Nonlinear Constitutive Behavior Of Ferroelectric Materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

Exploring the Kinetics of Domain Switching in Ferroelectrics for Structural Applications

The complex domain structure in ferroelectrics gives rise to electromechanical coupling, and its evolution (via domain switching) results in a time-dependent (i.e. viscoelastic) response. Although ferroelectrics are used in many technological applications, most do not attempt to exploit the viscoelastic response of ferroelectrics, mainly due to a lack of understanding and accurate models for their description and prediction. Thus, the aim of this thesis research is to gain better understanding of the influence of domain evolution in ferroelectrics on their dynamic mechanical response. There have been few studies on the viscoelastic properties of ferroelectrics, mainly due to a lack of experimental methods. Therefore, an apparatus and method called Broadband Electromechanical Spectroscopy (BES) was designed and built. BES allows for the simultaneous application of dynamic mechanical and electrical loading in a vacuum environment. Using BES, the dynamic stiffness and loss tangent in bending and torsion of a particular ferroelectric, viz. lead zirconate titanate (PZT), was characterized for different combinations of electrical and mechanical loading frequencies throughout the entire electric displacement hysteresis. Experimental results showed significant increases in loss tangent (by nearly an order of magnitude) and compliance during domain switching, which shows promise as a new approach to structural damping. A continuum model of the viscoelasticity of ferroelectrics was developed, which incorporates microstructural evolution via internal variables and associated kinetic relations. For the first time, through a new linearization process, the incremental dynamic stiffness and loss tangent of materials were computed throughout the entire electric displacement hysteresis for different combinations of mechanical and electrical loading frequencies. The model accurately captured experimental results. Using the understanding gained from the characterization and modeling of PZT, two applications of domain switching kinetics were explored by using Micro Fiber Composites (MFCs). Proofs of concept of set-and-hold actuation and structural damping using MFCs were demonstrated.

Computation of high-stability DC balancing scheme for ferroelectric liquid crystal on silicon holograms using graphics processing units.

Spatial light modulators based around liquid crystal on silicon have found use in a variety of telecommunications applications, including the optimization of multimode fibers, free-space communications, and wavelength selective switching. Ferroelectric liquid crystals are attractive in these areas due to their fast switching times and high phase stability, but the necessity for the liquid crystal to spend equal time in each of its two possible states is an issue of practical concern. Using the highly parallel nature of a graphics processing unit architecture, it is possible to calculate DC balancing schemes of exceptional quality and stability.

Mechanical constraint and loading on ferroelectric memory capacitors

The influence of mechanical constraint imposed by device geometry upon the switching response of a ferroelectric thin film memory capacitor is investigated. The memory capacitor was represented by two-dimensional ferroelectric islands of different aspect ratio, mechanically constrained by surrounding materials. Its ferroelectric non-linear behaviour was modeled by a crystal plasticity constitutive law and calculated using the finite element method. The switching response of the device, in terms of remnant charge storage, was determined as a function of geometry and constraint. The switching response under applied in-plane tensile stress and hydrostatic pressure was also studied experimentally. Our results showed that (1) the capacitor's aspect ratio could significantly affect the clamping behaviour and thus the remnant polarization, (2) it was possible to maximise the switching charge through the optimisation of the device geometry, and (3) it is possible to find a critical switching stress at zero electric field and a critical coercive field at zero residual stress. © 2009 Materials Research Society.

Ferroelectric liquid crystal mixture integrated into optical waveguides

We report an on-chip integrated ferroelectric liquid crystal (FLC) waveguide structure suitable for telecommunication applications. Single gaps with different widths of 5, 10, and 20 μ m inside individual silica waveguides were filled with an FLC mixture. The waveguide devices operate as a binary switch or an attenuator in a temperature range from 30 °C to 60 °C. The FLC mixture exhibited a good alignment quality in these gaps without alignment layers. A good extinction ratio of up to 33.9 dB and a low insertion loss of <4.3 dB at λ = 1550 nm were observed. Switching times of <100 μs were obtained for the low electric fields applied in this experiment. © 2012 IEEE.

Nucleation, growth, and control of ferroelectric-ferroelastic domains in thin polycrystalline films

The unique response of ferroic materials to external excitations facilitates them for diverse technologies, such as nonvolatile memory devices. The primary driving force behind this response is encoded in domain switching. In bulk ferroics, domains switch in a two-step process: nucleation and growth. For ferroelectrics, this can be explained by the Kolmogorov-Avrami-Ishibashi (KAI) model. Nevertheless, it is unclear whether domains remain correlated in finite geometries, as required by the KAI model. Moreover, although ferroelastic domains exist in many ferroelectrics, experimental limitations have hindered the study of their switching mechanisms. This uncertainty limits our understanding of domain switching and controllability, preventing thin-film and polycrystalline ferroelectrics from reaching their full technological potential. Here we used piezoresponse force microscopy to study the switching mechanisms of ferroelectric-ferroelastic domains in thin polycrystalline Pb 0.7Zr0.3TiO3 films at the nanometer scale. We have found that switched biferroic domains can nucleate at multiple sites with a coherence length that may span several grains, and that nucleators merge to form mesoscale domains, in a manner consistent with that expected from the KAI model. © 2012 American Physical Society.

Photomechanically Induced Phase Transitions in Ferroelectric Liquid Crystals

We report optically induced phase transtions occurring in two different host ferroelectric liquid crystals; SCE13 a multicomponentmixture optimised for room temperature performance, and CE8 a single component liquid crystal. These act as host liquid crystals for a novel guest azo dye, which can be made to photoisomerise using low power density U.V. illumination, resulting in dramatic changes in sample properties. We have shown that the magnitude of spontaneous polarisation of systems can be isothermally and reversibly induced or reduced, with the consequent appearance or disappearance of optical switching hysteresis. We discuss the parameters controlling the behaviour of the systems under U.V. illumination and suggest mechansims by which the transitions may occur. © 1993, Taylor & Francis Group, LLC. All rights reserved.

Programmable ZnO nanowire transistors using switchable polarization of ferroelectric liquid crystal

We demonstrate modulations of electrical conductance and hysteresis behavior in ZnO nanowire transistors via electrically polarized switching of ferroelectric liquid crystal (FLC). After coating a nanowire channel in the transistors with FLCs, we observed large increases in channel conductance and hysteresis width, and a strong dependence of hysteresis loops on the polarization states associated with the orientation of electric dipole moments along the direction of the gate electric field. Furthermore, the reversible switching and retention characteristics provide the feasibility of creating a hybrid system with switch and memory functions. © 2013 American Institute of Physics.

High performance non-volatile ferroelectric copolymer memory based on a ZnO nanowire transistor fabricated on a transparent substrate

A high performance ferroelectric non-volatile memory device based on a top-gate ZnO nanowire (NW) transistor fabricated on a glass substrate is demonstrated. The ZnO NW channel was spin-coated with a poly (vinylidenefluoride-co-trifluoroethylene) (P(VDF-TrFE)) layer acting as a top-gate dielectric without buffer layer. Electrical conductance modulation and memory hysteresis are achieved by a gate electric field induced reversible electrical polarization switching of the P(VDF-TrFE) thin film. Furthermore, the fabricated device exhibits a memory window of ∼16.5 V, a high drain current on/off ratio of ∼105, a gate leakage current below ∼300 pA, and excellent retention characteristics for over 104 s. © 2014 AIP Publishing LLC.

Controllable nanodomain defects in ferroelectric/ferroelastic biferroic thin films

Ferroelectric thin films have been intensively studied at the nanometre scale due to the application in many fields, such as non-volatile memories. Enhanced piezo-response force microscopy (E-PFM) was used to investigate the evolution of ferroelectric and ferroelastic nanodomains in a polycrystalline thin film of the simple multi-ferroic PbZr0.3Ti0.7O 3 (PZT). By applying a d.c. voltage between the atomic force microscopy (AFM) tip and the bottom substrate of the sample, we created an electric field to switch the domain orientation. Reversible switching of both ferroelectric and ferroelastic domains towards particular directions with predominantly (111) domain orientations are observed. We also showed that along with the ferroelectric/ferroelastic domain switch, there are defects that also switch. Finally, we proposed the possible explanation of this controllable defect in terms of flexoelectricity and defect pinning. © 2013 IEEE.

V5+-doped Bi3.4Yb0.6Ti3O12 fatigue resistant ferroelectric thin films

In this paper, a serial of Bi3.4Yb0.6Ti3-xVxO12 (BYTV) thin film with different V5+ contents were deposited on Pt/Ti/SiO2/Si substrates by chemical solution deposition (CSD). The crystallized phase and electrical properties of the films were investigated using X-ray diffraction, polarization hysteresis loops, leakage current-voltage, and fatigue test. From our experimental results, it can be found that the ferroelectric properties can be improved greatly using V5+-doped in Bi3.4Yb0.6Ti3O12 (BYT) thin film, compared with the reported BYT thin film. The remanent polarization was enhanced and excellent leakage current characteristic with 10(-11)A at the bias voltage of 4V, which is much lower than the BYT thin film or some reported bismuth layer-structure ferroelectric films. Fatigue test shows that the fabricated films have good anti-fatigue characteristic after 10(10) switching cycles. (c) 2008 Published by Elsevier B.V.

Nanostructured ferroelectric materials

Nanostructured materials are central to the evolution of future electronics and information technologies. Ferroelectrics have already been established as a dominant branch in the electronics sector because of their diverse application range such as ferroelectric memories, ferroelectric tunnel junctions, etc. The on-going dimensional downscaling of materials to allow packing of increased numbers of components onto integrated circuits provides the momentum for the evolution of nanostructured ferroelectric materials and devices. Nanoscaling of ferroelectric materials can result in a modification of their functionality, such as phase transition temperature or Curie temperature (TC), domain dynamics, dielectric constant, coercive field, spontaneous polarisation and piezoelectric response. Furthermore, nanoscaling can be used to form high density arrays of monodomain ferroelectric nanostructures, which is desirable for the miniaturisation of memory devices. This thesis details the use of various types of nanostructuring approaches to fabricate arrays of ferroelectric nanostructures, particularly non-oxide based systems. The introductory chapter reviews some exemplary research breakthroughs in the synthesis, characterisation and applications of nanoscale ferroelectric materials over the last decade, with priority given to novel synthetic strategies. Chapter 2 provides an overview of the experimental methods and characterisation tools used to produce and probe the properties of nanostructured antimony sulphide (Sb2S3), antimony sulpho iodide (SbSI) and lead titanate zirconate (PZT). In particular, Chapter 2 details the general principles of piezoresponse microscopy (PFM). Chapter 3 highlights the fabrication of arrays of Sb2S3 nanowires with variable diameters using newly developed solventless template-based approach. A detailed account of domain imaging and polarisation switching of these nanowire arrays is also provided. Chapter 4 details the preparation of vertically aligned arrays of SbSI nanorods and nanowires using a surface-roughness assisted vapour-phase deposition method. The qualitative and quantitative nanoscale ferroelectric properties of these nanostructures are also discussed. Chapter 5 highlights the fabrication of highly ordered arrays of PZT nanodots using block copolymer self-assembled templates and their ferroelectric characterisation using PFM. Chapter 6 summarises the conclusions drawn from the results reported in chapters 3, 4 and 5 and the future work.