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The effects of depolarization field on the dielectric and piezoelectric properties of ferroelectric ceramic particle-filled polymer-matrix composites are investigated at the underlying domain level. Phase field modeling and simulation reveals that the macroscopic properties of the composites are dominated by depolarization field effect, which depends on the arrangement and alignment rather than the size or internal grain structure of the ferroelectric particulates. It is found that 0-3 particulate composites with random dispersion of ferroelectric particles behave essentially like linear dielectric rather than ferroelectric materials, and domain-level analysis reveals the physical mechanism for lack of domain switching or hysteresis as attributed to strong depolarization effect. Thus, without effective reduction or elimination of the depolarization field, the composites cannot benefit from the functional fillers regardless of their superior properties. In order to exhibit the desired ferroelectric behaviors, it necessitates continuous ferroelectric phase connectivity in the composites. [ABSTRACT FROM AUTHOR]

Phase field modeling and computer simulation is employed to study dielectric composites with core-shell filler particles for high-energy-density applications. The model solves electrostatic equations in terms of polarization vector field in reciprocal space using fast Fourier transform technique and parallel computing algorithm. Composites composed of linear constituent phases (matrix, core, and shell materials) of different dielectric constants are considered. Inter-phase boundary conditions are automatically taken into account without explicitly tracking inter-phase interfaces in the composites. The core-shell structures of filler particles are systematically investigated in terms of shell thickness and dielectric constant with respect to core size and matrix dielectric constant, respectively. The effects of filler particle size, shape, and orientation are considered. It is found that core-shell structures of filler particles provide effective means to mitigate local electric field concentration in dielectric composites, improving dielectric breakdown strength and energy density of the composites. Optimal design of core-shell filler particles requires low shell dielectric constant and thick shell coating as compared to core material and core size, respectively. [ABSTRACT FROM AUTHOR]

Phase field modeling and computer simulation is employed to study the relations between filler microstructures and effective properties of dielectric composites. The model solves electrostatic equations in terms of polarization vector field in reciprocal space using a fast Fourier transform technique and parallel computing algorithm. Composites composed of linear constituent phases of different dielectric constants are considered. Interphase boundary conditions are automatically taken into account without explicitly tracking interphase interfaces in the composites. Various factors associated with filler microstructures are systematically investigated, including dielectric constant mismatch between fillers and matrix, particle size, shape, orientation, volume fraction, and spatial arrangement as well as directional alignment. Heterogeneous distributions of polarization, charge density, and local electric field are calculated for each composite microstructure, based on which effective dielectric constant and dielectric anisotropy of the composites are determined. It is found that electrostatic interactions among high-dielectric-constant fillers embedded in low-dielectric-constant matrix play critical roles in determining the composite properties, which sensitively depend on filler arrangement and, especially, directional alignment into fibrous microstructures (chains). Such microstructurally engineered composites, whose fillers are not randomly dispersed, exhibit strong dielectric anisotropy despite all constituent components being isotropic. [ABSTRACT FROM AUTHOR]

Three-dimensional micromagnetic simulations are used to study the effect of crystallographic textures on the magnetic properties ofuniaxial nanocrystalline films of hard magnetic materials with arbitrary grain shapes and size distributions. The correlation lengths (effective ferromagnetic exchange interaction radius and domain wall width) are assumed to be smaller than the typical grain size. The Landau-Lifshitz equations of magnetization dynamics are employed to describe the distribution of magnetization in ferromagnetic domains, domain evolution during magnetization switching, and the hysteresis curve. The equations are solved numerically in reciprocal space using the fast Fourier transform technique. Simulations are performed for films of different grain textures. The results show that magnetic coupling between grains in thin films significantly affects the morphology of the magnetic domains and their response to the magnetic field applied. The greater the deviation of the uniaxial directions of the grains from the film normal, the smaller the coercivity and the remanence magnetization. It is also shown that the remanence magnetization and coercivity respond differently to the variations in film texture and that the magnetic reversal process is a collective process involving groups of grains. In particular, it is found that the crystallographic texture of the grains has a more complicated effect on the coercivity than on the remanence magnetization and on the character of topological changes during the magnetization reversal process. [ABSTRACT FROM AUTHOR]

The phase field microelasticity theory of a three-dimensional elastically anisotropic solid of arbitrarily inhomogeneous modulus also containing arbitrary structural inhomogeneities is proposed. The theory is based on the equation for the strain energy of the elastically and structurally inhomogeneous system presented as a functional of the phase field, which is the effective stress-free strain of the "equivalent" homogeneous modulus system. It is proved that the stress-free strain minimizing this functional fully determines the exact elastic equilibrium in the elastically and structurally inhomogeneous solid. The stress-free strain minimizer is obtained as a steady state solution of the time-dependent Ginzburg-Landau equation. The long-range strain-induced interaction due to the elastic and structural inhomogeneities is explicitly taken into account. Systems with voids and cracks are the special cases covered by this theory since voids and cracks are elastic inhomogeneities that have zero modulus. Other misfitting defects, such as dislocations and coherent precipitates, are also integrated into this theory. Examples of elastic equilibrium of elastically inhomogeneous solid under applied stress are considered. [ABSTRACT FROM AUTHOR]

The phase field microelasticity theory of a three-dimensional elastically anisotropic single crystal with multiple voids and cracks is developed. It is extended to the case of elastically isotropic polycrystal. The theory is based on the exact equation for the strain energy of the “equivalent” continuous elastically homogeneous body presented as a functional of the phase field. This field is the equivalent stress-free strain. It is proved that the equivalent stress-free strain minimizing the strain energy of the elastically homogeneous body fully determines the elastic strain and displacement of the body with voids/cracks. The geometry and evolution of multiple voids and cracks are described by the phase field, which is a solution of the stochastic time-dependent Ginzburg–Landau equation. Other stress-generating defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on the configuration of multiple voids and cracks or on possible configurations and evolutions of cracks along their propagation paths. Examples of computations of the elastic equilibrium of systems with voids and/or cracks, the evolution of cracks in single crystals and polycrystals, and material toughening due to second-phase obstacles are considered. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Mechanisms of nucleation and growth of domains during ferroelectric phase transformation are investigated by using theoretical and computational approaches. It is shown that ferroelectric phase transformation exhibits some peculiar behaviors due to strong long-range dipole-dipole-like interactions involved in the system. Incorporation of electrostatic and elastostatic energies into the classical Landau-Ginzburg-Devonshire theory effectively modifies the coefficients of the polynomial free energy function and introduces extra energy barrier for ferroelectric phase transformation. It is found that independent nucleation of ferroelectric phase in the context of classical nucleation theory is prohibited, because electrostatic interaction generates an insurmountable energy barrier to isolated nucleus. Phase field modeling and computer simulation reveals that, in order to circumvent such an energy barrier, ferroelectric nucleation exhibits strong spatial correlation and self-organization behaviors from the very beginning, and ferroelectric phase transformation proceeds via spatial and temporal evolution of self-accommodating domains that provide a low-energy kinetic pathway throughout the phase transformation process. Theoretical analysis of the critical wavelength of correlated nucleation agrees with the computer simulation. Heterogeneous nucleation as induced by externally applied local electric field and subsequent polarization evolution process is also simulated to further demonstrate such self-organized pattern formation behaviors. [ABSTRACT FROM AUTHOR]

Electric field-induced antiferroelectric-ferroelectric phase transition and the associated nonlinear dielectric behavior in particulate composites are investigated for achieving a high dielectric capacity. A phenomenological thermodynamic model based on the Landau theory is first developed to discuss the generic phenomena of a temperature-electric field phase diagram, coexistence of antiferroelectric and ferroelectric phases, field-induced antiferroelectric-ferroelectric phase transition, and nonlinear dielectric behavior. The model is then used to carry out the phase field simulation of particulate nonlinear dielectric composites. It is found that the composites exhibit nonlinear dielectric behaviors, and the depolarization field in the composites helps reduce the dielectric hysteresis and enhance the reversibility of antiferroelectric-ferroelectric phase transitions, which are desired for energy storage applications. The simulations also reveal the underlying domain-level mechanisms for nucleation and growth processes of the phase transitions. It is shown that the macroscopic properties of the composites sensitively depend on the directional alignment of the antiferroelectric filler particles, and thus the filler morphology is an effective control variable in designing nonlinear dielectric composites. [ABSTRACT FROM AUTHOR]

Quantitative relationships between processing, microstructure, and properties in textured ferroelectric polycrystals and the underlying responsible mechanisms are investigated by phase field modeling and computer simulation. This study focuses on three important aspects of textured ferroelectric ceramics: (i) grain microstructure evolution during templated grain growth processing, (ii) crystallographic texture development as a function of volume fraction and seed size of the templates, and (iii) dielectric and piezoelectric properties of the obtained template-matrix composites of textured polycrystals. Findings on the first two aspects are presented here, while an accompanying paper of this work reports findings on the third aspect. In this paper, grain microstructure evolution in the polycrystalline matrix with different template volume fractions and seed sizes is simulated. To quantitatively characterize the crystallographic texture development during templated grain growth processing, a numerical algorithm is developed to compute the diffraction peak intensities and Lotgering factor of the simulated polycrystals during grain microstructure evolution. This novel approach provides a direct link between phase field simulation and diffraction experiment. This computational study clarifies the effects of the template volume fraction and template seed size on the final grain microstructure and texture. It is found that, while the degree of crystallographic texture generally increases with increasing template volume fraction, it is the average distance between template seeds that plays an important role. This finding suggests that reducing the template seed size and shortening the seed distance is an effective way to achieve higher texture at a lower template volume fraction, which is highly desired for enhancing the piezoelectric properties of ferroelectric polycrystals. The computational results are compared with complementary experiments, where good agreement is obtained. [ABSTRACT FROM AUTHOR]

Three-dimensional computer simulations are used to examine the development of magnetic domains and migration of domain walls in hard ferromagnetic thin films of polytwinned microstructure. The polytwinned microstructure, consisting of three different orientation variants of the L1[sub 0] ordered phase with orthogonal c-axes, is characterized by a multi-component long-range order (LRO) parameter. The coupling between the magnetic domains and the polytwinned microstructure is described by the coupling between magnetization and the LRO parameter in the anisotropy free energy of the system. The magnetodynamics is described by Landau-Lifshitz equations that are solved numerically in the reciprocal space using a parallel Fast Fourier Transform algorithm. It is found that the coupling results in a multilevel hierarchy in the magnetic domain structure, with intracolony boundaries (across multiple variants within a single polytwinned colony) and intercolony boundaries (across multiple colonies). In thin films of high magnetic anisotropy we find the intracolony boundary to be of {100} type and the intercolony one to be on average of {110} type. The migration of the magnetic domain boundaries in external magnetic fields is studied in a number of simple cases in which the fields are applied along different directions. The simulation results are analyzed and compared with existing experimental observations. [ABSTRACT FROM AUTHOR]