Planar Hexagonal Lattice Research Articles

Interdigitated immunoglobulin arrays form the hyperstable surface layer of the extremophilic bacterium Deinococcus radiodurans

Deinococcus radiodurans is an atypical diderm bacterium with a remarkable ability to tolerate various environmental stresses, due in part to its complex cell envelope encapsulated within a hyperstable surface layer (S-layer). Despite decades of research on this cell envelope, atomic structural details of the S-layer have remained obscure. In this study, we report the electron cryomicroscopy structure of the D. radiodurans S-layer, showing how it is formed by the Hexagonally Packed Intermediate-layer (HPI) protein arranged in a planar hexagonal lattice. The HPI protein forms an array of immunoglobulin-like folds within the S-layer, with each monomer extending into the adjacent hexamer, resulting in a highly interconnected, stable, sheet-like arrangement. Using electron cryotomography and subtomogram averaging from focused ion beam-milled D. radiodurans cells, we have obtained a structure of the cellular S-layer, showing how this HPI S-layer coats native membranes on the surface of cells. Our S-layer structure from the diderm bacterium D. radiodurans shows similarities to immunoglobulin-like domain-containing S-layers from monoderm bacteria and archaea, highlighting common features in cell surface organization across different domains of life, with connotations on the evolution of immunoglobulin-based molecular recognition systems in eukaryotes.

Graphene: Preparation, tailoring, and modification.

Graphene is a 2D material with fruitful electrical properties, which can be efficiently prepared, tailored, and modified for a variety of applications, particularly in the field of optoelectronic devices thanks to its planar hexagonal lattice structure. To date, graphene has been prepared using a variety of bottom-up growth and top-down exfoliation techniques. To prepare high-quality graphene with high yield, a variety of physical exfoliation methods, such as mechanical exfoliation, anode bonding exfoliation, and metal-assisted exfoliation, have been developed. To adjust the properties of graphene, different tailoring processes have been emerged to precisely pattern graphene, such as gas etching and electron beam lithography. Due to the differences in reactivity and thermal stability of different regions, anisotropic tailoring of graphene can be achieved by using gases as the etchant. To meet practical requirements, further chemical functionalization at the edge and basal plane of graphene has been extensively utilized to modify its properties. The integration and application of graphene devices is facilitated by the combination of graphene preparation, tailoring, and modification. This review focuses on several important strategies for graphene preparation, tailoring, and modification that have recently been developed, providing a foundation for its potential applications.

Gas‐Phase Fluorination of Hexagonal Boron Nitride

Hexagonal boron nitride (hBN) has received much attention in recent years as a 2D dielectric material with potential applications ranging from catalysts to electronics. hBN is a stable covalent compound with a planar hexagonal lattice and is relatively unreactive to most chemical environments, making the chemical functionalization of hBN challenging. Here, a simple, scalable strategy to fluorinate hBN using a direct gas-phase fluorination technique is reported. The nature of fluorine bonding to the hBN lattice and their chemical coordination are described based on various characterization studies and theoretical models. The fluorine functionalized hBN shows a bandgap reduction and displays a semiconducting behavior due to the fluorination process. Additionally, the fluorinated hBN shows significant improvement in its thermal and friction properties, which could be substantial in applications such as lubricants and thermal fluids. Theory and simulations reveal that the enhanced friction properties of fluorinated hBN result from reduced inter-planar interaction energy by electrostatic repulsion of intercalated fluorine atoms between hBN layers without significant disruption of the in-plane lattice. This technique paves the way for the fluorination of several other 2D structures for various applications such as magnetism and functional nanoscale electronic devices.

First-principles study of a 2-dimensional C-silicyne monolayer as a promising anode in Na/K ion secondary batteries.

With the depleting resources of energy and increasing demand, the need for sustainable and renewable energy resources has become the need of the hour. The low storage capacity of current materials for Na/K ion batteries has led to the quest to identify suitable materials for an electrode with excellent electrochemical properties. In the present work, a systematic theoretical investigation of C-silicyne, a planar 2-dimensional hexagonal lattice, is performed to establish the geometric and thermal properties and stability. The electronic properties illustrate the metallic nature of C-silicyne, which is conserved even after the effective adsorption of Na/K ions on the surface of the monolayer. For the practical functionality, the storage capacity of C-silicyne is evaluated as 591 mA h g-1 for Na ions and 443 mA h g-1 for K ions. Moreover, the low diffusion barriers for the Na (0.57 eV) and K (0.34 eV) ions display their feasible movement across the monolayer as the electrochemical cycle progresses. The average working voltage is found to lie in the range of 0.1-1 V, which is required for the effective functioning of the anode in a Na/K ion battery. These results demonstrate the potential of C-silicyne as a material for the anode in Na/K ion batteries.

The COMPASS force field: Validation for carbon nanoribbons

Abstract The COMPASS force field has been successfully applied in a large number of materials simulations, including the analysis of structural, electrical, thermal, and mechanical properties of carbon nanoparticles. This force field has been parameterized using quantum mechanical data and is based on hundreds of molecules as a training set, but such analysis for graphene sheets was not carried out. The objective of the present study is the verification of how good the COMPASS force field parameters can accurately describe the frequency spectrum of atomic vibrations of graphene, graphane and fluorographene sheets. We showed that the COMPASS force field allows us to describe with good accuracy the frequency spectrum of atomic vibrations of graphane and fluorographene sheets, whose honeycomb hexagonal lattice is formed by sp 3 hybridization. On the other hand, the force field does not describe very well the frequency spectrum of graphene sheet, whose planar hexagonal lattice is formed by sp 2 banding. In that case the frequency spectrum of out-of-plane vibrations differs greatly from the experimental data — bending stiffness of a graphene sheet is strongly over estimated. We present the correction of parameters of out-of-plane and torsional potentials of the force field, which allows achieving the coincidence of vibration frequency with experimental data. After such corrections, the COMPASS force field can be used to describe the dynamics of flat graphene sheets and carbon nanotubes.

Brownian motion of a plasma crystal

The dynamics of a plasma crystal under the action of random external forces is considered. The pair correlation functions of the particle displacements are calculated in the harmonic approximation by using the Langevin equations. The case of a planar hexagonal lattice is analyzed in more detail. Analogues of the Van Hove singularities in the spectral densities are discovered.

A unit-compressible modular robotic system and its self-configuration strategy using meta-module

Abstract Many modular robots can be configured together to constitute a system. However, it is yet difficult to accomplish the configuration tasks by modules themselves since there are many constraints in a system. Introducing the meta-module into control strategy may realize the self-configuration by reducing constraints. Based on this idea, this paper presents a novel self-configuration strategy for a unit-compressible modular robotic system. First, a hardware system called M-Lattice that allows to construct a planar hexagonal lattice of robots is introduced. By using a special motion mode to move modules, this system is able to reduce the local constraints. A kinematics analysis and two prototype robots are presented to demonstrate this ability. Then, a novel self-configuration strategy based on the concept of meta-module is proposed. The meta-module is a small group of basic modules that work cooperatively as one intelligent unit. Every meta-module can self-configure in the system by itself and the global constraints are effectively reduced at the same time. The overall performance of the proposed strategy is evaluated with simulations and the simulation results show that it has a fine performance in scalability as well as robustness.

Relaxation of interstitials in spherical colloidal crystals

Spherical colloidal crystals (CCs) self-assemble on the interface between two liquids. These 2D structures unconventionally combine local hexagonal order and spherical geometry. Nowadays CCs are actively studied by altering their structures. However, the statistical analysis of such experiments results is limited by uniqueness of self-assembled structures and their short lifetime. Here we perform numerical experiments to investigate pathways of CC structure relaxation after the intrusion of interstitial. The process is simulated in the frames of overdamped molecular dynamics method. The relaxation occurs due to interaction with extended topological defects (ETDs) mandatory induced in spherical CCs by their intrinsic Gaussian curvature. Types of relaxation pathways are classified and their probabilities are estimated in the low-temperature region. To analyze the structural changes during the relaxation we use a parent phase approach allowing us to describe the global organization of spherical order. This organization is preserved by only the most typical relaxation pathway resulting in filling one of vacancies integrated inside the ETD areas. In contrast with this pathway the other ones shift the ETDs centers and can strongly reconstruct the internal structure of ETDs. Temperature dependence of the relaxation processes and the mechanism of dislocation unbinding are discussed. Common peculiarities in relaxation of spherical structures and particular fragments of planar hexagonal lattice are found.

A Model for Gaussian Perturbations of Graphene

Graphene consists nominally of a regular planar hexagonal carbon lattice monolayer. However, its structure experiences perturbations in the presence of external influences, whether from substrate properties, thermal or electromagnetic fields, or ambient fluid movement. Here we give an information geometric model to represent the state space of perturbations as a Riemannian pseudosphere with scalar curvature close to -1/2. This would allow the representation of a trajectory of states under a given ambient or process change, so opening the possibility for geometrically formulated dynamical models to link structural perturbations to the physics.

The Coincidence Site Lattices in 2D Hexagonal Lattices Using Clifford Algebra

The problem of characterizing the coincidence site lattices obtained by superimposing a planar hexagonal lattice with its rotated version is solved using simple reflections handled with Clifford algebras. For any possible coincidence rotation, analytical expressions for the coincidence index and for a basis of the coincidence site lattices are deduced.

Large nonlinear optical rectification in atomic hexagonal layers with broken space inversion symmetry

Motivated by possible applications in optoelectronics, we consider nonlinear optical rectification (NOR) in two planar hexagonal lattice structures with broken space inversion symmetry—namely, in graphene epitaxially grown on a SiC substrate and in boronitrene (a monolayer of BN). For both structures, we calculate the second-order nonlinear optical susceptibility χ(2)(0;ω, − ω) relevant to the NOR effect and evaluate a bias voltage V0 appearing at the structure terminals under strong laser irradiation. We show that the reason for the χ(2)(0;ω, − ω) being nonvanishing in the examined structures is their sublattice (inversion) asymmetry combined with the trigonal symmetry of their π-electron energy bands near the corners of the hexagonal Brillouin zone of those structures. In spite of being rather small, the trigonal warping of the energy bands involved is found to provide a remarkably large magnitude of the NOR susceptibility, reaching the order of 5 × 10−4 esu for the graphene/SiC overlayer system when the pump photon energy ħω approaches the bandgap energy EG (≈0.26 eV) of the overlying graphene. For a graphene sample of a few microns length, irradiated by a normally incident laser beam with a relatively moderate power density of 10 kW cm−2, the corresponding optical rectification voltage V0 is estimated to be as large as several millivolts. Moreover, the sign of the voltage (i.e., its polarity) can be sharply reversed by sweeping the photon energy through the inter-π-band resonance condition ħω = EG. This frequency-controlled optical switching, if realized, will be a potent technique for graphene-based photonics and optoelectronics.

Relationship between triple and pair correlations in an A y B 1 − y solid solution with a planar hexagonal lattice

An analytical relationship is found between triple correlations and nearest neighbor pair correlations in an AyB1 − y solid solution with a planar hexagonal lattice (plane group p6mm). The range of variations in the triple correlation is determined as a function of the composition of the AyB1 − y solid solution and the value of the pair correlation. It is assumed that periodically ordered planar hexagonal and square island nanostructures can be considered as solid solutions A1/4□3/4 with vacancy sites □ and sites occupied by nanoparticles A. In this case, an ordered distribution of nanoparticles over the planar-lattice sites occurs because the nearest neighbor pair correlation is negative and has a maximum magnitude.

Periodized discrete elasticity models for defects in graphene

The cores of edge dislocations, edge dislocation dipoles, and edge dislocation loops in planar graphene have been studied by means of periodized discrete elasticity models. To build these models, we have found a way to discretize linear elasticity on a planar hexagonal lattice using combinations of difference operators that do not symmetrically involve all the neighbors of an atom. At zero temperature, dynamically stable cores of edge dislocations may be heptagon-pentagon pairs (glide dislocations) or octagons (shuffle dislocations) depending on the choice of initial configuration. Possible cores of edge dislocation dipoles are vacancies, pentagon-octagon-pentagon divacancies, Stone-Wales defects, and 7--5-5--7 defects. While symmetric vacancies, divacancies, and 7--5-5--7 defects are dynamically stable, asymmetric vacancies and 5--7-7--5 Stone-Wales defects seem to be unstable.

Simulation of pair and three-particle correlations in a binary solid solution with a hexagonal lattice

The correlations revealed in an AyB1 −y disordered solid solution in which atoms occupy sites in the planar hexagonal lattice are investigated. It is demonstrated that pair correlations in the first coordination shell necessarily result in the appearance of pair correlations in the second and subsequent coordination shells. These induced pair correlations decay to the tenth coordination shell. The atomic ordering in solid solutions of all compositions is studied using the computer simulation. It is shown that, within the limits of computational error, the functional dependence between the pair correlation parameter of the first coordination shell and the parameters of the induced pair correlations in the second to ninth coordination shells is described by a third-degree polynomial. The results of the computer simulation of three-particle correlations are in agreement with the analytical solution for the corresponding correlations in the first coordination shell of the hexagonal lattice.

Triple correlations in a A y B1 − y solid solution with a planar hexagonal lattice

It is shown that triple correlations in a AyB1 − y solid solution with a planar hexagonal lattice are due to the presence of nearest-pair correlations. The admissible range of the triple correlation as a function of the composition of the AyB1 − y solid solution and pair correlation value is determined. It is shown that periodically ordered planar hexagonal and square-island nanostructures can be considered as A1/4□ 3/4 solid solutions with vacant sites □ and sites occupied by nanoparticles A. In this case, the ordered distribution of the nanoparticles over the sites of the planar lattice is caused by the nearest-air correlation that is negative in sign and maximal in absolute value.

Structural properties of a monolayer graphite film on the (111)Ir surface

The structural properties of a monolayer graphite film prepared on the (111)Ir surface through thermal decomposition of benzene molecules were studied. The study was carried out in ultrahigh vacuum using scanning tunneling microscopy, which allowed observation of the atomic structure of the film. It is shown that, on extended smooth regions of the Ir surface, a continuous graphite film with a regular arrangement of carbon atoms in a planar hexagonal lattice is formed. The orientation of zigzag carbon atom chains coincides with the 〈110〉 direction on the Ir surface. Structural defects of the (5, 7) configuration were revealed in the film. A comparison of the topographies of the film and the (111)Ir surface shows that the graphite layer smoothly (without discontinuities) flows over subnanometer topographical features existing on the Ir surface and that the distance between the graphite film and the metal surface in this case can reach 1 nm.

Symmetry restrictions in the chirality dependence of physical properties of single-wall nanotubes

We investigate the chirality dependence of physical properties of nanotubes which are wrapped by the planar hexagonal lattice including graphite and boron nitride sheet, and reveal its symmetry origin. The observables under consideration are of scalar, vector, and tensor types. These exact chirality dependences obtained are useful to verify the experimental and numerical results and propose accurate empirical formulas. Some important features of physical quantities can also be extracted by considering the symmetry restrictions without complicated calculations.

Compact and almost compact breathers: A bridge between an anharmonic lattice and its continuum limit

We demonstrate that certain strictly anharmonic one-dimensional FPU lattices with a suitable quartic site potential appended support almost-compact discrete breathers over a macroscopic localized domain that is essentially fixed independently of the sparseness of the lattice. Beyond that domain the discrete breather tails decay at a double-exponential rate in the lattice-cell index, becoming truly compact in the continuum limit. Furthermore, the discrete breather is stable for amplitudes below a sharp threshold that depends on the sparseness of the lattice. For the two-dimensional version of the problem, the continuum limit of a planar hexagonal lattice with a purely quartic interaction potential begets an isotropic multidimensional nonlinear wave equation. When a quartic site potential of the appropriate sign is appended, the continuum equation has a compactly supported radial breather solution.

Almost Compact Breathers in Anharmonic Lattices near the Continuum Limit

Certain strictly anharmonic one-dimensional lattices support discrete breathers over a macroscopic localized domain that in the continuum limit becomes exactly compact. The discrete breather tails decay at a double-exponential rate, so such systems can store energy locally, especially since discrete breathers appear to be stable for amplitudes below a sharp stability threshold. The effective width of other solutions broadens over time, but, under appropriate conditions, only after a positive waiting time. The continuum limit of a planar hexagonal lattice also supports a compact breather.

A tunneling spectroscopy study of the temperature dependence of the forbidden band in Bi2Te3 and Sb2Te3

Bi 2 Te 3 and Sb 2 Te 3 semiconductors are layered crystals with rhombohedral structures, space group R 3 m ( ). The crystal lattice is formed by periodically ordered layers lying in the planes perpendicular to the C 3 symmetry axis. Each layer comprises five atomic planes (quintets) that form the sequence Te 1 ‐Bi‐Te 2 ‐ Bi‐Te 1 . Here, Te 1 and Te 2 are Te atoms in different sites. The atoms in separate layers are identical and form a planar hexagonal lattice. The atoms of each subsequent layer are situated above the centers of the triangles formed by the atoms of the preceding layer (close hexagonal packing); that is, the Te 1 and Bi atoms occupy octahedral sites in the tetradymite structure. The chemical bonds within the quintets are covalentionic. Between the quintets, the distance is comparatively long and bonds are van der Waals in nature and weak. This determines the anisotropy of the electrophysical properties of the single crystals [1].