Polycrystalline Ferroelectric Ceramics Research Articles

A micromechanics method to study the effect of domain switching on fracture behavior of polycrystalline ferroelectric ceramics

The effect of domain switching on anisotropic fracture behavior of polycrystalline ferroelectric ceramics was revealed on the basis of the micromechanics method. Firstly, the electroelastic field inside and outside an inclusion in an infinite ferroelectric ceramics is carried out by the way of Eshelby-Mori-Tanaka's theory and a statistical model, which accounts for the influence of domain switching. Further, the crack extension force (energyrelease rate) Gext for a penny-shape crack inside an effective polycrystalline ferroelectric ceramics is derived to estimate the averaged effect of domain switching on the fracture behavior of polycrystalline ferroelectric ceramics. The simulations of the crack extension force for a crack in a BaTiO3 ceramics are shown that the effect of domain switching must be taken into consideration while analyzing the fracture behavior of polycrystalline ferroelectric ceramics. These results also demonstrate that the influence of the applied electric field on the crack propagation is more profound at smaller mechanical loading and the applied electric field may enhance the crack extension in a sense, which are consistent with the experimental results.

Structural, dielectric and electrical properties of Sm-modified Pb(SnTi)O3 ferroelectric system

We have synthesized (Pb1-xSmx)(SnyTi1-y)1-x/4O3 (PSmST) polycrystalline ferroelectric ceramics with x = 005, 007, 01 and y = 0.45 by a solid-state reaction technique and performed preliminary X-ray diffraction (XRD) analysis, detailed temperature and frequency dependence dielectric measurements on them. The a.c. conductivity has been investigated over a wide range of temperature and the activation energy (E a.c) has also been calculated. It is observed that (i) the dielectric permittivity (e) and loss tangent (tan °) are dependent on frequency, (ii) the temperature of dielectric permittivity maximum shifts toward lower temperature side with the increase of samarium ion (Sm3) concentration at the Pb sites, and (iii) observed and calculated d-values of XRD patterns show that the compounds have been formed in orthorhombic single phase.

A statistical model prediction of effective electroelastic properties of polycrystalline ferroelectric ceramics with randomly oriented defects

In terms of the microstructure characteristics of polycrystalline ferroelectric ceramics, a statistical micromechanics model is employed to predict the effective electroelastic properties of polycrystalline ferroelectric ceramics with randomly oriented defects, such as voids and microcracks, by the method of Eshelby’s equivalent inclusion theory and Mori–Tanaka’s mean field concept. The model incorporates the effects of crystallographic domain switching under external mechanical or electric field and the randomly oriented defects on the macroscopic behaviors of the polycrystalline ferroelectric ceramics. The analytical predictions of BaTiO 3 polycrystalline ceramics are shown that the defects can enhance the effective piezoelectric properties but reduce the elastic properties, which are consistent with the experimental results.

A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics

A phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed. The framework of the law is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field that determines when non-linear response is possible. The size and shape of the switching surface in a modified electric field space remains fixed during non-linear behavior but its center moves around and thus is controlled by a kinematical hardening process. In general, the remanent polarization and the remanent strain are used as the internal variables that control how the center of the switching surface moves. However, the form presented in this paper has a one-to-one relationship between the remanent strain and the remanent polarization, simplifying the constitutive law and allowing remanent polarization to be used as the only internal variable controlling the kinematic effects. The constitutive law successfully reproduces hysteresis and butterfly loops for ferroelectric ceramics. The hysteresis and butterfly loops respond appropriately to the application of a fixed compressive stress parallel to the electric field. In addition, the law successfully handles remanent polarization rotation due to the application of electric field at an angle to the polarization direction.

Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics

In this paper, a general form for multi-axial constitutive laws for ferroelectric ceramics is constructed. The foundation of the theory is an assumed form for the Helmholtz free energy of the material. Switching surfaces and associated flow rules are postulated in a modified stress and electric field space such that a positive dissipation rate during switching is guaranteed. The resulting tangent moduli relating increments of stress and electric field to increments of strain and electric displacement are symmetric since changes in the linear elastic, dielectric and piezoelectric properties of the material are included in the switching surface. Finally, parameters of the model are determined for two uncoupled cases, namely non-remanent straining ferroelectrics and purely ferroelastic switching, and then for the fully coupled ferroelectric case.

Self-consistent modelling of non-linear effective properties of polycrystalline ferroelectric ceramics

A constitutive model for the non-linear effective behaviour of ferroelectric ceramics is presented. The model is developed on the basis of the effective medium approximation (EMA), which describes the interaction of the crystallites in a statistical way. Additionally, a particular simplified domain configuration within the crystallites and the possibility of domain wall motion are taken into account. In connection with a thermodynamic criterion for the domain wall displacement the volume fractions of the domains can be calculated dependent on the crystallite orientation and the applied load in a self-consistent manner. This mechanism leads to an extrinsic contribution to the effective behaviour. If the domain wall displacement is associated with energy dissipation the macroscopic behaviour is non-linear and hysteretic.

A statistical model for predicting effective electroelastic properties of polycrystalline ferroelectric ceramics with aligned defects

This work is focused on the analysis of the effects of domain switching and defects on the effective electroelastic properties of polycrystalline ferroelectric ceramics. On the basis of experimental results and the classical nucleation theory, a statistical micromechanics model is developed in order to describe the microstructural evolution of polycrystalline ferroelectric ceramics. Further, the methods of Eshelby’s equivalent inclusion and Mori–Tanaka’s mean field theory are used to predict the effective electroelastic properties of polycrystalline ferroelectric ceramics with aligned defects, taking the effects of the shapes of individual crystal and defect into consideration. Some numerical results for BaTiO 3 polycrystalline ceramics with aligned defects are carried out in order to illustrate the effects of the domain switching and defects on the effective electroelastic properties of polycrystalline ferroelectric ceramics. It has been shown that the simulations are in good agreement with the experimental results.

Effective electroelastic properties of polycrystalline ferroelectric ceramics predicted by a statistical model

The effective electroelastic properties and moduli of ferroelectric ceramics are calculated. Based on a statistical model, the effects of the shape of individual domain and crystallographic domain switching under an external field are firstly taken into consideration to predict the effective electroelastic constants. The model's prediction of the effective electroelastic properties and moduli of a BaTiO3 ceramic was found to be in agreement with the experimental results.

Time dependence of effective properties of polycrystalline ferroelectric ceramics

In this paper, based on Merz[7] experimental results and classical nucleation theory, a micromechanics statistical model is proposed to describe the relation between the special microstructure-level evolution phenomena-domain switching and macro-response. The polycrystalline ferroelectric ceramics treated as a composition of switched domain and unswitched domain, the approaches of Eshelby's equivalent inclusion and Mori-Tanaka's mean field theory are used to analyze and predict its effective electroelastic properties. The model can incorporate the effects of time dependence of domain switching and shape of individual crystalline. To the BaTiO 3 polycrystalline ceramics, the analytical results are in good agreement with the experimental results.

A micro-electro-mechanical model for polarization switching of ferroelectric materials

Ferroelectric and ferroelastic switching are the major source of nonlinearity and hysteresis in ferroelectric materials subjected to high electric field or mechanical stress. A computational micromechanics model for polycrystalline ferroelectric ceramics is developed based on consideration of the constitutive behavior of single crystals. This model simulates the tetragonal and the rhombohedral crystal structures. Saturation of the linear piezoelectric effect is included. Interaction between different grains in the polycrystalline ceramic is considered. A switching criterion is developed that accounts for different energy levels associated with 90° and 180° switching for the tetragonal structure (or 70.5°, 109.5°, and 180° for the rhombohedral structure). Experimental results on 8/65/35 PLZT are simulated and a parametric study of the effects of crystal structure, intergranular interaction, and phase transformation is performed.

The simulation of switching in polycrystalline ferroelectric ceramics

A polarization switching model for polycrystalline ferroelectric ceramics has been developed. It is assumed that a single ferroelectric crystallite in a ceramic, which is subjected to an electric field and/or a stress, undergoes a complete polarization change and a corresponding strain change if the resulting reduction in potential energy exceeds a critical value per unit volume of switching material. The crystallite’s switch causes a change in the interaction of its field and stress with the surrounding crystallites, which is modeled by the Eshelby inclusion method to provide a mean field estimate of the effect. Thus the model accounts for the effects of the mean electric and stress fields arising from the constraints presented by surrounding crystallites as well as the externally applied mechanical and electrical loads. The switching response of the ceramic polycrystal is obtained by averaging over the behavior of a large number of randomly oriented crystallites. The model, along with the linear dielectric, elastic, and piezoelectric behavior of the material, is implemented in a computer simulation. A fit to experimental electric displacement versus electric field, strain versus electric field, and strain versus stress curves of a ceramic lead lanthanum zirconate titanate PLZT at room temperature is used to obtain material parameters. The model then successfully predicts the electric displacement and strain hysteresis loops for the PLZT under varying electric fields with a constant applied stress.

A Model for Simulating Polarization Switching and AF-F Phase Changes in Ferroelectric Ceramics

A computational micromechanics model for polycrystalline ferroelectric ceramics developed by Chen and Lynch (1997) is modified and applied to the simulation of ferroelectric and ferroelastic switching of the tetragonal and the rhombohedral crystal structures, and to antiferroelectric to ferroelectric phase changes. Interactions between different grains in the ceramic are considered. Two switching criteria are used, one for ferroelectric switching and one or phase changes. Experimental results for both types of materials are simulated.

Modeling of domain switching in ferroelectric ceramics: An example

The authors have recently proposed a continuum model for domain switching in polycrystalline ferroelectric ceramics in which each crystallite is modeled as a mixture of various domains characterized by their mass fractions, and domain switching corresponds to changes of the mass fractions of the corresponding domains. In order to explore the implications of this model, the authors present the explicit solution to an idealized one-dimensional ferroelectric system. The solution indicates that the orientation misalignment of crystallites results in a local electric field of strong inhomogeneity. The local electric field does not necessarily vanish in the absence of an externally applied electric field and its magnitude at certain locations can be substantially larger than that of the externally applied electric field. With a postulated domain switching criterion, the model produces the hysteretic response of the macroscopic polarization to the applied electric field due to local domain switching.

The prediction of switching in polycrystalline ferroelectric ceramics

A computer simulation for three dimensional polarization switching in a polycrystalline tetragonal ferroelectric ceramic is developed. The method is used to predict the electric displacement and strain of a polycrystalline ferroelectric ceramic under electromechanical load. The model is fitted to experimental strain versus electric field and strain versus stress curves of a ceramic lead lanthanum zirconate titanate (PLZT) at room temperature. Depolarizations of a poled ceramic are predicted when axial stress and a fixed field are applied parallel to the polarization direction and either uniaxial stress or shear stress is applied perpendicular to the poled direction. Simulated electric displacement versus electric field hysteresis loops and the corresponding strain versus electric field butterfly loops are given with uniaxial stress and shear stress applied perpendicular to the polarization of the poled ceramic.

A finite element model of ferroelectric polycrystals

A finite element model of polarization switching in polycrystalline ferroelectric ceramics is developed. A polarization switch in a ferroelectric is the reorientation of the unit cell dipole to a new crystallographic direction. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. The crystallite's transformation causes a disruption of the local field which is computed by the finite element method. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model involves electric field induced (i.e., ferroelectric) switching and strain effects are neglected. Different values for the energy barrier to the switch are selected to model the electric displacement versus electric field hysteresis loop of a ceramic lead lanthanum zirconate titanate (PLZT) at room temperature and a best fit is obtained.

Modeling of domain switching in polycrystalline ferroelectric ceramics

This paper is concerned with the modeling of domain switching in polycrystalline ferroelectric ceramics. In the present analysis, each grain is modeled as a mixture, consisting of distinct types of domains which are characterized by their mass fractions as internal variables. Domain switching corresponds to changes of mass fractions of the corresponding domains, and the driving force of domain switching is the difference in Gibbs' energies. A thermodynamics-based criterion is proposed to govern domain switching in quasi-static processes. Some numerical results for an idealized one-dimensional ferroelectric system are included to illustrate the polycrystalline effect on the grain-level electric field distribution and the polarization response to applied electric fields.

Modeling of domain pinning effect in polycrystalline ferroelectric ceramics

Abstract Experimental observations indicate that electric fatigue of polycrystalline ferroelectric ceramics is partially recoverable through thermal treatments at temperatures that are too low to heal microcracking which is considered to be the primary cause of electric fatigue. It has been conjectured that this thermally-recoverable fatigue is due to domain pinning. This paper presents a theoretical model for the domain pinning effect on macroscopic properties of polycrystalline ferroelectric ceramics. The numerical results suggest that domain pinning can indeed lead to the type of fatigue behavior as observed.

Microcracking and electric fatigue of polycrystalline ferroelectric ceramics

The major obstacle preventing ferroelectric actuators from enjoying wide application is the so-called electric fatigue which results in reduction of actuation displacement/force after actuators have been subjected to many cycles of applied electric field. Experimental observations reveal that fatigued specimens often contain scattered microcracks, and hence suggest that microcracking may be the cause of electric fatigue. This paper presents a theoretical model developed within the framework of continuum electrodynamics for deformable dielectrics, to study the microcracking effect upon macroscopic properties of polycrystalline ferroelectric ceramics. The numerical results indicate that microcracking can indeed cause the observed fatigue behavior.

Sintering and characterization of Bi4Ti3O12 ceramics

Polycrystalline ferroelectric Bi4Ti3O12 ceramics have been prepared by the method of reactive liquid phase sintering. The sintering behaviour of the Bi2O3-TiO2 composite was examined by plotting the isothermal densification curves. The results indicate that the starting oxides are involved in the reaction even at temperatures lower than or equal to 800°C, but the reaction advances at a very slow rate. Above solidus, the liquid phase promotes an extended reaction. Saturation observed in two densification curves, at 875 and 1100°C demonstrate that the reaction proceeds by two steps. A completion of the Bi4Ti3O12 formation occurs after 60 min of sintering at 1100°C. Optical micrographs of sintered bismuth titanate ceramics show randomly oriented ferroelectric grains separated by a paraelectric intergranular layer. The Bi4Ti3O12 crystallites exhibit a platelike morphology, similar in the appearance to mica, as evidenced by scanning electron micrographs. Isothermal annealing (750 to 950°C) does not affect the microstructure and electric properties of sintered bismuth titanate. The considerable value of dielectric permittivity and the appearance of hysteresis have been correlated to the presence of oxygen vacancies within the pseudotetragonal structure of Bi4Ti3O12. The oxygen vacancies are preferentially sited in the vicinity of bismuth ions as evidenced by X-ray photoemission data. XPS and AES measurements confirm that the surface concentration of cations comprising the Bi4Ti3O12 ceramics does not deviate from the nominal bulk composition.

LOW FREQUENCY DIELECTRIC PROPERTIES OF PZT-8 FERROELECTRIC PIEZOELECTRIC CERAMICS

This article presents results of our studies on PZT-8 polycrystalline ferroelectric ceramics of lead zirconate titanate. We have measured the dielectric constant and dielectric loss over a low frequency range (from . 100kHz-20MHz) and temperature range from room temperature to 500℃. The mechanism of dielectric loss, the relaxation process and the impurity effects are discussed. The main loss above Tc is attributed to conducting loss.We also propose some suggestions for improving electrical properties of PZT-8 ferroelectric ceramics.