Sides Of Hexagon Research Articles

One-dimensional gallium nitride micro/nanostructures synthesized by a space-confined growth technique

Hexagonal GaN prismatic sub-micro rods and cone nanowires have been synthesized in a large scale by a novel and controllable space-confined growth method. The as-synthesized GaN products are highly crystalline with a wurtzite structure. The prismatic rods have lengths of 15∼20 μm and diameters of 400∼500 nm enclosed by hexagonal smooth side surfaces and a pyramidal end. And the cone nanowires have average diameters of 150∼200 nm and lengths up to several tens of μm with a cone tip. The photoluminescence (PL) studies reveal prominent band-gap UV emission properties of GaN products and narrow FWHM, indicating the excellent luminescent performance and high crystal quality. For field emission characteristic of GaN nanowires, the turn-on field is about 9.5 V/μm and the current density reaches 1.0 mA/cm2 at an electric field of 18 V/ μm. The contrast experiments indicate a novel growth control can be achieved by using a graphite tube as reaction vessel. The sealed graphite tube combined with metallic initiator is greatly responsible for large-scale and uniform preparation of GaN prismatic rods and cone nanowires. Highly symmetric GaN hexagonal micropyramids are grown on a bare Si substrate. The growth mechanism and the control function of the graphite tube are demonstrated. These low-dimensional structures not only enrich semiconducting GaN family, but also are good building blocks for optoelectronic devices.

308 表面粗さに及ぼすハニカム型平面研削砥石の有効砥粒率の影響(新材料・新加工技術)

Sapphire is commonly used as substrate for white light emitting diodes. Smooth surface after a grinding process is required to reduce a processing period for fabrication of flat surface. In this paper, surface roughness was controlled by a number of abrasive grains which pass through sample surfaces. This number is obtained by a quantity of abrasive grains on grinding wheel surface, a wheel rotation speed and a table feeding speed. Newly developed diamond grinding wheels are assembled by hexagonal grinding stones, which have layers with abrasive grains at sides of hexagons and filled up porous material without abrasive grains inside of the hexagons. The quantity of diamond grains on a grinding wheel surface is controlled by a size of hexagonal grinding stone and a layer thickness at edge of grinding stone. When the number of abrasive grains that pass through sample surface increases, surface of sapphire becomes smooth. Surface roughness decreases at a larger quantity of diamond grains on a grinding wheel surface, a higher wheel rotation speed and a higher table feeding speed. Surface roughness ground by a conventional wheel which has abrasive grains on all grinding wheel surface is rougher than that by developed diamond grinding wheels. The results indicate that almost abrasive grains on developed diamond grinding wheels are used for grinding of sapphire, and 1/5 of abrasive grains on a conventional wheel are contributed for grinding of sapphire.

FORMATION AND HARD MAGNETIC PROPERTIES OF A HEXAGONAL NETWORK OF NICKEL FERRITE NANOPARTICLES

A novel hexagonal network structure formed by self-assembly of discrete nickel ferrite nanoparticles on a carbon-coated Cu grid is reported. Each hexagon consists of about 22 discrete nanoparticles with sizes from 120 to 250 nm. The side of the regular hexagon contains 4–6 discrete nanoparticles. The sample displays a large coercivity of 622.6 Oe, exhibiting a hard magnetic feature different from those of the corresponding bulk materials, and is closely related to the hexagonal network structure of nickel ferrite nanoparticles.

Morphology of hepatitis C and hepatitis B virus particles as detected by immunogold electron microscopy.

We performed indirect immunogold electron microscopy (EM) for immunological identification and characterization of hepatitis C virus (HCV). To clarify the morphology of HCV, an indirect immunogold EM of two plasma samples from patients with high HCV RNA titers was carried out using antibodies specific for the putative HCV envelope protein (E) 1. Spherical virus particles 55-65 nm in diameter with delicate spike projections were detected in the 1.14-1.16 g/ml fractions after sucrose density gradient centrifugation. Polyclonal and monoclonal antibodies to the putative HCV E1 specifically recognized these particles. In addition, immunogold EM of the samples was also performed to uncover the morphology of HCV core particles. Spherical particles 33-40 nm in diameter (average, 37 nm) were detected in the 1.22- to 1.25-g/ml fractions by conventional EM after sucrose density gradient centrifugation. Immunogold EM using rabbit polyclonal antibody (RR8) specific for the putative HCV core protein and colloidal gold-labeled goat antirabbit IgG showed binding of the gold particles with RR8. Some of the HCV core particles showed icosahedric morphology. Optical rotation technique showed that the HCV core particles exhibit sixfold symmetry and that the length of the regular hexagon side is approximately 20 nm, suggesting that they have an icosahedric structure. Further, the detection limit of the indirect immunogold EM was evaluated in 11 plasma samples from chronic hepatitis B patients with different degrees of hepatitis B virus (HBV) DNA titers using antihepatitis B surface antigen antibody. The study showed that the detection limit of virus using this method is 10(7) virions/ml.

P-122: High Density Packing of Submicrometer Spherical Particles of the Y[sub 2]O[sub 3]: Eu[sup 3+] Phosphor for Low Voltage FPDs

Spherical, sub-micrometer Y2O3: Eu3+ phosphor particles have been synthesized by a homogenous solution method. These cubic Y2O3: Eu spherical phosphor particles (ca. 300 nm) will be ideal for FED devices as they can densely close-pack in very small pixels on screens (as shown herein.). The pixels are approximately hexagonal in shape where the length of the hexagonal side is about 5μm. The particles manifest high luminous efficiency (better than a commercial sample) under low voltage electron beam excitation. It is also shown herein that these particles are useful in voltage ranges up to 5000 V and perform well at such voltages.

The role of original surface roughness in laser-induced periodic surface structure formation process on poly-carbonate films

Poly-carbonate films containing different types of original surface roughness were illuminated by a polarized ArF excimer laser beam having a fluence of 4 mJ/cm2. Atomic force microscopy was applied to study the laser-induced periodic surface structure formation process at 0°, 30° and 45° angles of incidence. The effect of initial surface structures on the intensity distribution was investigated in cases of: (a) grains on oriented and amorphous thick films; (b) holes on thin spin-coated films; and (c) nanoparticles arranged along micrometer long sides of hexagons below the spin-coated films. The presence of the scattering objects caused symmetry breaking, if the samples were illuminated by oblique incident ‘s’ polarized beam. The Fourier analysis of the AFM pictures has shown the competition of structures having different periods. The characteristic of the permanent surface patterns proved that the interference of the incoming beam and the beams scattered on previously existing structures is the LIPSS generating feedback process. Ring-shaped structures having 228 nm diameter were produced.

On the relative lengths of sides of convex polygons

Let C be a convex body. By the relative distance of points p and q we mean the ratio of the Euclidean distance of p and q to the half of the Euclidean length of a longest chord of C parallel to pq. The aim of the paper is to find upper bounds for the minimum of the relative lengths of the sides of convex hexagons and heptagons.

A Molecular Dynamics Simulation of the Surface-Ordered Phase of n-Alkanes: the Effect of Chain Length

Behavior of realistic n -pentadecane, n -C 15 H 32 ; n -tridecane, n -C 13 H 28 and n -undecane, n -C 11 H 24 on the free surface of the melt is investigated searching for the effect of chain-length on the surface-ordered phase of n -alkanes, with larger simulation cells than that in our previous work. By very slow heating in each sample we find a temperature range (those are 325–340 K, 305–320 K and 288–293 K, for n -C 15 H 32 , n -C 13 H 28 and n -C 11 H 24 , respectively) where the middle layers prefer to be in the melt state with both free surfaces remaining crystalline; these observations are considered to correspond to the surface freezing recently found in n -alkanes. It is observed that the orientation of molecular axes in the surface monolayer is nearly perpendicular to the surface, and the molecules form regular hexagonal side packing similar to that observed in the rotator phases in crystals. It is found that the temperature of surface freezing, the translational disorder in the surface normal ...

Hepatitis C virus core particle detected by immunoelectron microscopy and optical rotation technique

Hepatitis C Virus (HCV) are 55–65 nm spherical particles, but the internal structure of the virion remains to be clarified. To clarify the morphology of HCV core particles, we performed an immune electron microscopy (IEM) using plasma samples from two blood donors with high HCV RNA titers and a detergent-treated anti-HCV core antibody-free plasma sample with high HCV RNA titer (1.5×10 8 copies/ml). Spherical particles, with 33–40 nm in diameter (an average diameter of 37 nm) were found in 1.22–1.25 g/ml fractions after sucrose density gradient centrifugation by conventional electron microscopy (EM). IEM using rabbit polyclonal antibody (RR8) specific to the putative HCV core protein and goat anti-rabbit IgG colloidal gold particles revealed that these spherical particles specifically reacted with RR8. This finding indicates that the spherical particles are naked HCV core particles. Some of the HCV core particles had an icosahedron-like structure. Optical rotation technique showed that the HCV core particle exhibits six-fold symmetry and that the length of regular hexagon side is approximately 20 nm. These findings showed that HCV core particles are spherical particles of 33–40 nm in diameter and that HCV core particles may possess an icosahedron-like structure and a buoyant density of 1.22–1.25 g/ml.

The mechanism of the evolution of hydrogen on palladium and associated internal damage phenomena

The mechanism of the hydrogen evolution reaction has been examined and the knowledge thus obtained applied to the interpretation of various aspects of internal damage found above a critical overpotential in alkaline solution. Tafel slopes showed a change at η=−0.3 V; the stoichiometric number is 1< ν<1.2, separation factor ( S TH=8±1); FTIR measurements give ∂ln θ/∂ η=(4.7 RT/ F) −1, and permeation measurements show ∂ln P ∞/∂ η=(6.1RT/F) −1. These facts are consistent (up to an overpotential ( η) of −0.3 V) with a rate determining proton discharge, coupled to Tafel recombination; at η more negative than −0.3 V, the mechanism changes to a fast proton discharge with rate determining electrochemical desorption to H 2. Damage within the Pd electrode appears markedly at pinholes along the hexagonal sides of grain boundaries. The number of hexagonal units and pinholes increases with overpotential and time. An increased solubility of hydrogen at points of high stress is seen as the cause of damage discernible at triaxial points and that generated along the sides of grain boundaries. The high fugacities of hydrogen in voids around these regions serves to interpret the further deterioration of the structure observed with increasing overpotential. Calculations of pressures inside the voids suggest that initiation of damage to the Pd corresponds to a change in reaction mechanism at η≃−0.3 V.

Development of an Omnidirectional Rolling Leg Mechanism for Application in a Locomotion Machine

The wheelchair is a superior assistive apparatus in open and flat spaces; however, in Japanese style houses, the conventional wheelchair has several drawbacks, including difficulty in negotiating tight corners and moving over obstacles such as thresholds, as well as damage to delicate surfaces such as Tatami mats. Therefore, we developed a new six-legged mobility assisting machine. The individual legs are designed to have a semi-circular arced sole, which can be made to roll like a wheel in the stance phase using a cam and crank mechanism. Therefore, the machine can move efficiently without vertical sway and can pass over step-like obstacles twice as high as those that can be passed over in a wheelchair having wheels with the same radius of curvature. Furthermore, the machine can move in any direction while keeping the passenger facing in the same direction. This is accomplished by simultaneously rotating all six legs around their respective vertical axes at the sole contact point. A 2/3-scale prototype machine (hexagon side: 232mm, height: 222mm, leg length: 100mm, and total weight: 8kg) produced smooth movement. The prototype has a velocity of 2.7m/min and a turning speed of 90degree/sec and has a passable step height of 13mm. The machine is easy to control because it is driven by only two motors: one for propulsion and one for turning.

Analysis of ice crystal growth for a crystal surface containing adsorbed antifreeze proteins

The adsorption of antifreeze protein (AFP) molecules to the ice crystal surface during melt growth from an AFP solution results in disturbance of the growth kinetics at the surface interface. In this paper, the growth pattern related to the potential for crystal growth as well as the crystal surface topography have been studied. The crystal shape and size were found to be strongly dependent on the supercooling in the crystal's surrounding liquid. In between a transition temperature and the freezing temperature, needle-type crystals were formed, growing rapidly in the c-axis direction. The surface was investigated using a scanning tunneling microscope (STM) and a systematic groove/ridge pattern aligned 65° (±5°) to the hexagonal side on one bipyramidal plane observed with length and width similar to the size of the AFP molecule. The depth of the grooves, ranging from 2 to 10 nm indicates the curvature of ice.

Microscopic Observation of Ice Crystal Surface Containing Adsorbed Silane Coupling Agents.

In order to clarify the growth of ice crystals containing adsorbed silane coupling agents (SCAs), a fundamental and microscale analysis has been conducted. By using an optical microscope, the growth patterns of the ice crystals were experimentally investigated while neglecting the influence of heat flux. It was found that some SCAs that particularly have three hydrophilic groups in a molecule can be adsorbed by the ice crystal surface preventing further growth of the crystals towards a-axis direction. We also investigated the surface of the ice crystals by using a scanning tunneling microscope (STM) in order to determine the influence of SCA on the microscale surface structure. Systematic grooves aligned about 75° to the hexagonal side on one bipyramidal plane were observed. Those grooves were at least 500 nm long, 30∼70nm deep, and existed at about 200 nm intervals.

Microscale Analysis of Crystals in Ice Slurry Made from an Antifreeze Protein Solution.

In order to clarify the crystal growth mechanism and to tealize the low-terperature heat transportation system of ice slurry made from an antifreeze protein (AFP) solution which consists of ice crystals resistant to recrystallization, a fundamental and microscale analysis has been conducted on the ice crystals. Since the thermophysical propertics of ice slurry used for ice storage applications, such as energy storage ability and flowability, depend on the shape and size of individual crystals, crystal growth patterns were experimentally investigated by changing the local supercooling temperature while neglecting the influence of heat flux. At low temperatures, when supercooling exceeded a certain transition value, dendritic crystals were generated, which were apparently unaffected by the existence of AFP. In between the transition terperature and the freezing point, needle-like crystals were observed to grow rapidly in the c-axis direction. If these needle-like crystals were held at terperatures within the hysteresis gap (between the freezing and the melting point), bipyramidal crystals within a maximum tip angle of approximately 30° were formed. Since protein adsorption to the ice crystal surface will strongly affect the crystal growth, the surface of crystals was investigated by using a Scanning Tunneling Microscope (STM) in order to determine the influence of AFP on the microscale surface struture. A systematic groov/ridge pattern that was aligned 65° (±5°) to the hexagonal side on one bipyramidal plane was observed. The grooves' length and width were similar to the length and width of AFP, indicating adsorption of single protein molecules to ice with an orientation corresponding to the alignment angle. Their depth, ranging from 2 nm to 10 nm, gives information about the surface curvature. Knowledge from microscale analysis can be used in order to create cost-effective artificial additives for ice slurry systems.

The hexagonal toroidal air-core magnet of the CHORUS detector

We report on the hexagonally shaped toroidal air-core magnet used in the magnetic spectrometer of the CHORUS experiment at CERN. The novel and unique features of this magnet are the radially-constant field over its entire volume, with field lines straight and parallel to the hexagonal sides, and the negligibly small field-free region along its central axis. A detailed description of its construction and performance is given.

A quintuple turning-joint to be linked with all sides of a symmetrical hexagon-linkage having parallel running diagonals

Two perspective and symmetrical hexagon-linkages both having parallel running diagonals perpendicular to the common axis of symmetry that contains their center of perspectivity, are to be interconnected by six turning-joints being the intersections of corresponding sides of the hexagons. All six of them join a common line perpendicular to the axis of symmetry. The 12-bar chain, obtained this way, represents an overconstrained linkage with two redundant (i.e. superfluous) turning-joints. The kinematic chain so designed, simultaneously contains three paris of reflected four-bars being folding ones when only one of them is. In case one of the perspective hexagons contracts into the center of perspectivity, a quintuple turning-joint is to be linked with all sides of the other hexagon.

Tubular graphic carbon structures

We define two classes of infinite graphitic carbon tubes (buckytubes) depending on the underlying morphology of their hexagonal ring structures. The principal axis of a cylindrical (1, 0) tube (type one, helical pitch zero) is parallel to two of the sides of each regular hexagon, and the orientation of hexagon sides in a (2, 0) cylinder (type two, pitch zero) lies at 90° to the tube axis. Helical graphitic tubes where the pitch is larger than zero can also be constructed. The tubes in which the helical pitch takes on the values zero and unity are considered in this work. Based on HMO level calculations, we obtain general formulae and/or recurrence relationships for characteristic polynomials of these tubes. From the formulae, it is found that (1,0) tubes with a circumference of 3R hexagonal rings (R is an integer) have zero HOMO-LUMO band gaps; other (1, 0) tubes always have nonzero band gaps. This pattern is slightly altered when the pitch equals one. In this case, the (1,1) tubes with a circumference of...

A theory of rotating elasto-plastic shrink fits

The paper gives a rigorous theory of rotating elasto-plastic shrink fits under the assumptions of infinitesimal strain, ideal plasticity and validity of Tresca's yield condition. The plastic strain increments are computed by the associated flow rule. Furthermore, it is assumed that the shaft remains purely elastic during the entire loading history. It is shown that, below a limit speed, the plastic deformation is governed by one side of the Tresca hexagon only. Beyond this speed, a second face of Tresca's hexagon becomes involved. In this case plastic prestrains accumulated below the limit speed have to be considered. For both speed regimes, solutions comprising stresses and radial displacement are obtained. Finally a numerical example is given.

Incommensurability Proofs: A Pattern that Peters Out

The concept of incommensurable magnitudes can be traced back to the ancient Greeks. Recall that two magnitudes are incommensurable if their ratio is not given by a pair of positive integers. Our main interest here is not to make a historical study, but rather to examine the scope of a proof technique, which, though sometimes attributed to the Greeks, may well be of more recent origin. It is a method of infinite descent which can be applied to show the incommensurability of the diagonal and side of a square [2, p. 270]; [11, p. 44]; [13, p. 23]. This technique can also be employed to prove incommensurable the diagonal and a side of a regular pentagon and similarly the shortest diagonal and a side of a regular hexagon. Thus we have a method which works for three cases in a row, and we may well believe that it will apply to n-sided regular polygons for n > 6. Alas, such a hope is unfounded. While the shortest diagonal and a side of a regular n-gon may be incommensurable, the pattern that seems to emerge in establishing the result for n = 4, 5, 6 fails for n > 6. In this paper, we first discuss the reason for this failure. In doing so, we utilize some elementary algebraic facts about the roots of unity. Later, we consider the question of when the second shortest diagonal and a side of a regular polygon are incommensurable. Finally, we note the connection of these questions with the Euclidean algorithm.

Spectral Domain Analysis of a Hexagonal Microstrip Resonator

The capacitance of an open regular hexagonal microstrip resonator is calculated with the quasi-static spectral domain technique. From the capacitance values, the effective hexagonal side and the effective dielectric constant are determined, yielding resonant frequencies which agree well with measured values. Numerical data for several dielectric constants are included. The capacitance values are also compared with those of circular and triangular microstrip resonators. A simple formula relates the resonant frequencies of commensurate hexagonal and circular resonators.