Effect Of Domain Switching Research Articles

A New One-Dimensional Rate-Based Phenomenological Model to Describe the Non-Linear Behaviour of Piezoelectric Actuators for Real-Time Applications

In this paper, a new rate-based phenomenological model of piezoelectric actuators for real-time applications is developed. This compact theoretical approach employs the Arrhenius equation for chemical reaction kinetics in order to describe the non-linear effect of domain switching. It needs only nine model parameters to account for the complete non-linearity of a piezoelectric actuator as well as the dependence of its non-linear effect on the electric field, the mechanical stress, and the temperature. This general validity for a wide range of operation conditions, which is based on a simplified description of the real behaviour, is the optimum prerequisite for a technically inexpensive control loop strategy for fast piezoelectric actuators as they are employed in state-of-the-art gasoline and diesel injectors for combustion engines. Moreover, other interfering physical effects, such as ageing, which may cause an injector's dosing function to deteriorate severely can be tackled by making use of this approach in electronic control units. All this is possible because the extremely compact theoretical formulation with a compact set of parameters does not need access to complex characteristic diagrams so that the most essential requirements of an automotive control unit such as a minimum computation time and a modest requirement of storage space can be fulfilled.

A FSDT—MITC Piezoelectric Shell Finite Element with Ferroelectric Non-linearity

A shell finite element based on the Reissner/Mindlin first-order shear deformation theory and integrating a bi-dimensional phenomenological ferroelectric constitutive law for domain switching effects is proposed. An electric switching function is considered to indicate the onset of domain switching. Only one internal variable (the remanent polarization) is used in the model. An implicit integration technique based on the return-mapping algorithm is adopted. The shell element is implemented into the commercial finite element code Abaqus ® via the subroutine user element. Some linear (piezoelectric) and non-linear (ferroelectric) tests are considered to validate first, the element formulation and second, the implementation of the bi-dimensional ferroelectric model. It is shown by studying a complex example (the spiral actuator) that the Reissner/Mindlin kinematic hypothesis (no variation of the displacement across the thickness or no thickness variation) is not sufficient for some electromechanical applications for which the d33 effect is of major importance.

Nonlinear ferro-electro-elastic beam theory

Motivated by the uniqueness and potential of the nonlinear range of piezoelectric and ferroelectric smart materials and structures, a static physically nonlinear ferro-electro-elastic beam theory which takes the effect of domain switching into account is developed. The kinematic assumptions adopt the geometrically linear Bernoulli–Euler form for the mechanical components and a first-order theory for the electrical potential, and lay the basis for further augmentation to higher order theories. The beam theory includes the field equations that correspond to the static case, the boundary conditions and the constitutive equations of ferro-electro-elasticity. The general 3-D constitutive equations are reduced to comply with the beam theory and formulated as ordinary differential equations by means of a set of generalized electro-mechanical stiffnesses. A micromechanical constitutive model that accounts for the loading history and for the domain switching phenomenon is adopted and an iterative solution procedure that incorporates the micromechanical approach is suggested. A numerical example that demonstrates the impact of the domain switching on the nonlinear electromechanical static response of a ferro-electro-elastic beam is presented and discussed. The quantitative assessment of this behavior takes a step towards new structural applications that cope with or even take advantage of the nonlinear ferro-electro-elastic range.

Theory and Numerics of Rate‐Dependent Incremental Variational Formulations in Ferroelectricity

AbstractThis paper is concerned with macroscopic continuous and discrete variational formulations for domain switching effects at small strains, which occur in ferroelectric ceramics. The developed new three–dimensional model is thermodynamically–consistent and determined by two scalar–valued functions: the energy storage function (Helmholtz free energy) and the dissipation function, which is in particular rate–dependent. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for ferroelectric ceramics. The rate–dependent character of the dissipation function allows us also to reproduce the experimentally observed rate dependency of the above mentioned hysteresis phenomena. An important aspect is the numerical implementation of the coupled problem. The discretization of the two–field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric format. The performance of the proposed methods is demonstrated by means of a benchmark problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Identification of a Putative Intracellular Allosteric Antagonist Binding-Site in the CXC Chemokine Receptors 1 and 2

The chemokine receptors CXCR1 and CXCR2 are G-protein-coupled receptors (GPCRs) implicated in mediating cellular functions associated with the inflammatory response. Potent CXCR2 receptor antagonists have been discovered, some of which have recently entered clinical development. The aim of this study was to identify key amino acid residue differences between CXCR1 and CXCR2 that influence the relative antagonism by two compounds that have markedly different chemical structures. By investigating the effects of domain switching and point mutations, we found that the second extracellular loop, which contained significant amino acid sequence diversity, was not important for compound antagonism. We were surprised to find that switching the intracellular C-terminal 60 amino acid domains of CXCR1 and CXCR2 caused an apparent reversal of antagonism at these two receptors. Further investigation showed that a single amino acid residue, lysine 320 in CXCR2 and asparagine 311 in CXCR1, plays a predominant role in describing the relative antagonism of the two compounds. Homology modeling studies based on the structure of bovine rhodopsin indicated a potential intracellular antagonist binding pocket involving lysine 320. We conclude that residue 320 in CXCR2 forms part of a potential allosteric binding pocket on the intracellular side of the receptor, a site that is distal to the orthosteric site commonly assumed to be the location of antagonist binding to GPCRs. The existence of a common intracellular allosteric binding site at GPCRs related to CXCR2 may be of value in the design of novel antagonists for therapeutic intervention.

A principle of virtual work and governing equations for nonlinear ferro-electro-elasticity

The variational principle of virtual work, the governing equations, and the boundary conditions for nonlinear ferroelectric structures are developed. The variational principle takes into account the presence of electrical body forces and body moment as well as the physical nonlinearity that results from the dissipative domain switching effect. The switching phenomenon also involves large strains. Hence, the geometrical nonlinearity is also taken into account and the electro-mechanical principle of virtual work is formulated in an Eulerian and Lagrangian type of description. The variational principle is used for the derivation of the generalized equilibrium equations (field equations) and the generalized boundary conditions. The governing equations for the ferroelectric structure are derived taking into account the nonlinear constitutive equations, the large deformations, and the spatial variation of the material tensors associated with the domain switching phenomenon.

Quasi-static thermo-electro-mechanical behaviour of piezoelectric stack actuators

Quasi-static thermo-electro-mechanical performance of annular and solid cylindrical piezoelectricactuators was studied by experimental means under electric fields varying from 0.3 to1.8 kV mm−1 with a preload of 4.6 MPa over the temperature range of−30 to125 °C. It was found that, for both annular and solid actuators, the electrically inducedstroke increases steadily with temperature. Under electric fields larger than1.0 kV mm−1, a nonlinear transition zone exists in the stroke–temperature plot over the temperature range25–50 °C. The dielectric constant was also found to increase with temperature. Preload dependence ofdisplacement was measured up to 42 MPa at room temperature and found to be negligiblebelow 30 MPa. A mathematical model that includes the linear piezoelectric effect and90° domain switching effect was used to model the experimental results. The model showsreasonable agreement with experimental results at low and high driving fields.

Two models to simulate rate-dependent domain switching effects—application toferroelastic polycrystalline ceramics

The aim of this paper is to study rate-dependent switching in ferroelastic materials. Morespecifically, a micro-mechanically motivated model is embedded into an iterativethree-dimensional and electromechanically coupled finite-element framework. Anestablished energy-based criterion serves for the initiation of domain switching processes asbased on reduction in (local) Gibbs free energy. Subsequent nucleation and propagation ofdomain walls is captured via a linear kinetics theory with rate-dependent effects beingincorporated in terms of a deformation-dependent limit-time parameter. Withthis basic model in hand, two different switching formulations are elaborated inthis work: on the one hand, a straightforward volume-fraction ansatz is appliedwith the volume-fraction value depending on the limit-time parameter; on theother hand, a reorientation–transformation formulation is proposed, whereby theorientation tensor itself is assumed to depend on the limit-time parameter. Macroscopicbehaviour such as stress versus strain curves or stress versus electrical displacementgraphs are obtained by applying straightforward volume-averaging techniquesto the three-dimensional finite-element-based simulation results which providesimportant insights into the rate-dependent response of the investigated ferroelasticmaterials.

Phase field simulation of crack tip domain switching in ferroelectrics

This paper presents a new application of the phase field method. Two-dimensional phase field simulations of domain switching in the crack tip vicinity of a crack embedded in a ferroelectric single crystal, which was subjected to mechanical and electric loading, have been carried out. Khachaturyan–Shatalov (KS) theory [1] was adopted to account for the elastic energy. The domain switching zones induced by the mechanical and electric loading were plotted. The stress field near the crack tip was also plotted to investigate the effect of domain switching on the crack. The obtained domain switching zones are in good agreement with reported theoretical predictions and experimental observations. The stress field shows that the positive electric field inhibits while the negative field promotes the crack propagation.

Introduction to the special issue on Nanoscale Ferroelectrics

As ferroelectrics-based devices are entering the realm of nanoscale dimensions, it is expected that properties of ferroelectrics will start exhibiting a pronounced size effect due to high surface-to-volume ratio, increased effect of local nonstoichiometry and interfaces, polarization fluctuations, etc. This poses serious problems to the development of nanoscale ferroelectric-based devices, such as high-density non-volatile memories, photonic and electrooptic devices, piezoelectric sensors an da ctuators, smart systems, and probe-based storage devices. Apparently, advances in understanding the nanoscale ferroelectric phenomena have not been following the progress in deposition and nanofabrication techniques at a sufficiently high pace. Research on various aspects of nanoscale ferroelectric phenomena is receiving great attention from scientific community. Hundreds of papers are published every year in different journals devoted to physics, chemistry, materials science, microelectronics, etc. In this Special Issue, to provide an overview of the current status in nanoscale ferroelectric research, the editors are bringing together review papers on subjects ranging from processing of ferroelectric nanoislands to theoretical analysis of the switching of polarization in confined geometries to realspace characterization of ferroelectric structures. Several papers in this Special Issue are devoted to fabrication of ferroelectric nanostructures using sol-gel method that allows forming isolated nanoislands where the properties of ferroelectrics can be investigated as a function of their size. Modeling of the nanostructures including domain switching and stress-mediated effects is also presented. Recent progress in an understanding of dielectric anomaly in ultrathin capacitors is discussed. Development in characterizing domain configurations in 3-D shape-constrained ferroelectrics fabricated by ion etching is also presented. The current status of Piezoresponse Force Microscopy (PFM) as a reliable tool for probing nanoscopic ferroelectric structures is overviewed in this Issue. Further insights into highorder frequency and geometry effects in PFM are presented as well.

A 1D constitutive law for hysteresis effects in piezoceramics

AbstractThis paper is concerned with a macroscopic constitutive law for domain switching effects, which occur in piezoelectric ceramics. The thermodynamical framework of the law is based on two scalar valued functions: the Helmholtz free energy and a switching surface. In common usage, the remanent polarization and the remanent strain are employed as internal variables. The novel aspect of the present work is to introduce an irreversible electric field, which serves besides the irreversible strain as internal variable. The irreversible electric field has only theoretical meaning, but leads to advantages within the finite element implementation, where displacement and the electric potential are the nodal degrees of freedoms. A common assumption is a one‐to‐one relation between the irreversible strain and the polarization. This simplification is not employed in the present paper. To accomplish enough space for the polarization, resulting from an applied electric field, the irreversible strains are additively split and a special hardening function is introduced. This balances the amount of space and the domain switching due to polarization. The constitutive model reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for piezoelectric ceramics and it accounts for the mechanical depolarization effect. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of domain switching on kinking of a crack in a ferroelectric material

Crack kinking induced by domain switching in a ferroelectric material under purely electric loading is investigated. Boundaries of domain switching zones for the asymptotic problem of a semi-infinite crack under the small scale conditions are determined based on the nonlinear electric theory. Stress intensity factors induced by the domain switching are numerically evaluated using the solution of the switching zone. Numerical results of the kink angle are obtained as a function of the ratio of the coercive electric field to the yield electric field for various polarization angles. Crack kinking in ferroelectric materials subjected to a cyclic electric field is also examined. The crack in the fully poled materials branches with different directions at application of the positive and negative electric fields, respectively. The electric fatigue crack is shown to have a forked crack pattern in the fully poled materials.

A phenomenological constitutive model for ferroelastic and ferroelectric hysteresis effects in ferroelectric ceramics

This paper is concerned with a macroscopic constitutive law for domain switching effects, which occur in ferroelectric ceramics. The three-dimensional model is thermodynamically consistent and is determined by two scalar valued functions: the Helmholtz free energy and a switching surface. In a kinematic hardening process the movement of the center of the switching surface is controlled by internal variables. In common usage, the remanent polarization and the irreversible strain are employed as internal variables. The novel aspect of the present work is to introduce an irreversible electric field, which serves instead of the remanent polarization as internal variable. The irreversible electric field has only theoretical meaning, but it makes the formulation very suitable for a finite element implementation, where displacements and the electric potential are the nodal degrees of freedom. The paper presents an appropriate implementation into a hexahedral finite brick element. The uni-axial constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for ferroelectric ceramics. Furthermore it accounts for the mechanical depolarization effect, which occurs if the polarized ferroelectric ceramic is subjected to a compression stress.

Interplay between Fracture and Domain Switching of Ferroelectrics

Applications of above-coercive electric fields lead to domain switching of a large or global scale. Large scale switching model is proposed to deal with load-induced domains witching in experiment. Both a discussion of crack initiation via the stress intensity factor and a discussion of crack path stability via T-stress are presented. The theoretical predictions and the experimental data roughly coincide for crack initiation, propagation and stability phenomena. Attention is also extended to consider the effect of non-uniform ferro-elastic domain switching in the vicinity of a crack. The domain switching zone is divided into a saturated inner core and an active surrounding annulus. Toughening for ferroelectrics with different poling states is estimated via Reuss type approximation. Solutions obtained according to spherical and cylindrical inclusions cover the range of experimental data.

A thermodynamic consistent 1D model for ferroelastic and ferroelectric hysteresis effects in piezoceramics

This paper represents a macroscopic constitutive law for domain switching effects, which occur in piezoelectric ceramics. The thermodynamical framework of the law is based on two scalar valued functions: the Helmholtz free energy and a switching surface. In the general sense of a kinematic hardening process, the movement of the centre of the switching surface is controlled by internal variables. In common usage, these are the remanent polarization and the irreversible strain. The novel aspect of the present work is to introduce an irreversible electric field, which serves besides the irreversible strain as internal variable. The irreversible electric field has only theoretical meaning, but it makes the formulation very suitable for a finite-element implementation, where displacement and the electric potential are the nodal degrees of freedom. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for piezoelectric ceramics. Furthermore, it accounts for the mechanical depolarization effect, which occurs if the polarized piezoceramic is subjected to a compression stress. Copyright © 2005 John Wiley & Sons, Ltd.

Toughening under non-uniform ferro-elastic domain switching

The existing models of switch-toughening seldom consider the effect of non-uniform ferro-elastic domain switching in the vicinity of a crack. To explore this issue, an evolution law for the volume fraction of the switched portion under applied electromechanical loading is established from the minimum energy principle. Based on this law, a switching model capable of dealing with the non-uniform distribution of switching strain is developed. The domain switching zone is divided into a saturated inner core and an active surrounding annulus. Mono-domain solution of ferro-elastic toughening is obtained under the model of small scale domain switching. Toughening for ferroelectrics with different poling states is estimated via Reuss type approximation. Two sets of solutions are obtained according to spherical and cylindrical inclusions. The interval of toughening defined by these two models covers the range of experimental data. The same conclusion is reached for the size of the switching zone.

Field-induced displacement properties of nanoscale domain structure in PZT thin film

Nanoscale characterization of fieldinduced displacement was made in compositionally graded PZT thin film according to the inverse piezoelectric effects by SFM in contact mode. The nanoscale piezoelectric displacement  electric field butterfly loop was obtained due to the combined contribution from linear piezoelectric effect and domain switching effect, which substantiate nanoscale validity of CaspariMerz theory. The nanoscale imprint phenomena were also observed in the thin film.

Simulation of nonlinear properties of ferroelectric and piezoceramicmaterials

AbstractFerroelectric and piezoelectric materials are becoming a very significant part of smart materials that are used widely as actuators, sensors and most common applications such as vibration control, precision positioning, precision cutting and microelectromechanical systems (MEMS). Piezoceramic materials show nonlinear characteristics when they are under high electromechanical loading. In this study, nonlinear behaviour of tetragonal perovskite type piezoceramic materials is simulated using micromechanical model. In the simulations uni‐axial loading is applied. The calculations which are based on a linear constitutive model, nonlinear domain switching model and a model of probability to switch are performed at each grain. The different domain switching effects (900 or 1800 domain switching for tetragonal perovskite structure) due to energy differences, different probability functions, different statistical random generators and material parameters are analyzed. Finally, simulation results are compared with the data of experiments are giving in literature. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thickness effect of ferroelectric domain switching in epitaxial PbTiO3 thin films on Pt(001)/MgO(001)

Epitaxial PbTiO3 thin films of various thicknesses were prepared by pulsed laser deposition on Pt(001)/MgO(001) substrates. Their ferroelectric domain structures and switching behavior were then investigated mainly using scanning force microscopy as a function of film thickness. Direct evidence of a-domain switching was observed under an external electric field, while its contribution to the total piezoelectric response was found negligible. Thinner epitaxial PbTiO3 films with higher c-domain population and larger tetragonality resulted in enhanced d33 piezoelectric coefficients. The results suggest that the key factor determining the piezoelectric response in epitaxial ferroelectric films is not the a-to-c domain switching but apparently the population of c-domains and their tetragonality.

Fabrication and physical properties of permalloy nano-size wires

Nano-size NiFe wires with patterned shapes in half-ring-in-series, octagon-in-series, and zigzag-in-series configurations were fabricated. Their magnetoresistance was studied below room temperature and their magnetic domain images were investigated at room temperature by a magnetic force microscope. In general, we have experimentally demonstrated that the variation of the magnetoresistance of our patterned nano-size wires can be related to different domain configurations and explained by the domain switching effect. The number of magnetic domain walls in our patterned wires can be controlled by the shape anisotropy and the size of each section of patterns that form the wires.