Role of grain orientation distribution in the ferroelectric and ferroelastic domain switching of ferroelectric polycrystals

The non-linear electromechanical behavior of ferroelectric polycrystals stems from polarization/domain switching, which are affected by the grain boundaries and grain orientations. The effects of grain orientation distribution on the domain switching and non-linear behavior of a two-dimensional ferroelectric polycrystal subjected to an electric or/and mechanical load are investigated by computer simulations with a real-space phase-field model. Phase-field simulations indicate that the macroscopic coercive field, remanent polarization and remanent strain in the polycrystal with a random distribution of grain orientation are correspondingly smaller than those in the polycrystal with a uniform distribution of grain orientation. However, the polycrystal with randomly distributed grain has a larger strain variation with the electric field than the polycrystal with uniformly distributed grains, which suggests that the random polycrystal has a better piezoelectric property than the uniform one. The different macroscopic non-linear behaviors of the ferroelectric polycrystals are attributed to different microscopic domain switching processes. For the polycrystal with randomly distributed grains, the domain switching takes place from the regions near the large angle grain boundaries, while new domains nucleate from the cross sections between the grain boundaries and the material surface in the polycrystal with uniform grain orientation.     

Conducting crack propagation driven by electric fields in ferroelectric ceramics

Ferroelectric ceramics are susceptible to fracture under high electric fields, which are commonly generated in the vicinity of electrodes or conducting layers. In the present work, we extend a phase-field model of fracture in ferroelectric single crystals to the simulation of the propagation of conducting cracks under purely electrical loading. This is done by introducing the electrical enthalpy of a diffuse conducting layer into the phase-field formulation. Simulation results show oblique crack propagation and crack branching from a conducting notch, forming a tree-like crack pattern in a ferroelectric sample under positive and negative electric fields. Microstructure evolution indicates the formation of tail-to-tail and head-to-head 90° domains, which results in charge accumulation around the crack. The charge accumulation, in turn, induces a high electric field and hence a high electrostatic energy, further driving the conducting crack. Salient features of the results are compared with experiments.     

Phase-field simulation of solidification morphology in laser powder deposition of Ti-Nb alloys

A phase-field model of alloy solidification is coupled to a new heat transfer finite element model of the laser powder deposition process. The robustness and accuracy of the coupled model is validated by studying spacing evolution under the directional solidification conditions in laser powder deposition of Ti-Nb alloys. Experimental Ti-Nb samples reveal the microstructure on a longitudinal section with significant change in the size of the dendrites across the sample. Quantitative phase-field simulations of directional solidification under local steady-state conditions extracted from the results of the finite element thermal model confirmed this behavior. Specifically, the phase-field simulations agree with the results of the analytical model of Hunt in predicting a minimum spacing value, which is due to the mutual effects of the increasing temperature gradient and decreasing solidification velocity towards the bottom of the microstructure. This work demonstrates the potential of coupling the phase-field method to complex heat transfer conditions necessary to simulate topologically complex microstructure morphologies present in laser powder deposition and other industrially relevant casting conditions.     

Phase-field simulation of domain structure for PbTiO3/SrTiO3 superlattices

Phase-field modeling has been performed to study the domain morphologies of ferroelectric PbTiO₃/SrTiO₃ superlattice grown on SrTiO₃ substrates. Taking into account contributions of the interfacial and depolarization field effects, the polarization, phase transition temperature and critical thickness are calculated as functions of sample dimensions and temperature. The results show that interfacial and depolarization field effects are the main reasons behind the dependence of the domain structures and critical properties (i.e., the phase transition temperature and critical thickness) on the thicknesses of the constituent layers of the PbTiO₃/SrTiO₃ superlattices.     

Phase-field study of competitive dendritic growth of converging grains during directional solidification

The microstructure evolution of grains with different orientations during directional solidification is investigated by the phase-field method. For converging dendrites, in addition to the usually accepted overgrowth pattern wherein the favorably oriented dendrites block the unfavorably oriented ones, the opposite pattern of overgrowth observed in some recent experiments is also found in our simulations. The factors which may induce this unusual overgrowth are analyzed. It is found that in addition to the difference in tip undercooling, the solute interaction of converging dendrites, which has been ignored in the classical theoretical model, also has a significant effect on the nature of the overgrowth at low pulling velocities. Solute interaction can retard the growth of dendrites at the grain boundary (GB) and induce a lag of these dendrites relative to their immediate neighbors, which gives the unfavorably oriented dendrite the possibility to overgrow the favorably oriented one. However, this unusual overgrowth only occurs when the spacing between the favorably oriented GB dendrite and its immediate favorably oriented neighbor decreases to a certain level through lateral motion. These findings can broaden our understanding of the overgrowth mechanism of converging dendrites.     

Phase-field simulation of abnormal grain growth due to inverse pinning

The possibility of abnormal grain growth due to inverse pinning was verified using phase-field simulations. In bicrystalline systems with circular precipitates, the perfect wetting condition is required for the long-distance migration of the interface between the matrix grains. If the distance between precipitates that are perpendicular to the interface exceeds a critical value, the migration is not observed irrespective of the wetting condition. In polycrystalline systems, abnormal grain growth occurs with the aid of the driving force for grain growth even though l_lim exceeded the critical value, where l_lim is the minimum distance between precipitates. Furthermore, the perfect wetting condition is not required for the abnormal grain growth in the polycrystalline systems. These facts enlarge the possibility of inverse pinning in real alloy systems.     

湿度对恒电场下BaTiO3单晶中畴变的影响

通过偏振光显微镜观察了在恒电场作用下湿空气对BaTiO3单晶畴变的影响.结果表明,在恒电场下,湿度对不同的畴结构有不同的影响.较低的湿度对a-b和b-c畴结构没有影响.而在较高的湿度下,随着放置时间的增加,b-c畴结构发生了变化,b畴逐渐向c畴转变;但是较高的湿度对a-b畴结构无影响.可用水分子在a(b)畴和c畴上的吸附差别解释上述现象.     

Phase-field study for the splitting mechanism of coherent misfitting precipitates in anisotropic elastic media

Through a phase-field study upon the splitting behavior and morphological evolution of coherent precipitates, we show that an interface instability driven by elastic anisotropy and a diffusion field can generate elastically induced splitting during diffusional phase transition. Particle splitting is triggered by interface grooving which advances by penetrating grooves into the interior of the particle. The sequential evolution of shapes during the splitting process is in good agreement with previous experiments.     

Study of electrical and mechanical contribution to switching in ferroelectric/ferroelastic polycrystals

Polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is simulated with a finite element model. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite, represented by a cubic element in a finite element mesh, is a single domain that switches completely without a simulated domain wall motion. The possible dipole directions of each crystallite are assigned randomly subject to crystallographic constraints. The model accounts for electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching without piezoelectric interaction. Different weights for the mechanical and electrical contribution to switching are selected phenomenologically to simulate electric displacement vs electric field and strain vs electric field of a ceramic lead lanthanum zirconate titanate (PLZT). Although the critical energy barriers for 90° and 180° switching are assumed to be the same, 90° switching is favored when the electrical contribution to switching (i.e. electrical energy) is dominant, but 180° switching is favored when the mechanical contribution to switching (i.e. elastic strain energy) is dominant. With increasing mechanical contribution and decreasing electrical contribution, the simulated electric displacement deviates from the Rayleigh law under a low applied electric field, and the shape of a switching region (or a process zone) changes from a prolonged ellipsoid to a sphere.     

相场模型及其在凝固组织模拟中的研究进展

相场法作为一种模拟凝固微观组织的有效方法,是目前研究的热点.对相场模型的基本原理、数值计算方法以及在凝固组织模拟中的研究进展进行了综述,提出了相场模型在微观组织模拟中存在的主要问题以及今后的发展方向.     

Three-dimensional phase-field modeling of martensitic microstructure evolution in steels

In the present work a 3-D elastoplastic phase-field (PF) model is developed, based on the PF microelasticity theory proposed by A.G. Khachaturyan and by including plastic deformation as well as anisotropic elastic properties, for modeling the martensitic transformation (MT) by using the finite-element method. PF simulations in 3D are performed by considering different cases of MT occurring in an elastic material, with and without dilatation, and in an elastic perfectly plastic material with dilatation having isotropic as well as anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to an Fe-0.3%C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The simulation results clearly show autocatalysis and morphological mirror image formation, which are some of the typical characteristics of a martensitic microstructure. The results indicate that elastic strain energy, anisotropic elastic properties, plasticity and the external clamping conditions affect MT as well as the microstructure.     

Fe-C合金等温凝固过程的相场法模拟

基于KKS模型,采用耦合相场和溶质场的方法,对Fe-0．5mol％C合金凝固过程中的枝晶生长进行了模拟,并研究了过冷度、各向异性强度和扰动强度对枝晶生长形貌的影响。结果表明：随着过冷度的减小,枝晶主干细化,各向异性程度增大,晶粒生长速度减小,溶质扩散层厚度增加,枝晶的最高溶质浓度降低,溶质梯度减小;随着各向异性的增加,晶粒由海藻状转变为枝晶态,枝晶生长速度也随之增大;扰动强度引发了侧向分枝,侧枝间互相竞争生长,根部出现“颈缩”现象,但扰动强度的加入并不改变枝晶尖端的稳态行为。     

合金过冷熔体中枝晶生长的相场法研究进展

相场法作为一种模拟晶粒长大的有效方法,是目前国内外研究的热点。对铸件的凝固组织进行数值模拟,有利于深入理解凝固组织形成机制,预测铸件的凝固微观组织,优化铸件的工艺。概述了目前国内外三维晶粒微观组织数值模拟的研究进展、相关基本原理和模型,以及在模拟过程中常用的计算方法,提出了相场模型在微观组织模拟中存在的主要问题以及今后的发展方向。     

各向异性对过冷熔体中枝晶生长影响的相场法模拟

文中采用二元合金的等温相场模型，通过在相场参数中引入界面能各向异性强度参数，以A1-4．5％Cu合金为例模拟了各向异性强度对二元合金凝固过程的枝晶生长的影响。结果表明：各向异性强度小时，枝晶形貌呈海藻态，随着各向异性强度的增大，枝晶形貌从海藻态向枝晶态转变，主枝不再分叉，成为光滑枝晶，枝晶尖端生长速度增大，曲率半径减小并逐渐趋于定值，同时模拟的结果与经典枝晶生长理论相吻合。     

Effect of grain orientation and grain size on ferroelectric domain switching and evolution: Phase field simulations

Phase field simulations were conducted in order to understand the effect of grain orientation, grain boundary and grain size on ferroelectric domain switching, stress distribution and evolution behavior under an applied electric field. Tetragonal ferroelectric domains were considered. Hysteresis loops were obtained for a single crystal, a bi-crystal and a polycrystal and the differences in their coercive fields were examined. It was found that the magnitude of the coercive field was closely related to the domain structures at the maximum electric field. Nucleation of new domains at a grain boundary led to local high stress. The effect of a reduced ferroelectric transition temperature at the grain boundary on the polarization distribution, domain structure and switching was studied.     

Phase-field modelling of as-cast microstructure evolution in nickel-based superalloys

A modelling approach is presented for the prediction of microstructure evolution during directional solidification of nickel-based superalloys. A phase-field model is coupled to CALPHAD thermodynamic and kinetic (diffusion) databases, so that a multicomponent alloy representative of those used in industrial practice can be handled. Dendritic growth and the formation of interdendritic phases in an isothermal (2-D) cross-section are simulated for a range of solidification parameters. The sensitivity of the model to changes in the solidification input parameters is investigated. It is demonstrated that the predicted patterns of microsegregation obtained from the simulations compare well to the experimental ones; moreover, an experimentally observed change in the solidification sequence is correctly predicted. The extension of the model to 3-D simulations is demonstrated. Simulations of the homogenization of the as-cast structure during heat treatment are presented.     

相场法模拟Cu-Ag合金时效过程中组织演变

基于相场方法,模拟研究了Cu-20和40 at%Ag合金在等温时效过程中相分解与微观组织的演变.系统自由能中耦合了体化学能、浓度梯度能和共格错配应变能,化学自由能是直接利用相图热力学数据计算得到的,因此,计算的微结构变化与真实合金系统是相对应的.通过模拟,获得了合金的形态和浓度分布随时间、温度和组分的变化规律.模拟结果表明,对称合金(Cu-40at%Ag)分解和粗化的速度均高于相应的非对称合金,其相分离的早期阶段形成规则的、相互连接的微观形态.在Cu-20at% Ag合金中,沉淀相Ag经历了调幅分解和粗化过程,其形态呈立方状,沿[110]方向排列.     

Domain microstructure evolution in magnetic shape memory alloys: Phase-field model and simulation

A phase-field micromagnetic microelastic model is employed to simulate domain microstructure evolution in magnetic shape memory alloys. The simulations reveal that coupled motions of martensite twin boundaries and magnetic domain walls depend not only on the external magnetic field but also on internal domain configurations. It is shown that a twin boundary can continue its motion under a decreasing magnetic field or even reverse motion direction without changing magnetic field. The domain microstructure-dependent driving forces for the coupled motions of martensite twin boundaries and magnetic domain walls are analyzed; these explain the complex domain processes and resultant peculiar magnetomechanical behavior of magnetic shape memory alloys.     

Lateral size and thickness dependence in ferroelectric nanostructures formed by localized domain switching

Ferroelectric nanostructures can be formed by local switching of domains using techniques such as piezo-force microscopy (PFM). Understanding the dependence of the switching behavior on the lateral size of the electrode is important to determine the minimum feature size for writing ferroelectric nanostructures. To understand these lateral size effects, we use the time-dependent Ginzburg–Landau equations in a two-dimensional square to rectangle ferroelectric transition to simulate localized switching of domains for PFM-type and parallel-plate capacitor configurations. Our investigations indicate that fringing electric fields lead to switching via intermediate 90° domains even in the absence of substrate or clamping effects for films of sufficient thicknesses, and via 180° rotations at smaller thicknesses. The voltage required to switch the domain increases by decreasing the lateral size, and at very small lateral sizes the coercive voltage becomes so large that it becomes virtually impossible to switch the domain.