Signature of antiphase boundaries in iron oxide nanoparticles

Iron oxide nanoparticles find a wide variety of applications, including targeted drug delivery and hyperthermia in advanced cancer treatment methods. An important property of these particles is their maximum net magnetization, which has been repeatedly reported to be drastically lower than the bulk reference value. Previous studies have shown that planar lattice defects known as antiphase boundaries (APBs) have an important influence on the particle magnetization. The influence of APBs on the atomic spin structure of nanoparticles with the γ-Fe2O3 composition is examined via Monte Carlo simulations, explicitly considering dipole–dipole interactions between the magnetic moments that have previously only been approximated. For a single APB passing through the particle centre, a reduction in the magnetization of 3.9% (for 9 nm particles) to 7.9% (for 5 nm particles) is found in saturation fields of 1.5 T compared with a particle without this defect. Additionally, on the basis of Debye scattering equation simulations, the influence of APBs on X-ray powder diffraction patterns is shown. The Fourier transform of the APB peak profile is developed to be used in a whole powder pattern modelling approach to determine the presence of APBs and quantify them by fits to powder diffraction patterns. This is demonstrated on experimental data, where it could be shown that the number of APBs is related to the observed reduction in magnetization.

Planar Lattice Subsets with Minimal Vertex Boundary

A subset of vertices of a graph is minimal if, within all subsets of the same size, its vertex boundary is minimal. We give a complete, geometric characterization of minimal sets for the planar integer lattice $X$. Our characterization elucidates the structure of all minimal sets, and we are able to use it to obtain several applications. We show that the neighborhood of a minimal set is minimal. We characterize uniquely minimal sets of $X$: those which are congruent to any other minimal set of the same size. We also classify all efficient sets of $X$: those that have maximal size amongst all such sets with a fixed vertex boundary. We define and investigate the graph $G$ of minimal sets whose vertices are congruence classes of minimal sets of $X$ and whose edges connect vertices which can be represented by minimal sets that differ by exactly one vertex. We prove that G has exactly one infinite component, has infinitely many isolated vertices and has bounded components of arbitrarily large size. Finally, we show that all minimal sets, except one, are connected.

Discrete Harmonic Functions in the Three-Quarter Plane

In this article we are interested in finding positive discrete harmonic functions with Dirichlet conditions in three quadrants. Whereas planar lattice (random) walks in the quadrant have been well studied, the case of walks avoiding a quadrant has been developed lately. We extend the method in the quarter plane—resolution of a functional equation via boundary value problem using a conformal mapping—to the three-quarter plane applying the strategy of splitting the domain into two symmetric convex cones. We obtain a simple explicit expression for the algebraic generating function of harmonic functions associated to random walks avoiding a quadrant.

B2N Monolayer: a Direct Band-Gap Semiconductor with High and Highly Anisotropic Carrier Mobility

Two-dimensional materials with a planar lattice, a suitable direct band-gap, high and highly anisotropic carrier mobility are desirable for the development of advanced field-effect transistors. Here we predict three thermodynamically...

Cylindric Hecke Characters and Gromov–Witten Invariants via the Asymmetric Six-Vertex Model

We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as structure constants the 3-point genus zero Gromov–Witten invariants of Grassmannians and are spanned by what we call cylindric Hecke characters, a particular set of virtual characters for whose computation we give several explicit combinatorial formulae. One of these expressions is a generalisation of Ram’s formula for irreducible Hecke characters and uses cylindric broken rim hook tableaux. We show that the latter are in bijection with so-called ‘ice configurations’ on a cylindrical square lattice, which define the asymmetric six-vertex model in statistical mechanics. A key ingredient of our construction is an extension of the boson-fermion correspondence to Hecke algebras and employing the latter we find new expressions for Jing’s vertex operators of Hall–Littlewood functions in terms of the six-vertex transfer matrices on the infinite planar lattice.

Kinematic analysis and deformation of a planar lattice with an arbitrary number of panels

Formulae are obtained for calculating the deformations of a statically determinate lattice under the action of two types of loads in its plane, depending on the number of panels located along one side of the lattice. Two options for fixing the lattice are analyzed. Cases of kinematic variability of the structure are found. The distribution of forces in the rods of the lattice is shown. The dependences of the force loading of some rods on the design parameters are obtained. Keywords: truss, lattice, deformation, exact solution, deflection, induction, Maple system. [email protected]

Mechanical characterization of 3D printed, non-planar lattice structures under quasi-static cyclic loading

Purpose While additive manufacturing via melt-extrusion of plastics has been around for more than several decades, its application to complex geometries has been hampered by the discretization of parts into planar layers. This requires wasted support material and introduces anisotropic weaknesses due to poor layer-to-layer adhesion. Curved-layer manufacturing has been gaining attention recently, with increasing potential to fabricate complex, low-weight structures, such as mechanical metamaterials. This paper aims to study the fabrication and mechanical characterization of non-planar lattice structures under cyclic loading. Design/methodology/approach A mathematical approach to parametrize lattices onto Bèzier surfaces is validated and applied here to fabricate non-planar lattice samples via curved-layer fused deposition modeling. The lattice chirality, amplitude and unit cell size were varied, and the properties of the samples under cyclic-loading were studied experimentally. Findings Overall, lattices with higher auxeticity showed less energy dissipation, attributed to their bending-deformation mechanism. Additionally, bistability was eliminated with increasing auxeticity, reinforcing the conclusion of bending-dominated behavior. The analysis presented here demonstrates that mechanical metamaterial lattices such as auxetics can be explored experimentally for complex geometries where traditional methods of comparing simple geometry to end-use designs are not applicable. Research limitations/implications The mechanics of non-planar lattice structures fabricated using curved-layer additive manufacturing have not been studied thoroughly. Furthermore, traditional approaches do not apply due to parameterization deformations, requiring novel approaches to their study. Here the properties of such structures under cyclic-loading are studied experimentally for the first time. Applications for this type of structures can be found in areas like biomedical scaffolds and stents, sandwich-panel packaging, aerospace structures and architecture of lattice domes. Originality/value This work presents an experimental approach to study the mechanical properties of non-planar lattice structures via quasi-static cyclic loading, comparing variations across several lattice patterns including auxetic sinusoids, disrupted sinusoids and their equivalent-density quadratic patterns.

Eighty-three sublattices and planarity

Let L be a finite n-element lattice. We prove that if L has at least $$83\cdot 2^{n-8}$$83·2n-8 sublattices, then L is planar. For $$n>8$$n>8, this result is sharp since there is a non-planar lattice with exactly $$83\cdot 2^{n-8}-1$$83·2n-8-1 sublattices.