induced favored domain orientation distribution depends on position within the plane of the CT specimen and correlates with projected deviatoric stresses and strains. Some issues concerning shortcomings in the experimental and simulation results are raised and discussed. The outcome of this type of simulations forms the basis for more realistic fracture mechanical evaluations in future.

Low temperature dielectric relaxation in ordinary perovskite ferroelectrics: enlightenment from high-energy x-ray diffraction

Ordinary ferroelectrics exhibit a second order phase transition that is characterized by a sharp peak in the dielectric permittivity at a frequency-independent temperature. Furthermore, these materials show a low temperature dielectric relaxation that appears to be a common behavior of perovskite systems. Tetragonal lead zirconate titanate is used here as a model system in order to explore the origin of such an anomaly, since there is no consensus about the physical phenomenon involved in it. Crystallographic and domain structure studies are performed from temperature dependent synchrotron x-ray diffraction measurement. Results indicate that the dielectric relaxation cannot be associated with crystallographic or domain configuration changes. The relaxation process is then parameterized by using the Vogel–Fulcher–Tammann phenomenological equation. Results allow us to hypothesize that the observed phenomenon is due to changes in the dynamic behavior of the ferroelectric domains related to the fluctuation of the local polarization.

Analysis of the state of poling of lead zirconate titanate (PZT) particles in a Zn-ionomer composite

ABSTRACTThe poling behaviour of tetragonal lead zirconate titanate (PZT) piezoelectric ceramic particles in a weakly conductive ionomer polymer matrix is investigated using high energy synchrotron X-ray diffraction analysis. The poling efficiency, crystallographic texture and lattice strain of the PZT particles inside the polymer matrix are determined and compared with the values for corresponding bulk ceramics reported in literature. The volume fraction of c-axis oriented domains and the lattice strain of the PZT particles are calculated from the changes in the integral intensities of the {200} peaks and the shift in the position of the {111} peaks respectively. It is shown that for an applied macroscopic field of 15 kV.mm−1, the PZT particles are effectively poled, leading to a maximum ν(002) domain reorientation volume fraction, of around 0.70. It is also found that a significant tensile lattice strain, ϵ{111}, of 0.6% occurs in the direction of the applied electric field, indicating the occurrence of residual stresses within the 2–4 μm size diameter particles. Although lower than that observed in poled tetragonal PZT ceramics, this level of lattice strain does indicate that the PZT particles within the composite experience significant elastic constraint. The correlation between the poling induced structural changes and the macroscopic piezoelectric and dielectric properties is discussed.

Revisiting the blocking force test on ferroelectric ceramics using high energy x-ray diffraction

The blocking force test is a standard test to characterise the properties of piezoelectric actuators. The aim of this study is to understand the various contributions to the macroscopic behaviour observed during this experiment that involves the intrinsic piezoelectric effect, ferroelectric domain switching, and internal stress development. For this purpose, a high energy diffraction experiment is performed in-situ during a blocking force test on a tetragonal lead zirconate titanate (PZT) ceramic (Pb0.98Ba0.01(Zr0.51Ti0.49)0.98Nb0.02O3). It is shown that the usual macroscopic linear interpretation of the test can also be performed at the single crystal scale, allowing the identification of local apparent piezoelectric and elastic properties. It is also shown that despite this apparent linearity, the blocking force test involves significant non-linear behaviour mostly due to domain switching under electric field and stress. Although affecting a limited volume fraction of the material, domain switching is responsible for a large part of the macroscopic strain and explains the high level of inter- and intra-granular stresses observed during the course of the experiment. The study shows that if apparent piezoelectric and elastic properties can be identified for PZT single crystals from blocking stress curves, they may be very different from the actual properties of polycrystalline materials due to the multiplicity of the physical mechanisms involved. These apparent properties can be used for macroscopic modelling purposes but should be considered with caution if a local analysis is aimed at.

Domain pinning near a single-grain boundary in tetragonal and rhombohedral lead zirconate titanate films

The interaction of grain boundaries with ferroelectric domain walls strongly influences the extrinsic contribution to piezoelectric activity in Pb(Zr,Ti)O3 (PZT), ubiquitous in modern transducers and actuators. However, the fundamental understanding of these phenomena has been limited by complex mechanisms originating from the interplay of atomic-level domain wall pinning, collective domain wall dynamics, and emergent mesoscopic behavior. This contribution utilizes engineered grain boundaries created by depositing epitaxial PZT films with various Zr:Ti ratio onto 24o SrTiO3 tilt bicrystals. The nonlinear piezoelectric response and surface domain structure across the boundary are investigated using piezoresponse force microscopy whilst cross section domain structure is studied using transmission electron microscopy. The grain boundary reduces domain wall motion over a width of 800±70 nm for PZT 45:55 and 450±30 nm for PZT 52:48. Phase field modeling provides an understanding of the elastic and electric fields associated with the grain boundary and local domain configurations. In conclusion, this study demonstrates that complex mesoscopic behaviors can be explored to complement atomic-level pictures of the material system.

In situ measurement of increased ferroelectric/ferroelastic domain wall motion in declamped tetragonal lead zirconate titanate thin films

Ferroelectric/ferroelastic domain reorientation was measured in a 1.9 μm thick tetragonal {001} oriented PbZr0.3Ti0.7O3 thin film doped with 1% Mn under different mechanical boundary constraints. Domain reorientation was quantified through the intensity changes in the 002/200 Bragg reflections as a function of applied electric field. To alter the degree of clamping, films were undercut from the underlying substrate by 0%, ∼25%, ∼50%, or ∼75% of the electrode area. As the amount of declamping from the substrate increased from 0% to ∼75%, the degree of ferroelectric/ferroelastic domain reorientation in the films increased more than six fold at three times the coercive field. In a film that was ∼75% released from the substrate, approximately 26% of 90° domains were reoriented under the maximum applied field; this value for domain reorientation compares favorably to bulk ceramics of similar compositions. An estimate for the upper limit of 90° domain reorientation in a fully released film under these conditions was determined to be 32%. It was also found that the different clamping conditions strongly influence the amount of reorientation upon removing the applied field, with higher remanence of preferred domain orientations observed in declamped films.

Ferroelectric/Ferroelastic domain wall motion in dense and porous tetragonal lead zirconate titanate films.

Direct evidence of ferroelectric/ferroelastic domain reorientation is shown in Pb(Zr0.30Ti0.70)O3 (PZT30/70) thin films clamped to a rigid silicon substrate using in situ synchrotron X-ray diffraction during application of electric fields. Both dense films and films with 3 to 4 vol% porosity were measured. On application of electric fields exceeding the coercive field, it is shown that the porous films exhibit a greater volume fraction of ferroelastic domain reorientation (approximately 12 vol% of domains reorient at 3 times the coercive field, Ec) relative to the dense films (~3.5 vol% at 3Ec). Furthermore, the volume fraction of domain reorientation significantly exceeded that predicted by linear mixing rules. The high response of domain reorientation in porous films is discussed in the context of two mechanisms: local enhancement of the electric field near the pores and a reduction of substrate clamping resulting from the lowering of the film stiffness as a result of the porosity. Similar measurements during weak-field (subcoercive) amplitudes showed 0.6% volume fraction of domains reoriented for the porous films, which demonstrates that extrinsic effects contribute to the dielectric and piezoelectric properties.

A multiscale model for reversible ferroelectric behaviour of polycrystalline ceramics

A multiscale model for the behaviour of ferroelectric polycrystalline materials under electro-mechanical loading is proposed. It is based on an energetic description of the equilibrium at the single crystal scale using a statistical estimate of the ferroelectric domain structure. A self-consistent scheme is then used to establish the behaviour of polycrystalline materials. The approach is anhysteretic but hysteresis effects can be added afterwards so as to obtain butterfly ferroelectric loops. It is applied to a tetragonal Lead Zirconate Titanate (PZT). The model allows the investigation of crystallographic texture effects on the overall behaviour and provides an estimate of internal stresses within the material. By way of an example a 〈100〉 fibre texture is predicted to generate as much as 150% more longitudinal strain and 33% more electric induction at 1MV/m compared to an isotropic polycrystal.

Residual stress relief due to fatigue in tetragonal lead zirconate titanate ceramics

High energy synchrotron XRD was employed to determine the lattice strain ε{111} and diffraction peak intensity ratio R{200} in tetragonal PZT ceramics, both in the virgin poled state and after a bipolar fatigue experiment. It was shown that the occurrence of microstructural damage during fatigue was accompanied by a reduction in the gradient of the ε{111}–cos2 ψ plot, indicating a reduction in the level of residual stress due to poling. In contrast, the fraction of oriented 90° ferroelectric domains, quantified in terms of R{200}, was not affected significantly by fatigue. The change in residual stress due to fatigue is interpreted in terms of a change in the average elastic stiffness of the polycrystalline matrix due to the presence of inter-granular microcracks.

Converse longitudinal piezoelectric response of a ferroelectric thick film elastically coupled with a supporting substrate or underlayer

Effects of elastic coupling between a ferroelectric thick film and a supporting substrate or underlayer with finite thickness on the apparent longitudinal piezoelectric coefficients are analysed in this work. General analytical solutions of the effective d33 converse piezoelectric coefficients of a film–substrate couple are given as a function of the electromechanical properties, crystalline structure and orientation, as well as the thickness ratio of the couple. Computations of effective d33 coefficients as a function of the thickness ratio are performed for typical tetragonal and rhombohedral lead zirconate titanate ferroelectric films with a composition near its morphotropic phase boundary. These results are compared with those for thin films with the same compositions, where the substrate clamping effect is dominant.

Modes of Domain Wall Motion and Polarization of Lead Zirconate Titanate Polycrystals

Domain wall motion depending on polarization field has been studied for tetragonal lead zirconate titanate (PZT) polycrystals. The domain structure of PZT polycrystals was observed in a backscattered electron image obtained with a scanning electron microscope under various poling conditions. Domain wall reorientation was observed when the applied polarization field strength became higher than the coercive electric field. An in situ X-ray diffraction (XRD) measurement was also done to evaluate the domain wall motion contribution, under a polarization field. The XRD intensity ratio of (002) vs (200) reached as much as 0.72, which was explained by taking the both contributions of domain wall reorientation and translation. The experimental data and consideration by a geometrical domain wall motion model confirmed that the domain wall translation has zero threshold energy and the domain wall reorientation occurs beyond the coercive electric strength, corresponding to a finite threshold energy.

Spontaneous polarization estimation from the soft mode in strain-free epitaxial polar axis-oriented Pb(Zr,Ti)O3 thick films with tetragonal symmetry

The ferroelectric property, crystal structure, and A1(1TO) soft mode of almost strain-free epitaxial polar axis-oriented tetragonal lead zirconate titanate thick films grown on CaF2 substrates were investigated by changing the Zr/(Zr+Ti) ratio and the temperature. The square of spontaneous polarization (Ps), Ps2, monotonically increased as tetragonal distortion, (c/a)−1, increased where a and c are the lattice parameters of the films and as the square of frequency in A1(1TO), ω2[A1(1TO)], increased. Additionally, the relationships of Ps2, (c/a−1), and ω2[A1(1TO)] were experimentally obtained, which confirmed the Ps value obtained from (c/a−1) and ω[A1(1TO)] without direct polarization measurements.

Evaluation of Ferroelectric Domain Behaviors Using Acoustic Emission Method

Two kinds of acoustic emission (AE) signals are used to evaluate the ferroelectric domain behaviors in tetragonal lead zirconate titanate (PZT) ceramics: AE related to the ferroelectric domain and vibro acoustic emission (vibro-AE) caused by sample vibration. The signal level of vibro-AE caused by the sample vibration is suppressed using an external resistor, and the vibro-AE and AE related to the ferroelectric domain are observed simultaneously. It is shown that the vibro-AE measured as an AE signal Vrms reflects the piezoelectricity of the sample. The Kaiser effect in terms of electrical loading is found to be valid for ferroelectric PZT ceramics. From the vibro-AE measurement, it is shown that domain clamping occurs at critical fields at which the vibro-AE signal vanishes. It is also shown that domain-related AE takes place above the coercive field Ec and after domain clamping occurs. From these obtained AE activities, conflicts among ferroelectric domains in the sequence of domain reorientation from the clamped state to the aligned domain state and the resulting stress relaxations are considered to be the origin of AE.

Measurement of Structural Changes in Tetragonal PZT Ceramics under Static and Cyclic Electric Fields Using a Laboratory X-ray Diffractometer

In situ structural characterization techniques that are capable of characterizing piezoelectric ceramics under different electrical loading conditions are important to understand the behavior of materials during their use. In this work, we report the use of a laboratory X-ray diffractometer for the measurement of various structural changes in tetragonal La-doped lead zirconate titanate (PZT) ceramics under the application of static and cyclic electric fields. The changes in the volume fractions of the 90 degrees domains parallel to the electric field direction are calculated from the intensities of the {002} diffraction peaks. In addition, the components of lattice strains are monitored from the changes in the (111) crystallographic planes. It is observed that, under the application of static electric fields, both 90 degrees domain switching and the 111 lattice strains showed similarity with the macroscopic strain-electric field hystersis loop. To measure the structural changes under cyclic electric fields, a time-resolved X-ray diffraction technique was used. Under application of a square-wave electric field of amplitude +/-650 V/mm and frequency 0.3 Hz, a change of approximately 5% in the volume fraction of the 90 degrees domains and approximately 0.07% strain of the 111 lattice planes are observed. Both the amount of 90 degrees domain switching and the 111 lattice strains are observed to increase with an increase in the amplitude of the cyclic electric field. The implications of the measured structural changes for the macroscopic piezoelectric properties of ceramics are discussed.

Effects of preferred orientation on the piezoelectric properties of Pt/Pb(Zr0.3Ti0.7)O3/Pt thin films grown by sol–gel process

Tetragonal lead zirconate titanate (PZT) films with different orientations and 200 nm film thicknesses were prepared on platinized silicon substrates. Types of substrate and control of thermal processes, such as layer-by-layer and one-crystallization heat treatments, result in highly (111) or (100)-oriented PZT films. The piezoelectric, dielectric, and ferroelectric properties of polycrystalline PZT films have been investigated as a function of preferred orientation. The property difference between (111) and (100)-oriented films appears to be induced by the effect of ferroelastic domain existence (90° domain in tetragonal composition). From a modified phenomenological equation, the higher electrostrictive coefficient value of 5.6 × 10−2 m4/C2 for (100)-oriented PZT may be responsible for the larger piezoelectric coefficients in (100)-oriented polycrystalline PZT films of 44 pm/V in comparison to (111)-oriented PZT films with about 3.1 × 10−2 m4/C2 of Q 33 and 40 pm/V of d 33,f . It was also observed that two (100)-oriented films prepared by different heat treatments showed different values in piezoelectric, dielectric, and ferroelectric properties even though only (100) orientation was characterized for both cases. This process-induced difference may also play an important role in determining both intrinsic and extrinsic contribution to the properties, even though these parameters seem to be more responsible for extrinsic components, such as domain wall motion.

Ferroelastic domain switching fatigue in lead zirconate titanate ceramics

The influence of the frequency and amplitude of cyclic mechanical loading on soft, tetragonal lead zirconate titanate (PZT) ceramics was investigated via neutron diffraction. Intensity change in the {2 0 0} reflections provided quantitative measurements of domain switching behavior, domain texture and the strain resulting from domain switching. The results are explained using a viscoelasticity model. It was found that the magnitude of applied stress affects the level of strain accumulated, while its frequency affects the time taken for the strain to reach saturation. Furthermore, markedly different behaviors are exhibited by poled and unpoled samples. For samples loaded under identical conditions, the frequency effect is more pronounced in unpoled samples and the accumulated ferroelastic strain is greater in poled samples.

Indentation size effect in soft PZT ceramics with tetragonal structure close to the MPB

Nanoindentation measurements in tetragonal lead zirconate–titanate (PZT) ceramics doped with 0.8 mol% of La2O3 with a composition close to the morphotropic phase boundary (MPB) were performed using indenters with different tip radii. The elastic modulus was independent of indenter size but varied as expected with the Zr/Ti ratio of the samples. On the other hand, the calculated mean pressure remained constant for each indenter above the first pop-in, also varying with the Zr/Ti ratio, but was in all samples clearly dependent on the indenter radius. Indentation size effect (ISE) in tetragonal PZT was partially explained by the concept of ‘geometrically necessary dislocations’. However, the experimental data also indicate that the actual ISE model needs to be slightly extended to include the ferroelastic domain switching contribution.

Thermal effects on mechanical grinding-induced surface texture in tetragonal piezoelectrics

The effect of temperature on grinding-induced texture in tetragonal lead zirconate titanate (PZT) and lead titanate (PT) has been investigated using in situ x-ray diffraction (XRD) with an area detector. In contrast with previous results on electrical poling, mechanically-ground PT and soft PZT materials retain strong ferroelastic textures during thermal cycling, even after excursions to temperatures slightly above the Curie temperature. The relationship between the residual stresses in the surface region, caused by grinding, and those resulting from domain wall motion is elucidated by in situ texture measurements obtained during thermal cycling.