铁电电容系统非线性电滞参数模型研究

为解决铁电电滞模型中特性参数确定困难的问题,改善模型在工程应用中受限现状,本文利用遗传算法提出一种实用的铁电模型特性参数识别方法,可根据随机试验数据完成特性参数的提取,继而重构铁电模型以模拟各种铁电电容系统的非线性电滞行为．以上方法不但可以预测各种电场条件下的电极化响应,还可预测反映系统特性的理想饱和极化响应．最后,为验证所提方法的有效性,本文进行了仿真计算验证,其结果表明,基于优化参数的电滞模型能够很好地与试验数据吻合,具有较好的精确性和鲁棒性,为铁电系统在实际工程的应用提供有效参考．     

Two-scale micromechanics-based probabilistic modeling of domain switching in ferroelectric ceramics

A two-scale micromechanics model is developed in this paper to analyze domain switching in ferroelectric ceramics, using a probabilistic domain switching criterion based on energetic analysis. The microstructure of ferroelectric ceramics at two distinct length scales, domains and grains, has been carefully analyzed. The interaction at domain level is accounted for by energy minimization theory, while the fluctuation at grain level is analyzed using ellipsoidal two-point correlation function. The model has been implemented by Monte Carlo method, and applied to simulate the electric poling and mechanical depoling of Pb(Zr_xTi_1-x)O₃ (PZT) ceramics across morphotropic phase boundary (MPB). The drastically different switching characteristics of PZT ceramics across MPB has been captured, and good agreement with experiments has been observed. The effects of the transformation strains and spontaneous polarizations are highlighted, confirming the proposition of Li et al. [2005. Domain switching in polycrystalline ferroelectric ceramics. Nature Materials 4, 776–781] that the strain compatibility plays a dominant role in domain switching in ferroelectric ceramics.     

铁电单晶Pb(Mg1/3Nb2/3)O3-0.32PbTiO3的实验及本构模型研究

对压力作用下沿[001]晶向极化的Pb(Mg弛豫型铁电单晶;极化旋转(相变);黏塑性模型;本构;细观力学国家自然科学基金,教育部全国优秀博士学位论文作者专项基金2006-11-06对压力作用下沿[001]晶向极化的Pb(Mg1/3Nb2/3)O3-0.32PbTiO3(PMN0.32PT)弛豫型铁电单晶的应力应变行为进行了实验研究,实验结果表明铁电单晶〈001〉晶向的应力应变行为和铁电多晶有本质的不同,是传统的电畴翻转机理所难以解释的,所提出的极化旋转(相变)模型合理地解释了实验中观察到的现象;基于提出的极化旋转(相变)模型,采用细观力学方法建立了铁电单晶的细观本构模型.在模型中采用黏塑性公式描述铁电单晶可能的8个相变系统的相变行为.为了验证模型的可靠性,用该模型模拟了铁电单晶〈001〉晶向的应力应变实验曲线.计算表明,该模型能较好地模拟铁电单晶〈001〉晶向的相变行为.     

Single amplifier biquad based autonomous electronic oscillators for chaos generation

Two simple autonomous chaotic electronic circuits have been proposed in this paper. The core of each of the circuits consists of a single amplifier biquad (SAB). We have proposed two configurations of converting this SAB into chaotic oscillators using suitable passive nonlinear element and a storage element in the form of an inductor. The mathematical models of the proposed chaotic circuits have been constructed, which are fourth order autonomous nonlinear differential equations. The behavior of the proposed circuits has been investigated through numerical simulations, Spice-based circuit simulations and electronic hardware experiments and they agree well with each other. It has been found that both the circuits show complex behaviors like bifurcations and chaos for a certain range of circuit parameters.     

Synchronization and circuit simulation of a new double-wing chaos

A new three-dimensional double-wing chaotic system with three quadratic terms was proposed. And the parameters which can induce the system are analyzed. The system with five equilibrium points has sophisticated dynamical behaviors and it is further investigated in details, including phase trajectory, Lyapunov exponent spectrum, Poincaré map, spectrogram map and dissipativity analysis. The circuit simulation results of the chaotic attractors are in agreement with numerical simulations. Furthermore, numerical simulations indicate that mismatch synchronization can be achieved and circuit simulations of the system synchronization are also presented.     

On hidden twin attractors and bifurcation in the Chua’s circuit

Recently a new attractor, called hidden attractor, has been found in the well-known Chua’s circuit, whose basin of attraction does not contain neighborhood of any equilibrium. This paper will restudy this circuit, showing that two hidden attractors can coexist in this circuit for some parameters, and characterizes the basins of these two attractors by means of computer method as well. In addition, a computer-assisted proof of the chaoticity of these attracters is presented by a topological horseshoe theory.     

The influence of mechanical constraint upon the switching of a ferroelectric memory capacitor

The role of mechanical constraint upon the switching response of a ferroelectric thin film memory capacitor is explored. The memory capacitor is represented by a two dimensional ferroelectric island whose non-linear behaviour is modelled by a crystal plasticity constitutive law within the finite element method. The switching response of the device, in terms of remnant charge storage, is determined as a function of geometry and constraint. Various types of constraint on the ferroelectric capacitor are considered, including the presence of a silicon dioxide passivation layer, a silicon substrate and metallic electrodes. The effect of the relative resistance to 90 degree switching and 180 degree switching is also explored in a tetragonal ferroelectric device. Throughout the study, the finite element calculations are compared with the behaviour of a material element subjected to various degrees of mechanical constraint.     

Unconventional domain band structure at the crack tip in ferroelectric ceramics

Domain polarization switch near the tip of a crack or an electrode plays a critical role in the fracture or toughening of ferroelectric ceramics. The intensive electric field near a crack tip stimulates local domain switching. Experiment indicates that the domain band structure in front of an indentation crack under lateral electric loading is unconventional, attributed to the highly localizing crack tip electric field. The partially switched ferroelectric grain resembles a banded Eshelby inclusion embedded in a polycrystalline ferroelectric matrix. The domain wall energy for unconventional domain structures is estimated via arrays of misfit dislocations. Mesomechanics analysis quantifies the unconventional domain band structures. The predicted parameters include the volume fraction, the thickness, and the orientation of switched domain bands.     

Minimizing electrostatic interactions from piezoresponse force microscopy via capacitive excitation

Piezoresponse force microscopy(PFM) has emerged as one of the most powerful techniques to probe ferroelectric materials at the nanoscale, yet it has been increasingly recognized that piezoresponse measured by PFM is often influenced by electrostatic interactions. In this letter, we report a capacitive excitation PFM(ce-PFM) to minimize the electrostatic interactions. The effectiveness of ce-PFM in minimizing electrostatic interactions is demonstrated by comparing the piezoresponse and the effective piezoelectric coefficient measured by ce-PFM and conventional PFM. The effectiveness is further confirmed through the ferroelectric domain pattern imaged via ce-PFM and conventional PFM in vertical modes, with the corresponding domain contrast obtained by ce-PFM is sharper than conventional PFM. These results demonstrate ce-PFM as an effective tool to minimize the interference from electrostatic interactions and to image ferroelectric domain pattern, and it can be easily implemented in conventional atomic force microscope(AFM)setup to probe true piezoelectricity at the nanoscale.     

铁电陶瓷电致疲劳失效的研究进展

铁电陶瓷是具备力电转换功能的典型高技术材料.本文概述铁电陶瓷电致疲劳失效的研究进展.首先介绍电致疲劳的定义和特点,然后讨论电致疲劳失效在不同尺度下的表现行为,包括宏观尺度下裂纹的疲劳扩展;细观尺度下裂纹的萌生;微观尺度下点缺陷在循环电场下的积聚.随即阐述了铁电陶瓷在循环电场下缺陷汇聚的理论分析,运用微结构演化方法计算了单个孔洞随畴界的移动距离,推导了循环电场下铁电陶瓷内点缺陷浓度的演化方程,给出了点缺陷浓度与其汇聚程度之间的定量关系,从而提出了贯通不同尺度的铁电陶瓷电致疲劳失效机理.      

Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading

Complex, non-linear, irreversible, hysteretic behavior of polycrystalline ferroelectric materials under a combined electro-mechanical loading is a result of domain wall motion, causing simultaneous expansion and contraction of unlike domains, grain sub-divisions that have distinct spontaneous polarization and strain. In this paper, a 3-dimensional finite element method is used to simulate such a polycrystalline ferroelectric under electrical and mechanical loading. A constitutive law due to Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47, 1663-1697] for switching by domain wall motion in multidomain ferroelectric single crystals is employed in our model to represent each grain, and the finite element method is used to solve the governing conditions of mechanical equilibrium and Gauss's law. The results provide the average behavior for the polycrystalline ceramic. We compare the outcomes predicted by this model with the available experimental data for various electromechanical loading conditions. The qualitative features of ferroelectric switching are predicted well, including hysteresis and butterfly loops, the effect on them of mechanical compression, and the response of the polycrystal to non-proportional electrical loading.     

Analysis of the electromechanical behavior of ferroelectric ceramics based on a nonlinear finite element model

A nonlinear finite element (FE) model based on domain switching was proposed to study the electromechanical behavior of ferroelectric ceramics. The incremental FE formulation was improved to avoid any calculation instability. The problems of mesh sensitivity and convergence, and the efficiency of the proposed nonlinear FE technique have been assessed to illustrate the versatility and potential accuracy of the said technique. The nonlinear electromechanical behavior, such as the hysteresis loops and butterfly curves, of ferroelectric ceramics subjected to both a uniform electric field and a point electric potential has been studied numerically. The results obtained are in good agreement with those of the corresponding theoretical and experimental analyses. Furthermore, the electromechanical coupling fields near (a) the boundary of a circular hole, (b) the boundary of an elliptic hole and (c) the tip of a crack, have been analyzed using the proposed nonlinear finite element method (FEM). The proposed nonlinear electromechanically coupled FEM is useful for the analysis of domain switching, deformation and fracture of ferroelectric ceramics.The project supported by the National Natural Science Foundation of China (10025209, 10132010 and 90208002), the Research Grants of the Council of the Hong Kong Special Administrative Region, China (HKU7086/02E) and the Key Grant Project of the Chinese Ministry of Education (0306)     

Utilizing mechanical loads and flexoelectricity to induce and control complicated evolution of domain patterns in ferroelectric nanofilms

We have conducted a systematical investigation to reveal the stability and evolution path of various ferroelectric domain patterns in nanofilms subjected to mechanical loads and related flexoelectric field. Within a rigorous framework of flexoelectricity, a phase-field approach has been established for simulating the domain structure of ferroelectric nanofilms. The electromechanical fields of the nanofilms are numerically solved by a fast Fourier transform technique (FFT) based on the combination of Khachaturyan's microscopic elastic theory and Stroh's formalism of anisotropic elasticity. Using this approach, we simulate eight types of domain patterns that can be stabilized in the nanofilms. It is further demonstrated that these domain patterns can be significantly affected by the mechanical loads and related flexoelectric field and exhibit fruitful evolution paths. To adapt the applied mechanical strain and strain gradient, the domain pattern may remain stable, evolve into another polydomain pattern, or become a monodomain state (an effect of domain erasing). The domain fraction, detailed domain morphology, average stresses in the nanofilms, average polarization and temporal evolution characteristics of the domain patterns under various mechanical loads and sources of flexoelectric field have been analyzed. This investigation should provide instructive information for the practical application of ferroelectric nanofilms under complex and changeable mechanical conditions.     

Effect of electric boundary conditions on crack propagation in ferroelectric ceramics

In this paper, the effect of electric boundary conditions on Mode I crack propagation in ferroelectric ceramics is studied by using both linear and nonlinear piezoelectric fracture mechanics. In linear analysis, impermeable cracks under open circuit and short circuit are analyzed using the Stroh formalism and a rescaling method. It is shown that the energy release rate in short circuit is larger than that in open circuit. In nonlinear analysis, permeable crack conditions are used and the nonlinear effect of domain switching near a crack tip is considered using an energy-based switching criterion proposed by Hwang et al.（Acta Metal. Mater.,1995）. In open circuit, a large depolarization field induced by domain switching makes switching much more diffcult than that in short circuit. Analysis shows that the energy release rate in short circuit is still larger than that in open circuit, and is also larger than the linear result. Consequently,whether using linear or nonlinear fracture analysis, a crack is found easier to propagate in short circuit than in open circuit, which is consistent with the experimental observations of Kounga Njiwa et al.（Eng. Fract. Mech., 2006）.     

Electrically excitable purely mechanical resonances in piezoelectric and ferroelectric materials - geometrical considerations

Mechanical displacements of electrically excited specimens of piezoelectric and ferroelectric materials are determined using a displacement laser interferometer system. It is found that purely mechanical resonances can exist in these specimens independent of any detectable electrical disturbance, including virgin and depoled specimens of ferroelectric ceramics. For specimens of the ceramic PZT8 it is shown that the number of purely mechanical resonances increases with decreasing specimen thicknesses, but there seems to be no other correlation between the resonances and the geometries of the specimens. Preliminary experimental evidence indicates that for the case of ferroelectric ceramics occurrence of the resonances may be due to the coupling of the driving voltage to the unit cell dipoles of the domains - this is suggestive of a dependence of domain structure.     

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.     

铁电材料的疲劳失效行为

在航空航天、核能发电等重大装备技术领域, 作为高温传感/驱动/能量收集器件的敏感材料——铋层状结构铁电(BLSF)陶瓷在复杂载荷环境下的疲劳失效问题严重限制着器件寿命和可靠性的提高. 本文以BLSF陶瓷的应用需求为背景, 围绕铁电材料的疲劳裂纹扩展与电畴极化翻转及其相互作用机制等关键问题, 综述了铁电材料在热、力、电三种载荷及其耦合作用下疲劳失效行为的研究现状, 并根据当前铁电材料的一些新发展、新应用对其未来研究方向进行了展望, 旨在为高性能、长寿命铁电/压电器件设计提供参考.      

Nonlinear characteristic of a circular composite plate energy harvester: experiments and simulations

Conservative chaotic systems are rare, especially autonomous smooth dynamical systems. This paper reports two four-dimensional (4D) autonomous conservative systems. The conservation of these two systems has been verified using the trace of Jacobian matrix, perpetual point theory and Hamiltonian energy theory. Numerical analyses, including phase portrait, Poincaré section, Lyapunov exponent spectrum and bifurcation diagram, verify the existence of the chaotic and quasiperiodic flows. Moreover, a electronic circuit in Multisim is built to demonstrate their chaotic dynamics, whose circuit experimental results agree well with the numerical results.     

铁电陶瓷微观电畴的成核率模型

大量的实验已经证实电畴翻转是铁电材料非线性和迟滞性本构曲线的根本原因。研究者已经对铁电陶瓷的微观电畴翻转行为进行了大量详细的研究。针对描述电畴成核的物理实验结果和经典的成核率实验数据,为了建立电畴翻转体积分数的演化方程提出了反应微观电畴翻转的成核率模型。针对铁电试样电畴随机分布的情况,应用该模型对铁电陶瓷的非线性本构行为进行了研究。理论结果与实验数据的比较表明,模型能较好的描述铁电材料的非线性本构行为。同时模型所揭示的微观反转的物理本质可进一步的指导宏观唯象模型的改进。     

A constitutive model for thermo-electro-mechanical behavior of ferroelectric polycrystals near room temperature

A constitutive model that can be used to predict thermo-electro-mechanical linear and nonlinear behavior of ferroelectric polycrystals near room temperature is proposed. A ferroelectric polycrystal is modeled by an agglomerate of 210 single crystallites that are distributed regularly over all directions. A variant in a single crystallite is characterized by a Gibbs free energy function whose coefficients have linear dependency on temperature. A dissipation inequality for domain switching is derived from the restriction of the second law of thermodynamics. Domain switching process is governed by a viscoplastic switching law with temperature-dependent switching parameters. The responses of the proposed model to electric field and mechanical stress loading at room and elevated temperatures are calculated and compared qualitatively with experimental observations available in literature.