Hexagonal Base Research Articles

Perluasan Masalah Isoperimetrik pada Bangun Ruang

In this paper, several extensions of the isoperimetric problem in solid figures are explored, focusing on oblique and right prisms with rectangular, right-angled triangular, and regular hexagonal bases. The objective of this research is to find the prism with the largest volume while keeping the surface area constant. Through manipulations of algebra and simple trigonometry, evidence is obtained that a right prism provides a larger volume than an oblique prism if their surface areas are equal. By utilizing partial derivatives of a two-variable function and the Lagrange multiplier method, conditions for the side lengths are derived to obtain the prism with the maximum volume. The results show that a cube is the solution to the isoperimetric problem, meaning it has the largest volume among prisms with rectangular bases, while for the isoperimetric solution on prisms with right-angled triangular bases, the base of the prism must be an isosceles right-angled triangle. A regular hexagonal prism has a larger volume than prisms with rectangular and right-angled triangular bases if their surface areas are the same.

A new class of discrete conformal structures on surfaces with boundary

We introduce a new class of discrete conformal structures on surfaces with boundary, which have nice interpretations in 3-dimensional hyperbolic geometry. Then we prove the global rigidity of the new discrete conformal structures using variational principles, which is a complement of Guo–Luo’s rigidity of the discrete conformal structures in Guo and Luo (Geom Topol 13(3):1265–1312, 2009) and Guo’s rigidity of vertex scaling in Guo (Commun Contemp Math 13(5):827–842, 2011) on surfaces with boundary. As a byproduct, new results on the convexity of the volume of generalized hyperbolic pyramids with right-angled hyperbolic hexagonal bases are obtained. Motivated by Chow–Luo’s combinatorial Ricci flow and Luo’s combinatorial Yamabe flow on closed surfaces, we further introduce combinatorial Ricci flow and combinatorial Calabi flows to deform the new discrete conformal structures on surfaces with boundary. The basic properties of these combinatorial curvature flows are established. These combinatorial curvature flows provide effective algorithms for constructing hyperbolic metrics on surfaces with totally geodesic boundary components of prescribed lengths.

GaN-based pyramidal quantum structures for micro-size light-emitting diode applications

GaN-based pyramidal quantum structures, InGaN nanostructures located on top of micro-sized GaN pyramids, were fabricated by selective-area growth on SiC substrates by means of hot-wall metal-organic chemical vapor deposition. Arrays of GaN-based pyramidal structures exhibit micro-size pyramids possessing high uniformity, precise hexagonal bases, and InGaN/GaN quantum-well layers with well-defined interfaces. Each pyramid comprises a p-i-n InGaN/GaN structure, which is separated from that of other pyramids by a dielectric layer, serving as a building block for micro-emitters. Moreover, interconnected micro-size light-emitting diodes (microLEDs) built on the GaN-based pyramidal quantum structures were demonstrated, resulting in well-determined electroluminescence in the near-ultraviolet regime with negligible spectral shifts at high current levels. The results elucidated the rewards for development of these light-emitting designs and their potential for microLED applications.

Ultrasound wave exchange between COVID-19 virus and host cells

A way to control or cure viral diseases like the Coronavirus is the use of exchanged waves between viral RNAs and cellular DNAs. In this research, we propose a model to compare the structure of cells and Corona viruses with the structure of speakers/microphones and obtain the frequency and the shape of exchanged waves. This is a theoretical and a mathematical model. Real material of this model are both Coronaviruses and host cells. METHODS: In this model, the cellular DNA and viral RNA are formed from charged particles and by their motions, some electromagnetic waves are emerged. In fact, they act like the inductors within speakers/microphones and produce some magnetic fields. These fields interact with charges around nuclear and viral membranes and produce some currents along them. In these conditions, membranes act like the magnet within speakers/microphones and emit some new magnetic fields. These fields interact with DNA and viral inductors, move them and produce some extra magnetic waves, These waves move charges along viral and nuclear membranes, vibrate them and produce some sound waves. RESULTS : Shape of DNA ultrasound waves depend on their RNA/DNA sources. A cellular DNA coils several times around the histone and supercoiled axes and produce linear, toroid and round inductors. A viral RNA coils and creates round viral inductor. These inductors are formed from hexagonal and pentagonal bases and emit hexagonal/pentagound linear/curved sound waves. CONCLUSIONS: Frequency of DNA sound waves could be between 107-1020 (Hz). Also, frequency of viral sound waves could be between 107-1011 [KVirus/KCell] where KVirus, KCell are some constants depending on the genus of liquids within viral and cell membranes. In some conditions, KVirus/KCell=1 and virus could be absorbed by cells.

Twinned nanoparticle structures for surface enhanced Raman scattering

This work dealt with the preparation of twinned nanostructures for the optimization of substrates for SERS. At first GaP nanocones with hexagonal bases were prepared on GaP substrates by metal organic vapour phase epitaxy (MOVPE) at 650 °C. The substrates were then covered with Ag nanoparticles by RF sputtering. The Ag nanoparticles had very short inter–particle distances if they formed from thin Ag layers. The nominally 5 nm thick Ag layer resulted in the formation of an Ag nanoparticle assemblage with inter–particle distances shorter than 5 nm. The GaP nanocones and Ag nanoparticles worked in synergy to yield a substantial increase of SERS signal. This was verified with Rhodamine 6G molecules (at a concentration of 10-6M) at the typical Raman lines of 611 cm−1 and 773 cm−1. The enhancement of SERS was estimated to be as high as 106 for the nanocone substrate decorated with Ag nanoparticles from a nominally 5 nm thick Ag layer.

Microfabrication of Microlens by Timed-Development-and-Thermal-Reflow (TDTR) Process for Projection Lithography.

This paper presents a microlens fabrication process using the timed-development-and-thermal-reflow process, which can fabricate various types of aperture geometry with a parabolic profile on a single substrate in the same batch of the process. By controlling the development time of the uncrosslinked negative photoresist, a state of partial development of the photoresist is achieved, called the timed development process. The thermal reflow process is followed after the timed development, which allows the photoresist to regain its liquid state to form a smooth meniscus trench surrounded by a crosslinked photoresist sidewall. Microlens with larger aperture size forms deeper trench with constant development time. With constant aperture size, longer developing time shows deeper meniscus trench. The depth of the meniscus trench is modeled in the relationship of the development time and aperture size. Other characteristics for the microlens including the radius of curvature, focal length, and the parabolic surface profile are modeled in the relationship of the microlens thickness and diameter. Microlens with circular, square, and hexagonal bases have been successfully fabricated and demonstrated where each geometry of the lens-bases shows different fill factors of the lens arrays. To test the fabricated lenses, a miniaturized projection lithography scheme was proposed. A centimeter-scale photomask pattern was photo-reduced using the fabricated microlens array with a ratio of 133, where the smallest linewidth was measured as 2.6 µm.

Magnetic properties of six-legged spin-1 nanotube in presence of a longitudinal applied field

In this paper, we investigate the magnetic behavior of a single-walled hexagonal spin-1 Ising nanotube by using the effective field theory (EFT) with correlations and the differential operator technique (DOT). The system consists of six long legs distributed parallel to each other on a hexagonal basis. Within each chain, spin sites are regularly positioned and magnetically coupled through a J// exchange interaction along the chains and J⊥ between adjacent chains. Key equations of magnetization, susceptibility and critical temperatures are established, numerically resolved and carefully analyzed for some selected exchange couplings and various applied magnetic fields. In addition to the phase diagram, interesting phenomena are noted, particularly for opposite exchange interactions where magnetization plateaus and frustration are discovered.

Growth of InAs Wurtzite Nanocrosses from Hexagonal and Cubic Basis.

Epitaxially connected nanowires allow for the design of electron transport experiments and applications beyond the standard two terminal device geometries. In this Letter, we present growth methods of three distinct types of wurtzite structured InAs nanocrosses via the vapor-liquid-solid mechanism. Two methods use conventional wurtzite nanowire arrays as a 6-fold hexagonal basis for growing single crystal wurtzite nanocrosses. A third method uses the 2-fold cubic symmetry of (100) substrates to form well-defined coherent inclusions of zinc blende in the center of the nanocrosses. We show that all three types of nanocrosses can be transferred undamaged to arbitrary substrates, which allows for structural, compositional, and electrical characterization. We further demonstrate the potential for synthesis of as-grown nanowire networks and for using nanowires as shadow masks for in situ fabricated junctions in radial nanowire heterostructures.

Orthorhombic YBaCo4O8.4 crystals as a result of saturation of hexagonal YBaCo4O7 crystals with oxygen

Hexagonal YBaCo4O7 crystals (sp. gr. P63mc, ah = 6.3058(4) A, ch = 10.2442(7) A, Z = 2) are saturated with oxygen to the YBaCo4O8.4 composition and studied by X-ray diffraction (XRD) analysis. The saturation is completed by a structural first-order phase transition to orthorhombic crystals (sp. gr. Pbc21, ao = 31.8419(2) A, bo = 10.9239(5) A, co = 10.0960(5) A, Z = 20). The connection of two lattices is expressed in terms of the action of matrix (500/120/001) on the hexagonal basis. Five structural fragments of the same type but with different degrees of order alternate along the long axis of the oxygen-saturated orthorhombic structure. The XRD data on single crystals differ from the results obtained by other researchers on ceramic samples; possible causes of these differences are discussed.

Mysterious hexagonal pyramids on the surface of Pyrobaculum cells.

In attempts to induce putative temperate viruses, we UV-irradiated cells of the hyperthermophilic archaeon Pyrobaculum oguniense. Virus replication could not be detected; however, we observed the development of pyramidal structures with 6-fold symmetry on the cell surface. The hexagonal basis of the pyramids was continuous with the cellular cytoplasmic membrane and apparently grew via the gradual expansion of the 6 triangular lateral faces, ultimately protruding through the S-layer. When the base of these isosceles triangles reached approximately 200nm in length, the pyramids opened like flower petals. The origin and function of these mysterious nanostructures remain unknown.

Fractal random series generated by Poisson-Voronoi tessellations

In this paper, we construct a new family of random series defined on R D \mathbb {R}^D , indexed by one scaling parameter and two Hurst-like exponents. The model is close to Takagi-Knopp functions, save for the fact that the underlying partitions of R D \mathbb {R}^D are not the usual dyadic meshes but random Voronoi tessellations generated by Poisson point processes. This approach leads us to a continuous function whose random graph is shown to be fractal with explicit and equal box and Hausdorff dimensions. The proof of this main result is based on several new distributional properties of the Poisson-Voronoi tessellation on the one hand, and an estimate of the oscillations of the function coupled with an application of a Frostman-type lemma on the other hand. Finally, we introduce two related models and provide in particular a box-dimension calculation for a derived deterministic Takagi-Knopp series with hexagonal bases.

Novel simple methods for the synthesis of single-phase valentinite Sb2O3

Several methods with solid and dissolved reactants were investigated as possible routes for synthesis of single-phase valentinite Sb2O3. The methods are based on simple chemical reaction between SbCl3 and NaOH. The method with solid state reactants was established on self-propagating room temperature reaction (SPRT), while wet syntheses were based on the same chemical reaction, and performed in either distilled water or absolute ethanol. The prepared powders were characterized by X-ray powder diffraction, scanning electron microscopy and field emission scanning electron microscopy, high-resolution transmission electron microscopy, selected area electron diffraction (SAED) and UV/vis diffuse reflectance spectroscopy. SPRT and aqueous solution syntheses resulted in single-phase valentinite Sb2O3, but with significantly different morphologies. In the case of SPRT method the obtained powder contains well crystallized prismatic shaped submicronic particles, with hexagonal or lozenge basis typical for valentinite crystal structure, while aqueous solution synthesis resulted in powder containing micronic agglomerates. The ethanolic solution synthesis product was Sb2O3 with cubic senarmontite as predominant phase and traces of orthorhombic valentinite. It was confirmed that not only the aggregate state, but also the choice of solvent has a great influence on the structural and optical characteristics of synthesized Sb2O3 powders.

Hexagonalization of Aluminogermanate Imogolite Nanotubes Organized into Closed-Packed Bundles

Imogolite nanotubes are promising building blocks for nanotechnologies with potential applications in molecular separation, molecular storage, or catalysis. We present an experimental study of the structure of germanium-based imogolite nanotubes Al2O3Ge(OH)4 arranged in bundles. It combines cryo-transmission electron microscopy, infrared spectroscopy, thermogravimetric measurements, and X-ray scattering experiments. Thanks to a systematic method developed to analyze X-ray scattering diagrams as a function of the nanotube shape, single-walled germanium-based imogolite nanotubes, known as cylindrical for more than 30 years, are shown to take an hexagonal base shape when arranged in bundles. Physical and chemical properties of hexagonal imogolite nanotubes should markedly differ from those of cylindrical ones, making hexagonal basis nanotubes a ?new? member, of particular interest, of the rich family of imogolites.

A Multiple-Electron Reaction in Rechargeable Lithium Batteries with a Positive Electrode Li9V3P8-δO29-δ'

The oxygen and phosphorus deficient material of monodiphosphate Li 9 V 3 (P 2 O 7 ) 3 (PO 4 ) 2 with a trigonal layered structure, or Li 9 V 3 P 8-δ O 29-δ' has been synthesized, where the lattice constants are a = 9.7422(4) and c = 13.6145(8) Å in the hexagonal basis. The electrochemical characteristics using this material with δ≈0.4 and δ' ≈1 as a positive electrode exhibit a double-electron reaction with a capacity 170 A h kg -1 and an energy density 670 W h kg -1 . The V atoms are ionized significantly to reduce the V–O electronic admixture and are in a state with the orbital singlet–doublet separation 1370 cm -1 within the Γ 4 manifold. The Li ionic motion at 295 K is suggested from a microscopic viewpoint.

Seeded growth of ZnO nanorods from NaOH solutions

Perpendicularly aligned arrays of corrugated ZnO nanorods were grown onto gold patterned LiTaO 3 substrates, coated with a sputtered ZnO seed layer. During the growth process, these substrates were held submerged in an aqueous solution comprising a 1:40 mol ratio mix of zinc nitrate hexahydrate to sodium hydroxide. The substrates were placed in a custom apparatus residing in an autoclavable storage bottle. Scanning electron micrographs, which were taken at different deposition intervals, suggest that the growth mechanism of ZnO nanorods initiates with the etching of the ZnO sputtered seed layer into hexagonal bases (> 500 nm across), from where multiple protrusions (40 nm–100 nm in width) grow atop these hexagonal bases. Such nanoprotrusions later coalesce into larger nanorods. Uniformly distributed high density corrugated nanorods, with proximal spacing between adjacent nanorods of approximately 20 nm–50 nm, were observed over the entire surface.

Stacking faults and metallic properties of triangular latticeCoO2 with a three-layer structure

A triangular lattice system CoO2 is synthesized through chemical extraction of Li fromLiCoO2 with H2SO4. On the basis of the x-ray powder diffraction and various composition analyses, thestructure approximately modelled with space group and cell dimensions a = 2.8388(6) and c = 13.439(1) Å in the hexagonal basis has three oxygen layers with a prismatic oxygen environment (P3)between the layers. It also has stacking faults with shift vectors and along the shift of . Through measurements of the thermoelectric power and magnetic susceptibility,CoO2 (P3) is suggested to be a weakly correlated metal with a mass enhancement of 2.6.Na0.09CoO2 synthesized throughNa extraction from Na0.7CoO2 also shows metallic properties with correlation effects probably stronger than those ofCoO2 (P3).

Self-Assembled c-Plane GaN Nanopillars on γ-LiAlO2 Substrate Grown by Plasma-Assisted Molecular-Beam Epitaxy

We have grown M-plane GaN films with self-assembled C-plane GaN nanopillars on a γ-LiAlO2 substrate by plasma-assisted molecular-beam epitaxy. The diameters of the basal plane of the nanopillars are about 200 to 900 nm and the height is up to 600 nm. The formation of self-assembled c-plane GaN nanopillars is through nucleation on hexagonal anionic bases of γ-LiAlO2. Dislocation defects were observed and analyzed by transmission electron microscopy. From the experimental results, we developed a mechanism underlying the simultaneous growth of three-dimensional c-plane nanopillars and two-dimensional M-plane films on a γ-LiAlO2 substrate.

Photoluminescence studies of GaN epilayer–nanocrystals grown on γ-LiAlO 2 substrate

We report the optical studies of the properties of M-plane GaN/ c-plane GaN nanocrystal heterostructure on γ-LiAlO 2 substrate grown by plasma-assisted molecular beam epitaxy. In this structure, in addition to the M-plane epilayer, nanocrystals grown in c-direction could also be observed in the step edges of the M-plane GaN terraces and the hexagonal basis of the γ-LiAlO 2 substrate. X-ray diffraction (XRD) with peaks at 2 θ=32.295°, 34.680° and 34.505° are attributed to the M-plane GaN, LiAlO 2 and c-plane GaN, respectively. Two peaks were observed in the photoluminescence spectra at low temperature. The peak at 3.33 to 3.35 eV is attributed to the emission from c-plane GaN nanocrystals and the peak at 3.50 eV is attributed to the emission from M-plane GaN epilayers. The relative intensity of these peaks is position-dependent. In the area with higher concentration of the GaN nanocrystals the emission for the nanocrystals is stronger and vice versa. Cathodoluminescence shows that the emission peak at 3.33–3.35 eV is originated from the nanocrystals GaN.

Epitaxial growth of copper silicides by “bilayer” technique on monocrystalline silicon with and without native SiO x

Cu/Au and Au/Cu multilayered films were thermally evaporated alternatively on (1 0 0) and (1 1 1) monocrystal silicon substrates with and without native silicon oxide. After heat treatment in situ either at 400 or at 600 °C, the interfacial transformations were analyzed by Rutherford backscattering spectrometry, θ–2 θ X-ray diffraction and scanning electron microscopy. It was found, that the samples surface was covered with Cu 3Si and Cu 4Si crystallites of square, rectangular and hexagonal basis shapes well-oriented on Si(1 0 0) and of triangular shape on Si(1 1 1) owing to the strong intermixing between the different elements. The dilution of the entire gold deposited layer in the Cu–Au–Si formed mixture suggests that gold atoms have a high limit solubility in the formed polycrystalline Cu 3Si and Cu 4Si silicides.

New heterometallic organosiloxanes

Among a diversity of bimetallic1 organometallo siloxanes (OMSO), compounds simultaneously contain ing transition and main group metals remained unknown. Combinations of transition and alkaline earth metals are of particular interest because alkali and alkaline earth metals are similar in electronegativity. Hence, the char acteristics of the structure formation of OMSO would be expected to be similar for such compounds. In addition, it is worthwhile to compare the influence of alkaline earth and other main group metals in the OMSO structure. We synthesized bimetallic OMSO, viz., calcium cop per phenylsiloxane (1) and cadmium copper phenyl siloxane (2), according to a procedure described earlier.2 This procedure involves the alkaline hydrolysis of phenyl triethoxysilane followed by the exchange reaction of the resulting organosilanolate and polyvalent metal halides. X ray diffraction study of OMSO 1 and 2 demon strated that these compounds are structurally similar and can be described as hexagonal prisms, whose upper and lower bases are formed by the six membered organo siloxane rings linked to each other by the metal oxide fragments O—M—O (Fig. 1). In all sandwich type bimetallic OMSO synthesized earlier, the prismatic cage has a cylindrical shape. By contrast, the cage in complexes 1 and 2 has an ellipsoid shape, the ellipsoid being elongated along the line be tween two main group metals, which is due to the fact that the ionic radii of the Ca and Cd atoms (1.00 and 0.87 A, the coordination numbers are 5 and 6, respec tively)3 substantially differ from that of the Cu atom (0.65 A, the coordination number is 5).3 The deviation from the cylindrical shape can be estimated from the dis tance between the opposite copper atoms. In μ6 (hexa phenylcyclohexasiloxanolato)hexacopper(II), which has been synthesized earlier,4 the corresponding distance is 5.5—5.7 A. In complex 2, this distance is substantially shorter (4.462(1) A). The replacement of the Cd atom by Ca leads to a further decrease in this distance (to 4.004(1) A), and the latter is comparable to the analogous distance (3.958(1) A) in the "globular" Cu,Na OMSO complex.5 Therefore, the partial replacement of Cu atoms by atoms with larger ionic radii leads to a distortion of the cylindrical shape of the cage, the degree of distortion being more likely determined by the ionic radius rather than by the nature of the introduced metal atom.