Unpoled Material Research Articles

Depolarization field effect on elasticity of unpoled piezoelectric ceramics

Multiple poling steps and complex electrode configurations are indispensable for high-performance state-of-the-art piezoelectric devices, yet those create partially poled or utterly unpoled regions that significantly change behaviors of piezoelectric devices. Several studies have dealt with method to obtain elastic compliance, yet little attention has been paid to method to obtain elastic loss. Furthermore, physical mechanism to explain the behavior of unpoled piezoelectric ceramic is missing. In this study, we experimentally obtain both effective elastic compliance and elastic loss of unpoled piezoelectric ceramics, using recently developed method called partial electrode (PE), and propose physical mechanism to explain the elasticity. The derivation process for analytical admittance equation for PE is explained and verified with finite element analysis (FEA) simulation. The complex elastic compliance was determined by fitting experimental admittance curve with derived analytical solutions. With the aid of intensive and extensive elastic compliances and elastic losses, we concluded that elasticity of unpoled piezoelectric material lies in between intensive-ness and extensive-ness. We explained this “elastic intermediacy” with depolarization field effect, which is one of the most important phenomena in piezoelectricity.

Temperature-dependent anhysteretic behavior of co-doped PZT

The anhysteretic behavior of a soft Pb(Zr,Ti)O3 was measured from 25 °C to 175 °C. The experimental determination of the anhysteretic polarization curve, combined with classical P-E and S-E loop measurements, allows for an experimental separation of the reversible and dissipative contributions to the ferroelectric behavior. This approach offers insight into the different mechanisms originating at the microscopic scale and the contribution to the macroscopic ferroelectric properties. It was found that the reversible anhysteretic susceptibility χa of the unpoled material increases by 30% from room temperature to 150 °C. On the other hand, the effect on the total susceptibility for a null polarization χc increases only by 17% over the same temperature range. Since the difference between χa and χc reflects the dissipative contribution to the macroscopic ferroelectric behavior, this reveals that dissipation reduces the improvement of susceptibility under increasing temperature. This work illustrates the benefits of separating experimentally the reversible and dissipative contributions to describe the ferroelectric behavior, which can serve as a basis for advanced modeling approaches.

Electric field-induced changes in the ferroelastic behavior of (Na1/2Bi1/2)TiO3-BaTiO3

In this study, the macroscopic mechanical behavior was characterized for poled and unpoled polycrystalline (1−x)(Na1/2Bi1/2)TiO3-xBaTiO3 (NBT-xBT) for compositions across the morphotropic phase boundary (MPB). Due to a field-induced ferroelectric phase transformation, NBT-xBT compositions near the MPB (x = 6–7 mol%) showed a significant decrease in the coercive stress for electrically poled samples. The apparent difference in mechanical behavior is suggested to be due to an irreversible electric-field-induced transformation to long-range ferroelectric order in the poled samples. The results indicate a significant difference in the critical stresses for the relaxor-ferroelectric transition and ferroelastic domain wall motion, which can have important effects on applications for lead-free ferroelectrics. To further illustrate this, a method was developed to electrically depole NBT-xBT at room temperature, resulting in an unpoled NBT-xBT material with long-range ferroelectric order. Mechanical testing revealed analogous macroscopic ferroelastic behavior to the poled samples, despite the lack of a piezoelectric response.

Quantitative evaluation of the piezoelectric response of unpoled ferroelectric ceramics from elastic and dielectric measurements: Tetragonal BaTiO3

A method is proposed for evaluating the potential piezoelectric response, that a ferroelectric material would exhibit after full poling, from elastic and dielectric measurements of the unpoled ceramic material. The method is based on the observation that the softening in a ferroelectric phase with respect to the paraelectric phase is of piezoelectric origin, and is tested on BaTiO3. The angular averages of the piezoelectric softening in unpoled ceramics are calculated for ferroelectric phases of different symmetries. The expression of the orientational average with the piezoelectric and dielectric constants of single crystal tetragonal BaTiO3 from the literature reproduces well the softening of the Young's modulus of unpoled ceramic BaTiO3, after a correction for the porosity. The agreement is good in the temperature region sufficiently far from the Curie temperature and from the transition to the orthorhombic phase, where the effect of fluctuations should be negligible, but deviations are found outside this region, and possible reasons for this are discussed. This validates the determination of the piezoelectric response by means of purely elastic measurements on unpoled samples. The method is indirect and, for quantitative assessments, requires the knowledge of the dielectric tensor. On the other hand, it does not require poling of the sample, and therefore is insensitive to inaccuracies from incomplete poling, and can even be used with materials that cannot be poled, for example, due to excessive electrical conductivity. While the proposed example of the Young's modulus of a ceramic provides an orientational average of all the single crystal piezoelectric constants, a Resonant Ultrasound Spectroscopy measurement of a single unpoled ceramic sample through the ferroelectric transition can in principle measure all the piezoelectric constants, together with the elastic ones.

A new method to determine the un-poled elastic properties of ferroelectric materials

Piezoelectric devices with complex electrode geometries often contain ferroelectric regions that experience little or no electric field and remain unpolarised. Since the un-poled and poled material properties differ it is desirable to account for these regions in a device when developing predictive models or to design piezoelectric transducers. The lack of published data on the elastic properties for un-poled ferroelectrics, specifically the numerous commercial compositions such as lead zirconate titanate, reflects the difficulty of experimental measurement. In this work, a method for predicting un-poled properties from more commonly available poled data has been developed. A new method of calculating these properties is presented which provides a rapid and practical solution to the problem of evaluating the isotropic stiffness and Poisson’s ratio for an un-poled ferroelectric material. The way in which this calculation has been derived and validated is presented and detailed comparisons are made with alternative methods and experimental data.

Aging in the relaxor and ferroelectric state of Fe-doped (1-x)(Bi1/2Na1/2)TiO3-xBaTiO3 piezoelectric ceramics

Aging of piezoelectric properties was investigated in lead-free (1 − x)(Bi1/2Na1/2)TiO3-xBaTiO3 doped with 1at. % Fe. The relaxor character of the un-poled material prevents macroscopic aging effects, while in the field-induced ferroelectric phase aging phenomena are similar to those found in lead zirconate titanate or barium titanate. Most prominent aging effects are the development of an internal bias field and the decrease of switchable polarization. These effects are temperature activated, and can be explained in the framework of defect complex reorientation. This picture is further supported by electron paramagnetic resonance spectra indicating the existence of (FeTi′−VO••)• defect complexes in the Fe-doped material.

Microstructural modelling of the polarization and properties of porous ferroelectrics

Micromechanical models of porous ferroelectric ceramics have often assumed that thematerial is fully polarized in a particular direction and/or consists of a single isolated pore.In this work the polarization state in three-dimensional porous polycrystalline ferroelectricnetworks has been modelled to eradicate the oversimplification of these idealized unit cells.This work reveals that microstructural network models more closely represent a porousferroelectric microstructure since they are able to take into account the complexpolarization distribution in the material due to the presence of high and low permittivityregions. The modelling approach enables the prediction of the distribution ofpoled and unpoled material within the structure. The hydrostatic figures of meritand permittivity were determined for a variety of porous lead zirconate titanatemicrostructures and found to be in good agreement with experimental data. The decreasein piezoelectric activity with porosity was observed to be associated with thecomplex polarization state within the material. Model results were shown to bemuch improved when compared to a model assuming a fully polarized model.

Evolving morphotropic phase boundary in lead-free (Bi1/2Na1/2)TiO3–BaTiO3 piezoceramics

The correlation between structure and electrical properties of lead-free (1−x)(Bi1/2Na1/2)TiO3–xBaTiO3 (BNT-100xBT) polycrystalline piezoceramics was investigated systematically by in situ synchrotron diffraction technique, combined with electrical property characterization. It was found that the morphotropic phase boundary (MPB) between a rhombohedral and a tetragonal phase evolved into a morphotropic phase region with electric field. In the unpoled material, the MPB was positioned at the transition from space group R3m to P4mm (BNT-11BT) with optimized permittivity throughout a broad single-phase R3m composition regime. Upon poling, a range of compositions from BNT-6BT to BNT-11BT became two-phase mixture, and maximum piezoelectric coefficient was observed in BNT-7BT. It was shown that optimized electrical properties are related primarily to the capacity for domain texturing and not to phase coexistence.

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.

Dielectric breakdown of an unpoled piezoelectric material with a conductive channel

ABSTRACTThe dielectric breakdown of an unpoled piezoelectric ceramic, PZT807, with a conductive channel, is investigated. Cylindrical bar specimens with a conductive channel are used for breakdown tests of the unpoled piezoelectric ceramic under purely electrical loads. Narrow tubular channels emanating from the head of the initial channel are observed in the specimens after breakdown occurs. The radius of the tubular channel that is created at the surface of the initial channel head is insensitive to various types of channel formation. The problem of a fine tubular channel that emanates from the initial channel head is numerically solved to evaluate the three‐dimensional J integral, which is directly related to the energy that is available at breakdown, at the initiation of a new channel in the specimen. The critical J integral at the onset of breakdown is obtained.

Indentation strength of a piezoelectric ceramic: Experiments and simulations

The spherical indentation strength of a lead zirconate titanate (PZT) piezoelectric ceramic was investigated under poled and unpoled conditions and with different electrical boundary conditions (arising through the use of insulating or conducting indenters). Experimental results show that the indentation strength of the poled PZT is higher than that of the unpoled PZT. The strength of a poled PZT under a conducting indenter is higher than that under an insulating indenter. Poling direction (with respect to the direction of indentation loading) did not significantly affect the strength of material. Complementary finite element analysis (FEA) of spherical indentation of an elastic, linearly coupled piezoelectric half-space is conducted for rationalizing the experimental observations. Simulations show marked dependency of the contact stress on the boundary conditions. In particular, contact stress redistribution in the coupled problem leads to a change in the fracture initiation, from Hertzian cracking in the unpoled material to subsurface damage initiation in poled PZT. These observations help explain the experimental ranking of strength the PZT in different material conditions or under different boundary conditions.

A Note on Tensile Testing of Poled and Unpoled Piezoelectric Ceramics

Abstract: Tensile tests were carried out on unpoled and poled soft lead zirconate titanate (PZT) ceramic materials: APC #855 (APC International) and PZT‐5H (Morgan Electro Ceramics). The tests were performed on a dog‐bone specimen with holes at its edges. A methodology is presented for carrying out these tests. A tensile stress was applied by means of Kevlar strings through the specimen holes. The poling direction was perpendicular to the longitudinal specimen axis. For the poled specimens, two electrical boundary conditions were applied, namely, E = 0 and D = 0. Strains were measured at four points on the sample. For each specimen, the bending percentage was calculated. For all specimens, stress–strain curves were found to be initially linear; at a strain of approximately 0.0001, the curves became nonlinear. Young’s modulus was measured in the linear region of the stress–strain curve. Young’s modulus values were highest for the poled material with an open circuit boundary condition (D = 0) and lowest for the unpoled material.

Micromechanical modeling and simulation of rate-dependent effects in ferroelectric polycrystals

In this contribution, rate-dependent switching effects of ferroelectric materials are studied by means of a micromechanically motivated approach. The onset of domain switching is thereby initiated based on the reduction in Gibbs free energy by means of energy-based criterion. The subsequent nucleation and propagation of domain walls during switching process are incorporated via a volume fraction concept combined with a simple linear kinetics theory. The key aspect in modeling of the interaction between the individual grains (intergranular effects) are incorporated in this model by making use of a probabilistic ansatz; to be specific, a phenomenologically motivated Weibull distribution function is adopted. The developed framework is incorporated into a finite element formulation whereby each domain is represented by a single finite element and initial dipole directions are randomly oriented so that the virgin state of the particular bulk ceramics of interest reflects an un-poled material. Based on a staggered iteration technique and straightforward volume averaging concept, the model is simulated to capture the non-linear behavior for different loading, for various loading amplitudes and frequencies. Attributes of the model, both symmetric major loops and biased minor loops are illustrated through examples. Simulation results for the rate-independent case are in good agreement with experimentally measured data reported in the literature and, moreover, are extended to rate-dependent computations which captures some important insights.

Raman scattering investigation of poled and unpoled PbMg1/3Nb2/3O3-PbTiO3single crystals and textured ceramics

Relaxor ferroelectrics PbMg1/3Nb2/3O3-PbTiO3single crystals exhibit outstanding electromechanical properties and are potential materials for sonar applications. Since the methods of obtaining large single crystals are very expensive, the low cost textured ceramics are a very good alternative. Poled (FC or RT) and unpoled PMN-29%PT (single crystals) and PMN-34.5%PT (textured ceramics, L= 0.9) were investigated. The Rayleigh lines and Raman modes were studied between 20 and 240°C. The temperature dependences of intensities, frequencies and FWHMs were used to better understand the phase transitions. Differences are evidenced for poled and unpoled materials in good agreements with the thermal expansion and dielectric results. Although NbO6 sublattice remains stable over the 20-240°C temperature range, a continuous softening of the TiO6 and step transitions of the Pb2+ sublattices are evidenced. Rayleigh wings intensity appears sensitive to the nanostructure rearrangement.

Thermal diffusivity by laser intensity modulation method (LIMM-TD): a novel technique for the determination of thermal diffusivities and conductivities and its application to porous PZT and silica samples

A modification of a technique for the measurement of the thermal diffusivity of thin solid materials is presented. The technique is called Thermal Diffusivity by Laser Intensity Modulation Method (LIMM-TD). It is based on the measurement of the phase retardation of a thermal wave passing through the test material by means of a lead-zirconate-titanate ceramic (PZT) pyroelectric detector. It is not necessary to know either the pyroelectric coefficient of the detector or the intensity of the laser beam. The method was tested on quartz samples to verify its accuracy. It was then applied to the study of several sets of ceramic samples with porosities of 20, 25, and 30%. One sample set was poled and the pores were partially filled with the fluid used during poling. A second set was not poled. The poled porous samples had thermal conductivities intermediate between that of a commercial dense sample and those of unpoled materials. Thermal diffusivities and conductivities were also measured on micron-thickness porous silica samples. The experimental results were compared with calculations using several composite mixing theories.

Effective elastic properties for unpoled barium titanate

Piezoelectric devices with complex electrode geometries may contain regions of ferroelectric material that remain unpoled. It is desirable to account for these non-piezoelectric regions for device optimization, since the unpoled and poled material properties differ. The lack of published elastic properties for unpoled ferroelectrics, specifically the numerous commercial PZT compositions, reflects the difficulty of experimental measurement. In this work, a method was developed to predict unpoled properties from more commonly available poled material data. Barium titanate was chosen for study as a representative ferroelectric, with both single crystal and polycrystalline (ceramic) properties available. Finite element micro-mechanical models were created with a focus on computational economy. This allowed larger ensembles of results to be computed, providing accurate effective compliances when averaged. The modelling methodology predicted the elastic properties for unpoled barium titanate to within ∼10% of measured experimental values.

On the fracture toughness of ferroelectric ceramics with electric field applied parallel to the crack front

Mode I steady crack growth is analyzed to determine the toughening due to domain switching in ferroelectric ceramics with electric field applied parallel to the crack front. A multi-axial, electromechanically coupled, incremental constitutive theory is applied to model the material behavior of the ferroelectric ceramic. The constitutive law is then implemented within the finite element method to study steady crack growth. The effects of electric field on the fracture toughness of both initially unpoled and poled materials are investigated. Results for the predicted fracture toughness, remanent strain and remanent polarization distributions, and domain switching zone shapes and sizes are presented. The effects of the plane-strain constraint and transverse stress are also established. Finally, the model predictions are discussed in comparison to recent experimental observations.

Electrical fracture toughness for a conducting crack in ferroelectric ceramics

Conducting cracks in ferroelectric ceramics under purely electrical loading are analyzed to investigate the effects of electric fields on fracture behavior. The asymptotic problem of conducting cracks in a mono-domain ferroelectric material as well as in a poly-domain ferroelectric material is considered and the relation between the crack tip stress intensity factor and the applied intensity factor of electric field under small scale conditions is investigated. In order to evaluate the crack tip stress intensity factors due to the domain switching, the shape of the domain switching zone attending the crack tip must be determined. The evaluation of the shape is carried out based on the nonlinear domain switching model. It is shown that the switching zone boundary and the crack tip stress intensity factors due to the switching depend strongly on the angle of the polarization vector and the ratio of the coercive electric field to the yield electric field. The electrical fracture toughness of unpoled poly-domain ferroelectrics is examined. Employing a Reuss type approximation, the crack tip stress intensity factors for an unpoled poly-domain material are obtained. The ratio of the critical electrical energy release rate to the critical mechanical energy release rate is obtained.

R-curve effect, influence of electric field and process zone in BaTiO3 ceramics

Abstract Double cantilever beam (DCB) specimens were used to measure fracture toughness and R-curve effect of coarse grained BaTiO 3 doped with 0.5 mol% TiO 2 and fine grained BaTiO 3 doped with 1.5 mol% La 2 O 3 and 3.3 mol% TiO 2 . The coarse grained BaTiO 3 had an average grain size of 20 μm compared to 0.4 μm for the fine grained material. Coarse grained BaTiO 3 showed increasing crack resistance with rising crack length for crack elongations up to 2 mm. The R-curve behaviour can be attributed to mechanisms shielding the crack tip from applied loads, such as ferroelastic domain switching in a process zone ahead of the crack tip, which was observed in situ. Since domain switching events left a pattern on the polished surface of the DCB specimen, it was possible to visualise the domain switching during crack propagation using Nomarski differential interference contrast. The method allowed to measure the size and shape of the process zone in unpoled and poled material. The maximum width of the process zone was 120 μm in both cases but the spatial distribution of switching events showed remarkable differences. An electrical DC field applied to the DCB samples while the cracks were propagating promoted crack growth in coarse grained, unpoled samples. In specimens poled perpendicularly to the crack, a rising toughness was found, if negative electric fields were applied. Fine grained samples were not affected by electrical fields of up to 1 kV/mm.

Polarization measurements on PZT under transverse tensile loading

The present paper deals with the influence of uniaxial tensile stresses on polarization of a commercial soft PZT ceramic. It is found that for an electric field of E < 0.75 kV/mm the polarization in field direction of the initially unpoled material increases under tensile stresses acting normally to the applied electric field. Above 0.75 kV/mm, the polarization under the tensile stresses is slightly lower than the polarization in unstressed specimens. For initially poled PZT depolarization occurs under tensile stresses acting perpendicularly to the poling direction. This effect is small if an electrical field is applied in poling direction, but increases strongly for an electric field applied against the poling direction.