Structure of weiss domains in elastic ferroelectric crystals

In this work a variational principle is proposed to study the existence and structure of Weiss domains in elastic ferroelectric crystals. Weiss domains are defined as certain subregions of the crystal in each of which the polarization vector is uniform and has a constant magnitude which is equal to the saturation polarization per unit mass for the crystal. The variational principle differs from previous ones in that the variations of the domain walls are also taken into account and it is a direct generalization of the one corresponding to the rigid crystals which we have proposed earlier. In deriving the general theory the dependence on the polarization gradients are also considered and the effect of this dependence when passing from one domain to another is represented by an appropriately chosen surface energy on domain walls. The domain structure is studied under homogeneous deformation. The effect of a small deformation field on the shape of domains is illustrated in the case of a rectangular uniaxial crystal which has initially no electric field inside. It is shown that the deformation creates a small electric field in the crystal and domain walls change slightly.     

Simulation of the initial polarization curves and hysteresis loops for ferroelectric films by an extensive time-dependent Ginzburg–Landau model

The polarization hysteresis loops as well as the initial curves of ferroelectric films with 180° domain boundaries perpendicular to the film surface are simulated based on an extensive time-dependent Ginzburg–Landau model. The result shows that the curve and loop strongly depend on the frequency ω of the applied electric field, the effective mass density ρ, and the viscosity coefficient K of the material, however, the constant ωK/ρ can induce the same curve and loop. The hysteresis area of the saturated loop is increased with field amplitude, which is consistent with the previous experimental observation. In addition, it is found that the latent domains in the film can result in a remarkable decrease in the remanent polarization and coercive field.     

Electrical properties of sol-gel processed PLZT thin films

Sol-gel processed lanthanum-modified lead zirconate titanate (PLZT) thin films consisting of two different perovskite phase contents were fabricated on indium tin oxide coated Corning 7059 glass substrates with two different heating schedules: direct insertion at 650° C for 30 min and at 500° C for 2h. Optical transmittance spectra, polarization versus electric field curves, relative dielectric constant versus frequency and capacitance versus d.c. bias voltage curves of the samples were investigated. The samples showed a good transparency of over 70% and interference oscillation. A thin film consisting of mainly perovskite phase showed a slim loop hysteresis in the polarization versus electric field curve and in the capacitance versus d.c. bias voltage curve, indicating the presence of ferroelectric domains, but a film consisting of mainly pyrochlore phase did not. The dielectric constant and loss factor of the thin film consisting of mainly perovskite phase were about 90 and about 0.2, respectively, at relatively low frequency and showed dispersion of the dipolar polarization of permanent dipole moment in the ferroelectric perovskite phase in the frequency range between 10 kHz and 1 MHz.     

Structural visualization of polarization fatigue in epitaxial ferroelectric oxide devices

Ferroelectric oxides, such as Pb(Zr,Ti)O(3), are useful for electronic and photonic devices because of their ability to retain two stable polarization states, which can form the basis for memory and logic circuitry. Requirements for long-term operation of practical devices such as non-volatile RAM (random access memory) include consistent polarization switching over many (more than 10(12)) cycles of the applied electric field, which represents a major challenge. As switching is largely controlled by the motion and pinning of domain walls, it is necessary to develop suitable tools that can directly probe the ferroelectric domain structures in operating devices-thin-film structures with electrical contacts. A recently developed synchrotron X-ray microdiffraction technique complements existing microscopic probes, and allows us to visualize directly the evolution of polarization domains in ferroelectric devices, through metal or oxide electrodes, and with submicrometre spatial resolution. The images reveal two regimes of fatigue, depending on the magnitude of the electric field pulses driving the device: a low-field regime in which fatigue can be reversed with higher electric field pulses, and a regime at very high electric fields in which there is a non-reversible crystallographic relaxation of the epitaxial ferroelectric film.     

Dielectric energy storage densities in Ba1-xSrxTi1-yZryO3 ceramics

This paper presents measurements of the Weiss temperature, the Curie constant, the spontaneous polarization and the stored dielectric energy density of Ba_1-xSr_xTi_1-yZr_yO₃ ceramics for compositions with 0≤x≤1 and 0≤y≤0.5. The first three of these dielectric parameters are used to predict the density of energy storage that can be obtained when ceramics of these compositions are used as capacitor dielectrics. These predictions are compared with direct measurements of energy densities which show that for moderate electric field strengths (-50 kV mm ^-1) the stored dielectric energy densities were the largest for ceramics with x>0.7 and y?～0.2. © 2000 Kluwer Academic Publishers     

An approach for analysis of poled/depolarized piezoelectric materials with a crack

In this paper, the influence of dielectric medium inside a crack on crack growth, in an infinite poled or depolarized ceramic, has been studied by employing an electric boundary condition derived from the exact boundary conditions proposed by Sosa (1996). The effect of remanent polarization has also been examined. The results obtained show that electric displacement on crack surfaces is not always zero. Hence, for studying fracture problems of piezoelectric ceramics with cracks accurately, the exact boundary conditions should be implemented. In addition, the results indicate that the effect of remanent polarization is equivalent to that of a positive electric field and it cannot be neglected. It is also found that a positive electric field always has a tendency to open a crack, and a negative electric field tends to close a crack.     

Nanoscale domain switching in Bi3.15Eu0.85Ti3O12 thin films annealed at different temperature by scanning probe microscopy

The nanoscale domain switching behavior of Bi_3.15Eu_0.85Ti₃O₁₂ (BET) thin films annealed at temperatures of 600, 650 and 700 °C is investigated by scanning probe microscopy (SPM) via the direct observation on their domain structure. It is shown that most ferroelectric domains are clearly detectable and confined in the grains. Some domains opposite to the polarizing electric field were observed by SPM, and their formations are attributed to the grain boundaries playing an active roles in pinning a preferential polarization state. The remnant polarization (2P_r) values of BET thin films increase with the annealing temperature due to the increase of nanoscale domains switched into the direction of polarizing electric field.     

THE EFFECTIVE DIELECTRIC CONSTANT OF DUST LAYERS

The electrical breakdown of a dust layer usually occurs at average electric fields which appear to be too small to initiate the breakdown. This suggests that the local electric field where breakdown occurs is somehow enhanced over that of the average field across the layer. AC dielectric measurements performed on the dust layer can be used to determine an effective static dielectric constant at a given temperature. The use of this dielectric constant in an expression for the local electric field, which combines the effects of dielectric polarization and space charge in the layer, results in predicted values of the local electric field which can be more than an order of magnitude larger than the applied field. In studies involving 11 different dust species, the dielectric constant was found to depend on temperature and layer thickness, as well as the concentration of alkali and alkaline earth metals in the dust.     

Optical Study of Domains in Antiferroelectric Ceramics

Antiferroelectric ceramics are now highly focused as giant strain actuator materials. In this study, domain formation in antiferroelectric lead zirconate based ceramics (Pb_0.99Nb_0.02[(Zr_0.6Sn_0.4)_1-yTi_y]_0.98O₃) was observed dynamically under an electric field at various temperatures using a high-resolution charge-coupled-device (CCD) microscope system. Field induced polarization and field induced strain were also measured. No domain was observed without an electric field, but clear domains appeared with an electric field due to the phase transition from an antiferroelectric to a ferroelectric state. Results of the optical study can explain well the electrical properties. The behavior of the field induced domains showed a shape memory effect and the domains were well oriented compared with normal ferroelectric ceramics.     

The effect of a constant electric field on the structural parameters of ferroelectric PbSc<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> crystals

The effect of a constant electric field on the polarization and structural parameters of ferroelectric lead scandium niobate (PbSc_0.5Nb_0.5O₃) crystals was studied using X-ray diffraction. Application of a constant electric field leads to splitting of the Bragg diffraction peaks. It is shown that this behavior is most probably explained by the formation of a new phase.     

Variational‐based modeling of micro‐electro‐elasticity with electric field‐driven and stress‐driven domain evolutions

Recently, increasing interest in so‐called functional or smart materials with electromechanical coupling has been shown such as ferroelectric piezoceramics. These materials are characterized by microstructural properties, which can be changed by external stress and electric field stimuli, and hence find use as the active components in sensors and actuators. The electromechanical coupling effects result from the existence and rearrangement of microstructural domains with uniformly oriented electric polarization. The understanding and efficient simulation of these highly nonlinear and dissipative mechanisms, which occur on the microscale of ferroelectric piezoceramics, are a key challenge of the current research. This paper does not offer a substantially new physical model of these phenomena but a new mathematical modeling approach based on a rigorous exploitation of rate‐type variational principles. This provides a new insight in the structure of the coupled problem, where the governing field equations appear as the Euler equations of a variational statement. We outline a variational‐based micro‐electro‐elastic model for the microstructural evolution of both electrically and mechanically driven electric domains in ferroelectric ceramics, which also incorporates the surrounding free space. To this end, we extend recently developed multifield incremental variational principles of electromechanics from local to gradient‐extended dissipative response and specialize it by a Ginzburg–Landau‐type phase field model, where the thickness of the domain walls enters the formulation as a length scale. This serves as a natural starting point for a canonical compact, symmetric finite element implementation, considering the mechanical displacement, the microscopic polarization, and the electric potential induced by the polarization as the primary fields. The latter is defined on both the solid domain and a surrounding free space. Numerical simulations treat domain wall motions for electric field‐driven and stress‐driven loading processes, including the expansion of the electric potential into the free space. Copyright © 2012 John Wiley & Sons, Ltd.     

Microstructure and dielectric properties of BF–PFN ceramics with negative dielectric loss

Multiferroics with negative value of dielectric constant are very promising materials because of their modern applicability. These materials can be used as materials for the construction of electromagnetic radiation shields. The subject of the research is multiferroic BiFeO₃–PbFe_1/2Nb_1/2O₃ (BF–PFN) ceramics. For all multiferroic materials the following studies are conducted: SEM, EDS and the temperature dependence of dielectric constant ε′(T). Above a certain temperature (different for different chemical compositions) the value of dielectric constant reaches negative values. Such the behavior of the dielectric constant may indicate that the polarization inside the material has a reverse direction to the external electric field. That is, the electric field inside the material counteracts the applied external electric field. The obtaining materials also show negative dielectric losses. The Axelrod model is used to explain the mechanism that causes negative dielectric loss.     

掺锰钛酸钡PTC陶瓷复合材料介电特性的研究

应用标准的陶瓷制备工艺制备掺锰钛酸钡ＰＴＣ陶瓷复合材料，在不同电场频率下测试样品的相对介电常数－温度特性，发现当温度高于居里点后，开始不同掺锰浓度样品的相对介电常数随温升级慢变化，到达某特殊温度时，出现异常跃升；异常跃升的起始温度依赖于掺杂浓度和测试电场频率，其峰值随测试电场频率的降低而增大。通过分析相关的物理过程应用离子极化理论对测试结果进行讨论。     

Ferroelectric control of magnetic anisotropy

We demonstrate unambiguous evidence of the electric field control of magnetic anisotropy in a wedge-shaped Co film of varying thickness. A copolymer ferroelectric of 70% vinylidene fluoride with 30% trifluoroethylene, P(VDF-TrFE) overlays the Co wedge, providing a large switchable electric field. As the ferroelectric polarization is switched from up to down, the magnetic anisotropy of the Co films changes by as much as 50%. At the lowest Co thickness the magnetic anisotropy switches from out-of-plane to in-plane as the ferroelectric polarization changes from up to down, enabling us to rotate the magnetization through a large angle at constant magnetic field merely by switching the ferroelectric polarization. The large mismatch in the stiffness coefficients between the polymer ferroelectric and metallic ferromagnet excludes typical magnetoelectric strain coupling; rather, the magnetic changes arise from the large electric field at the ferroelectric/ferromagnet interface.     

Young's experiment with electromagnetic spatial coherence wavelets

We discuss Young's experiment with electromagnetic random fields at arbitrary states of coherence and polarization within the framework of the electric spatial coherence wavelets. The use of this approach for the electromagnetic spatial coherence theory allows us to envisage the existence of polarization domains inside the observation plane. We show that it is possible to locally control those polarization domains by means of the correlation properties of the electromagnetic wave. To show the validity of this alternative approach, we derive by means of numerical modeling the classical Fresnel-Arago interference laws.     

Polarization independent blue-phase liquid crystal cylindrical lens with a resistive film

We propose a new electrode design for polarization-independent cylindrical lens using a polymer-stabilized blue phase liquid crystal (BPLC). The top electrode is coated with a transparent and resistive film to generate linearly varying electric potential from center to edge; while the bottom iridium tin oxide electrode has a constant potential. Therefore, the vertical electric field across the BPLC layer varies linearly over the lens aperture and a desired parabolic phase profile is obtained automatically according to the Kerr effect. Simulation results show that this simple device is polarization independent and it has parabolic-like phase profile in a large tuning range.     

Miniaturized flow fractionation device assisted by a pulsed electric field for nanoparticle separation

Electric field flow fractionation (EFFF) is a powerful separation technique based on an electrical field perpendicular to a pressure-driven flow. Previous studies of microelectric field flow fractionation (micro-EFFF) indicate that separation performance was limited due to a weak effective electric field caused by polarization layers on the electrode surfaces. In this work, we report on a micro-EFFF device that uses a pulsed voltage scheme to overcome these limitations. The device was fabricated in indium tin oxide (ITO)-coated glass with ITO as electrodes. The effective electric field for pulsed voltage operation was found to be 50-fold stronger when compared with constant voltage operation. A strong influence of pulsed voltage frequency on nanoparticle retention times was observed. Using pulsed voltage, improved separation of polystyrene particles of different surface charge and particle size is demonstrated. Pulsed voltage also offers more parameters compared to the constant voltage mode, e.g., pulse frequency, duty cycle, and waveform to optimize the retention behavior of analytes.     

Analysis of transient electric field for epoxy spacer under lightning impulse voltage

A transient electric field takes place in gas-insulated switch-gears (GIS) while lightning impulse voltage is imposed on it. Taking permittivity, conductivity, and polarization loss into consideration, the differential equations of transient field are deduced, where the response caused by lightning impulse voltage is expressed by Duhamel integration. The equivalent conductivity contributed by polarization loss of epoxy spacer is obtained from the experiment. The potential distribution curves of epoxy spacer in GIS are given at representative time, and the electric intensity distribution curves on the spacer surface with respect to time are illustrated. The maximum of intensity on the spacer surface is also calculated, which is compared with the one in the static field. Some distinguishing features of the transient field in GIS are also discussed.     

Electromechanical coupling properties of [001], [011] and [111] poled Pb(Mg1/3Nb2/3)O3-0.32PbTiO3 single crystals

The electric field induced “butterfly” curves and polarization loops, and the stress induced strain and polarization responses of [001], [011] and [111] oriented Pb(Mg_1/3Nb_2/3)O₃-0.32PbTiO₃ (PMN-0.32 PT) relaxor ferroelectric single crystals have been systematically investigated by experiment study. The focus is on the effect of constant compressive bias stress on the electromechanical coupling behavior along three crystallographic directions of PMN-0.32 PT single crystals. Dependence of the coercive field, remnant polarization, dielectric constant, and piezoelectric coefficient on the bias stress has been quantified for PMN-0.32 PT single crystals oriented in three different directions. Obtained results show that the large piezoelectric responses under zero compressive stress in [001] and [011] orientation are dominated by intrinsic crystal lattice while the engineered domain structure has a relatively minor effect. It is found that observed responses under stress cycle for [001] oriented crystals are due to polarization rotation and phase transformations. However, those for [011] and [111] oriented crystals are due to domain switching. The “butterfly” curves and polarization loops driven by electric field under different bias compression are described by two non-180° domain switching.     

Dynamics of phase-separated fluids under external fields

Phase separation in external fields has attracted much attention recently. The reason is twofold. Since kinetics of phase separation and morphology of growing domains can be controlled by external fields, it is of technological importance. The other is that existence of mesoscale domains causes curious dynamical properties in fields, which provides us with a fundamental statistical dynamic problem. One example is a phase separation of binary fluids under shear flow. Phase-separated domains are deformed under the field, which causes burst, fusion, and reconnection of domains so that extra energy dissipation occurs in these processes. Because of this large deformation of domains, the system exhibits quite unusual rheological behavior. The kinetics of phase separation of binary fluids is also influenced by an external electric field when the new phases have different dielectric constants. Deformation and interaction of domains in an electric field are investigated by means of an interfacial approach.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.