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Li-Intercalation in nano-rutile TiO2-anodes induces loss of long-range order with the formation of ∼5 nm layered LixTiO2 domains with ∼1 nm columbite-like grain boundaries.

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 modelled 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 modelled. 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 40W/m 2 .

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 modelling 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.

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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.

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.

Intercalation materials are promising candidates for reversible energy storage and are, for example, used as lithium-battery electrodes, hydrogen-storage compounds, and electrochromic materials. An important issue preventing the more widespread use of these materials is that they undergo structural transformations (of up to ~10% lattice strains) during intercalation, which expand the material, nucleate microcracks, and, ultimately, lead to material failure. Besides the structural transformation of lattices, the crystallographic texture of the intercalation material plays a key role in governing ion-transport properties, generating phase separation microstructures, and elastically interacting with crystal defects. In this review, I provide an overview of how the structural transformation of lattices, phase transformation microstructures, and crystallographic defects affect the chemo-mechanical properties of intercalation materials. In each section, I identify the key challenges and opportunities to crystallographically design intercalation compounds to improve their properties and lifespans. I predominantly cite examples from the literature of intercalation cathodes used in rechargeable batteries, however, the identified challenges and opportunities are transferable to a broader range of intercalation compounds.