- Related item:
- Scale effects and the formation of polarization vortices in tetragonal ferroelectrics
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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- and short-circuit boundary conditions. The results indicate a narrow range of conditions where single vortices are energetically favorable: nanowire widths less than about 30 nm, open-circuit boundary condition, and surface energy of less than 4 N/m. Short-circuit boundary conditions tend to favor the formation of a monodomain, while surface energy greater than 4 N/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.
- Related item:
- Study of Periodic Domain Patterns in Tetragonal Ferroelectrics Using Phase-Field Methods
- Description:
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A sharp-interface model based on the linear constrained theory of laminates identifies eight distinct rank-2 periodic patterns in tetragonal ferroelectrics. While some of the periodic solutions, such as the herringbone and stripe patterns are commonly observed, others such as the checkerboard pattern consisting of repeating polarization vortices are rarely seen in experiments. The linear constrained theory predicts compatible domain arrangements, but neglects gradient effects at domain walls and misfit stresses due to junctions of domains. Here, we employ a phase-field model to test the stability of the periodic domain patterns with in-plane polarizations, under periodic boundary conditions which impose zero average stress and electric field. The results indicate that domain patterns containing strong disclinations are of high energy and typically unstable in the absence of external stresses or electric fields. The study also provides insight into the internal stresses developed in the various domain patterns.
- Related item:
- Nano-actuator concepts based on ferroelectric switching
- Description:
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The concept of a nano-actuator that uses ferroelectric switching to generate enhanced displacements is explored using a phase-field model. The actuator has a ground state in the absence of applied electric field that consists of polarized domains oriented to form a flux closure. When electric field is applied, the polarization reorients through ferroelectric switching and produces strain. The device is mechanically biased by a substrate and returns to the ground state when electric field is removed, giving a repeatable actuation cycle. The mechanical strains which accompany ferroelectric switching are several times greater than the strains attained due to the piezoelectric effect alone. We also demonstrate a second design of actuator in which the displacements are further increased by the bending of a ferroelectric beam. Phase-field modeling is used to track the evolution of domain patterns in the devices during the actuation cycle, and to study the design parameters so as to enhance the achievable actuation strains.
- Related item:
- Nanoscale domain patterns and a concept for an energy harvester
- Description:
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The current work employs a phase-field model to test the stability of nanoscale periodic domain patterns, and to explore the application of one pattern in an energy harvester device. At first, the stability of several periodic domain patterns with in-plane polarizations is tested under stress-free and electric field-free conditions. It is found that simple domain patterns with stripe-like features are stable, while patterns with more complex domain configurations are typically unstable at the nanoscale. Upon identifying a stable domain pattern with suitable properties, a conceptual design of a thin film energy harvester device is explored. The harvester is modeled as a thin ferroelectric film bound to a substrate. In the initial state a periodic stripe domain pattern with zero net charge on the top electrode is modeled. On bending the substrate, a mechanical strain is induced in the film, causing polarized domains to undergo ferroelectric switching and thus generate electrical energy. The results demonstrate the working cycle of a conceptual energy harvester which, on operating at kHz frequencies, such as from vibrations in the environment, could produce an area power density of about 40Wm−2.
- Related item:
- Nanoscale periodic domain patterns in tetragonal ferroelectrics: A phase-field study
- Description:
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Ferroelectrics form domain patterns that minimize their energy subject to imposed boundary conditions. In a linear, constrained theory, that neglects domain-wall energy, periodic domain patterns in the form of multirank laminates can be identified as minimum-energy states. However, when these laminates (formed in a macroscopic crystal) comprise domains that are a few nanometers in size, the domain-wall energy becomes significant, and the behavior of laminate patterns at this scale is not known. Here, a phase-field model, which accounts for gradient energy and strain energy contributions, is employed to explore the stability and evolution of the nanoscale multirank laminates. The stress, electric field, and domain-wall energies in the laminates are computed. The effect of scaling is also discussed. In the absence of external loading, stripe domain patterns are found to be lower-energy states than the more complex, multirank laminates, which mostly collapse into simpler patterns. However, complex laminates can be stabilized by imposing external loads such as electric field, average strain, and polarization. The study provides insight into the domain patterns that may form on a macroscopic single crystal but comprising nanoscale periodic patterns, and on the effect of external loads on these patterns.
- Related item:
- Design optimization of a ferroelectric nano-actuator using phase-field modeling
- Description:
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A ferroelectric crystal with charge-free surface conditions contains polarized domains which can form a flux closure with zero net polarization. In the presence of an external electric field, the flux closure in a two-dimensional continuum reorients its spontaneous polarization to align with the field. Based on this concept of ferroelectric switching coupled with mechanical straining, we demonstrate the working principle of a ferroelectric nano-actuator. The behavior of the actuator is explored under the action of electro-mechanical loading and its mechanism is simulated with a 2D phase-field model. The design of nano-actuator is modified to achieve greater actuation displacements by bending a thin device.
