Ferroelectric Properties of Polycrystalline Ceramics with Dipolar Defect Simulated from the Potts--Ising Model

Physical properties of polycrystailine ferroelectrics including the contributions of the fixed dipolar defects and the average grain size in the Potts-Ising model are simulated by using the Monte Carlo method. Domain pattern, hysteresis loop and switching current of the polarization reversal process are obtained. Two processes are considered in our simulation. In the first one, the grain texture of ferroelectric ceramics are produced from the Ports model, and then the Ising model is implemented in the obtained polycrystailine texture to produce the domain pattern, hysteresis loop and switching current. It is concluded that the defect has the ability to decrease the remnant polarization P~ as well as the coercive field E~. The back switching is obviously observed after the electric field is off, and it shows some variation after introducing the fixed dipolar defect. Meanwhile, the spike of the switching current is found to lower with the increasing defect concentration and the decreasing average grain size.     

Dynamic hysteresis for Potts spin system: a Monte Carlo simulation

A Monte Carlo approach based on the Q-state Potts model is developed to describe and simulate the dynamic hysteresis of Potts spin lattice against periodic time-varying external field E. The dynamic responses of the hysteresis loops against frequency P of applied field and domain size R are studied. It is revealed that the hysteresis loops for the system energy W, polarization P, and domain wall fraction @ depend considerably on the frequency and domain size. The remnant polarization P_r shows a single-peak pattern as a function of P. The P-E loop exhibits thin rhomb and fat rhomb patterns at low P, whereas a tip-smoothed rhomb and roughly elliptical pattern is observed at high P. The loop area can be scaled with Q,P^1/3 at low P. The frequency dependency of the dynamic hysteresis is explained in terms of a simplified phenomenological model. At very small domain size, the dynamic hysteresis is significantly compressed, predicting the polarization weakening effect at small domain size.     

Simulation on dielectric susceptibility and domain evolution of relaxor ferroelectrics

Dielectric susceptibility and domain evolution of the relaxor ferroelectrics have been simulated using the Monte Carlo method upon the Potts-Ising model. The grain size effect and the applied ac field frequency effect on the dielectric susceptibility were theoretically investigated. We found that the dielectric susceptibility increases and the T_m (the temperature at which the dielectric susceptibility reaches the maximum) shifts to lower temperature with increasing average grain size or decreasing frequency. In addition, we obtained the value of the relaxation parameter γ estimated from the linear fit of the modified Curie-Weiss law; its changing trend with increasing average grain size or increasing frequency was well consistent with the experimental observation. From the results of the domain pattern evolution process, we observed the differences between relaxor ferroelectrics and normal ferroelectrics subjected to an applied ac field.     

Mathematical Modeling of the Polarization of Polycrystalline Ferroelectrics

General patterns of the polarization models of Rayleigh, Preisach, and Jiles–Atherton are found. The limiting dependence of the polarization is confirmed. A way of constructing it based on the energy criterion for domain switching for polycrystalline ferroelectrics with perovskite structure is proposed. Differential equations are constructed for determining the irreversible components of polarization and deformation, and large loops of dielectric hysteresis are calculated.     

Specific features in the permittivity of polycrystalline ferroelectrics: The role of Schottky regions

This paper reports on the results of investigations into the influence of Schottky regions formed in the vicinity of crystallite boundaries in polycrystalline ferroelectrics on their permittivity. The dependence of the dielectric properties of the Schottky regions on the orientation of the spontaneous polarization in the adjacent region of the crystallite is taken into consideration. It is demonstrated that nonmonotonic dependences of the permittivity and its relative change on the crystallite size under uniaxial compression are associated with the presence of the domain structure in polycrystalline ferroelectrics.     

Simulation of hysteresis loops for polycrystalline ferroelectrics by an extensive Landau-type model

Landau-type phenomenological theory is extended to the polycrystalline ferroelectrics by defining a volume fraction of polarization to simulate polarization hysteresis loops. Using this simple model, polarization hysteresis loops of a model Pb(Zr_0.52Ti_0.48)O₃ ceramic at different fields or temperatures are simulated, it is found that our results are in very good agreement with the experimental data for the saturated as well as the unsaturated loops. Moreover, this model can accurately predict the coercive fields and remnant polarizations under arbitrary applied fields.     

Relation between the microstructural properties of electrical steels and the Preisach modelling

In this paper, the relation of the microstructural properties of electrical steels and the material parameters in the dynamic Preisach model is established. Particular experimental work was performed in order to separate the influence of grain size from the crystallographic texture. First, the parameters defined in the dynamic Preisach model has been fitted using the hysteresis loss characteristics. Next, we identified and separated the effect of average grain size from the crystallographic texture on each material parameter defined in the Lorentzian–Preisach distribution function. Here, the same texture dependence was identified for all kinds of magnetisation processes, i.e. for the irreversible and reversible parts of the quasi-static magnetisation and for the AC excess loss behaviour. Finally, the Preisach distribution function is rewritten explicitly including the grain size and crystallographic texture dependence.     

铁电体中偶极子的滞后对剩余极化的影响

铁电体的剩余极化强度随温度降低而下降的特性引起了人们对铁电体存储数据失效的担心.运用铁电体的唯象理论和偶极子对交变电场的响应,提出了在电滞回线测量中偶极子的滞后冷冻效应模型,对极化的低温退化现象做了合理解释:温度下降导致吉布斯自由能势垒增大,致使偶极子对交变电场的响应时间延长.引入响应的滞后因子发现,极化强度随温度降低会出现峰值,在低温下降直至为零,可用偶极子的滞后与冻结效应描述.详细研究结果表明:因材料组份变化导致热力学参量的变化是重要因素:铁电-顺电相变中软模系数的增大会导致剩余极化峰移向高温;铁电性的增强,温度极化系数的增大和耐压强度或饱和电场的增强均会抑制滞后效应,从而使低温滞后效应移向低温.运用导出的公式数值模拟Ba Ti O_3/Bi Sc O_3复合陶瓷剩余极化强度的实验结果发现,Bi Sc O3含量的增加,使居里温度略有减小,但导致了软模系数较大幅度的增加,其结果是使偶极子的滞后效应发生在较高的温度.软模系数与铁电体的极化特性、铁电性、介电性和力学性均密切相关.研究结论表明:在低温下铁电体的铁电性没有失效,偶极子的低温冻结效应更有利于铁电体长久地保存数据.     

Dynamics of the domain structure in a ferroelectric triglycinesulfate crystal

The dynamics of the domain structure in ferroelectrics of order-disorder type like triglycinesulfate is studied. The polarization properties of ferroelectrics with relaxation-type absorption are described in terms of the pseudospin formalism. A kinetic equation describing the polarization dynamics of ferroelectrics is derived using the Hamiltonian of the problem. The domain structure dynamics is obtained for different problem parameters and initial conditions. Analytical results are compared with experimental data.     

Low temperature properties of the random field Potts chain

The random field q-states Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case (q = 2). This is also the expected outcome based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field perturbations (`chaos') and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,..., 5. Finally for q = 2 (Ising case) the domain length distribution is studied for correlated random fields. Received 27 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: rieger@lusi-sb.de     

Experimental study of polarization bremsstrahlung from small-grained polycrystals

The spectrum of polarization Bremsstrahlung is measured in backscattering geometry for 7-MeV electrons and a polycrystalline Ni foil without texture. The average size of grains in the foil is 300 nm. The results show the possibility of using a new method in the diagnostics of the atomic structure of polycrystalline materials with nanosized grains. The method is based on measuring the coherent component of polarization Bremsstrahlung.     

Dynamics of the domain structure in ferroelectrics with an incommensurate phase

The dynamics of the domain structure of ferroelectrics with an incommensurate phase (like sodium nitrite) is considered. The polarization properties of these ferroelectrics are described using the pseudospin formalism. The equation for the polarization is numerically solved together with the equation for acoustic waves. The obtained results are analyzed for various values of the parameters of the crystal and different initial conditions. It is shown that, after a sufficiently large time, the domain structure of the crystal becomes localized.     

Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.     

Improved phenomenological renormalization schemes

An analysis is made of various methods of phenomenological renormalization based on finite-dimensional scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made using two-dimensional Ising and Potts lattices and the three-dimensional Ising model. Variants of equations for the phenomenological renormalization group are obtained which ensure more rapid convergence than the conventionally used Nightingale phenomenological renormalization scheme. An estimate is obtained for the critical finite-dimensional scaling amplitude of the internal energy in the three-dimensional Ising model. It is shown that the two-dimensional Ising and Potts models contain no finite-dimensional corrections to the internal energy so that the positions of the critical points for these models can be determined exactly from solutions for strips of finite width. It is also found that for the two-dimensional Ising model the scaling finite-dimensional equation for the derivative of the inverse correlation length with respect to temperature gives the exact value of the thermal critical index.     

Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a three-dimensional model of ferroelectrics with quenched disorder and varying domain sizes. We study (1) bursts of the switching current at slow driving along the hysteresis loop (electrical Barkhausen noise) and (2) the polarization reversal when a strong electric field was applied and back-switching after the field was removed. We show how these processes are related to the underlying structure of domain walls, which in turn is controlled by the pinning at quenched local electric fields. When the depolarization fields of bound charges are properly screened we find that the fractal switching current noise may appear with two distinct universal behaviors. The critical depinning of plane domain walls determines the universality class in the case of weak random fields, whereas for large randomness the massive nucleation of domains in the bulk leads to different scaling properties. In both cases the scaling exponents decay logarithmically when the driving frequency is increased. The polarization reverses in the applied field as a power-law, while its relaxation in zero field is a stretch exponential function of time. The stretching exponent depends on the strength of pinning. The results may be applicable for uniaxial relaxor ferroelectrics, such as doped SBN:Ce. Received 7 February 2002 / Received in final form 10 April 2002 Published online 9 July 2002     

Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices

The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.     

Unusual domain evolution in semiconducting ferroelectrics: A phase field study

The effect of electrical conductivity on the domain evolution of semiconducting ferroelectrics is investigated using a phase field model which includes the drift of space charges. Phase field simulations show that the tail-to-tail 90° charged domain wall appears during the domain formation in the semiconducting ferroelectrics at zero field, which is prohibited in common insulating ferroelectrics. Due to the screening of polarization charges, the domain switching takes place through the motion of head-to-head 180° charged domain wall in the semiconducting single-domain ferroelectrics subjected to an electric field. Comparing to the insulating ferroelectrics, the semiconducting ferroelectrics have a lower speed of domain evolution due to the decrease of mobility of charged domain walls. The response of semiconducting ferroelectrics to a mechanical load is also found different from that of insulating ferroelectrics.     

A viscoelastic model of polarization switching in polymer ferroelectrics

The theoretical aspects of the viscoelastic model for polarization switching in ??soft?? organic ferroelectrics have been considered. The model describes the amplitude-frequency dependences of the hysteresis loops obtained upon polarization switching in thin films of the ferroelectric copolymer poly(vinylidene fluoride-trifluoroethylene).     

Investigation into the domain structure dynamics in ferroelectrics with an incommensurate phase

The domain structure dynamics in ferroelectrics with an incommensurate phase is studied. Sodium nitrite is considered to be a prominent representative of the above ferroelectrics. The polarization properties of these ferroelectrics are described using pseudospin formalism. A kinetic equation for describing polarization of ferroelectrics is derived using the Hamiltonian. This equation is numerically solved simultaneously with the sound-vibration equation. The results are analyzed for various crystal parameters and initial conditions. The crystal domain structure is shown to be localized for reasonably long times. This circumstance makes it possible to conclude that these domain-structure states are long-lived states of a soliton type. The importance of finding and describing these states is emphasized. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 66–70, August, 2006.     

晶粒尺寸及衬底应力对铁电薄膜特性的影响

考虑衬底应力、畴壁运动和畴结构变化, 建立了修正的Landau-Devonshire热力学模型, 计算了生长在不同衬底上的含有纳米晶粒的PbZr_0.4Ti_0.6O₃(PZT)薄膜的电滞回线, 研究了矫顽场、剩余极化强度和相对介电常数对晶粒尺寸以及薄膜厚度的依赖关系. 结果表明, 矫顽场和相对介电常数对晶粒尺寸的依赖关系呈类抛物线状;衬底压应力使矫顽场和剩余极化强度增大, 使相对介电常数减小;随着厚度增加, 矫顽场先缓慢增加, 到200 nm 关键词： 铁电体 晶粒尺寸 衬底应力 薄膜厚度