Nonequilibrium hyperuniform states in active turbulence.

We demonstrate that the complex spatiotemporal structure in active fluids can feature characteristics of hyperuniformity. Using a hydrodynamic model, we show that the transition from hyperuniformity to nonhyperuniformity and antihyperuniformity depends on the strength of active forcing and can be related to features of active turbulence without and with scaling characteristics of inertial turbulence. Combined with identified signatures of Levy walks and nonuniversal diffusion in these systems, this allows for a biological interpretation and the speculation of nonequilibrium hyperuniform states in active fluids as optimal states with respect to robustness and strategies of evasion and foraging.

Morphological Evolution of Pit-Patterned Si(001) Substrates Driven by Surface-Energy Reduction.

Lateral ordering of heteroepitaxial islands can be conveniently achieved by suitable pit-patterning of the substrate prior to deposition. Controlling shape, orientation, and size of the pits is not trivial as, being metastable, they can significantly evolve during deposition/annealing. In this paper, we exploit a continuum model to explore the typical metastable pit morphologies that can be expected on Si(001), depending on the initial depth/shape. Evolution is predicted using a surface-diffusion model, formulated in a phase-field framework, and tackling surface-energy anisotropy. Results are shown to nicely reproduce typical metastable shapes reported in the literature. Moreover, long time scale evolutions of pit profiles with different depths are found to follow a similar kinetic pathway. The model is also exploited to treat the case of heteroepitaxial growth involving two materials characterized by different facets in their equilibrium Wulff's shape. This can lead to significant changes in morphologies, such as a rotation of the pit during deposition as evidenced in Ge/Si experiments.

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model.

One of the major difficulties in employing phase-field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work, we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free-energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite-element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

Complex dewetting scenarios of ultrathin silicon films for large-scale nanoarchitectures.

Dewetting is a ubiquitous phenomenon in nature; many different thin films of organic and inorganic substances (such as liquids, polymers, metals, and semiconductors) share this shape instability driven by surface tension and mass transport. Via templated solid-state dewetting, we frame complex nanoarchitectures of monocrystalline silicon on insulator with unprecedented precision and reproducibility over large scales. Phase-field simulations reveal the dominant role of surface diffusion as a driving force for dewetting and provide a predictive tool to further engineer this hybrid top-down/bottom-up self-assembly method. Our results demonstrate that patches of thin monocrystalline films of metals and semiconductors share the same dewetting dynamics. We also prove the potential of our method by fabricating nanotransfer molding of metal oxide xerogels on silicon and glass substrates. This method allows the novel possibility of transferring these Si-based patterns on different materials, which do not usually undergo dewetting, offering great potential also for microfluidic or sensing applications.

Stress Induced Branching of Growing Crystals on Curved Surfaces.

If two-dimensional crystals grow on a curved surface, the Gaussian curvature of the surface induces elastic stress and affects the growth pathway. The elastic stress can be alleviated by incorporating defects or, if this is energetically unfavorable, via an elastic instability which leads to anisotropic growth with branched ribbonlike structures. This instability provides a generic route to grow defect-free crystals on curved surfaces. Depending on the elastic properties of the crystal and the geometric properties of the surface, different growth morphologies with two-, four-, and sixfold symmetry develop. Using a phase field crystal type modeling approach, we provide a microscopic understanding of the morphology selection.

Two-dimensional liquid crystalline growth within a phase-field-crystal model.

By using a two-dimensional phase-field-crystal (PFC) model, the liquid crystalline growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from an isotropic phase is compared with that grown from a columnar or smectic-A (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of the classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process, we analyze the topological structure of the nematic order, which starts from nucleation of +1/2 and -1/2 disclination pairs at the PTC growth front and evolves into hexagonal cells consisting of +1 vortices surrounded by six satellite -1/2 disclinations. It is found that the orientational and the positional order do not evolve simultaneously; the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.

Engineered Coalescence by Annealing 3D Ge Microstructures into High-Quality Suspended Layers on Si.

The move from dimensional to functional scaling in microelectronics has led to renewed interest toward integration of Ge on Si. In this work, simulation-driven experiments leading to high-quality suspended Ge films on Si pillars are reported. Starting from an array of micrometric Ge crystals, the film is obtained by exploiting their temperature-driven coalescence across nanometric gaps. The merging process is simulated by means of a suitable surface-diffusion model within a phase-field approach. The successful comparison between experimental and simulated data demonstrates that the morphological evolution is driven purely by the lowering of surface-curvature gradients. This allows for fine control over the final morphology to be attained. At fixed annealing time and temperature, perfectly merged films are obtained from Ge crystals grown at low temperature (450 °C), whereas some void regions still persist for crystals grown at higher temperature (500 °C) due to their different initial morphology. The latter condition, however, looks very promising for possible applications. Indeed, scanning tunneling electron microscopy and high-resolution transmission electron microscopy analyses show that, at least during the first stages of merging, the developing film is free from threading dislocations. The present findings, thus, introduce a promising path to integrate Ge layers on Si with a low dislocation density.

The influence of membrane bound proteins on phase separation and coarsening in cell membranes.

A theoretical explanation of the existence of lipid rafts in cell membranes remains a topic of lively debate. Large, micrometer sized rafts are readily observed in artificial membranes and can be explained using thermodynamic models for phase separation and coarsening. In live cells such domains are not observed and various models are proposed to describe why the systems do not coarsen. We review these attempts critically and show within a phase field approach that membrane bound proteins have the potential to explain the different behaviour observed in vitro and in vivo. Large scale simulations are performed to compute scaling laws and size distribution functions under the influence of membrane bound proteins and to observe a significant slow down of the domain coarsening at longer times and a breakdown of the self-similarity of the size-distribution function.

Particles on curved surfaces: a dynamic approach by a phase-field-crystal model.

We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the minimal energy configuration. We study annihilation of dislocations within the ordered system and premelting along grain-boundary scars. The obtained minimal energy configurations on a sphere are compared with existing results and scaling laws are computed for the number of excess dislocations as a function of system size.

Derivation of the phase-field-crystal model for colloidal solidification.

The phase-field-crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field-crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density-functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field-crystal model is proposed which involves less approximations than the standard phase-field-crystal model. We finally test the validity of these phase-field-crystal models against dynamical density-functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field-crystal model in order to match the bulk freezing transition point.

Phase-field simulation of stripe arrays on metal bcc(110) surfaces.

By using a phase-field model, we simulate formation and growth of stripe arrays starting with anisotropic growth of islands under the Ehrlich-Schwoebel barrier on metal bcc(110) surfaces. The anisotropy is incorporated in terms of attachment kinetics that is locally limited at the island edge aligned to the y axis (or 100 ) and instantaneous at the island edge aligned to the x axis (or 110 ). By reproducing the stripe arrays under various anisotropy magnitudes, we investigate dynamics of formation and growth of the stripe arrays. While enhancing coarsening in the y direction, the anisotropy suppresses coarsening in the x direction at the early stage, which contributes to formation of stripe arrays. At long times, the stripe arrays develop the quasiperiodic uniaxial structure with the selected transversal slope and the decreasing longitudinal slope as consequence of competition between coarsening and roughening. At the case of the large anisotropy magnitude, the fast roughening is caused by the strongly limited attachment kinetics, where the transversal coarsening turns fast and then the uniaxial growth is broken finally. For the weak roughening at the case of the reduced anisotropy magnitude, the slow transversal coarsening is achieved with the fast longitudinal coarsening, which contributes to the stripe arrays of the regular period and the increasing uniaxial length. Such arrays have the potential to be used as templates to grow one-dimensional nanostructures.