Prism Axis Research Articles

Formalization of calculations of the basing error when installing a shaft-type workpiece in a prism

The error of the position of the axis of the cylindrical workpiece in height is considered, depending on the tolerance for the angular size of the prism. The relationship between the manufacturing error of the angle of the prismatic support for basing cylindrical workpieces for technological impact and the position of the workpiece axis in the direction of the prism axis is revealed. Nomograms are constructed to determine the position of the workpiece in a standard prism depending on the diameter of the workpiece and the error of its diametrical size. Practical recommendations for working with the nomogram are given and the scope of application of the results of the work is determined.

Growth twins and deformation twins of sodalite-type microporous compounds

The tendency of sodalite-group minerals and synthetic materials with the sodalite-type structure to form growth twins has long been known. Judging by faceting, the twin components are connected by a 180-degree turn around the [111] axis of the cubic lattice. In this work, the structure of growth twins, including simple prismatic twins elongated in the [111] direction and V-shaped twins, has been studied in detail at the atomic level. It is shown for elongated twins that the boundary between the twin components passes in the (111) plane through the common vertices of TO4 tetrahedra (T = Al, Si). The coordinates of these vertices are connected by pseudosymmetry operators, each of which can be a twinning operator. This can be either a 180-degree turn around the [111] axis or a reflection in any of the planes (2‾ 11), (12‾ 1), or (112‾). Twinning by a plane is accompanied by smaller distortions of the motif at the twin boundary and, therefore, is energetically more favorable. V-shaped twins are regular intergrowths of two simple twins, the prism axes of which are directed along different ⟨111⟩ directions of the cubic lattice. In addition to growth twins, deformation twins of sodalite and related materials are discussed. Their symmetry is usually lower than cubic, and twinning is often combined with modulation of the crystal structure or the formation of a superstructure. Crystal twinning can be a consequence of a phase transition from a high-temperature cubic phase with a symmetry lowering. So far, no examples are known when growth twinning is combined with deformation twinning, but such a possibility is not ruled out.

Effect of Kind of Deformation on Young's Modulus, Damage Parameter, Texture and Structure of Alloy Mg – 5% Li (wt)

Effect of deformation by extrusion, rolling after extrusion (in combination with annealing and changing the rolling direction), and subsequent alternating bending (AB) with the number of cycles 0.5, 1, 3, and 5 on the elastic modulus (E), damage accumulation parameter (damage parameter ω), crystallographic texture, and substructure parameters of the binary Mg-5%Li alloy have been studied. The damage parameter (0 ≤ ω ≤ 1), which is interpreted as the relative reduction in the effective load-bearing cross-sectional area due to damage accumulation, was found by the change in the elastic modulus after various above types of deformation. At this, we used to compare equivalent deformation and equivalent elastic energy models. The substructure parameters (crystalline domains sizes D, lattice distortion ε, dislocation density ρ) were estimated by analyzing the physical broadening of the lines diffraction on the crystal lattice of studied alloy of the penetrating hard X-ray synchrotron radiation. It was found that in the studied alloy, sheet forms a texture, at which the hexagonal prism axis is 90° deviated from the normal direction (ND) to the sheet up to transverse direction (TD) after extrusion of the ingot at 350°C in combination with its further rolling in the direction of extrusion axis (rolling direction RD) to a thickness of 4.5 mm and annealing at 350°C after each pass. At this the crystallographic directions and coincide with RD. The texture, at which the hexagonal prism axis is deviated from ND to TD by angles ranging from 15 to 70° (unlike from texture of basal type of the pure magnesium) is formed after further rolling of studied alloy to a thickness of 1 mm with the changing of the RD on 90° in combination with annealing at 350°C after each pass. The crystallographic direction coincides with RD. The anisotropy of above mentioned characteristics was found. Correlation and regression analysis showed that the anisotropy and the values of E, D, ε, and ρ, are decreased, and the values of ω are increased with an increase of alternating bend cycles’ number. It is shown that changes in the above characteristics are mainly due to the crystallographic texture formed during thermomechanical processing and subsequent alternating bending of Mg-5%Li alloy sheets, which is confirmed by data of correlation and regression analysis.

Three-parameter error analysis method based on rotating coordinates in rotating birefringent polarizer system.

We propose error analysis using a rotating coordinate system with three parameters of linearly polarized light--incidence angle, azimuth angle on the front surface, and angle between the incidence and vibration planes--and demonstrate the method on a rotating birefringent prism system. The transmittance and angles are calculated plane-by-plane using a birefringence ellipsoid model and the final transmitted intensity equation is deduced. The effects of oblique incidence, light interference, beam convergence, and misalignment of the rotation and prism axes are discussed. We simulate the entire error model using MATLAB and conduct experiments based on a built polarimeter. The simulation and experimental results are consistent and demonstrate the rationality and validity of this method.

Elastic anisotropy of iron carbides with trigonal-prismatic coordination of C by Fe

Elastic anisotropies obtained by density functional theory (DFT) calculations of four iron carbides exhibiting trigonal prismatic coordination of C by Fe are presented and compared. The elastic anisotropy is considerable for the carbides θ-Fe3C, χ-Fe5C2 and a hypothetical Fe2C with Pbcm symmetry, all with sheet-like arrangement of the trigonal prisms which results in a largely parallel arrangement of the prism axes. It is found that the easy shear which is mainly responsible for the large elastic anisotropy in these carbides occurs in all these three carbides in a plane perpendicular to the average axis of the prisms. In contrast to these three elastically anisotropic carbides, Fe7C3, in which the axes of the trigonal prisms are much more regularly distributed in space, shows a negligible elastic anisotropy.

Structure of prismatic halloysite

The crystal structure of halloysite, despite being one of the most commonly occurring clay minerals on the Earth’s surface, remains elusive. This paper reports on a multi-methodological study to shed more light on the atomic arrangement of halloysite from Olkhon Island, Lake Baikal, Russia, which has a prismatic morphology. It has been investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM), selected-area electron diffraction (SAED) and, in particular, high-resolution transmission electron microscopy (HRTEM), to reveal its atomic structure and formation process. XRD analysis indicated a basal spacing of ca. 7.2 A and two characteristic peaks with d = 4.28 and 4.03 A on the tail of the 02,11 band. The halloysite grain cross sections displayed various prismatic forms, ranging from a rectangle to a regular 18-sectored polygon in SEM and TEM. The SAED pattern from a sector of the polygonal prisms with the incident beam parallel to the prism axes showed a regular one-layer oblique reciprocal lattice, similar to that of kaolinite along Y i -directions. HRTEM imaging performed with the new computer-assisted minimal-dose system and an incident beam perpendicular to the prism axis showed stacking of most dioctahedral 1:1 layers with their pseudo-mirror plane perpendicular to the prism axis and an almost random, or rather, alternating lateral stagger to the right or left from the preceding layer, which corresponds to interlayer displacements of τ + and τ − in Zvyagin symbols, or layer displacements of t 1 and t 2 used to describe the stacking in kaolinite. This stacking feature explains the SAED pattern from the side of the prismatic grains and the two characteristic peaks on the tail of the 02,11 band in the XRD pattern. Based on these results, it is proposed that tubular halloysite initially forms as a hydrated one with the pseudo-mirror plane of the kaolinite layers perpendicular to the tube axis, then dehydrates with, possibly, partially hydrogen-bonded interlayers, and finally transforms to a prismatic one consisting of sectored flat layers with the complete hydrogen-bonded interlayers. During this transformation, stacking with comparable ratio and frequent alternation of τ + and τ − is formed, to minimize morphological change of the tubes.

Mode Indices Measurement of a Special Ti-Diffused $ \hbox{LiNbO}_{3}$ Waveguide Structure: A Strip Waveguide Array Embedded in a Planar Waveguide

We demonstrate the feasibility of using a commercial Metricon 2010 prism coupler to characterize the mode indices (at 1.5- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> wavelength) of a special Ti-diffused <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{LiNbO}_{3}$</tex></formula> waveguide structure where a single-mode strip waveguide is embedded in a multimode planar waveguide. To achieve it, a structure of a strip waveguide array embedded in a planar waveguide was fabricated. The characterization involves simultaneously coupling light from a prism into an array of identical strip waveguides and a planar waveguide. As a result, the modes of the strip waveguide and planar waveguides simultaneously appear on the light reflection pattern measured in the case where the strip waveguide axis is parallel to the prism axis. The mode belonging to the strip waveguide is assigned by comparing the pattern with that measured either from the clear planar waveguide area or also from the strip waveguide array area but in the case where the strip waveguide axis is perpendicular to the prism axis. The direct observation for the near-field mode pattern of the strip waveguide and the numerical results of both the strip and planar waveguides provide evidences for the mode assignment.

Solving the torsion problem for an anisotropic prism by the advanced Kantorovich–Vlasov method

Introduction. The torsion problem for elastic prismatic bodies has been addressed by engineers and mathematicians for the last 100 years. The unremitting interest in this problem is due to practical needs (many structural elements are designed to resist torsion) and theoretical needs (the deformation of such elements should be studied to reveal the mechanism of their failure). Only two classical special cases of torsion of a rod acted upon by opposite torques at its ends are completely understood: pure torsion described by the rigorous theory developed by Saint Venant [5, 6] and generalized torsion theoretically studied by Voight [16] and Lekhnitskii [3]. In the former case, only two tangential stresses appear nonzero, the prism axis remains straight, and cross-sectional warping is constant throughout the height. Such a behavior is typical of isotropic, orthotropic, and anisotropic materials with the plane of elastic symmetry perpendicular to the prism axis. In the latter case, all the stresses are nonzero yet constant throughout the height, the prism axis bends, and the cross-sectional warping linearly varies throughout the height. This case of torsion is observed in materials with general anisotropy or anisotropic materials with one plane of elastic symmetry nonorthogonal to the prism axis. The classical torsion problem was generalized in different ways such as inclusion of large strains or stress concentration around cracks, analysis of stability and vibrations under various torsional loads, complication of the body shape, material properties (viscosity), and loading and boundary conditions [10–15, 17]. The present paper addresses the torsion problem for a rectangular prism made of anisotropic materials with low order of symmetry and the stress–strain state varying throughout the height. Use will be made of the general problem statement in linear elasticity. The problem-solving method to be used reduces the original three-dimensional problem to three coupled one-dimensional problems, each for one of the variables of the domain. The deformation of the cross-section and axis of a square-based prism will be studied for different types of anisotropy of the material. 1. Problem Statement. Consider a rectangular prism occupying a Cartesian domain VV x y z x a y b { , , :| | , | | , 0 zc }. The z-axis is directed along the height of the prism and the x- and y-axes along the principal axes of inertia of the cross-section. The prism base z 0is fixed, the opposite face zc (end) is free from loads. The prism is twisted about the z-axis by stresses a yz (, ) and b xz (, ) acting on the lateral surfaces along the tangent to the boundary and distributed nonuniformly

General Multiple Order Prism Vector Finite Macroelements for Planar Microwave Circuits and EBGs

We present a class of mixed order prism macroelements, appropriate for an efficient analysis of 3-D planar microwave circuits and electromagnetic bandgaps (EBGs). The multiple order concept used in this context implies arbitrary orders of variation toward different directions and is substantially different, compared to the well-known mixed order property, associated to any tangentially continuous vector element. Prism elements of first order in the planar directions and arbitrary high orders along the prism axis are developed by this approach.

Polyhedral serpentine: a spherical analogue of polygonal serpentine?

AbstractVugs in late hydrothermal veins in the serpentinite at Gew-graze, Lizard, Cornwall, UK, contain serpentine spheres ≤0.7 mm in diameter composed of a crystallographically controlled radial array of well crystallized lizardite-1T crystals. Examinations with optical and scanning electron microscopy reveal that the spheres actually have polyhedral morphology. The polyhedral facets at the sphere surface are the (0001) terminations of individual single crystals of lizardite. Each lizardite crystal is a hexagonal prism and tapers inwards to the core. The angle from prism axis to prism axis is always ∼24°, and this angle is consistent even though individual prisms have not maintained contact during growth. The space between prisms is filled by smaller crystals of lizardite in more random orientations, forming a solid sphere. Collectively, the tapering prisms form a growth array that produces a surface tessellation consisting of mainly 6-fold neighbours, but with some 5-fold arrangements to accommodate a closed spherical structure. A ‘buckybalF, modified by adding face-centring points to each hexagon and pentagon, provides a useful model to describe the space filling adopted by the polyhedral lizardite spheres. Cross sections (close to an equatorial plane) through these polyhedral spheres resemble cross sections of polygonal serpentine, with 15 sectors at 24° to each other, though very much larger in diameter.

Technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides

We propose a technique of applying the prism-coupler method for accurate measurement of the effective indices of channel waveguides, which can have step- or graded-index profiles. The technique involves coupling light from a prism into an array of waveguides, varying the angle between the prism axis and the array axis, and curve fitting of the measurement data. We demonstrate the technique with arrays of polymer waveguides and ion-exchanged glass waveguides.

Er3Si5-x – a modulated derivative of the structure type AlB2

The crystal structure of the new compound Er3Si5-х (x = 0.24) obtained at 600oС was studied by X-ray single-crystal diffraction. This orthorhombic structure can be derived from the structure type AlB2 by considering an ordered distribution of vacancies on the small-atom sites and appeared to be modulated along one crystallographic direction: superspace group Amm2(α00), a = 0.40872(2), b = 1.13516(5), c = 0.65739(3) nm, q = 0.2223(1)a*. In contrast to the hexagonal structure type Th3Pd5 with empty triangular channels, in the structure of Er3Si5-x Si atoms move from one trigonal prism to a neighboring one according to the modulation wave, the direction of the modulation vector being parallel to the prism axes.

Coherent and intense multibeam generation by the apex of sharp nano-objects: Electron half-circular prism

Mutually coherent multiple electron beams (multibeam) were generated from diffraction at the apex of sharp nano-objects, especially carbon nanotubes, in a field emission projection microscope. Simulation using a simple scalar diffraction model showed that the apex of sharp nano-objects played the role of an electron half-circular prism, deflecting an electron beam through a constant angle toward the prism axis. The multibeam diffraction pattern gave a high visibility of ∼0.8 and high intensity.

Crystal Structure of Helicobacter pylori Formamidase AmiF Reveals a Cysteine-Glutamate-Lysine Catalytic Triad

Helicobacter pylori AmiF formamidase that hydrolyzes formamide to produce formic acid and ammonia belongs to a member of the nitrilase superfamily. The crystal structure of AmiF was solved to 1.75A resolution using single-wavelength anomalous dispersion methods. The structure consists of a homohexamer related by 3-fold symmetry in which each subunit has an alpha-beta-beta-alpha four-layer architecture characteristic of the nitrilase superfamily. One exterior alpha layer faces the solvent, whereas the other one associates with that of the neighbor subunit, forming a tight alpha-beta-beta-alpha-alpha-beta-beta-alpha dimer. The apo and liganded crystal structures of an inactive mutant C166S were also determined to 2.50 and 2.30 A, respectively. These structures reveal a small formamide-binding pocket that includes Cys(166), Glu(60), and Lys(133) catalytic residues, in which Cys(166) acts as a nucleophile. Analysis of the liganded AmiF and N-carbamoyl d-amino acid amidohydrolase binding pockets reveals a common Cys-Glu-Lys triad, another conserved glutamate, and different subsets of ligand-binding residues. Molecular dynamic simulations show that the conserved triad has minimal fluctuations, catalyzing the hydrolysis of a specific nitrile or amide in the nitrilase superfamily efficiently.

Unique shape, surface and porosity of dried electrified alginate gels

Alginate gels after electrification and freeze-drying produced moieties (cellular solids) exhibiting major increases in surface area and porosity. Gel size and gum concentration were not limiting factors. The spherical spaces created by the freezing, drying or electrification were round and paralleled the circumference of the gel, forming circles within the circle. The phenomenon was dependent on shape and did not occur on the outer surfaces of alginate beads. In contrast, cut beads, even if only a thin layer had been removed, changed character with the observed space formation. Before drying, a steeper pH gradient (∼2 near the anode and ∼12 near the cathode) was observed in the alginate gels. Agarose gels yielded similar pH values as the alginate gels if they included CaCl 2 added by diffusion, but no spaces were produced on their outer surface. Alginate gels that contained no extra ions (having previously diffused out) did not produce surface pores after electrification. pH was another factor involved in the formation of the new structures. Low methoxy pectin (LMP) gels resemble alginate in their cross-linking mechanism, and produced similar shapes upon electrification. If gels (alginate or LMP) were manufactured in a cubic shape, the created spaces were parallel to the rectangular base and ran along the prism's axis. Combinations of increased pH, gel composition, electrification and freezing caused these changes in structure and porosity, which could potentially be beneficial in many uses that involve the release of ingredients into different types of mediums.

Luminescence of CVD ZnO nanocrystals of different shapes

The effect of the shape and dimensions of zinc oxide nanocrystals on the threshold and directionality of UV lasing in the nanocrystals has been investigated. The results indicate that hexagonal columnar nanocrystals have the lowest optical threshold pump power at nanoresonator diameters of 100–200 nm, comparable to the absorption path length of the excitation light. The laser radiation is shown to have a mode structure, being directed predominantly along the prism axis. The lasing mechanism in prismatic nanocrystals differs from that in hexagonal-pyramidal nanocrystals. Electron microscopy results show that the ZnO nanocrystals are highly uniform in shape and size and that these parameters depend on the chemical vapor deposition conditions.

Performance comparison of two dual‐head coincidence cameras of the first and latest generation

This study compares the performance and image quality of two gamma camera based PET systems of the first and latest generation. We investigated two dual head coincidence gamma cameras (PRISM 2000XP and AXIS, manufactured in 1997 and 2001 by Picker/Philips) predominantly in accordance with the NEMA NU2-1994 and NU2-2001 protocols. All performance parameters except for spatial resolution and image quality were determined after measuring a standard cylinder over several half-life periods. Scatter and random fractions were evaluated with the sinogram technique. In order to determine spatial resolution and image quality we used phantoms as described in the NEMA NU2-2001 protocol. The efficiency of the new system was found to be increased. True count rate at activity levels used in clinical conditions is improved and scatter fraction is decreased substantially. Accordingly, improved spatial resolution and image quality were observed with the new system. Altogether, the AXIS represents a further approach to the performance of dedicated positron emission tomographs.

Design of Sandwich Panels With Prismatic Cores

The paper focuses on optimization of lightweight sandwich panels with prismatic cores subject to bending loads in the two principal in-plane directions. Comparisons are made with optimal designs of panels with corrugated cores: a limiting case. When optimized for loading transverse to the prism axis, prismatic panels outperform those with corrugated cores, especially at lower loads. In contrast, when optimized for longitudinal loading, the corrugated core panel is always superior. Both panels exhibit significant anisotropy: a deficiency mediated by optimizing jointly for both orientations. The designs emerging from joint optimizations have only slightly lower load capacity than those optimized singly, but with the benefit of equal strengths in the two principal directions. Moreover, jointly optimized corrugated and prismatic panels perform equally well. Both are competitive with honeycomb core panels, especially at high load capacities. With the additional potential for multifunctionality (notably active cooling), the corrugated panels appear to be particularly promising thermostructural elements.

INCLUSION COMPOUN DS OF α AND γ -CYCLODEXTRINS WITH n-ALKYL AMINE (n= 12, 18)

We report the synthesis of - and -ciclodextrin inclusion compounds with dodecylamine (DDA), and octadecylamine (ODA). Elemental analysis, 13C CP- MAS NMR spectroscopy, scanning electron microscopy (SEM) and powder X-ray diffraction analysis confirm the inclusion process. The basic host structure of the products is similar to that of typical cyclodextrin inclusion compounds. Depending on the guest's molecular length they could present two possible conformations. The extended linear (zig-zag) conformation occurs when the space periodicity along the prism axis, calculated from spacing of these crystallographic layer lines, is comparable to the predicted length of the guest (DDA guest). When the predicted lengths of the guest (ODA guest) are longer than the periodicity matrix layer lines, a helicoidal guest conformation is predicted

Alumino-magnesiohulsite, a new member of the hulsite group, in kotoite marble from east of Verkhoyansk, Sakha-Yakutia, Russia

Alumino-magnesiohulsite, the Al- and Mg-dominant analogue of hulsite, (Fe 2+ ,Mg) 2 (Fe 3+ ,Sn, Mg)O 2 BO 3 , is a new, optically spectacular mineral with pleochroism from brown to blue-green discovered in a magnesian skarn from northeastern Siberia. It forms prismatic, twinned crystals in a spinel-bearing kotoite marble at the contrct of a Mesozoic granosyenite against Palaeozoic dolomite marbles. EMP analyses give: MgO 33.94; FeO 15.97; Al 2 O 3 15.86; SnO 2 11.88; TiO 2 0.75; MnO 0.42; CaO 0.11; B 2 O 3 (calc.) 17.07; total 96.00 wt.%, which can be recalculated to the formula (Mg1.55Fe 2+ 0.45 )Σ2.00(Al 0.63 Mg 0.17 Mn 0.01 Ti 0.02 Sn 0.16 )Σ0.99 O 2 (BO 3 ). Optically, it is biaxial (+), α9about 1.78, γ9about 1.805, 2V z (measured from extinction data) = 33(5)°, α is parallel to the prism axis b. Alumino-magnesiohulsite is monoclinic, space group P 2/ m , with a = 5.3344(7), b = 3.0300(5), c = 10.506(1) A, β = 94,46°, V = 169.29(4) A 3 , Z = 2 and D calc = 3.84 g/cm 3 . Its cell parameters are significantly smaller than those of previously studied members of the hulsite group. A single-crystal X-ray study provided a pattern of cation distribution over the five distinct octahedral sites (M1-M5), which is not consistent with the formula given above. Despite this discrepany, the IMA-Commission on New Minerals and Mineral Names agreed for nomenclature and classification purposes with using the conventional stoichiometric formula in which the amount of R 2+ cations attributed to the tin-bearing unit equals that of the tetravalent ions, so that this attains an overall charge of 3.0 + . Taking into account variable tin contents as usual in hulsites, an ideal general formula of alumino-magnesiohulsite is Mg 2 (Al 1–2x Mg x Sn x )O 2 (BO 3 ) with x expected to be in the range 0.15–0.20. Alumino-magnesiohulsite occurs within bimineralic aggregates in the rock together with aluminous, tin-bearing ludwigite of the formula (Mg 1.62 Fe 2+ 0.38 )(Fe 3+ 0.50 Al 0.31 Fe 2+ 0.07 Mn 0.01 Ca 0.01 Sn 0.05 Ti 0.05 ) O 2 (BO 3 ). These aggregates may be pseudomorphs after a preexisting high-temperature mineral intermediate in composition between ludwigite and alumino-magnesiohulsite. The reason for the exceptionally high Al-content of the new hulsite-group mineral can only partly be due to its Al-saturation by coexisting spinel, because hulsites from other localities also coexisting with spinel contain much less Al.