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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]

A thermodynamic theory for the lower-bound hysteresis in martensitic transformations is developed. It is shown that the elastic energy generated by the transformation-induced crystal lattice misfit makes the system free energy a nonlinear function of the volume fractions of the phases, lifts the additivity principle and ergodicity hypothesis of the conventional Gibbsian thermodynamics, and produces a macroscopic energy barrier between the parent and product phases. Since the energy barrier is proportional to the macroscopic volume of the system and thus cannot be surmounted by the thermally assisted nucleation of the new phase, a rate-independent hysteresis of thermodynamic nature is produced, which sets the lower bound for the total transformation hysteresis. This lower-bound hysteresis is characterized by two critical temperatures of the martensitic and reverse transformations, one during cooling and another during heating, with their difference defining the corresponding transformation hysteresis. The necessary undercooling and overheating are intrinsic material properties determined by the transformation elastic energy. The theory is tested against experimental observations, explains the ubiquitous temperature hysteresis in the martensitic transformations, and correlates the hysteresis with the volumetric misfit strain of the transformations. The proposed theory is generic and is applicable to any displacive (diffusionless and martensitic) phase transformations. Image 1 [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]

Highlights: [•] Diffuse interface field approach is adopted to model multi-liquid colloidal system. [•] Gibbs–Duhem-type formalism is developed to treat heterogeneous Laplace pressure. [•] Isolated anisotropic particles do not disturb uniform curvature of liquid interface. [•] Interacting particles alter shape and local curvature of liquid interface. [•] Morphology and stability of Pickering emulsion droplets depend on Laplace pressure. [ABSTRACT FROM AUTHOR]

[001]-textured Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ceramics were synthesized by using templated grain growth method. Significantly high [001] texture degree corresponding to 0.98 Lotgering factor was achieved at 1 vol. % BaTiO3 template. Electromechanical properties for [001]-textured PMN-PT ceramics with 1 vol. % BaTiO3 were found to be d33 = 1000 pC/N, d31 = 371 pC/N, &eh;r = 2591, and tanδ = ∼0.6%. Elastoelectric composite based modeling results showed that higher volume fraction of template reduces the overall dielectric constant and thus has adverse effect on the piezoelectric response. Clamping effect was modeled by deriving the changes in free energy as a function of applied electric field and microstructural boundary condition. [ABSTRACT FROM AUTHOR]

Computer modeling and simulations are performed to investigatecapillary bridges spontaneously formed between closely packed colloidalparticles in phase separating liquids. The simulations reveal a self-stabilizationmechanism that operates through diffusive equilibrium of two-phaseliquid morphologies. Such mechanism renders desired microstructuralstability and uniformity to the capillary bridges that are spontaneouslyformed during liquid solution phase separation. This self-stabilizationbehavior is in contrast to conventional coarsening processes duringphase separation. The volume fraction limit of the separated liquidphases as well as the adhesion strength and thermodynamic stabilityof the capillary bridges are discussed. Capillary bridge formationsin various compact colloid assemblies are considered. The study shedslight on a promising route to in situ(in-liquid)firming of fragile colloidal crystals and other compact colloidalmicrostructures via capillary bridges. [ABSTRACT FROM AUTHOR]

Abstract: The DLVO theory treats the total interaction force between two surfaces in a liquid medium as an arithmetic sum of two components: Lifshitz–van der Waals and electric double layer forces. Despite the success of the DLVO model developed for homogeneous surfaces, a vast majority of surfaces of particles and materials in technological systems are of a heterogeneous nature with a mosaic structure composed of microscopic and sub-microscopic domains of different surface characteristics. In such systems, the heterogeneity of the surface can be more important than the average surface character. Attractions can be stronger, by orders of magnitude, than would be expected from the classical mean-field DLVO model when area-averaged surface charge or potential is employed. Heterogeneity also introduces anisotropy of interactions into colloidal systems, vastly ignored in the past. To detect surface heterogeneities, analytical tools which provide accurate and spatially resolved information about material surface chemistry and potential — particularly at microscopic and sub-microscopic resolutions — are needed. Atomic force microscopy (AFM) offers the opportunity to locally probe not only changes in material surface characteristic but also charges of heterogeneous surfaces through measurements of force–distance curves in electrolyte solutions. Both diffuse-layer charge densities and potentials can be calculated by fitting the experimental data with a DLVO theoretical model. The surface charge characteristics of the heterogeneous substrate as recorded by AFM allow the charge variation to be mapped. Based on the obtained information, computer modeling and simulation can be performed to study the interactions among an ensemble of heterogeneous particles and their collective motions. In this paper, the diffuse-layer charge mapping by the AFM technique is briefly reviewed, and a new Diffuse Interface Field Approach to colloid modeling and simulation is briefly discussed. [Copyright &y& Elsevier]

Abstract: We present a novel mesoscale simulation approach to modeling the evolution of solid particles segregated at fluid–fluid interfaces. The approach involves a diffuse-interface field description of each fluid phase in addition to the set of solid particles. The unique strength of the model is its generality to include particles of arbitrary shapes and orientations, as well as the ability to incorporate electrostatic particle interactions and external forces via a previous work [P.C. Millett, Y.U. Wang, Acta Mater. 57 (2009) 3101]. In this work, we verify that the model produces the correct capillary forces and contact angles by comparing with a well-defined analytical solution. In addition, simulation results of rotations of various-shaped particles at fluid–fluid interfaces, external force-induced capillary attraction/repulsion between particles, and spinodal decomposition arrest due to colloidal particle jamming at the interfaces are presented. [ABSTRACT FROM AUTHOR]

The diffraction behaviors of imperfect nanotwin superlattices were considered and the effects of random variations in nanotwin layer thicknesses and variant volume fractions on the diffraction peak intensity profiles investigated. Imperfect nanotwin superlattices exhibit a pronounced adaptive diffraction phenomenon when the Brillouin zone-dependent condition, [image omitted], is met, where T is twin-related bilayer thickness, γ is twinning shear strain magnitude, s is twinning shear direction unit vector, and K is the reciprocal lattice vector of the constituent crystal denoting the fundamental reflection spots and Brillouin zones in reciprocal space. Nanotwin layer thickness variations produce little effect on the diffraction intensity distributions of adaptive Bragg reflection peaks, whereas variant volume fraction variations significantly reduce the height and broaden the width of adaptive peaks, but only affect their integrated intensities slightly and do not change their positions. In spite of imperfections, an extraordinary peak still appears at position k along twin peak splitting vector ΔK, as determined by a lever rule according to the average twin variant volume fraction [image omitted]: [image omitted]. Imperfect nanotwin superlattices exhibit a certain degree of diffuse reflection around the adaptive peaks with strong Lorentzian shape characteristics; adaptive peaks exhibit anisotropic broadening, i.e. peak is broader in the direction perpendicular to twin plane, and sharper parallel to the twin plane. The width of the adaptive peak does not provide direct information of nanodomain size, but the Brillouin zone-dependent diffraction behavior can be used to determine the nanodomain sizes. [ABSTRACT FROM AUTHOR]

Large, reversible and anhysteretic strain induced by external field is desired for multifunctional materials used in sensors, actuators and transducers. However, these desired attributes usually compromise each other, leading to trade-offs in materials’ properties and limiting their applicability. This paper focuses on field-induced inter-ferroelectric phase transformations. Some fundamental principles and domain mechanisms are systematized based on insights learned from phase field modeling and simulations, whose synergistic operations are expected to provide unique combination of large, reversible, and anhysteretic strain attributes. These working principles are: (i) Field-induced inter-ferroelectric structural phase transformation to achieve large strain; (ii) Field-induced stable-metastable phase transformation to maximize reversibility; (iii) Heterogeneous nucleation-and-growth process at domain walls to enhance low-field responses; (iv) Deactivation of domain wall motion by applying external fields along nonpolar axes to minimize hysteresis; (v) Domain wall broadening mechanism and domain size effect to exploit nanoscale engineered domain microstructures; and (vi) Bridging domain mechanism and phase coexistence to promote ferroelectric shape memory effects. It is shown that special initial domain microstructures and preferred evolution kinetic pathways can be achieved by crystallographic domain engineering technique, which allow multiple principles to work together without compromising one another. Due to the commonalities and fundamental interrelations among ferroelectric, ferromagnetic and ferroelastic materials, the gained understanding of thermodynamic and kinetic principles has general implications to displacive phase transformations in ferroic materials and is helpful for design of new functional materials with advanced field-induced strain properties. [ABSTRACT FROM AUTHOR]

Abstract: A novel mesoscale simulation approach to modeling the collective interactions of charged colloidal particles allowing investigation of complex self-assembly processes is presented. Diffuse interface field variables are used to describe the shape, size, location and orientation of each individual particle within the computational domain. In addition, these field variables are used to determine the spatially resolved particle charge density distributions as well as the magnitude and direction of the electric field throughout the medium. Individual particle positions and rotations are updated in time as a result of long-range electrostatic and short-range repulsive forces and torques. Illustrative results of the model’s capability to evolve both monodisperse and binary distributions of charged particles of various shapes and charge characteristics are presented. [Copyright &y& Elsevier]

Abstract: Field-directed dipolar particle self-assembly is explored by computer simulation as a processing route to advanced materials with controlled particulate microstructures. The computational model of arbitrarily shaped ferro-colloidal particles is developed by using a diffuse interface field approach. The model explicitly describes the evolving configuration of dipolar particles of arbitrary shapes and sizes, automatically treats short-range interaction between neighboring particles and accurately calculates long-range electrostatic/magnetostatic interaction, including dipole and all multipole contributions. No a priori constraint is imposed on any possible particle configuration or its evolution path. Ferro-colloidal processing of polymer-matrix composite via directed dipolar particle self-assembly under an external field is simulated. [Copyright &y& Elsevier]

Abstract: A phase field model of solid-state sintering is developed. The model treats multiple concurrent physical processes, i.e., rigid-body translation and rotation of powder particles, grain growth through boundary migration, and various diffusion mechanisms including surface diffusion, grain boundary diffusion, volume diffusion, and vapor transport through evaporation and condensation. The approach of centers of particles through rigid-body motions plays a key role in the densification of sintered powder compacts. The effective treatment of particle translation and rotation in phase field formalism is a necessary and critical step in developing a phase field sintering model. A scheme of particle translation and rotation is formulated based on a new formula of grain boundary force. The rigid-body motion modifies both the Cahn–Hilliard nonlinear diffusion equation and the Ginzburg–Landau (Allen–Cahn) structural relaxation equation by introducing advection terms. Computer simulations are presented. [Copyright &y& Elsevier]

The phase field microelasticity approach to mesoscale modelling of mobile crystal defects is reviewed. Various defects are modelled in the same theoretical framework, including dislocations, cracks and free surfaces in single crystals, polycrystals and heteroepitaxial films. The model is also applicable to diffusional and displacive phase transformations. The phase field microelasticity model is based on Ginzburg-Landau phase transition theory with modification by incorporating the transformation micromechanics. It numerically solves the exact elasticity equation that governs the long-range elastic interactions of structural defects which determine the mechanical properties of materials. The mesoscale microstructures of arbitrary geometrical complexity are described by a set of structure density fields or phase fields, without explicitly tracking the moving boundaries. The topological changes during nucleation, annihilation, coalescence of defects and formation of various metastable configurations are automatically taken into consideration. No ad hoc assumptions on possible microstructure morphologies during evolution are required. Various nano- and mesoscale processes are simulated. The models enable one to investigate the structure properly relationships of complex material systems which are determined by the interplays between multiple physical processes. [ABSTRACT FROM AUTHOR]

The phase field microelasticity approach to coherent phase transformations is extended to the case of a finite sample with free surfaces. The 3D simulation model is based on numerical solution of exact elasticity equation. No ad hoc assumptions on the microstructure morphology along evolution path are made. It is used to investigate the effects of free surfaces on multi-variant martensitic transformations in AuCd and FeNi alloys. The simulation shows that formation of free surfaces changes the martensite microstructures mostly in the surface layers, the thickness of these layers being commensurate with the size of martensite domains. It also shows that the free surfaces affect the microstructures of the high-symmetry FeNi more significantly than that of the low-symmetry AuCd because the latter has more orientation variants and can achieve better stress accommodation. [Copyright &y& Elsevier]

A development of the nonlinear surface instability of heteroepitaxial films during annealing process has been studied by using the phase field microelasticity model. The developed model considers the diffusional surface profile evolution of nonlinear grooved and coarsened regime, which is driven by the strain energy relaxation and is not constrained by any ad hoc assumptions concerning possible surface morphology. The method is based on the numerical solution of the exact elastic equilibrium equations. The simulation has shown that an initial small amplitude random roughening of a flat film develops to form a quasi-periodical array of islands under a certain balance between the strain and surface energies. This occurs through the competitive growth of amplitudes with different wavelengths. The surface morphology simultaneously grows and coarsens. The fully coarsened morphology exhibits a dominant wavelength that is significantly greater than the one that follows from the linear analysis of initial instability. The equilibrium morphology corresponding to a periodic array of islands is reached independent of the initial fluctuations of the surface profile. [Copyright &y& Elsevier]

Dislocation dynamics near a free surface and in heteroepitaxial thin films are simulated using an extended version of the nanoscale Phase Field Microelasticity model of dislocations [Acta Mater. 49 (2001) 1847]. The model automatically takes into account the effect of image forces on dislocation motions. In particular, the operations of Frank–Read sources in epitaxial films grown on infinitely thick and relatively thin substrates are investigated. The simulation reveals different misfit dislocation behaviors at the interface. Its implication on the interface susceptibility to crack nucleation is discussed. [Copyright &y& Elsevier]

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered. [ABSTRACT FROM AUTHOR]

Phase field model is developed to calculate heterogeneous distributions of polarization, charge, local field, and effective susceptibility of dielectric and magnetic composites with arbitrary multicomponent microstructures. It solves electrostatic and magnetostatic equations in terms of polarization vector field in reciprocal Fourier space, with interphase boundary conditions automatically satisfied without explicitly tracking interphase interfaces. This advantage allows the model to effectively treat arbitrarily complex multicomponent composites and seamlessly incorporate evolving microstructures from composite fabrication simulations. Evolution of internal field distributions and effective properties in composites during self-assembly fabrication process is presented to demonstrate the model’s capability and potential. [ABSTRACT FROM AUTHOR]

Computer modeling and simulation reveals a grain size- and composition-dependent behavior of phase coexistence around the morphotropic phase boundaries in polycrystals of ferroelectric solid solutions. It shows that the width of phase coexistence composition range increases with decreasing grain sizes; phase-coexisting domain microstructures effectively reduce elastostatic, electrostatic, and domain wall energies; and grain boundaries impose internal mechanical and electric boundary conditions, which affect the phase-coexisting domain microstructures in the grains and give rise to the grain size effect of phase coexistence. [ABSTRACT FROM AUTHOR]

Microstructures of coherent phase decomposition near morphotropic phase boundary in lead zirconate titanate are investigated by using computer modeling and simulation. The model is based on the recently proposed incoherent equilibrium phase diagram [G. A. Rossetti, Jr. et al., Appl. Phys. Lett. 88, 072912 (2006)] and takes into account the coherency strain energy and electrostatic energy. It reveals characteristic multidomain microstructures, where nanoscale lamellar domains of tetragonal and rhombohedral phases coexist with well-defined crystallographic orientation relationships and produce coherent diffraction effects. The simulated microstructures provide important information for interpretation of diffraction data and identification of phases near morphotropic phase boundary. [ABSTRACT FROM AUTHOR]

Computer modeling and simulation reveals a bridging domain mechanism that explains the phase coexistence commonly observed around the morphotropic phase boundaries of ferroelectric solid solutions. The simulation takes into account the important role of coupled ferroelectric and ferroelastic domain microstructures in phase coexistence phenomenon. It shows that minor domains of metastable phase spontaneously coexist with and bridge major domains of stable phase to reduce total system free energy, including bulk free energy, domain wall energy, and long-range electrostatic and elastostatic energies. The existence of bridging domains also explains the enhanced piezoelectric response in the vicinity of morphotropic phase boundaries. [ABSTRACT FROM AUTHOR]

Computer modeling and simulation reveal a domain wall broadening mechanism that explains the domain size effect of enhanced piezoelectric properties in domain engineered ferroelectric single crystals. The simulation shows that, under electric field applied along the nonpolar axis of single crystal without domain wall motion, the domain wall broadens and serves as embryo of field-induced new phase, producing large reversible strain free from hysteresis. This mechanism plays a significant role in the vicinity of interferroelectric transition temperature and morphotropic phase boundary, where energy difference between stable and metastable phases is small. Engineered domain configuration fully exploits this domain wall broadening mechanism. [ABSTRACT FROM AUTHOR]

A phase field microelasticity theory of a three-dimensional anisotropic solid with arbitrary elastic and structural inhomogeneities is proposed. The theory is based on the strain energy for the elastically and structurally inhomogeneous system as a functional of the phase field, which is the effective misfit strain of the "equivalent" homogeneous modulus system. It is demonstrated that the misfit strain minimizing this functional fully determines the exact elastic equilibrium in the elastically and structurally inhomogeneous solid. The misfit strain minimizer is obtained as a steady-state solution of the time-dependent Ginzburg-Landau equation. Examples of the elastic equilibrium of an elastically inhomogeneous solid under applied stress are considered. [ABSTRACT FROM AUTHOR]

A peculiar magnetic domain pattern (so-called cellular domain structure) was recently observed in Fe–Ga alloys, which was claimed to be responsible for desirable hysteresis-free and isotropic magnetization behaviors and to be associated with the reported non-Joulian magnetism [H. D. Chopra and M. Wuttig, Nature 521, 340 (2015)]. So far, such cellular domain phenomenon is observed only in Fe–Ga single crystal specimens of thin disk shape and with special thermal history. In this Letter, we report that the cellular domain structure is also observed in as-cast polycrystalline Fe–Ga alloys that are simply synthesized by arc-melting without special thermal treatment. For comparison, the cellular domains observed in an Fe–Ga single crystal specimen of rectangular prism shape are also presented. The cellular domain structure is discussed in light of a surface domain phenomenon and is found to be well interpreted by the Stephan model [Von W. Stephan, Exp. Tech. Phys. 4, 153 (1956)] based on classical domain theory, contrary to the Chopra–Wuttig model relying on the hypothesized charge density wave theory. [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]

Piezoelectric materials enable the conversion of mechanical energy into electrical energy and vice-versa. Ultrahigh piezoelectricity has been only observed in single crystals. Realization of piezoelectric ceramics with longitudinal piezoelectric constant (d33) close to 2000 pC N-1, which combines single crystal-like high properties and ceramic-like cost effectiveness, large-scale manufacturing, and machinability will be a milestone in advancement of piezoelectric ceramic materials. Here, guided by phenomenological models and phase-field simulations that provide conditions for flattening the energy landscape of polarization, a synergistic design strategy is demonstrated that exploits compositionally driven local structural heterogeneity and microstructural grain orientation/texturing to provide record piezoelectricity in ceramics. This strategy is demonstrated on [001]PC-textured and Eu3+-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ceramics that exhibit the highest piezoelectric coefficient (small-signal d33 of up to 1950 pC N-1 and large-signal d33* of ≈2100 pm V-1) among all the reported piezoelectric ceramics. Extensive characterization conducted using high-resolution microscopy and diffraction techniques in conjunction with the computational models reveals the underlying mechanisms governing the piezoelectric performance. Further, the impact of losses on the electromechanical coupling is identified, which plays major role in suppressing the percentage of piezoelectricity enhancement, and the fundamental understanding of loss in this study sheds light on further enhancement of piezoelectricity. These results on cost-effective and record performance piezoelectric ceramics will launch a new generation of piezoelectric applications. [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]

Abstract: A phase field model was developed to study the relationships between particulate microstructure and the magnetoelectric properties of magnetostrictive–piezoelectric composites. The model explicitly treats grain structures and domain processes in two-phase composites and automatically takes into account boundary conditions at inter-phase interfaces and grain boundaries. The model was used to investigate certain fundamental issues important for both rational design and practical application of magnetoelectric composites, such as connectivity of constituent phases, electrical conductivity of the magnetostrictive phase, in situ electric poling of ferroelectric phase within composite and the bias magnetic field during sensing. The evolution of magnetic and electric domains and their associated magnetostriction and electrostriction were simulated to study the strain-mediated domain-level coupling mechanisms that exist between magnetization and polarization. The simulations show that in situ poling of the ferroelectric phase within the composite microstructure is essential for piezoelectricity and thus the magnetoelectric effect, which requires 0–3 connectivity of the magnetostrictive–ferroelectric microstructure. Contrary to conventional wisdom that regards the conductivity of the magnetostrictive phase as detrimental to the magnetoelectric effect, it was found that a finite electrical conductivity of an isolated magnetostrictive phase can significantly enhance the magnetoelectric coefficient by both assisting effective poling and helping to stabilize the poled ferroelectric state. The simulations also show that the polarization response markedly lags behind the magnetization response, and a bias magnetic field effectively enhances the magnetoelectric effect. [Copyright &y& Elsevier]

Phase field modeling and simulation reveal that the magnetoelectric response of particulate magnetostrictive-piezoelectric composites sensitively depends on the magnetic domain structures of magnetostrictive phase. It is found that the longitudinal and transverse magnetoelectric coefficients of particulate composites with isotropic two-phase microstructures can be effectively tailored by controlling the magnetic domain structures. It is shown that engineered magnetic domains via controlled internal residual stress through appropriate processing, such as co-sintering under external stress (rather than isostatic pressing) in analogy to stress annealing of magnetostrictive materials, provide a powerful means to optimize magnetoelectric responses of particulate composites without fabricating anisotropic two-phase microstructures (e.g., laminate, fiber/rod). [ABSTRACT FROM AUTHOR]

Magnetoelectric voltage tunable inductors (VTIs) offer a new paradigm for power electronics circuit design. Here, air-gapped VTIs are demonstrated exhibiting a large inductance tunability of 220% with applied fields under 20 kVcm−1 and operational stability up to 5 MHz that covers the full frequency range of the state-of-the-art power electronics. The design of air-gapped VTI comprises of two C-shaped ferrite cores, one permeability-variable magnetic flux valve (MFV) in between C-shaped cores, and slotted air gap between cores and MFV. The tunability of VTIs is achieved through the electric field modulation of permeability in the MFV based on the magnetoelectric effect. There is a tradeoff between the tunability and saturation current. The introduction of air gap significantly reduces the tunability but provides methodology toward increasing the saturation current and power handling capability due to the increased reluctance. The inductance and tunability reduces by 50% with increase in the air-gap width from 0.07 mm to infinity (condition with no C-shaped cores). Phase field simulations demonstrate that the air gap affects the magnetization, permeability, and tunability of VTIs by tailoring the demagnetization field that further influences the magnetic domain rotation process. VTIs with increased frequency range and saturation current will strengthen the continued development of tunable power electronics. [ABSTRACT FROM AUTHOR]

The physical properties (dielectric, ferroelectric, piezoelectric, etc.) of complex perovskite ferroelectrics depend on the degree of order/disorder and the scale of the ordered domains. In this study, the electrocaloric (EC) properties of three representative complex perovskite ferroelectrics, Pb(Mg 1/3 Nb 2/3)O 3 –8PbTiO 3 (PMN-8PT), 1mol% Sm-doped Pb(Mg 1/3 Nb 2/3)O 3 –8PbTiO 3 (1S-PMN-8PT) and Pb(Sc 1/2 Ta 1/2)O 3 (PST) are evaluated. Multi-layer ceramic capacitors (MLCCs) with identical structural configurations were fabricated for these three compounds, and their EC properties were characterized by direct measurement using a thermocouple. The EC temperature change Δ T of PMN-8PT, 1S-PMN-8PT and PST MLCCs under 20 V μm−1 at room temperature were found to be 1.42 K, 1.54 K, and 3.10 K, respectively. X-ray diffraction and high-resolution transmission electron microscopy data suggests that the high EC performance of PST is related to the ordering of B-site cations (Sc3+ and Ta5+) with the ordering parameter S = 0.82 and a long coherence length of ∼100 nm, such that the sample transitioned from a relaxor ferroelectric to a normal ferroelectric. These results provide pathway towards design of high performance EC materials required for solid state refrigeration and air-conditioning technologies. Multi-layer ceramic capacitors for three representative complex perovskite ferroelectrics, Pb(Mg 1/3 Nb 2/3)O 3 –8PbTiO 3 (PMN-8PT), 1mol% Sm-doped Pb(Mg 1/3 Nb 2/3)O 3 –8PbTiO 3 (1S-PMN-8PT) and Pb(Sc 1/2 Ta 1/2)O 3 (PST), were fabricated. Their EC temperature change Δ T under 20 V μm−1 at room temperature were 1.42 K, 1.54 K, and 3.10 K, respectively. The high EC performance of PST is related to the long-range ordering of B-site cations (Sc3+ and Ta5+). [Display omitted] [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]

Computer modeling and simulation is performed to study the domain stabilization effect due to short-range ordering of charged point defects in aged ferroelectrics. Phase field model takes into account various energetic contributions involved in domain aging phenomenon, including chemical, domain wall, electrostatic and elastostatic energies, as well as domain-dependent internal electric field associated with the short-range ordering of charged point defects. The internal electric field strength is estimated by the computer simulation. Clausius–Clapeyron-type thermodynamic analysis of field-induced ferroelectric phase transition is used to evaluate aging-produced internal field strength from relevant experimental data, which is in agreement with the computer simulation. [ABSTRACT FROM AUTHOR]

Abstract Control of magnetic permeability through voltage in magnetoelectric materials promises to create novel voltage tunable inductors. Domain-level phase field modeling and computer simulation are employed to study magnetoelectric composites of Co-modified NiCuZn ferrite and PZT, where ferrite outperforms metallic magnetostrictive materials at high frequencies important for inductor applications. The simulations focus on the interplay between magnetocrystalline anisotropy and stress-induced anisotropy and reveal different regimes of permeability and tunability behaviors. It is shown that the permeability and its tunability can be significantly increased by reducing the intrinsic magnetocrystalline anisotropy through doping NiCuZn-ferrite with Co2+ to form solid solution (1- x)(Ni 0.6 Cu 0.2 Zn 0.2)Fe 2 O 4 - x CoFe 2 O 4 , and the optimal performance is achieved at vanishing magnetocrystalline anisotropy constant K 1 = 0 corresponding to composition x ∼0.02. The findings are confirmed by complementary experiments with good agreements. The effect of internal bias stress is further investigated, which is shown to shift the permeability regimes and thus provides an effective engineering technique to optimize the voltage tunable inductor performance. A tunability as high as ∼500% is obtained under the optimal condition, which is much higher than that obtained in conventional high-frequency voltage tunable inductors. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

Control of magnetic permeability through voltage promises to create novel electronic devices, such as voltage tunable inductors. The relationship between the structure and property of voltage tunable inductors comprising of magnetoelectric Metglas/PZT composites and the underlying domain-level mechanisms are investigated using theoretical analysis, computer simulation, and complementary experiments. A theoretical model is developed to analyze the roles of material anisotropy, inductor shape, and stress in controlling the Metglas permeability and its tunability. The analysis reveals key roles played by stress-induced anisotropy and the resultant ground magnetization state, and predicts two stress-dependent regimes of inductance tunability. The theory is validated using systematic experiments. The experimental results are used to determine the material and physical parameters. To further elucidate the underlying domain-level mechanisms responsible for controlling the behavior of voltage tunable inductor, phase field modeling is employed to simulate domain microstructures and magnetic permeability of Metglas/PZT composites under varying voltage. The computational results confirm the two regimes of inductance tunability and the controlling role of stress-induced anisotropy. The findings suggest engineering of internal bias stress as an effective means to optimize the inductance tunability of magnetoelectric Metglas/PZT composites. [ABSTRACT FROM AUTHOR]

Computer simulation is performed to study the mechanisms for controlling domain configurations and sizes in crystallographically engineered ferroelectric crystals. It is found that minimal domain sizes and highest domain wall densities are obtained with intermediate electric field applied along nonpolar axis of ferroelectric crystals, while lower and higher fields produce coarser domains, and temperature also plays important role in domain size control. The simulation shows that selection of polar domain variants by external electric field during nucleation stage of ferroelectric phase transition significantly affects subsequent domain growth and evolution kinetics, controlling the formation and sizes of lamellar domains. [ABSTRACT FROM AUTHOR]

We report on the direct observation of tetragonal nanodomains within an average monoclinic MC phase of Pb(Mg1/3Nb2/3)O3-0.35PbTiO3 single crystals by high-resolution transmission electron microscopy. These nanodomains are geometrically arranged in alternating layers of twins. The findings are consistent with the fundamental underlying assumptions of the ferroelectric adaptive phase theory [Y. M. Jin et al., Phys. Rev. Lett. 91, 197601 (2003)]. [ABSTRACT FROM AUTHOR]