Nanoscale periodic domain patterns in tetragonal ferroelectrics: A phase-field study

Balakrishna, Ananya Renuka; Huber, J. E.; Münch, Ingo von

doi:10.1103/physrevb.93.174120

Cited by 15 publications

(9 citation statements)

References 83 publications

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“…In this case, the final pattern is essentially 2-dimensional, with the polarization vector always lying in the e 1 − e 3 plane; this was not forced, but rather was a natural outcome of the relaxation towards a minimum energy state. The same pattern was noted in earlier work using a phase field model, but in a 2-dimensional simulation with a 40nm periodic cell size [14]. However, in that study a fixed average strain was imposed to stabilize the pattern.…”

Section: Evolution Of a 2-dimensional Domain Topologysupporting

confidence: 76%

“…However, thicker plates or bulk materials can form energy minimizing patterns with domains polarized in all three axial directions [3,12]. The formation of periodic or nearly periodic patterns of domains is commonly observed; the effect of specimen size and mechanical strain on the formation of such periodic domain patterns has also been widely reported [4,[12][13][14][15]. The spatial distribution of domains affects ferroelectric properties at both fine scale and macroscale [8,11,[16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…Exploring the spatiotemporal evolution of periodic polarization patterns in a theoretical framework would indicate the complexities in pattern formation and provide initial steps towards nanoscale experimentation. Recently, we used the same phase field model as in this work to explore nanoscale domain patterns [14]. Starting from the patterns predicted by energy minimization with sharp interfaces [5], it was found that several of the patterns dissolve into simpler, more stable arrangements such as single domains or alternating stripes.…”

Section: Introductionmentioning

confidence: 99%

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Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material

2018

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Periodic domain patterns in tetragonal ferroelectrics are explored using a phase field model calibrated for barium titanate. In this context, we discuss the standard periodic boundary condition and introduce the concept of reverse periodic boundary conditions. Both concepts allow the assembly of cubic cells in accordance with mechanical and electrical conditions. However, application of the reverse periodic boundary condition is due to an increased size of the RVE and enforces more complex structures compared to the standard condition. This may be of particular interest for other multiphysics simulations. Additionally, we formulate mechanical side conditions with minimal spherical (hydrostatic) stress, or conditions with controlled average strain. It is found that in sufficiently small periodic cells, only a uniform single domain, or the simplest stripe domains constitute equilibrium states. However, once the periodic cells are of order 20 domain wall widths in size, more complex, 3-dimensional patterns emerge. Some of these patterns are known from prior studies, but we also identify other domain patterns with long, ribbon-like domains threaded through them and some vortex-like structures.

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Section: Evolution Of a 2-dimensional Domain Topologysupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material

2018

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“…The considered average grain size ranges from 10 to 170 nm, and the selected electric-field frequency ranges from 10 up to 2,500 Hz. In recent years, phase-field approach was successfully employed in the study of domain patterns and structures in ferroelectric single crystals, [25,26] thin films [27][28][29] and polycrystals [18,30]. It is a robust and versatile method for studying interfacial problems of a wide spectrum of physical phenomena, such as the flexoelectric coupling [31,32] and fracturing [33,34] in ferroelectric solids.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic versus extrinsic effects of the grain boundary on the properties of ferroelectric nanoceramics

Kang

Wang

et al. 2017

Phys. Rev. B

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As the grain size decreases to the nanometer range, the characteristics of the ferroelectric nanoceramic can be ultimately determined by the competition between two effects: the intrinsic effect that is associated with the local properties of the grain boundary and the extrinsic effect that arises from the dynamics of domain structure which is highly influenced by the depolarization field caused by the grain boundary. In this work we investigate such a competition with a phase-field simulation based on the time-dependent Ginzburg-Landau (TDGL) kinetic equation.The study is performed on poled/unpoled nanoceramics under high-and low-amplitude bipolar alternating electric field with selected grain size and loading frequency. Our calculations for poled BaTiO 3 at 100 Hz show that, for the grain size from 170 to 50 nm, its properties are dominated by the extrinsic effect, and from 50 to 10 nm, they are dominated by the intrinsic one. As the grain size decreases, the dielectric and piezoelectric constants at the remnant state continuously rise in the extrinsic-dominated region and then drop sharply in the intrinsic-dominated region. Our frequency calculations from 10 to 2,500 Hz at the grain size of 100 nm indicate that the high-frequency behavior is very similar to that of the small grain-size, intrinsic-dominated one, whereas the low-frequency behavior is closely related to that of the large grain-size, extrinsic-dominated part, with the demarcation line occurring around 400 Hz. For the un-poled ceramics under small signal loading, the intrinsic effect is dominant over the entire range of grain size and frequency.

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“…This transformation introduces stress-free spontaneous strains in the ferroelectric system [1]. At present, theoretical models like phase field methods describe complex microstructures in electrode/ferroelectric systems as a function of the composition field (lithium-ion concentration, temperature or polarization) [10,11,12,13]. The Kobayashi-Warren-Carter phase field model [9] further accounts for crystallographic misorientation at grain boundaries during a phase transition process.…”

Section: Introductionmentioning

confidence: 99%

Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys

Balakrishna

Carter

2018

Phys. Rev. E

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Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in the electrode. The structural changes to the lattice symmetry affect the host material's properties. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model, which describes the composition field of a diffusing species, with a phase-field crystal (PFC) model, which describes the host-material lattice symmetry. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a diffusion-induced phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process.

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Nanoscale periodic domain patterns in tetragonal ferroelectrics: A phase-field study

Cited by 15 publications

References 83 publications

Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material

Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material

Intrinsic versus extrinsic effects of the grain boundary on the properties of ferroelectric nanoceramics

Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys

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