铁电薄膜在红外辐射作用下响应的解析解

本文研究了红外探测器中红外焦平面列阵的象元———铁电薄膜微桥在红外辐射作用下的输出信号。采用层合板作为力学模型,将铁电薄膜微桥结构简化为一块边长为微米量级、厚度为亚微米量级的夹层板,中间是铁电薄膜,上下表面为金属薄膜,上表面为金黑,下表面为铂(白金),上下表面都是电极。微桥的上表面接收周期为1/30秒的辐射方波脉冲信号。由于微桥十分微小,可以认为红外辐射在板面上均匀分布,又由于板的平面尺寸与厚度之比相当大,因此可以认为热传导只在板厚的方向进行,问题变为一维的。采用适当的力-电-热耦合的控制方程,利用级数解,算出铁电薄膜微桥在红外辐射作用下的力学响应和薄膜内的力、热、电输出信号,并对结果作了分析比较。     

铁电陶瓷PZT的实验本构研究

用低频高压电源和液压加力架实验研究了力电载荷下铁电陶瓷软性ＰＺＴ（Ｐ－５１）的单轴应力应变关系,在不同压应力下的电滞回线和蝶曲线,实验发现随着压应力的增加。ＰＺＴ的铁电特性发生很大的变化,尝试用电畴来解释ＰＺＴ在不同压力电性的变化规律和退极化效应,在本实验中,我们很好的解决了测试材料高压性能中常出现的绝缘问题和电弧放电问题,获得了比较系统的实验结果。     

弯曲衬底上应变异质外延薄膜形态失稳的相场模拟

论文旨在研究弯曲衬底上应变异质外延薄膜的表面非线性演化行为,研究采用了基于Eshelby等效方法的相场微弹性模型来模拟二维应变Si1-xGex/Si薄膜/衬底系统的形态失稳.建立了关于等效特征应变和长程序参量的自由能泛函,数值求解了时间相关的Ginzburg-Landau动力学方程.系统自由能包括化学能,弹性应变能以及薄膜、衬底与真空相两两之界面能.跟踪了全时的形态演化过程,给出了指定时刻的量子点形态轮廓图.结果表明,量子点倾向于沉积在弯曲衬底的波谷处,波谷处是能量有利位置,量子点在此处比在波峰处更加稳定.论文所做的相场模拟可以用来预测量子点形成的轮廓、尺寸和位置,可以为控制和生成周期性自组装表面纳米结构提供理论指导.     

BST铁电薄膜在红外辐射作用下响应的解析解

研究了红外探测器中红外焦平面列阵的象元-BST铁电薄膜微桥在红外辐射作用下输出信号的分析方法.将BST铁电薄膜微桥结构简化为一块微米尺度的夹层板,中间是BST铁电薄膜,在极化模式下工作.微桥的上表面接收辐射脉冲信号.由于微桥十分微小,可以认为红外辐射在板面上均匀分布,又由于板的平面尺寸比厚度大得多,可以认为热传导只在板厚的方向进行.采用适当的力-电-热耦合的控制方程和非线性的本构方程,得到了铁电薄膜微桥在红外辐射作用下的的力、热、电输出信号的解析解,并将计算结果与实验结果作了比较.     

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。     

铁磁纳米结构磁化状态及其磁-力耦合效应的相场模拟

基于随时间变化的Ginzburg-Landau(TDGL)方程,建立了模拟铁磁材料磁-力耦合效应的相场模型。从弱解形式出发,推导出了相关控制方程的有限元格式,然后编制程序进行数值求解。由于有限元对复杂边界有良好的适用性,该模型可用于不同形状铁磁材料的畴结构模拟。通过相场模拟,发现铁磁纳米结构中的磁化会形成涡旋结构,与实验观察到的磁化涡旋结构符合较好。由非均匀磁化引起的结构的变形、应力等力学参量都可以通过模拟一并得到。本文结果表明,改变结构形状可以有效控制磁畴结构的形态,适当的外应力可以改变磁畴结构及其对外磁性的大小。     

铁电陶瓷PZT53复杂力电耦合行为的实验研究

通过实验研究了平行和垂直于极化方向的正应力对铁电陶瓷锆钛酸铅(PZT53)的电滞回线(E3-P3)和电致应变曲线(E-ε)的影响. 实验发现平行于极化方向的压应力对PZT53陶瓷的电滞回线、电致应变曲线形状以及矫顽场大小都有明显的影响,但是垂直于极化方向的拉、压应力只对PZT53陶瓷的电致应变曲线形状有明显的影响,但对电滞回线形状和矫顽场大小都没有显著影响. 采用畴翻转的模型详细解释了观察到的实验现象,所得结果为建立铁电陶瓷的多轴力、电耦合本构模型,提供了物理基础.     

PZT压电陶瓷高温变形与失效的实验研究

随着工业设备集成化进程的加快,PZT压电陶瓷获得越来越广泛的应用,其工作环境也越来越复杂.例如,新一代节能环保型发动机中起致动作用的压电陶瓷叠层驱动器,工作时要承受力-热-电载荷的共同作用.因此,研究PZT压电陶瓷在高温下的变形与失效行为,对工业设计具有重要的指导意义.为此,本文利用自行搭建的压电陶瓷高温下电滞回线、蝶形回线和应力退极化曲线的测试装置,研究了PZT压电陶瓷在不同温度下的电致变形和应力退极化行为,得到了材料在不同温度下的电滞回线、蝶形回线、应力电位移曲线和应力应变曲线.实验结果表明,随着温度的升高,由电滞回线测得的剩余极化逐渐减小,蝶形回线逐渐变扁;由应力退极化产生的剩余极化和剩余应变也逐渐减小.极化量的改变是由材料的热释电效应(自发极化随温度的升高而减小)造成的,而应变量的变化是由晶胞畸变随着温度升高而减小所致.     

铁电陶瓷微观电畴演化的成核率模型

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.根据这些描述电畴运动的物理实验结果,提出了成核率模型来模拟铁电材料的非线性本构行为.进一步由模型建立了基于微观电畴运动的电畴翻转体积分数演化方程.应用该模型得到的理论计算结果与实验数据的比较表明,模型能够描述铁电材料的非线性本构行为.同时模型所揭示的微观电畴成核的演化行为可进一步的指导宏观唯象模型的建立与改进.     

铁电陶瓷宏细观本构模型

在居里温度以下，铁电陶瓷呈铁电相，具有许多取向不同的铁电畴，取向分布函数描述了铁电畴的取向分布情况文中推广了经典的内变量理论，采用宏细观相结合的方法，建立了铁电陶瓷的宏观行为与细观结构的关系，给出了铁电陶瓷的屈服条件，屈服面的演化规律及取向分布函数的演化规律计算得出了与实验比较符合的电位移－电场关系曲线及应变电场－蝶形关系曲线     

Strain tunability of dielectric and ferroelectric properties in epitaxial lead titanate thin films

Many distinguished properties of epitaxial ferroelectric thin films can be tunable through the misfit strain. The strain tunability of ferroelectric and dielectric properties in epitaxial lead titanate ultrathin films is numerically investigated by using a phase field model, in which the surface effect of polarization is taken into account. The response of polarization to the applied electric field in the thickness direction is examined with different misfit strains at room temperature. It is found that a compressive misfit strain increases the coercive field and the remanent polarization while a tensile misfit strain decreases both of them. The nonlinear dielectric constants of the thin films with tensile misfit strains are much larger than those of the thin films without misfit strains, which are attributed to the existence of the a/c/a/c multiple domains in the thin films under tensile misfit strains.     

Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: Experimental validation of the non-local stress/curvature relations

The classical Stoney formula relating local equibiaxial film stress to local equibiaxial substrate curvature is not well equipped to handle realistic cases where the film misfit strain, the plate system curvature, and the film thickness and resulting film stress vary with in-plane position. In Part I of this work we have extended the Stoney formula to cover arbitrarily non-uniform film thickness for a thin film/substrate system subject to non-uniform, isotropic misfit strains. The film stresses are found to depend non-locally on system curvatures. In Part II we have designed a demanding experiment whose purpose is to validate the new analysis for the case of radially symmetric deformations. To achieve this, a circular film island with sharp edges and a radially variable, but known, thickness is deposited on the wafer center. The plate system’s curvatures and the film stress distribution are independently measured by using white beam and monochromatic X-ray microdiffraction (μXRD) measurements, respectively. The measured stress field (from monochromatic μXRD) is compared to the predictions of various stress/curvature analyses, all of which have the white beam μXRD measurements as input. The results reveal the shortcomings of the “local” Stoney approach and validate the accuracy of the new “non-local” relation, most notably near the film island edges where stress concentrations dominate.     

Wrinkling of a charged elastic film on a viscous layer

A thin metallic film deposited on a compliant polymeric substrate begins to wrinkle under compression induced in curing process and afterwards cooling of the system. The wrinkle mode depends upon the thin film elasticity, thickness, compressive strain, as well as mechanical properties of the compliant substrate. This paper presents a simple model to study the modulation of the wrinkle mode of thin metallic films bonded on viscous layers in external electric field. During the procedure, linear perturbation analysis was performed for determining the characteristic relation that governs the evolution of the plane-strain wrinkle of the thin films under varying conditions, i.e., the maximally unstable wrinkle mode as a function of the film surface charge, film elasticity and thickness, misfit strain, as well as thickness and viscosity of the viscous layer. It shows that, in proper electric field, thin film may wrinkle subjected to either compression or tension. Therefore, external electric field can be employed to modulate the wrinkle mode of thin films. The present results can be used as the theoretical basis for wrinkling analysis and mode modulation in surface metallic coatings, drying adhesives and paints, and microelectromechanical systems (MEMS), etc.     

Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362–370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney’s Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483–2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.     

Three dimensional phase field study on the thickness effect of ferroelectric polymer thin film

The electromechanical behavior of poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] ferroelectric thin film was investigated using the three dimensional (3D) phase-field method. Various energetic contributions, including elastic, electrostatic, and domain wall energy were taken into account in the variational functional of the phase field model. Evolution of the microscopic domain structures of P (VDF-TrFE) polymer film was simulated. Effects of the in-plane residual stress, the film thickness and externally applied electric bias field on the electromechanical properties of the film were explored. The obtained numerical results showed that the macroscopic responses of the electric hysteresis loops are sensitive to the residual stress and electric bias field. It was also found that thickness has a great effect on the electric hysteresis loops and remanent polarization.     

Residual stresses in thin film systems: Effects of lattice mismatch,thermal mismatch and interface dislocations

This paper explores the mechanisms of the residual stress generation in thin film systems with large lattice mismatch strain, aiming to underpin the key mechanism for the observed variation of residual stress with the film thickness. Thermal mismatch, lattice mismatch and interface misfit dislocations caused by the disparity of the material layers were investigated in detail. The study revealed that the thickness-dependence of the residual stresses found in experiments cannot be elucidated by thermal mismatch, lattice mismatch, or their coupled effect. Instead, the interface misfit dislocations play the key role, leading to the variation of residual stresses in the films of thickness ranging from 100 nm to 500 nm. The agreement between the theoretical analysis and experimental results indicates that the effect of misfit dislocation is far-reaching and that the elastic analysis of dislocation, resolved by the finite element method, is sensible in predicting the residual stress distribution. It was quantitatively confirmed that dislocation density has a significant effect on the overall film stresses, but dislocation distribution has a negligible influence. Since the lattice mismatch strain varies with temperature, it was finally confirmed that the critical dislocation density that leads to the measured residual stress variation with film thickness should be determined from the lattice mismatch strain at the deposition temperature.     

多孔极化PZT95/5铁电陶瓷单轴压缩力学响应与放电特性

采用添加造孔剂的方法制备了四种不同孔隙率PZT95/5铁电陶瓷,对其进行电场极化,随后开展了准静态单轴压缩实验,讨论了畴变、相变以及孔隙率对极化PZT95/5铁电陶瓷的力学响应与放电特性的影响.研究结果表明:(1)多孔极化PZT95/5铁电陶瓷非线性力学响应行为主要归因于畴变和相变的共同作用,与内部孔洞变形和坍塌基本无关;(2)在准静态单轴压缩下极化PZT95/5铁电陶瓷的去极化机制是畴变和相变的共同作用;(3)孔隙率对极化PZT95/5铁电陶瓷的弹性模量、压缩强度有明显的影响,而对断裂应变的影响较小;(4)极化PZT95/5铁电陶瓷畴变和相变开始的临界应力都随着孔隙率的增大而线性衰减,但相变开始的临界体积应变却不依赖孔隙率;(5)极化PZT95/5铁电陶瓷电荷饱和释放量随着孔隙率呈线性减小,但孔隙率对电荷释放速率基本没有影响.     

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.     

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.     

Misfit dislocation dipoles in wire composite solids

Developed in this note is a theoretical model describing the mobility of a misfit screw dislocation dipole in a wire composite consisting of a stiff cylindrical substrate covered by a soft co-axial cylindrical film. A critical value of the film thickness, which is a function of the parameter measuring the stiffness of the film with respect to the substrate, is identified. It is observed that: (i) there exist two equilibrium positions of the misfit dislocation dipole (one stable and the other one unstable) when the film is thicker than the critical value; (ii) the two equilibrium positions of the misfit dislocation dipole converge to a single saddle point equilibrium position which is neither stable nor unstable when the thickness of the film is at the critical value; (iii) there exists no equilibrium position of the misfit dislocation dipole when the thickness of the film is below the critical value. These features could be useful to the design of wire composites and to the dislocation-related plasticity analysis.