Domain switching in polycrystalline ferroelectric ceramics

Ferroelectric ceramics are widely used as sensors and actuators for their electro-mechanical properties, and in electronic applications for their dielectric properties. Domain switching--the phenomenon wherein the ferroelectric material changes from one spontaneously polarized state to another under electrical or mechanical loads--is an important attribute of these materials. However, this is a complex collective process in commercially used polycrystalline ceramics that are agglomerations of a very large number of variously oriented grains. As the domains in one grain attempt to switch, they are constrained by the differently oriented neighbouring grains. Here we use a combined theoretical and experimental approach to establish a relation between crystallographic symmetry and the ability of a ferroelectric polycrystalline ceramic to switch. In particular, we show that equiaxed polycrystals of materials that are either tetragonal or rhombohedral cannot switch; yet polycrystals of materials where these two symmetries co-exist can in fact switch.     

Combined isotropic and kinematic hardening in phenomenological switching models for ferroelectric ceramics

A phenomenological model for ferroelectric switching is presented in this paper. The model is based on ideas of plasticity. A switching surface is used as the criterion for non-linear response of the material. Hardening models are used to control the size and position of the switching surface in electric field space. The distinctions between kinematic, isotropic and combined hardening models are discussed. The predicted response to electric loading is computed using combinations of isotropic and kinematic hardening. The calculated hysteresis loop and poling curve are in good agreement with experimental data.     

铁电陶瓷中电畴翻转研究进展

电畴为铁电陶瓷固有的独特微观组织特征之一,铁电陶瓷的许多性能均与其密切有关.综述了铁电陶瓷中的电畴结构,系统介绍了电场、机械作用引起的电畴翻转,概述了电畴翻转对铁电陶瓷断裂韧性的影响及其研究进展.     

Numerical analysis of ferroelectric/ferroelastic domain switching in ferroelectric ceramics

A numerical approach predicting the behavior of ferroelectric ceramics under electric field and mechanical loading is proposed in this paper. In the model, macroscopic properties of ferroelectric ceramics are determined by microscopic structures. Ferroelectric ceramics are seen to be composed of many domains with different orientations, and domain switching is the source of the nonlinear constitutive behavior of the ferroelectric ceramics. Numerical calculations based on the model were carried out, and the computational results are compared with the experimental results, which shows the two sets of results consist with each other. The calculation approach can provide a guidance for the ceramics component design.     

Nanoscale domain switching behaviour in polycrystalline ferroelectric thin films

We report on the nanoscale domain switching behaviour in polycrystalline tetragonal perovskite lead zirconate titanate (PZT) ferroelectric thin films investigated via piezoresponse force microscopy (PFM). Local domain structures were imaged as a function of varying biasing conditions and spatial location of the tip within 50-100?nm sized grains. Nanoscale piezoresponse images provided direct visual evidence of the complex interplay between electrical and mechanical fields in a polycrystalline system, which causes effects such as correlated switching between the grain of interest and neighbouring grains, ferroelastic domain switching, inhomogeneous piezostrain profiles and domain pinning on very minute length scales. Detailed investigations on mechanisms which induce such domain behaviour are presented.     

Variations in predicting domain switching of ferroelectric ceramics

In this article, a set of equivalent variational formulations for computing the driving forces for domain switching in ferroelectric materials is presented. It is proven that these formulations allow the free adoption of any couple of mechanical and electric fields as independent variables while obtaining consistent results. In addition, explicit expressions are provided for each formulation which allows for the study of the phase transformation process under different constraints.     

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.     

An evaluation of a class of phenomenological theories of ferroelectricity in polycrystalline ceramics

Various phenomenological theories of ferroelectricity in polycrystalline ceramics have been proposed in recent years. A particularly attractive class of multiaxial theories with a reduced number of internal variables hinges upon an additive decomposition of the strain and the dipole density into reversible internal variables associated with elasticity and dipole perturbations, and irreversible internal variables associated with dipole switching. It has, however, been recently recognized that these theories can provide unexpected predictions for certain—yet unexceptional—loading histories. The source of the problem was pinned down to the nonconvex dependence of the internal energy on the irreversible variables. The purpose of the present study is to evaluate this more thoroughly. It is found that predictions become unstable above a certain level of mechanical stress, which can be on the order of a few megapascals or even lower for typical sets of material parameters employed in the literature. It is argued that this class of theories should be used with caution, even within their presumed range of validity.     

Domain switching in ferroelectric single crystal/ceramics under electromechanical loading

Domain switching in PMN-PT single crystal and PZT-5 ceramics under electromechanical loading were studied in two different ways. For the single crystal, domain switching was in situ investigated with polarized light microscopy. A 90° domain-switching zone was observed near the crack tip and the size of the switching zone changed with the acuity of the crack tip. For PZT-5 ceramics, domain switching under orthogonal electromechanical loading (E₃ and compressive stress σ₁₁) was studied by measuring the hysteresis loops, butterfly curves and reversed butterfly curves (₁₁ versus E₃). Experimental results show that 90° domain switching is suppressed in the planes parallel to the compression direction. A domain-switching model dividing each 180° switching to two successive 90° switching was proposed to explain the experimental results.     

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

Summary 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.     

Effect of composition on rate dependence of ferroelastic/ferroelectric switching in perovskite ceramics

Abstract

The process of ferroelectric/ferroelastic switching is rate dependent as evidenced by the frequency dependence of the coercive field/stress in polarisation/strain–electric field/stress loops. The rate dependence of domain switching has been investigated in different compositions of ferroelectric/ferroelastic perovskites by studying their stress–strain hysteresis loops. Stress–strain loops were generated by applying a static compressive load and then superimposing cyclic compressive loads of different amplitudes and frequencies. The stress–strain loops were fitted using a Rayleigh type relationship, whose parameters characterise the intrinsic and extrinsic contributions to the strain. Using these parameters, the rate dependence of the extrinsic domain wall contribution was investigated.     

Preparation of polycrystalline BaTi2O5 ferroelectric ceramics

Polycrystalline BaTi₂O₅ (BT₂) was prepared by solid state sintering in air using BaCO₃ and TiO₂ as starting materials. A rod-like BT₂ sintered bodies in a single phase were obtained above 1025 °C by adding 5 wt.% B₂O₃. The densification of BT₂ sintered bodies decreased with increasing sintering temperature. The maximum permittivity of BT₂ sintered body was 640 at the Curie temperature (T_c) of 461 °C and the frequency of 100 kHz. The addition of B₂O₃ was effective to obtain BT₂ in a single phase at low temperatures with elongated microstructure and to improve the permittivity, indicating the formation of preferred orientation at low temperature was related with liquid-phase sintering mechanism.     

Developments in ferroelectric ceramics for capacitor applications

A brief overview of the materials and processes for making ceramic capacitors based on BaTiO₃ and relaxor ferroelectric compositions is presented with special emphasis on more recent developments.     

A phenomenological law for complex granular materials from Mohr-Coulomb theory

Manipulating powders still entails some clumsy and risky operations even now in the middle of the fourth industrial revolution. This is because there is a lack of well-understood theory about granular matter due to its ravelled complexity. However, granular matter is the second most handled material by man after water and is thus ubiquitous in daily life and industry only after water. Since the eighteenth century, mechanical and chemical engineers have been striving to manage the many difficulties of grain handling, most of which are related to flow problems. Many continuum models for dense granular flow have been proposed. Herein, we investigated Mohr–Coulomb failure analysis as it has been the cornerstone of stress distribution studies in industrial applications for decades. This research gathers over 130 granular materials from several industrial sectors, as varied as cement and flour, including raw materials, food, pharmaceuticals, and cosmetics. A phenomenological law derived from the yield locus and governed exclusively by one dimensionless number from adhesive interactions has been found. Surprisingly, and in contrast to the common perception, flow in the quasi-static regime is actually independent of the friction, the packing fraction and any other grains/bulk intrinsic properties. The simplicity and accuracy of the model are remarkable in light of the complex constitutive properties of granular matter.     

The influence of fabrication processing on domain structure and polarization switching in PZN-based ferroelectric ceramics

Lead zinc niobate (Pb(Zn_1/3Nb_2/3)O₃, PZN) based ceramics are prepared by using conventional mixing oxide and complex phase reaction-sintering ceramic techniques. From the results of X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM), it is clear that these two fabrication processing routes produce different microstructures and ferroelectric domains in the same Pb(Zn_1/3Nb_2/3)O₃–BaTiO₃–Pb(Zr_0.4Ti_0.6)O₃ composition. Furthermore, different phase transitions are observed for the temperature dependence of the dielectric permittivity that can be confirmed by differential scanning calorimetry (DSC). Different polarization switching characteristics are also examined by using high field-induced strain and ferroelectric hysteresis loop. It is suggested that the distribution of the inner stress and domain configuration should be related with the fabrication processing of ferroelectric ceramics.     

A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material’s properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions.     

Memory switching in polycrystalline silicon films

Non-volatile memory switching has been observed in polycrystalline silicon layers produced by chemical vapor deposition. Evidence for filamentary conduction is found for devices which are in their low impedance state. Devices have been cycled through high and low impedance states up to a maximum of 2x10⁴ times. Exposure to transient ionizing electron radiation caused the devices to switch to their low impedance state.     

A constitutive model for fcc crystals with application to polycrystalline OFHC copper

Based on the results of a series of experiments on commercially pure OFHC copper (an fcc polycrystal), a physically based, rate- and temperature-dependent constitutive model is proposed for fcc single crystals. Using this constitutive model and the Taylor averaging method, numerical calculations are performed to simulate the experimental results for polycrystalline OFHC copper. The model calculation is based on a new efficient algorithm which has been successfully used to simulate the flow stress of polycrystalline tantalum over broad ranges of temperature, strain rate, and strain (Nemat-Nasser, S., Okinaka, T., Ni, L., 1998. J. Mech. Phys. Solids 46, 1009). The model effectively simulates a large body of experimental data, over a broad range of strain rates (0.001–8000 s⁻¹), and temperatures (77–1096 K), with strains close to 100%. Few adjustable constitutive parameters of the model are fixed at the outset for a given material. All other involved constitutive parameters are estimated based on the crystal structure and the physics of the plastic flow.