Hexagonal Edge Research Articles

In plane mechanical properties of hexagonal V-chiral and Tri-chiral metamaterials

The reasonable design of man-made multifunctional metamaterials with advanced mechanical and physical properties that are not found in nature is both challenging and important. In this paper, novel chiral structures are designed by adding V- and Tri- chiral elements to the typical hexagonal honeycomb substrate, so as to realize the modulation of in plane mechanical properties. Finite element simulations show that the Poisson's ratio of the hexagonal V-chiral structure is negative when the strain is greater than 0.4, and that of the hexagonal Tri-chiral structure is always negative. Quasi-static compression tests show that the introduction of chiral properties results in a stronger load-bearing capacity, and the hexagonal Tri-chiral structure has a stronger energy absorption (EA) and specific energy absorption (SEA) capability. A parametric study is carried out by means of FEM, by adjusting the geometrical parameters of the proposed structures, the performance in terms of energy absorption and compressive stiffness can be improved. Subsequently, Bloch-Floquet theorem is employed for the dispersion relations of the chiral metamaterials and the results show that compared to conventional hexagonal honeycomb, chiral metamaterials are able to generate band gaps in a lower frequency range. Numerical simulation results show that the bandwidth of the proposed novel chiral metamaterials can be tuned through a reasonable selection of hexagonal edge length, wall thickness and radius. Experimental investigations are conducted to test the vibration transmission rate of Structure Ⅲ, and the results prove that the structure is capable of vibration suppression in the target frequency band range. Finally, by filling Structure Ⅲ with steel columns, the structure generates band gaps in the lower frequency range, hence the application of this chiral metamaterial is broadened.

Advancing digital earth modeling: Hexagonal multi-structural elements in icosahedral DGGS for enhanced geospatial data processing

Discrete Global Grid Systems (DGGSs) employ uniform cells for hierarchical Earth surface representation. However, prevalent software systems stemming from DGGS only focus on grid centers and lack the modeling of vertices and edges, which hindering efficient geospatial data computation and analysis. Consequently, we propose a novel mathematical model for hexagonal centers, vertices and edges of an icosahedral DGGS and provide corresponding hierarchical indexing methods and conversion rules with respect to integer coordinates. The proposed method was incorporated into the open-source software DGGRID, thereby enhancing its capabilities by integrating data fusion into the computation framework and expanding its application scope. The results show that the introduction of multi-structural elements could lead to higher-precision modeling of raster and vector data.

A New Framework for Canny Edge Detector in Hexagonal Lattice

Feature extraction is widely used in image processing applications such as face recognition, character recognition, fingerprint identification and medicine. Edge features is among the most important features for such applications. Canny edge detector is the most popular one and has many benefits in comparison with other methods. Since pixels in hexagonal domain have many benefits in comparison with square domain, this paper presents an efficient Canny edge detector in hexagonal domain. The proposed method includes square to hexagonal transformation and edge detection based on a new algorithm. The proposed method has been evaluated on synthetic and real image datasets with different signal to noise ratios (SNRs). Detected edges in synthetic images show that the proposed hexagonal edge detector outperforms existing methods in 44 cases out of 60 cases with respect to figure of merit (FoM). Finally, results of real images demonstrate the superiority of the proposed method in qualitative analysis of sub-images.

Platinum Nanosheets Intercalated into Natural and Artificial Graphite Powders.

Insertion of sheet-type platinum particles (platinum nanosheets) between graphite layers was achieved by a thermal treatment of a mixture of platinum chloride (IV) and graphite powder (natural graphite or artificial graphite) under 0.3 MPa of chlorine at 723 K, followed by the treatment under 40 kPa of hydrogen pressure. Similar platinum nanosheets, which were 1-3 nm in thickness and 100-500 nm in width and had a number of hexagonal holes and edges with 120° angle, were formed between the layers of both natural graphite or artificial graphite; however, their location in the graphite layers depended on the type of graphite used. A number of platinum nanosheets were observed in the edge region of natural graphite particles which have flat surface. On the other hand, a number of platinum nanosheets were found inside and away from the edge of the artificial graphite particles especially in the vicinity of the cracks. Both the platinum nanosheet-containing artificial and natural graphite samples showed high selectivity to cinnamyl alcohol in cinnamaldehyde hydrogenation under supercritical carbon dioxide conditions, while spherical platinum particles, which were located on the surface of natural and artificial graphite, showed lower selectivity.

Simulation of Natural Convection in a Concentric Hexagonal Annulus Using the Lattice Boltzmann Method Combined with the Smoothed Profile Method

This research work presents results obtained from the simulation of natural convection inside a concentric hexagonal annulus by using the lattice Boltzmann method (LBM). The fluid flow (pressure and velocity fields) inside the annulus is evaluated by LBM and a finite difference method (FDM) is used to get the temperature filed. The isothermal and no-slip boundary conditions (BC) on the hexagonal edges are treated with a smooth profile method (SPM). At first, for validating the present simulation technique, a standard benchmarking problem of natural convection inside a cold square cavity with a hot circular cylinder is simulated. Later, natural convection simulations inside the hexagonal annulus are carried out for different values of the aspect ratio, AR (ratio of the inner and outer hexagon sizes), and the Rayleigh number, Ra. The simulation results are presented in terms of isotherms (temperature contours), streamlines, temperature, and velocity distributions inside the annulus. The results show that the fluid flow intensity and the size and number of vortex pairs formed inside the annulus strongly depend on AR and Ra values. Based on the concentric isotherms and weak fluid flow intensity at the low Ra, it is observed that the heat transfer inside the annulus is dominated by the conduction mode. However, multiple circulation zones and distorted isotherms are observed at the high Ra due to the strong convective flow. To further access the accuracy and robustness of the present scheme, the present simulation results are compared with the results given by the commercial software, ANSYS-Fluent®. For all combinations of AR and Ra values, the simulation results of streamlines and isotherms patterns, and temperature and velocity distributions inside the annulus are in very good agreement with those of the Fluent software.

Effect of alkali metals and superalkali species on electronic properties of graphdiyne with open hexagonal edges

In the present work, we study the new two dimensional materials with tunable bandgap and high chemical reactivity via locating the alkali metals and superalkalis (Li, Na, K, Li3O, Na3O, and K3O) on the graphdiyne (GDY) sheets with open hexagonal edges. Our density functional theory (DFT) calculations reveal that the bandgap energy of GDY with a different open zigzag or armchair edges (ZGDY and AGDY) is decreased by interacting with alkali metals and superalkali species. We found that the alkali metals and superalkalis lowered the bandgap energy of AGDY and ZGDY by more than 170% and converted them into the semimetals. Our results also show that the M3O/ZGDY systems show higher chemical reactivity as compared to the other studied systems. Among the studied M(M3O)/ZGDY(AGDY) systems, the maximum binding energy, maximum means static polarisability, minimum bandgap energy, and minimum chemical hardness are related to the K3O/ZGDY complex. Consequently, the K3O/ZGDY is a promising chemically reactive material for applications in various fields such as gas detectors, catalysts in the oxygen reduction reactions, and drug delivery application.

Dynamic response of sandwich panel with hierarchical honeycomb cores subject to blast loading

This paper introduces a novel hierarchical core structure to sandwich panel for bearing the blast loading, in which each vertex of a regular hexagonal cell was replaced with a smaller hexagonal unit. The finite element (FE) models of such hierarchical honeycomb sandwich panels were established and validated with the experiments under different impulse loads. The hierarchical honeycomb cores were compared with the regular honeycomb counterpart in terms of the peak deflection on the back facesheet, compression and specific energy absorption (SEA) of the core. The results showed that the maximum deflection at the back facesheet of the hierarchical honeycomb sandwich panels were smaller than the regular honeycomb counterpart for a higher level of blast load (specifically, the dimensionless impulse higher than 0.06). It was found that the structural hierarchical parameter γ (i.e. the ratio of the newly-introduced smaller hexagonal edge length (L1) to the regular hexagon edge length (L0)), had limited influence on the maximum deflection of back facesheet of the sandwich panel, but had a significant effect on the SEA of the cores.

Characterization of hydrogen plasma defined graphene edges

We investigate the quality of hydrogen plasma defined graphene edges by Raman spectroscopy, atomic resolution AFM and low temperature electronic transport measurements. The exposure of graphite samples to a remote hydrogen plasma leads to the formation of hexagonal shaped etch pits, reflecting the anisotropy of the etch. Atomic resolution AFM reveals that the sides of these hexagons are oriented along the zigzag direction of the graphite crystal lattice and the absence of a D-peak within the noise background in the Raman spectra seems to suggest rather high quality zigzag edges. In a second step of the experiment, we investigate hexagon edges created in single layer graphene on hexagonal boron nitride and find a substantial D-peak intensity. Polarization dependent Raman measurements reveal that hydrogen plasma defined edges consist of a mixture of zigzag and armchair segments. Furthermore, electronic transport measurements were performed on hydrogen plasma defined graphene nanoribbons which indicate a high quality of the bulk but a relatively low edge quality, in agreement with the Raman data. These findings are supported by tight-binding transport simulations. Hence, further optimization of the hydrogen plasma etching technique is required to obtain pure crystalline graphene edges.

Platinum Nanosheets between Graphite Layers.

Two-dimensional platinum nanosheets were obtained by the hydrogen reduction of platinum tetrachloride intercalated between graphite layers, the latter was prepared by the treatment of the mixture of platinum tetrachloride and graphite powder under chlorine atmosphere. The size of platinum nanosheets was 1-3 nm in thickness with a width in the range of 5-300 nm. These nanosheets contain a number of hexagonal holes and edges with an angle of 120°. This review discusses the reduction and oxidation behavior of platinum species and structure of platinum nanosheets between graphite layers. The selective hydrogenation catalyzed by these platinum nanosheets entrapped between the graphite layers is also demonstrated.

Testing topological protection of edge states in hexagonal quantum spin Hall candidate materials

We analyze the detailed structure of topological edge mode protection occuring in hexagonal quantum spin Hall (QSH) materials. We focus on bismuthene, antimonene, and arsenene on a SiC substrate, which, due to their large bulk gap, may offer new opportunities for room-temperature QSH applications. While time reversal symmetry is responsible for the principal symmetry protected character of QSH states, the hexagonal edge terminations yield further aspects of crystal symmetry which affect the topological protection. We show that armchair QSH edge states remain gapless under an in-plane magnetic field in the direction along the edge, a hallmark of their topological crystalline protection. In contrast, an out-of-plane magnetic field opens a gap of the order of a few meV within realistic ranges of parameters. We use these intriguing signatures of armchair QSH edge states to predict experimentally testable fingerprints of their additional topological crystalline character and their helicity emerging in tunneling spectroscopy and ballistic magnetotransport.

Highly efficient infrared to visible up-conversion emission tuning from red to white in Eu/Yb co-doped NaYF4 phosphor.

Eu/Yb co-doped NaYF4 phosphors have been synthesized by the combustion method. The Eu doping was fixed and the effect of Yb doping concentration on the structural, morphological and luminescence properties has been investigated. X-ray diffraction analysis revealed that the phosphors consisted of mixed α- and β-phases, but the β-phase was dominant. All elements of the host and dopants, as well as adventitious C, were detected using X-ray photoelectron spectroscopy. The surface morphology showed a microrod-like structure with sharp hexagonal edges. Energy dispersive X-ray spectroscopy spectra proved the formation of the desired materials. The photoluminescence spectra illustrated the optical emission properties of Eu3+ in the red region when excited at 394 nm, while, under the same excitation, Yb3+ ions gave emission at 980 nm. The up-conversion (UC) emission of Eu/Yb co-doped NaYF4 produced a white color at the higher concentration of Yb excited by a 980 nm laser, which was made possible by green emission of Er contamination (from Yb source) and blue emission of Eu2+ ions. The lifetime of the Eu3+ UC luminescence at 615 nm was also affected by the Yb doping concentration. The temperature sensitivity associated with the Er3+ peaks at 520 and 542 nm was assessed as a function of temperature and the maximum of 0.0040 K-1 occurred at 463 K.

Selective excitation and imaging of ultraslow phonon polaritons in thin hexagonal boron nitride crystals

We selectively excite and study two new types of phonon-polariton guided modes that are found in hexagonal boron nitride thin flakes on a gold substrate. Such modes show substantially improved confinement and a group velocity that is hundreds of times slower than the speed of light, thereby providing a new way to create slow light in the mid-infrared range with a simple structure that does not require nano-patterning. One mode is the fundamental mode in the first Restrahlen band of hexagonal boron nitride thin crystals on a gold substrate; the other mode is equivalent to the second mode of the second Restrahlen band of hexagonal boron nitride flakes that are suspended in vacuum.The new modes also couple efficiently with incident light at the hexagonal boron nitride edges, as we demonstrate experimentally using photo-induced force microscopy and scanning near-field optical microscopy. The high confinement of these modes allows for Purcell factors that are on the order of tens of thousands directly above boron nitride and a wide band, with new perspectives for enhanced light-matter interaction. Our findings demonstrate a new approach to engineering the dispersion of polaritons in 2D materials to improve confinement and light-matter interaction, thereby paving the way for new applications in mid-infrared nano-optics.

Tuning transport properties of graphene three-terminal structures by mechanical deformation

Straintronic devices made of carbon-based materials have been pushed up due to the graphene high mechanical flexibility and the possibility of interesting changes in transport properties. Properly designed strained systems have been proposed to allow optimized transport responses that can be explored in experimental realizations. In multi-terminal systems, comparisons between schemes with different geometries are important to characterize the modifications introduced by mechanical deformations, specially if the deformations are localized at a central part of the system or extended in a large region. Then, in the present analysis, we study the strain effects on the transport properties of triangular and hexagonal graphene flakes, with zigzag and armchair edges, connected to three electronic terminals, formed by semi-infinite graphene nanoribbons. Using the Green's function formalism with circular renormalization schemes, and a single band tight-binding approximation, we find that resonant tunneling transport becomes relevant and is more affected by localized deformations in the hexagonal graphene flakes. Moreover, triangular systems with deformation extended to the leads, like longitudinal three-folded type, are shown as an interesting scenario for building nanoscale waveguides for electronic current.

Novel insight into the epitaxial growth mechanism of six-fold symmetrical β-Co(OH)2/Co(OH)F hierarchical hexagrams and their water oxidation activity

The six-fold symmetry widely presents in both natural and artificial architectures. Understanding the growth mechanism of six-fold symmetrical materials is of fundamental interest and significance. Herein, we report the formation process of β-Co(OH)2/Co(OH)F hierarchical hexagrams with a six-fold symmetrical arrangement. Our results demonstrate that hexagonal β-Co(OH)2 plates are first formed under the reaction condition. These hexagonal plates then act as templates for the growth of Co(OH)F nanorods. The intermediate material is therefore composed of plate-like β-Co(OH)2 hexagonal cores appended with six rod-like Co(OH)F branches, giving the β-Co(OH)2/Co(OH)F hybrid. After prolonged reaction, the β-Co(OH)2 hexagons can be completely converted, leading to authentic six-branched Co(OH)F nanorods as the final product. Consequently, for both intermediate and final materials, the Co(OH)F nanorods are arranged with a six-fold symmetry. Importantly, these Co(OH)F nanorods grow along β-Co(OH)2 hexagon edges as lateral branches instead of perpendicular to hexagons. This uncommon epitaxial growth mechanism is considered to be a result of the matching between the b-axis of Co(OH)F crystals and the a-axis of β-Co(OH)2 crystals, which is beneficial for the electrocatalysis. The β-Co(OH)2/Co(OH)F hierarchical hexagrams show enhanced water oxidation activity compared to the pure β-Co(OH)2 and Co(OH)F.

Selective Hydrogenation of Cinnamaldehyde Over Platinum Nanosheets Intercalated Between Graphite Layers.

Platinum nanosheets between graphite layers were prepared by a thermal treatment of the mixture of platinum chloride (IV) and graphite powder under 0.3 MPa of chlorine at 723 K for 7 days, followed by the reduction under 40 kPa of hydrogen at 573 K for 1 h. Two-dimensional platinum metal nanosheets of 1-3 nm thickness and of 100-200 nm width were intercalated between graphite layers (Pt-GIC). The platinum nanosheets had a number of hexagonal holes and edges with angle of 120°. Liquid phase hydrogenation of cinnamaldehyde (CAL) was studied over Pt-GIC which was compared with that over platinum metal particles supported on graphite layers (Pt/Gmix). The conversion of cinnamaldehyde over Pt-GIC was lower than that over Pt/Gmix; however, the selectivity to cinnamyl alcohol (COL) was higher than that over Pt/Gmix. For similar CAL conversion of around 25% (in 60 min over Pt-GIC and 15 min over Pt/Gmix), the COL selectivities over 5 and 10 wt% Pt-GIC (56 and 54%) were higher than those over 5 and 10 wt% Pt/Gmix (33 and 19%).

A Quantification Method for Fitting Directed Arcs to Hexagonal Grid Edges

A Quantification Method for Fitting Directed Arcs to Hexagonal Grid Edges

Nucleation mode selection during formation and growth of molten removal particles in Al2O3 ceramics laser cutting

Because of the multiple selections on different crystalline faces in nucleation process of α-alumina, it is necessary to confirm the nucleation mode and growth mechanism of molten removal particles produced by alumina ceramics laser cutting. A model based on driving force of Helmholtz and Gibbs free energies is built to compare different critical nucleation sizes and corresponding nucleation barriers among several crystal planes. The calculation shows that when alumina ceramic is cooled and solidified from a molten state, the material is preferably nucleated in the parallelepiped model with extension and stack along the (112¯0) plane. X-ray diffraction and scanning electron microscopy detections are taken to verify the nucleation mode that the morphologies thereof are shown as corners of an octahedron or edges of hexagons in different section directions. A pyramid stacking growth mode of spherical particles is proposed to coincide with the hollow micro morphology. The analysis concludes this model is feasible and it makes contribution to the potential application of removal particles for the field of ceramic powder metallurgy during laser processing.

Hardware implementation of hexagonal sampling based bio-inspired retinal encoder

This paper addresses hardware implementation of a power efficient retinal encoder system used in visual prosthesis equipment for blind people. The hardware architecture is inspired from the retinal receptive fields in mammalian vision system. The captured image is passed through several filter banks in different filtering stages in primate vision system. As the photoreceptors in the primate vision system are arranged in hexagonal fashion, the hexagonal tessellation scheme was found to be the most suitable sampling scheme for retinal image processing. In this work, the hardware implementation of different retinal filtering stages and final edge detection scheme is performed in Altera Cyclone II FPGA and in Synopsys Design Vision. An area efficient Cellular Logic Array Processing (CLAP) algorithm is used as the final stage edge detector. Both rectangular and hexagonal edge detection schemes were tested and their performance was analysed using Berkeley Segmentation Dataset and ROC performance scheme.

Hardware implementation of hexagonal sampling based bio-inspired retinal encoder

This paper addresses hardware implementation of a power efficient retinal encoder system used in visual prosthesis equipment for blind people. The hardware architecture is inspired from the retinal receptive fields in mammalian vision system. The captured image is passed through several filter banks in different filtering stages in primate vision system. As the photoreceptors in the primate vision system are arranged in hexagonal fashion, the hexagonal tessellation scheme was found to be the most suitable sampling scheme for retinal image processing. In this work, the hardware implementation of different retinal filtering stages and final edge detection scheme is performed in Altera Cyclone II FPGA and in Synopsys Design Vision. An area efficient Cellular Logic Array Processing (CLAP) algorithm is used as the final stage edge detector. Both rectangular and hexagonal edge detection schemes were tested and their performance was analysed using Berkeley Segmentation Dataset and ROC performance scheme.

Electro-absorption of silicene and bilayer graphene quantum dots

We study numerically the optical properties of low-buckled silicene and AB-stacked bilayer graphene quantum dots subjected to an external electric field, which is normal to their surface. Within the tight-binding model, the optical absorption is calculated for quantum dots, of triangular and hexagonal shapes, with zigzag and armchair edge terminations. We show that in triangular silicene clusters with zigzag edges a rich and widely tunable infrared absorption peak structure originates from transitions involving zero energy states. The edge of absorption in silicene quantum dots undergoes red shift in the external electric field for triangular clusters, whereas blue shift takes place for hexagonal ones. In small clusters of bilayer graphene with zigzag edges the edge of absorption undergoes blue/red shift for triangular/hexagonal geometry. In armchair clusters of silicene blue shift of the absorption edge takes place for both cluster shapes, while red shift is inherent for both shapes of the bilayer graphene quantum dots.