Soft Lead Zirconate Titanate Research Articles

Evaluation of piezoelectric material properties for a higher power output from energy harvesters with insight into material selection using a coupled piezoelectric-circuit-finite element method

Piezoelectric material properties have substantial influence on electrical power output from piezoelectric energy harvesters (PEHs). Understanding their influences is the first step in designing effective PEHs to generate higher power outputs. This paper uses a coupled piezoelectric-circuit-finite element method to study the power outputs of different types of piezoelectric materials, including single crystal, polyvinylidene fluoride (PVDF), and soft and hard lead zirconate titanate (PZT) materials. The purpose of this study is to try to gain an understanding of which piezoelectric material property--the elastic compliance s11, the piezoelectric strain constant d31, the piezoelectric stress constant g31, and the relative dielectric constant ϵ(T)r33, and the associated material properties of the d31 × g31, called the figure of merit (FOM), and the coupling coefficient k31--dominates the power output. A rectangular piezoelectric plate under a low-frequency excitation is used to evaluate piezoelectric material properties for a higher power output. It was found that 1) d31 is a more dominant material property over other material properties for higher power output; 2) FOM was more linearly related to the power output than either the k31 or the d31; and 3) ϵ(T)r33 had some role; when the materials have an identical d31; a lower ϵ(T)r33 was preferred. Because of unexplained outliers, no single material parameter was able to be recommended as selection criteria, but combined FOM with d31 parameters is recommended for selection of piezoelectric material for a higher power output from PEHs.

Calculation of Hysteresis Losses for Ferroelectric Soft Lead Zirconate Titanate Ceramics

The phenomenological Hamad model was modified to enable retracing of the hysteresis loop of ferroelectric soft lead zirconate titanate (PZT). Comparison with experimental results revealed the modified model can retrace polarization versus electric field for different electric field amplitudes and temperatures. Hysteresis loss per unit volume per cycle for soft PZT was predicted and estimated. The results revealed that energy loss increased with decreasing temperature and with increasing electric field amplitude.

Micropolar Theory of Flexoelectricity

The invalidities, including (i) the property of continuity and (ii) the irreversibility of thermodynamics, are investigated when characterizing flexoelectricity with classical continuum approach and Clausius-Duhem inequality. To avoid the invalidities, Micropolar field theory is introduced. The differences between classical continuum approach and the proposed approach are discussed and compared. As a special case, the linear constitutive equations for Micropolar electromagnetic elastic solids are derived. Moreover, the linear constitutive equations for isotropic EM elastic solids in Micropolar theory are further obtained for estimating the flexoelectric coefficient flexoelectric coefficients for unplowed soft lead zirconate titanate (PZT) ceramic.

Fatigue and retention properties of shape memory piezoelectric actuator with non-180° domain switching

A shape memory piezoelectric actuator can maintain a piezoelectric displacement without an operating voltage. It has two stable strain states at zero voltage: a poled state and a depoled state. The driving principle of the shape memory piezoelectric actuator is based on reorientation of the non-180° domains in the ferroelectric materials. In this study, a unimorph shape memory piezoelectric actuator with a soft lead zirconate titanate was fabricated. The fatigue and retention properties of this shape memory piezoelectric actuator were investigated. The fatigue behavior of the actuator in the early stages is considered to be closely related to the domain stabilization process. Continuous cycle fatigue tests revealed that the shape memory piezoelectric actuator continues to operate even after 106 cycles. Retention measurements revealed that the depoled state of the actuator was more stable than the poled state. The drift in the actuator displacement over one year was estimated to be less than 10% of the initial shape memory displacement.

Mechanically controlled domain structure in PZT piezoelectric ceramics

The influence of the mechanically applied load on the piezoelectric properties and domain switching characteristics has been investigated experimentally using a soft lead zirconate titanate (PZT) piezoceramic, which de-poled to make randomly orientated domain structures. Mechanical loads were applied to rectangular PZT ceramics under compressive and tensile stresses. With the applied stress, 90° domain switching occurred in many locations in the PZT ceramics, where the higher stress caused more severe domain switching. The domain switching occurred with different directions, depending on the stress direction. For instance, the (200) peak increased and the (002) peak decreased when more severe compressive stress was applied. The opposite trend was detected as more severe tensile stress was applied; the (200) peak decreased and the (002) peak increased. With the applied loading process, the domains (long tetragonal c-axis) were orientated regularly in the PZT ceramics. Furthermore, like the electrically poled PZT ceramics, the domain orientations were more aligned when the sample surfaces were constrained during the loading process.

Cyclic energy harvesting from pyroelectric materials

A method of continuously harvesting energy from pyroelectric materials is demonstrated using an innovative cyclic heating scheme. In traditional pyroelectric energy harvesting methods, static heating sources are used, and most of the available energy has to be harvested at once. A cyclic heating system is developed such that the temperature varies between hot and cold regions. Although the energy harvested during each period of the heating cycle is small, the accumulated total energy over time may exceed traditional methods. Three materials are studied: a commonly available soft lead zirconate titanate (PZT), a pre-stressed PZT composite, and single-crystal PMN-30PT. Radiation heating and natural cooling are used such that, at smaller cyclic frequencies, the temporal rate of change in temperature is large enough to produce high power densities. The maximum power density of 8.64 μW/cm3 is generated with a PMN-30PT single crystal at an angular velocity of 0.64 rad/s with a rate of 8.5°C/s. The pre-stressed PZT composite generated a power density of 6.31 μW/cm(3), which is 40% larger than the density of 4.48 μW/cm3 obtained from standard PZT.

Origin and magnitude of the large piezoelectric response in the lead-free (1–x)BiFeO3–xBaTiO3 solid solution

Abstract

Nonlinearity and scaling behavior in a soft lead zirconate titanate piezoceramic

Lead oxide-based ferroelectrics, represented by lead zirconate titanate [Pb(Zr,Ti)O3] or PZT), are the most widely used materials for piezoelectric actuators, sensors, and transducers due to their excellent piezoelectric properties. Most of these piezoelectric materials are employed under a variety of strains (stress, electrical field, and temperature). It would thus be interesting to predict their behaviors under different excitations without having to perform too much experimental work, i.e., just carry out a single experiment and still be able to provide the other experimental values. The purpose of this paper has thus been to propose several behavioral laws linking the electrical field, temperature and mechanical stress. The first law rendered it possible to express the mechanical stress by an equivalent electric field [ΔE≡αΔT×P(E,T0)]. Subsequently, a law linking the electrical field and temperature {ΔE≡[2β×P(E,θ0)]×Δθ} was proposed. From these two laws, a third law was identified reflecting the mechanical stress as an equivalent temperature; each expressed by a temperature equivalent stress (T≡δ×Δθ). After experimental validation of these laws, the mapping could be extended in order to predict the polarization behavior in the tensile stress zone as well as that as a function of the negative temperature.

High temperature blocking force measurements of soft lead zirconate titanate

Piezoelectric actuators outperform other technological solutions in the area of high-speed, high-force and high-accuracy displacement, but are only able to generate strains of about 0.2%. The load capability is generally quantified in terms of a blocking force, which is the force sustained under electric field at zero displacement. Stress–strain curves in a temperature regime from room temperature up to 150 °C on electrically loaded soft lead zirconate titanate (PZT) are generated to determine the blocking stress. The ensuing nonlinear behaviour is discussed in terms of ferroelectric and ferroelastic switching and contrasted to idealized linear constitutive behaviour as often assumed by manufacturers. The blocking stress is shown to increase with temperature due to an additional stiffening effect as a function of electric field. The actual mechanical work done is found to be larger than in the idealized case where linear constitutive behaviour is assumed.

Determination of reversible and irreversible contributions to the polarization and strain response of soft PZT using the partial unloading method

Experimental work is aimed at systematically investigating the non-linear ferroelectric and ferroelastic behavior of a commercially available soft lead zirconate titanate (PZT) material. The fast partial unloading method is used to measure the material properties of unpoled soft PZT under pure electric field and of initially pre-poled soft PZT under compressive stress loading. In the first experiment using unpoled PZT, the evolution of piezoelectric constants and dielectric permittivity is determined as a function of electric field. It is found that the piezoelectric constants and dielectric permittivity depend on the electric field history. The results are used to separate the reversible strain and polarization from the irreversible ones caused by domain switching. In the second experiment using initially pre-poled PZT, it is found that the strain response is significantly dependent on the stress loading rate. The elastic moduli and piezoelectric coefficients are evaluated with respect to the compressive stress history. The measured longitudinal and transverse irreversible strains change significantly during both loading and unloading processes. An attempt is made to discuss the use of irreversible strain and irreversible polarization as internal variables for constitutive modeling. This investigation provides valuable information for modeling to predict the performance and for improving the reliability of piezoelectric devices.

Comparison of the Temperature‐Dependent Ferroelastic Behavior of Hard and Soft Lead Zirconate Titanate Ceramics

The ferroelastic properties of a hard acceptor‐doped lead zirconate titanate (PZT) ceramic are investigated between room temperature and 300°C. Comparison with a soft PZT shows that acceptor doping has a stronger influence on mechanically induced domain switching than on switching caused by electric fields. A quantitative analysis of spontaneous and remanent strain and polarization indicates that poling in the soft material is dominated by 180° domain processes, while non‐180° processes dominate the strain behavior. If the mechanical load exceeds a threshold level, the “hardening” effect of the acceptor doping vanishes, and hard and soft materials behave identically. The results are discussed based on the defect dipole model and the charge drift model for hardening and aging in acceptor‐doped ferroelectric ceramics.

In situ neutron diffraction studies of a commercial, soft lead zirconate titanate ceramic: response to electric fields and mechanical stress

Structural changes in commercial lead zirconate titanate (PZT) ceramics (EC-65) under the application of electric fields and mechanical stress were measured using neutron diffraction instruments at the Australian Nuclear Science and Technology Organisation (ANSTO) and the Oak Ridge National Laboratory (ORNL). The structural changes during electric-field application were measured on the WOMBAT beamline at ANSTO and include non-180° domain switching, lattice strains and field-induced phase transformations. Using time-resolved data acquisition capabilities, lattice strains were measured under cyclic electric fields at times as short as 30 μs. Structural changes including the (002) and (200) lattice strains and non-180° domain switching were measured during uniaxial mechanical compression on the NRSF2 instrument at ORNL. Contraction of the crystallographic polarization axis, (002), and reorientation of non-180° domains occur at lowest stresses, followed by (200) elastic strains at higher stresses.

Polarization switching process of soft lead zirconate titanate bulk ceramics

The domain switching dynamics was investigated in Nb-doped Pb(Zr 0.52Ti 0.48)O 3 bulk ceramics through observing systematically the evolution of the hysteresis loops at frequencies ranging from 0.01 to 100 Hz and in a field of 7.5–35 kV/cm. The experimental results indicate that the hysteresis loops are remarkably dependent on the fields and the frequencies. The data are analyzed by the Merz equation. The analysis results reveal that the requirement to satisfy the Merz equation is saturated loops. Based on these results, we divided the polarization switching process into three regions.

Artificial Neural Network Modeling of Ferroelectric Hysteresis: An Application to Soft Lead Zirconate Titanate Ceramics

In this work, the Artificial Neural Network (ANN) was used to model ferroelectric hysteresis using data measured from soft lead zirconate titanate [Pb (Zr1−xTix)O3 or PZT] ceramics as an application. Data from experiments were split into training, testing and validation dataset. Four ANN models were developed separately to predict output of the hysteresis area, remnant, coercivity and squareness. Each model has two neurons in the input layer, which represent field amplitude and field frequency. The ANNs were trained with varying number of hidden layer and number of neurons in each layer to find the best network architecture with highest accuracy. After the networks have been trained, they were used to predict hysteresis properties of the unseen testing patterns of input. The predicted and the testing data were found to match very well which suggests the ANN success in modeling ferroelectric hysteresis properties obtained from experiments.

Creep in Soft PZT: The Effect of Internal Fields

The effect of internal fields on the activation energy of creep in polycrystalline ferroelectric ceramics is investigated. It is shown that the internal fields can be evaluated directly from the experimental curves for polarization creep under constant electric field. For this purpose a micro-mechanical model of thermally activated ferroelectric switching is modified by taking into account the dependence of the activation energy on the internal fields within the framework of a phenomenological mean-field approximation. The modified model has the form of an Arrhenius type equation containing the structural parameters like the spontaneous polarization only via the effective fields acting on the domain walls. As an example, a rationalization of the experimental room-temperature creep curves in a soft lead zirconate titanate piezoceramic PZT-5H on the basis of the model is carried out. It is shown that the main part of the internal field, which is linear in the spontaneous polarization and responsible for the logarithmic creep, can be directly extracted from such data sets.

Nonlinear Dynamic Bending and Self-sensing of Clamped-Clamped Functionally Graded Piezoelectric Transducers under AC Voltage

We study numerically and experimentally the nonlinear dynamic bending and sensing behavior of clamped-clamped functionally graded piezoelectric transducers under alternating current (AC) voltage. The contribution of domain wall motion to the elastic compliance, piezoelectric coefficient and dielectric permittivity in soft lead zirconate titanate (PZT) layers is evaluated, and a nonlinear finite element analysis is performed to discuss the effects of the amplitude and frequency of input voltage, number of layers and property gradation on the sound pressure, output voltage, and internal stresses and electric field for the transducers. In order to confirm the numerical results, bending tests on functionally graded piezoelectric transducers are conducted, and the sound pressure and output voltage are measured.

Investigation of the additive induced doping effects in gelcast soft lead zirconate titanate ceramics

Due to the high sensitivity of the electrical properties of electronic ceramics to various factors, knowledge about the possible influence of the processing procedure on their electrical performance is critical for applying a new technique to the fabrication of the materials. In this study, various electrical parameters, complex impedance spectra, ferroelectric hysteresis loops, and microstructures of soft lead zirconate titanate (PZT) ceramics formed by the gelcasting technique from suspensions with various dispersants were investigated in comparison with those of the conventional dry pressed ones. We found that the sodium ion, which is the main cation in many commercial surfactants, exhibited obvious hard doping effects; thus causing deteriorated performance of the gelcast PZT ceramics. While a certain impurity ion introduced by a dispersant was also found to induce soft doping characteristics and improve the electrical performance of the materials. The results suggest that the doping effects of the metal ions or impurities introduced by the dispersants, or other additives, should be generally considered for applying a wet processing technique to forming multicomponent electronic ceramics.

Temperature-dependent ferroelastic switching of soft lead zirconate titanate

The longitudinal strain and polarization of a soft polycrystalline ferroelectric ceramic (lead zirconate titanate, PZT) were measured under uniaxial compressive stress at elevated temperatures utilizing a novel testing fixture. Ferroelectric ceramics have not previously been characterized under these conditions due to experimental complexity. In addition to nonlinear macroscopic constitutive behavior, the linear elastic moduli have been measured throughout the loading cycle, allowing for the determination of the relative contributions from the linear and nonlinear ferroelastic behavior as a function of stress and temperature. Experimental results show a strong temperature dependence of ferroelastic switching. The ferroelastic properties of unpoled and poled materials for temperatures up to the Curie point are contrasted with the spontaneous strain, elucidating the role of tetragonality in ferroelastic switching. When thermal changes are considered, marked changes in the maximum strain are observed.

Determination of temperature dependence of piezoelectric coefficients matrix of lead zirconate titanate ceramics by quasi-static and resonance method

The piezoelectric coefficients (d33, −d31, d15, g33, −g31, g15) of soft and hard lead zirconate titanate ceramics were measured by the quasi-static and resonance methods, at temperatures from 20 to 300 °C. The results showed that the piezoelectric coefficients d33, −d31 and d15 obtained by these two methods increased with increasing temperature for both hard and soft PZT ceramics, while the piezoelectric coefficients g33, −g31 and g15 decreased with increasing temperature for both hard and soft PZT ceramics. In this paper, the observed results were also discussed in terms of intrinsic and extrinsic contributions to piezoelectric response.

Temperature- and dc bias field- dependent piezoelectric effect of soft and hard lead zirconate titanate ceramics

The dc bias field-dependent piezoelectric coefficient d 33 of lead zirconate titanate ceramics (PZT5, PZT8 and P5H) were determined by a quasi-static method. It was found that piezoelectric coefficient d 33 was almost independent of positive dc bias field for PZT8 and PZT5 ceramics, while for P5H ceramic an obvious decrease of coefficient d 33 was observed under positive dc bias field. On the other hand, the temperature-dependent piezoelectric response for PZT ceramics were investigated by both quasi-static and resonance methods. The piezoelectric coefficient d 33 was found to increase with increasing temperature for both PZT5 and PZT8 ceramics. For P5H ceramics, coefficient d 33 showed a first decreasing and then increasing tendency with respect to temperature. These results were discussed in terms of intrinsic and extrinsic contributions to piezoelectric response.