Triangular Holes Research Articles

The Effect of the Doping Amount on Electroelastic Coupled-Wave Scattering and Dynamic Stress Concentration around Defects in BNT Doped FN Materials.

Sodium bismuth titanate (Bi0.5Na0.5TiO3, BNT) has attracted much attention because of its excellent dielectric, piezoelectric and electromechanical properties. The microstructure of sodium bismuth titanate-doped ferrum niobium material (Bi0.5Na0.5TiO3 doped (Fe0.5Nb0.5)4+, BNT-xFN) shows a triangle as its typical defect shape. Since piezoelectric devices usually operate under dynamic loads, they fail easily owing to dynamic stress concentration or dynamic fracture. Elastic waves can simulate many types of dynamic loads, and the dynamic stress concentration caused by an anti-plane shear wave is the basis for the calculation of the stress field strength factor of type Ⅲ-dynamic fractures. In this study, the electroelastic coupled-wave diffraction and dynamic stress concentration of BNT-xFN materials with triangular defects under the incidence of anti-plane shear waves were studied. Maxwell equations are decoupled by auxiliary functions, and the analytical solutions of the elastic wave field and electric field are obtained. Based on the conformal mapping method, the triangle defect was mapped to the unit circle defect, and the dynamic stress concentration coefficient around the triangle defect was obtained by calculating the undetermined mode coefficients in the expression through boundary conditions. The numerical calculation shows that the size of the triangular hole, the frequency of the applied mechanical load, the incidence angle of mechanical load and the amount of FN doping have a great influence on the stress concentration of BNT-xFN materials.

Impact of aperture angle on magnetostatic shielding performances of magnetic shield cylinders

The spin exchange relaxation free (SERF) atomic magnetometer plays an important role in ultrahigh sensitive magnetic measurements. With the improvement of signal response and the reduction of sensor noise, the sensitivity of the SERF atomic magnetometer is limited mainly by environmental magnetic noise. In order to improve the performance of magnetic shielding, the models of a magnetic shielding cylinder with triangular holes were established in this paper, and the effect of aperture angle (θ) on the efficiency of shielding by a permalloy cylinder was investigated by the finite element analysis. The results showed that the shielding effectiveness decreases first and then increases with the augment of θ. The cylinder showed that the worst shielding effect at θ equals 60°, resulting from the magnetoresistance of leakage flux in the air dielectric. This research focuses on providing theoretical support for the design of magnetic shields and improvement of the magnetic shielding ability.

Investigation of impact performance of perforated plates and effects of the perforation arrangement and shape on failure mode

Searching for lighter protective structure and better energy absorption material is the key goal to improve the protection performance of moving platforms. The impact performance of perforated structures subjected to projectile impact and effects of the perforation arrangement and shape on failure mode are investigated experimentally and numerically. Three different impact velocities, three kinds of hole patterns (circle, triangle and square) and two types of hole arrangements (matrix type and dislocation type) of the perforated plate specimens are discussed in this research. The Mie-Grüneisen equation of states and Johnson-Cook strain-rate sensitive material models are selected in the numerical model. The numerical results agree well with the experimental results. The results show that when the impact velocity, hole shape and hole arrangement are different, the failure modes of perforated plate and witness plate can be divided into eight and four modes, respectively. The projectile deflection effects are observed when the projectile passes through the perforated plate. The deviation angle of projectile decreases with the increase of impact velocity. The deviation angle of perforated plate with circle hole and triangle hole by dislocation type is greater than that by matrix type at the same impact velocity, but the conclusion of perforated plate with square hole is just the opposite. The ballistic deflection effect of the perforated structure with triangular hole is greater than that with the circular hole and square hole. The results obtained from the study will provide a reference to the research of new spatial or layered armor systems containing the perforated plates.

Improvement of the Geometric Accuracy for Microstructures by Projection Stereolithography Additive Manufacturing

Projection stereolithography creates 3D structures by projecting patterns onto the surface of a photosensitive material layer by layer. Benefiting from high efficiency and resolution, projection stereolithography 3D printing has been widely used to fabricate microstructures. To improve the geometric accuracy of projection stereolithography 3D printing for microstructures, a compensation method based on structure optimization is proposed according to mathematical analysis and simulation tests. The performance of the proposed compensation method is verified both by the simulation and the 3D printing experiments. The results indicate that the proposed compensation method is able to significantly improve the shape accuracy and reduce the error of the feature size. The proposed compensation method is also proved to improve the dimension accuracy by 21.7%, 16.5% and 19.6% for the circular, square and triangular bosses respectively. While the improvements on the dimension accuracy by 16%, 17.6% and 13.8% for the circular, square and triangular holes are achieved with the proposed compensation method. This work is expected to provide a method to improve the geometric accuracy for 3D printing microstructures by projection stereolithography.

Efficient and selective capture of xenon over krypton by a window-cage metal–organic framework with parallel aromatic rings

Efficient capture and separation of xenon (Xe) and krypton (Kr) from nuclear fuel reprocessing plants is of great significance for the control of discharge of gaseous radioisotopes into the environment. However, due to the similar size and chemically inert spherical properties of Xe/Kr, the discovery of an adsorbent with both high adsorption capacity and high selectivity remains a challenge. Here, we report a microporous MOF (Ni-MOF, [Ni2IINiIII(μ3-OH)(bdc)3(tpt)]·guest) featuring two different cavities with an appropriate triangular hole window size. One is composed of parallel aromatic rings with spacings of approximately 4.3 Å comparable to the kinetic diameter of Xe (4.047 Å), affording excellent binding affinity for Xe while the larger one with narrow pore window provides sufficient space for gas adsorption. The Ni-MOF material exhibits an exceptionally high Xe uptake of 5.43 mmol/g and Xe/Kr selectivity of 7.66 at 298 K and 1 bar. The adsorption capacity is the highest among all MOFs without open-metal-sites. Furthermore, the sorption selectivity of Xe over Kr within Ni-MOF originates from a special sandwiched π-Xe-π interaction revealed by Van der Waals interaction calculations.

Endoepitaxial growth of monolayer mosaic heterostructures.

The controllable growth of two-dimensional (2D) heterostructure arrays is critical for exploring exotic physics and developing novel devices, yet it remains a substantial synthetic challenge. Here we report a rational synthetic strategy to fabricate mosaic heterostructure arrays in monolayer 2D atomic crystals. By using a laser-patterning and an anisotropic thermal etching process, we create periodic triangular hole arrays in 2D crystals with precisely controlled size and atomically clean edges, which function as robust templates for endoepitaxial growth of another 2D crystal, to obtain monolayer mosaic heterostructures with atomically sharp heterojunction interfaces. Systematic microstructure and spectroscopic characterizations reveal periodic modulation of chemical compositions, lattice strains and electronic band gaps throughout the mosaic heterostructures. The robust growth of the monolayer mosaic heterostructures with a high level of synthetic control opens a pathway for band structure engineering and spatially modulating the potential landscapes in the atomically thin 2D crystals, establishing a designable material platform for fundamental studies and development of complex devices and integrated circuits from 2D heterostructures.

Hydrogen Storage Performance of γ-Graphdiyne Doped Li Based on First Principles for Micro/Nano.

The rapid development of micro/nano systems promotes the progress of micro energy storage devices. As one of the most significant representatives of micro energy storage devices, micro hydrogen fuel cells were initially studied by many laboratories and companies. However, hydrogen storage problems have restricted its further commercialization. The γ-graphdiyne (γ-GDY) has broad application prospects in the fields of energy storage and gas adsorption due to its unique structure with rigid nano-network and numerous uniform pores. However, the existence of various defects in γ-GDY caused varying degrees of influence on gas adsorption performance. In this study, Lithium (Li) was added into the intrinsic γ-GDY and vacancy defect γ-GDY (γ-VGDY) to obtain the Li-GDY and Li-VGDY, respectively. The first-principles calculation method was applied and the hydrogen storage performances of them were analysed. The results indicated that the best adsorption point of intrinsic γ-GDY is H2 point, which located at the centre of a large triangular hole of an acetylene chain. With large capacity hydrogen storage, doping Li atom could improve the hydrogen adsorption property of intrinsic γ-GDY; meanwhile, vacancy defect inspires the hydrogen storage performance further of Li-VGDY. The mass hydrogen storage density for Li2H56-GDY and Li2H56-VGDY model were 13.02% and 14.66%, respectively. Moreover, the Li2H56-GDY and Li2H56-VGDY model had same volumetric storage density, with values that could achieve 5.22 × 104 kg/m3.

Hydrothermal characteristics of turbulent flow in a tube with solid and perforated conical rings

Metallic inserts are well-recognized in modern research as efficient passive thermal performance enhancement methods. However, only scarce studies examined conical rings mainly due to the high corresponding pressure drop. This study aims to achieve a balanced hydrothermal performance using solid and perforated conical rings by focusing -for the first time- on the number and shape of holes in both convergent and divergent rings. The results show that larger Nusselt numbers (up to 360.2 at Reynolds number of 26,000) can be achieved using solid divergent rings due to thermal boundary layer disruption and near-wall flow acceleration, but this configuration also shows the highest friction factors (5.04 at Reynolds number of 6000). Perforating the rings reduces both Nusselt number and friction factor for more balanced performances, especially for higher numbers of holes. Circular and triangular holes result in the highest and lowest values of both parameters, respectively. A maximum thermal enhancement factor of 1.1 is obtained when using solid divergent rings at Reynolds number of 6000. However, a thermal enhancement factor of 1.06 can be achieved using circularly perforated rings with significantly lower pumping power requirements. When referencing solid rings instead of the plain tube, thermal enhancement factors can reach 1.2.

Study on the influence of hole defects with different shapes on the mechanical behavior and damage law of coal and rock.

To study the effect of different shapes of hole defects in coal and rocks on their mechanical behavior and macro damage law, the microscopic mechanical parameters required for particle flow code (PFC) simulation were calibrated with laboratory test data, and then the evolution process of crack and stress field in coal and rocks with circle, square, triangular and trapezoidal holes under uniaxial compression were researched. The findings indicate that: the existence of hole defects lowers the elastic modulus, peak stress, peak strain and other mechanical parameters of coal and rock, and the reduction degree is influenced by the shape of defect. Meanwhile, the existence of hole defects promotes the generation and evolution of meso-cracks in coal and rock. For coal and rock with hole defects, the crack initiation stress and expansion stress are less than those of intact coal and rocks. The crack initiation stress and expansion stress of coal and rocks with trapezoidal hole defects are the smallest, and the coal and rocks with circular hole defects are the largest. The existence of hole defects weakens the damage degree of coal and rocks to some extent. With the increase of axial strain, the evolution curve of the number of meso-cracks shows stage characteristics, which consists of the calm period before the crack initiation point, the stable growth stage between the crack initiation point and the dilatation point, and the accelerated growth stage after the dilatation point. Before the initiation of crack, the concentration zone of compressive stress is located on the left and right sides of the hole defect, and the concentration zone of tensile stress is located on the upper and lower sides of the hole defect. The concentration of tensile stress is the main reason for the initiation and propagation of cracks, while the existence of compressive stress chain among macroscopic cracks is the cause of the residual strength of coal and rocks after failure.

Experiment and Modelling of Triangular Holes Array by Non-traditional Machining Process

Triangular holes array is a common structure of the specially shaped holes that can be used for various products in aerospace vehicles. These are commonly produced in the electrochemical machining (ECM) process. The high-quality and accuracy of a triangular grid are closely related to the processing parameters of cathode structure and sidewall insulation sleeve, power supply, electrolyte flow rate, feed speed, and machining gap. Simulations have been carried out to consider the influence of parameters including structure and dimension of the cathode, initial machining gap, feed speed, and current on the homogeneity of the flow field in the machining gap. Consequently, the modeling can support the design of the cathode. The paper is divided into two parts. Firstly, the tool cathode is simulated and fabricated. Secondly, the triangular holes array is produced by using the designed cathode tool. It was found that higher feed speed and lower machining gap increase the stability, accuracy, and efficiency of the machining process and the quality of the triangular holes array.

Comparison of estimated and measured sound-absorption coefficient and transmission loss by geometric dimensions of a collection of equilateral triangular holes of equilateral triangular holes

We performed a theoretical analysis on collection of equilateral triangular holes with consideration for sound wave attenuation within the tube and then calculated the sound-absorption coefficient and transmission loss. We then compared these results with experimental values. In the experiment, we measured the sound-absorption coefficient and transmission loss of a test sample using impedance measurement tubes with two and four microphones. We estimated the sound-absorption coefficient and transmission loss because of the dimensions of a collection of equilateral triangular holes through theoretical analysis and then compared these results with experimental values. In the present analysis, the propagation constant and characteristic impedance were introduced into a one-dimensional transfer matrix. Considering the effects of sound wave attenuation in the tubule from three-dimensional analysis, we derived the propagation constant and characteristic impedance. Values for the sound-absorption coefficient and transmission loss obtained through the analysis of holes as triangles rather than as circles gave calculation results closer to the experimental values. This is because this method more suitably simulates the effects of the boundary layer that occupies the space within the hole. The results show that the sound absorption coefficient and transmission loss of triangular honeycombs can be estimated with sufficient accuracy using only geometric dimensions and physical properties.

Tiling Enumeration of Hexagons with Off-Central Holes

This paper is the sequel of the author's previous paper about tiling enumerations of the cored versions of a doubly-intruded hexagon (Electron. J. Combin. 2020), in which we generalized Ciucu's work about $F$-cored hexagons (Adv. Math. 2017). This paper provides an extensive list of thirty tiling enumerations of hexagons with three collinear chains of triangular holes. Besides two chains of holes attaching to the boundary of the hexagon, we remove one more chain of triangles that is slightly off the center of the hexagon. Two of our enumerations imply two conjectures posed by Ciucu, Eisenkolbl, Krattenthaler, and Zare (J. Combin. Theory Ser. A 2001).

Unidirectional transmission of funnel-shaped waveguide with complete bandgap

It will be a future trend to apply quantum photonic technology to communication technology and information processing. One of major developing directions of quantum photonic technology is the miniaturization and on-chip integration. Like the diodes in integrated electric circuitry, optical unidirectional transmitter devices (UTDs) play an important role in processing the quantum information and also represent the main components of integrated optical devices. Thus, the design of UTDs has become one of the research hotspots. With photonic bandgap and localization characteristics, as well as easy micro-nano scaled integration, the photonic crystals (PCs) are often preferred when used to develop micro-nano integrated optical devices. At present, the common methods of achieving UTD with photonic crystals include directional bandgap mismatch, asymmetrical coupling by a micro-cavity, odd-even mode conversion, total reflection of photonic crystals with grating and photonic crystal heterostructure, etc. However, these optical unidirectional transmitters gained through the above methods generally have a low forward transmission, narrow working band, complex structure, etc. In the paper a novel method of UTD is put forward based on photonic crystal and a UTD of funnel-shaped waveguide is designed. The design of the device is divided into two parts: optimal funnel waveguide design and optimal point defect design. The band structure of TE polarized photonic crystal is calculated by R-soft. A triangular lattice circular air hole photonic crystal with complete photonic band gap is used as the initial structure and line defects are introduced to form a funnel-shaped waveguide structure (FSWS). The FSWS consists of the first waveguide W1, the second waveguide W2 and a funnel cavity. The funnel cavity is shaped like a funnel and located at the coupling between W1 and W2. Owing to the unique characteristics of the waveguide, the light wave transmission will be localized in the waveguide, which is conducive to improving the forward transmission. The influence of width variation of W2 with forward and backward incident light are analyzed by the finite difference time domain (FDTD) method, and W2 is selected as a waveguide formed by removing 11 rows of air holes. The FSWS achieves the initial asymmetric transmission, while the backward transmission remains high. Further studies are conducted to introduce four types of point defects to suppress the backward transmittance. The point defects refer to moving one or two air holes. In the work the FDTD is also used to calculate four kinds of point defect backward transmittance spectra and optimize the positions of point defects. Finally, it is found that when the optimal point defect mode is type I and <i>d</i> = 5<i>a</i>, the forward transmission (<i>T</i><sub>f</sub>) and transmission contrast (<i>C </i>) at 1550 nm are 0.716 and 0.929, respectively. Working bandwidth (<i>B</i>) can be increased up to 111 nm (1501–1612 nm). By mode analysis, it is found that the point defect introduces mode mismatch between W1 and W2, by converting the fundamental mode in W2 into high-order modes. Thus, the back-propagating light waves in W2 cannot effectively couple into W1, resulting in complete blockage of backward propagation. In addition, the structure is made of silicon based air hole photonic crystal. The 2D air-hole PC slab is mature and even compatible with conventional complementary metal oxide semiconductor (CMOS) processing. The designed UTD is easy to implement, and has the advantages of simplicity and high unidirectional transmission characteristics. Therefore, it can provide a new solution for UTDs with higher requirements for integrated optical path at present.

Stress Intensity Factors for a Non-Circular Hole with Inclusion Layer Embedded in a Cracked Matrix

The failure analysis of a non-circular hole with an inclusion layer embedded in an infinite cracked matrix under a remote in-plane uniform load is presented. In this study, a series solution of stress functions for both the matrix and inclusion layer is obtained using the complex variable theory in conjunction with the method of conformal mapping. The stress intensity factor (SIF) can then be determined numerically by solving the singular integral equation (SIE) for the interaction among different crack sites, material properties, and geometries of irregular holes with an inclusion layer. In particular, the failure behavior of composite structures associated with an approximately triangular hole and an approximately square hole with inclusion layers, such as those of oxides, nitrides, and sulfides, is examined in detail. The results demonstrate that a softer layer would enhance the SIF and a stiffer layer would restrain the SIF when a crack is near the inclusion layer. It can be concluded that crack propagation would be suppressed by a stiffer layer even when a micro-defect such as a hole resides in the inclusion layer.

Reversible structural transition of two-dimensional copper selenide on Cu(111)

Structural engineering opens a door to manipulating the structures and thus tuning the properties of two-dimensional materials. Here, we report a reversible structural transition in honeycomb CuSe monolayer on Cu(111) through scanning tunneling microscopy and Auger electron spectroscopy (AES). Direct selenization of Cu(111) gives rise to the formation of honeycomb CuSe monolayers with one-dimensional moiré structures (stripe-CuSe), due to the asymmetric lattice distortions in CuSe induced by the lattice mismatch. Additional deposition of Se combined with post annealing results in the formation of honeycomb CuSe with quasi-ordered arrays of triangular holes (hole-CuSe), namely, the structural transition from stripe-CuSe to hole-CuSe. Further, annealing the hole-CuSe at higher temperature leads to the reverse structural transition, namely from hole-CuSe to stripe-CuSe. AES measurement unravels the Se content change in the reversible structural transition. Therefore, both the Se coverage and annealing temperature play significant roles in the reversible structural transition in CuSe on Cu(111). Our work provides insights in understanding of the structural transitions in two-dimensional materials.

Strong coupling between an inverse bowtie Nano-Antenna and a J-aggregate

We demonstrate strong coupling between a single or few J-aggregates and an inverse bowtie plasmonic structure, when the J-aggregate is located at a specific axial distance from the metallic surface. Three hybrid modes are clearly observed, witnessing a strong interaction, with a Rabi splitting of up to 290 meV, the precise value of which significantly depends on the orientation of the J-aggregate with respect to the symmetry axis of the plasmonic structure. We repeated our experiments with a set of triangular hole arrays, showing consistent formation of three or more hybrid modes, in good agreement with numerical simulations.

Design of isotropic porous plates for use in hierarchical plate-lattices

This work deals with the elastic and plastic properties of two-dimensional periodic metamaterials. Design maps are developed to ensure their isotropic elastic response while attaining the theoretical stiffness limits. Numerical simulations of two different topologies - triangular and round hole staggered patterns - are performed to analyze their large deformation response for relative densities ranging from 0.1 to 0.9. The investigations show that the strength of triangular perforated plates is profoundly dependent on the unit cells’ direction concerning the axial loading; 0 and 30 degrees have the lowest and highest yield strength over the entire range of volume fractions. In contrast, the round hole staggered patterns exhibit an almost uniform yield strength in all directions. The yield strength of the circular patterns is significantly lower at low- and intermediate-density ranges; whereas they outperform the triangular ones at relative densities higher than 0.6. Additionally, validation experiments are performed on specimens of 0.3 relative density that have been extracted from DP980 steel sheets using micro waterjet cutting, showing good agreement in terms of force-displacement response and surface strain fields. A foam-like structure is built from periodic sheets and the scaling of the elastic properties of the resulting hierarchical 3D metamaterial are discussed.

On some peculiar fractures observed in tests of the Upper-Cretaceous fossil echinoid Micraster

Many skeletons (“tests”) of the fossil echinoid Micraster from the marl limestone strata of the Upper Cretaceous formation of western Navarra (Spain) show small triangular holes on their surface, caused by the loss of a pyramidal fragment. The base of the pyramidal borings is often close to an equilateral triangle. The test of echinoids is a mosaic structure constituted of interlocking monocrystalline plates of bio-calcite which possess a preferred crystalline orientation. In the case of the genus Micraster, the surface of the plates is near-parallel to the basal calcite plane (0001). The geometry of the observed holes, at first sight surprising, is simply explained by the intersection of cracks along the three easy 101¯4 cleavage planes of the calcite single crystalline plates constitutive of the skeletons. The fracture process leading to the pyramidal fractures is most likely due to stresses of thermo-elastic origin induced by the heterogeneous dilatational response of the anisotropic tests adhered to the isotropic marly limestone in which they are embedded and which is constitutive of their inner molds.

Electrically Pumped Epitaxially Regrown GaSb‐Based Type‐I Quantum‐Well Surface‐Emitting Lasers with Buried High‐Index‐Contrast Photonic Crystal Layer

Epitaxially regrown electrically pumped photonic crystal surface‐emitting lasers (PCSELs) emitting near 2 and 2.6 μm are designed, fabricated, and characterized. A high‐index‐contrast photonic crystal layer is incorporated into the GaSb‐based laser heterostructure by air‐hole‐retaining epitaxial regrowth. A square lattice of triangular holes is etched in the top waveguide core layer of the incomplete laser heterostructure. The nanopatterned surface is subsequently cleaned and regrown with AlGaAsSb p‐cladding material. Transmission electron microscopy studies demonstrate uniform regrowth over the nanopatterned GaSb surface. The selected regrowth regimes yield a buried 2D array of elongated air‐holes. The diode PCSELs based on moderately etched nanopatterns demonstrate band‐edge lasing near 2 μm up to room temperatures. The cascade diode PCSELs operate near 2.6 μm with minimum threshold current densities of about 500 A cm−2 achieved at 180 K. The devices generate mW level output in narrow divergence beam emitted from the window in substrate contact. The angle‐resolved electroluminescence measurements reveal a four‐sub‐band band structure with an apparent photonic bandgap corresponding to the buried high‐index‐contrast square photonic crystal layer. The PCSELs made of heterostructures supporting two modes in the vertical direction demonstrate two sets of sub‐bands showing anti‐crossing‐like interaction.

Binomial determinants for tiling problems yield to the holonomic ansatz

We present and prove closed form expressions for some families of binomial determinants with signed Kronecker deltas that are located along an arbitrary diagonal in the corresponding matrix. They count cyclically symmetric rhombus tilings of hexagonal regions with triangular holes. We extend a previous systematic study of these families, where the locations of the Kronecker deltas depended on an additional parameter, to families with negative Kronecker deltas. By adapting Zeilberger’s holonomic ansatz to make it work for our problems, we can take full advantage of computer algebra tools for symbolic summation. This, together with the combinatorial interpretation, allows us to realize some new determinantal relationships. From there, we are able to resolve all remaining open conjectures related to these determinants, including one from 2005 due to Lascoux and Krattenthaler.