Phase transitions and domain structures of ferroelectric nanoparticles: Phase field model incorporating strong elastic and dielectric inhomogeneity

Wang, J. J.; Q., X.; Li, Q.; Britson, Jason; Chen, Lei

doi:10.1016/j.actamat.2013.08.055

Cited by 157 publications

(125 citation statements)

References 58 publications

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“…However, at the nanoscale, both surface energy, γ, [41][42][43] and electrical boundary conditions [36,44] affect the formation of ferroelectric domains. For BaTiO3 nanowires, experiments and theoretical considerations suggest γ values of about 0.68N/m, [36,44] however the presence of depolarization field and surface layer effects can cause local variation in γ values and have led to greater estimates of γ, around 10N/m [44].…”

Section: Polarization Flux Closures In the Form Of Bundles Of 90mentioning

confidence: 99%

Scale effects and the formation of polarization vortices in tetragonal ferroelectrics

Balakrishna

Huber

2015

Applied Physics Letters

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Vortices consisting of 90• quadrant domains are rarely observed in ferroelectrics. Although experiments show polarization flux closures with stripe domains, it is as yet unclear why pure single vortices are not commonly observed. Here we model and explore the energy of polarization patterns with vortex and stripe domains, formed on the square cross-section of a barium titanate nanowire. Using phase-field simulations, we calculate the associated energy of polarization patterns as a function of nanowire width. Further, we demonstrate the effects of surface energy and electrical boundary conditions on equilibrium polarization patterns. The minimum energy equilibrium polarization pattern for each combination of surface energy and nanowire width is mapped for both open-circuit and short-circuit boundary conditions. The results indicate a narrow range of conditions where single vortices are energetically favorable: nanowire widths less than about 30nm, opencircuit boundary condition, and surface energy of less than 4N/m. Short-circuit boundary conditions tend to favor the formation of a monodomain, while surface energy greater than 4N/m can lead to the formation of complex domain patterns or loss of ferroelectricity. The length scale at which a polarization vortex is energetically favorable is smaller than the typical size of nanoparticle in recent experimental studies. The present work provides insight into the effects of scaling, surface energy and electrical boundary conditions on the formation of polarization patterns.

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Section: Polarization Flux Closures In the Form Of Bundles Of 90mentioning

confidence: 99%

Scale effects and the formation of polarization vortices in tetragonal ferroelectrics

Balakrishna

Huber

2015

Applied Physics Letters

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“…21 This SPM has been successfully used in solving the mechanical equilibrium equation in various elastically inhomogeneous systems [22][23][24][25] and electrostatic equilibrium equation in ferroelectric-nanoparticle systems. 26 Moreover, the physical laws in dielectric and magnetic composites are very similar. Therefore, the SPM should be a good and efficient tool for studying the magnetic composites.…”

Section: Introductionmentioning

confidence: 97%

Static magnetic solution in magnetic composites with arbitrary susceptibility inhomogeneity and anisotropy

Wang

Song

et al. 2015

Journal of Applied Physics

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The static magnetic solutions in magnetic composites with arbitrary susceptibility inhomogeneity and anisotropy are accurately computed using an efficient numerical algorithm based on a proposed Fourier spectral iterative perturbation method for 3-dimensional systems. An advantage of this method is that the interphase boundary conditions are automatically considered without explicitly tracking interphase interfaces in the composites. This method can be conveniently implemented in phase-field modeling of microstructure evolution in systems with inhomogeneous susceptibility as well as inhomogeneous spontaneous magnetization distributions. Based on the proposed method, the effects of microstructures including the susceptibility mismatch between the inclusions and matrix, inclusions volume fraction, and inclusions arrangement on the effective susceptibility and local static magnetic field distribution of the composite are investigated. It is found that the interactions among the inclusions embedded in the matrix play critical roles in determining the composite properties. V C 2015 AIP Publishing LLC.

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“…is the dielectric constant tensor of the background reference (Zheng and Woo, 2009;Woo and Zheng, 2008;Tagantsev, 2008;Wang et al, 2013). For a perovskite ferroelectric, e.g., PbTiO 3 , its background reference is in cubic paraelectric phase, the background dielectric constants in the three axis directions are thus the same, i.e., b…”

Section: Free Energy Constructionmentioning

confidence: 99%

“…Nevertheless, due to the bulky implement of these methods, the simulating supercells are generally small and the simulating time is limited. Recently, phase-field methods capable of simulating large-size systems and long-time period have been applied to simulate the mechanical behaviors of ferroelectric domain patterns (Li et al, 2002a;Wang et al, 2004;Su and Landis, 2007;Kontsos and Landis, 2010;Chen et al, 2012aChen et al, , 2012bWang et al, 2013). Although many works have been paid attention to two-dimensional geometries, the three-dimensional phase-field simulations (Li et al, 2002a;Wang et al, 2013) can capture the whole domain structure and complicated evolution of the domain pattern in ferroelectric thin films, with properly considering the effects of temperature, surfaces, external electric field and mechanical loads, etc.…”

mentioning

confidence: 99%

Utilizing mechanical loads and flexoelectricity to induce and control complicated evolution of domain patterns in ferroelectric nanofilms

Chen

Zheng

Feng

et al. 2015

Journal of the Mechanics and Physics of Solids

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Phase transitions and domain structures of ferroelectric nanoparticles: Phase field model incorporating strong elastic and dielectric inhomogeneity

Cited by 157 publications

References 58 publications

Scale effects and the formation of polarization vortices in tetragonal ferroelectrics

Scale effects and the formation of polarization vortices in tetragonal ferroelectrics

Static magnetic solution in magnetic composites with arbitrary susceptibility inhomogeneity and anisotropy

Utilizing mechanical loads and flexoelectricity to induce and control complicated evolution of domain patterns in ferroelectric nanofilms

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