Formation Of Tetrahedra Research Articles

Intermediate States on the Way to Edge‐Sharing BO4 Tetrahedra in M6B22O39⋅H2O (M=Fe, Co)

The new borates Fe(II)(6)B(22)O(39)·H(2)O (colourless) and Co(II)(6)B(22)O(39)·H(2)O (dichroic: red/bluish) were synthesised under the high-pressure/high-temperature conditions of 6 GPa and 880 °C (Fe)/950 °C (Co) in a Walker-type multi-anvil apparatus. The compounds crystallise in the orthorhombic space group Pmn2(1) (Z=2) with the lattice parameters a=771.9(2), b=823.4(2), c=1768.0(4) pm, V=1.1237(4) nm(3), R(1)=0.0476, wR(2)=0.0902 (all data) for Fe(6)B(22)O(39)·H(2)O and a=770.1(2), b=817.6(2), c=1746.9(4) pm, V=1.0999(4) nm(3), R(1)=0.0513, wR(2)=0.0939 (all data) for Co(6)B(22)O(39)·H(2)O. The new structure type of M(6)B(22)O(39)·H(2)O (M=Fe, Co) is built up from corner-sharing BO(4) tetrahedra and BO(3) groups, the latter being distorted and close to BO(4) tetrahedra if additional oxygen atoms of the neighbouring BO(4) tetrahedra are considered in the coordination sphere. This situation can be regarded as an intermediate state in the formation of edge-sharing tetrahedra. The structure consists of corrugated multiple layers interconnected by BO(3)/BO(4) groups to form Z-shaped channels. Inside these channels, iron and cobalt show octahedral (M1, M3, M4, M5) and strongly distorted tetrahedral (M2, M6) coordination by oxygen atoms. Co(II)(6)B(22)O(39)·H(2)O is dichroic and the low symmetry of the chromophore [Co(II)O(4)] is reflected by the polarised absorption spectra (Δ(t)=4650 cm(-1), B=878 cm(-1)).

Chemistry of Vanadaboranes: Synthesis, Structures, and Characterization of Organovanadium Sulfide Clusters with Disulfido Linkage

Vanadaborane, [(CpV)(2)(B(2)H(6))(2)] (Cp = eta(5)-C(5)H(5)), 1 reacts with elemental sulfur to afford the hexasulfide cluster [(CpV)(2)S(4)(mu-eta(1)-S(2))], 2 in high yield. Compound 2 is a notable example of an organovanadium sulfide cluster in which the [V(2)S(4)] atoms define a bicapped tetrahedron framework, with one mu-eta(1)-S(2) ligand bridged the two (CpV) moieties. The sulfur atom in [V(2)S(4)] core in 2 is a four-skeletal-electron donor isoelectronic with the BH(3) unit; therefore, the replacement of boron hydride in 1 by four sulfur atoms necessitates the formation of a bicapped tetrahedron [V(2)S(4)] framework. Furthermore, this is the only reported example of a bimetallic hexasulfide cluster containing vanadium. Pyrolysis of 1 with bis-chalcogenide ligands such as Ph(2)S(2) and Bz(2)Se(2) (Bz = PhCH(2)), results in the formation of substituted vanadahexaboranes [(CpV)(2)B(4)H(12-x)L(x)], 3-5 (3: L = SPh: x = 3; 4: L = SPh, x = 2; 5: L = SeBz: x = 1) in modest yield. All these new compounds have been characterized by mass, (1)H, (11)B, (13)C NMR spectroscopy, and elemental analysis, and the structural types were unequivocally established by crystallographic analysis of compounds 2-5.

Chemically anisotropic single-crystalline silicon nanotetrahedra

We describe a method based on silicon micromachining to machine single-crystalline siliconnanoparticles bounded by (111) faces in the form of tetrahedra. The technologyallows the fabrication of tetrahedra in a size range from 20 to 1000 nm side length,and gives the possibility to chemically modify sites (faces, edges and/or tips)within certain limits. The chemical modification is anticipated to facilitate theself-assembly into new supermaterials such as photonic crystals in the diamond lattice.

First Mixed Alkaline Uranyl Molybdates: Synthesis and Crystal Structures of CsNa3[(UO2)4O4(Mo2O8)] and Cs2Na8[(UO2)8O8(Mo5O20)

AbstractTwo new mixed alkaline uranyl molybdates CsNa3[(UO2)4O4Mo2O8] (1) and Cs2Na8[(UO2)8O8(Mo5O20)] (2) have been obtained by high‐temperature solid state reactions. Their crystal structures have been solved by direct methods: Compound 1: triclinic, P$\bar{1}$, a = 6.46(1), b = 6.90(1), c = 11.381(2) Å, α = 84.3(1), β = 91.91(1), γ = 80.23(1)°, V = 488.6(2) Å3, R1 = 0.06 for 2865 unique reflections with |Fo| ≥ 4σF; Compound 2: orthorhombic, Ibam, a = 6.8460(2), b = 23.3855(7), c = 12.3373(3) Å, V = 1975.2(1) Å3, R1 = 0.049 for 2120 unique reflections with |Fo| ≥ 4σF. The structure of 1 contains complex sheets of UrO5 pentagonal bipyramids and molybdenum polyhedra. The sheets have [(UO2)2O2(MoO5)] composition. Natrium and cesium atoms are located in the interlayer space. Cesium atoms are situated between the molybdenum clusters, whereas natrium atoms are segregated between the uranyl complexes. The large Cs+ ions are localized between the Mo2O9 groups and force the molybdenum polyhedra to rotate relative to the [(UO2)2O2(MoO5)] sheets. Such rotation is impossible for U6+ polyhedra due to their rigid edge‐sharing complexes. The distance between the U6+ polyhedra vertices of neighboring layers is 3.8 Å, that allows the Na+ ion to be positioned between the uranyl groups. The crystal structure of 2 is based upon a framework consisting of [(UO2)2O2(MoO5)] sheets parallel to (010). The sheets are linked into a 3‐D framework by sharing vertices with the Mo(2)O4 tetrahedra, located between the sheets. Each MoO4 tetrahedron shares two of its corners with two MoO6 octahedra in the sheet above, and the other two with MoO6 octahedra of the sheet below. Thus four MoO6 octahedra and one MoO4 tetrahedron form chains of composition Mo5O18. The resulting framework has a system of channels occupied by the Cs+ and Na+ ions.

Variational tetrahedral mesh generation from discrete volume data

In this paper, we propose a novel tetrahedral mesh generation algorithm, which takes volumic data (voxels) as an input. Our algorithm performs a clustering of the original voxels within a variational framework. A vertex replaces each cluster and the set of created vertices is triangulated in order to obtain a tetrahedral mesh, taking into account both the accuracy of the representation and the elements quality. The resulting meshes exhibit good elements quality with respect to minimal dihedral angle and tetrahedra form factor. Experimental results show that the generated meshes are well suited for Finite Element Simulations.

Cluster observations of the Earth's quasi‐parallel bow shock

Cluster observations of the Earth's quasi‐parallel shock are used to investigate properties of the transition and the role of magnetic pulsations in the shock process. We use crossings at small spacecraft separations to show that pulsations grow in only a few seconds. We then use an example when the spacecraft were only a few thousand kilometers apart, and yet at times the shock was located within the tetrahedron formation, to demonstrate that for a period of 10 min the thickness of the shock transition was less than 2500 km and that during several shorter intervals the shock thickness was less than 1000 km. In the context of evidence for the extent of SLAMS exceeding 1000 km, this suggests that the thickness of the shock layer over which the bulk of plasma thermalization occurs can be narrow, containing one or at most a few SLAMS. The small‐scale spatial properties of structures within the shock are difficult to extract independently of their time evolution, but we present a crossing at which two pairs of spacecraft observed the same magnetic signatures simultaneously. We show that signatures of these pulsations are consistent with their refraction as they are convected antisunward, as predicted by simulation work, and that they are coherent over a distance of at least 1300 km parallel to the expected shock surface.

Complex Topology of Uranyl Polyphosphate Frameworks: Crystal Structures of α‐, β‐K[(UO2)(P3O9)] and K[(UO2)2(P3O10)

AbstractThree new uranyl polyphosphates, α‐K[(UO2)(P3O9)] (1), β‐K[(UO2)(P3O9)] (2), and K[(UO2)2(P3O10)] (3), were prepared by high‐temperature solid‐state reactions. The crystal structures of the compounds have been solved by direct methods: 1 – monoclinic, P21/m, a = 8.497(1), b = 15.1150(1), c = 14.7890(1) Å, β = 91.911(5)°, V = 1898.3(3) Å3, Z = 4, R1 = 0.0734 for 4181 unique reflections with |F0| ≥ 4σF; 2 – monoclinic, P21/n, a = 8.607(1), b = 14.842(2), c = 14.951(1) Å, β = 95.829(5)°, V = 1900.0(4) Å3, Z = 4, R1 = 0.0787 for 3185 unique reflections with |F0| ≥ 4σF; 3 – Pbcn, a = 10.632(1), b = 10.325(1), c = 11.209(1) Å, V = 1230.5(2) Å3, Z = 4, R1 = 0.0364 for 1338 unique reflections with |F0| ≥ 4σF. In the structures of 1 and 2, phosphate tetrahedra share corners to form infinite [PO3]− chains, whereas, in the structure of 3, tetrahedra form linear [P3O10]5− trimers. The structures are based upon 3‐D frameworks of U and P polyhedra linked by sharing common O corners. The infinite [PO3]− chains in the structures of 1 and 2 are parallel to [100] and [–101], respectively. The uranyl polyphosphate frameworks are occupied by host K+ cations.

Analytic Solutions for Equal Mass Four-Craft Static Coulomb Formation

Analytic constant charge solutions are investigated for square planar and 3-D tetrahedron four-craft static Coulomb formations. The solutions are formulated in terms of the formation geometry and attitude. In contrast to the two- and three-spacecraft Coulomb formations, a four-spacecraft formation has new equality and multiple inequality constraints that need to be satisfied for the individual spacecraft charges to be both unique and real. Unique charge relative equilibriums are important to reduce the overall power requirement of the spacecraft charge emision. A spacecraft must not only satisfy three inequality three-craft constraints to yield a real charge solution, but it must also satisfy two additional equality constraints to ensure that the spacecraft charges are unique. Further, a method is presented to reduce the number of equality constraints arising due to the dynamics of a four-spacecraft formation. The unique and real spacecraft charges are determined as a function of the orientation of the square formation in a given principal orbit plane. For the 3-D tetrahedron formation scenario there is only a unique set of charged products. The implementability constraints are numerically evaluated to show that only trivial equal-mass tetrahedron formations are possible where one craft is on the along-track axis with zero charge.

A case of intramedullar epidermoid cyst

We use a combination of atom-swap Monte-Carlo (MC) and molecular dynamics (MD) to study the structure and mechanical properties of Cu1−xAgx|Ni multilayers with 6 nm layer width for which the Ag-content is used to tune the lattice misfit. We find that the multilayers form a semi-coherent interface with a network of partial dislocations arranged in a regular triangular pattern. A combination of MC and MD was used to equilibrate Cu1−xAgx|Ni with x = 0%, 5% and 10%. Ag does not enter the Ni-layer but segregates and precipitates from the Cu layers. We find alloying of Cu and Ni at 600 K. All these findings are in good agreement with the experimental binary phase diagrams of the Cu-Ag, Ag-Ni and Cu-Ni systems. The resulting multilayer structures were then sheared parallel and perpendicular to the normal of the bilayer interface. Initial sliding takes place at the Cu|Ni interface within the misfit dislocation network, followed by emission of partial dislocations into the Cu layer. Flow stress increases with increasing Ag content. Additional calculations of biaxial tension that suppress sliding at the heterointerface show a similar trend. Strengthening can be attributed to Ag precipitates pinning the Cu|Ni heterointerface and to the formation of sessile stacking-fault tetrahedra from the misfit dislocation network whose density increases with the concentration of Ag in the Cu layer.

格子間原子型転位ループ近傍での積層欠陥四面体の形成

格子間原子型転位ループ近傍での積層欠陥四面体の形成

Effect of nitrogen addition on the band gap, core level shift, surface energy, and the threshold field of electron emission of the SrTiO3 thin films

The effect of nitrogen (N) doping on the behavior of field emission, surface energy and the band structure of strontium titanate (SrTiO3) thin films coated on silicon tip arrays has been examined in detail. Measurements using x-ray photoelectron spectroscopy, ellipsometry, water contact angle and field emission testing revealed that the optimal 50%-nitrogen partial pressure (PN) could improve substantially the threshold field of electron emission of the SrTiO3 films accompanied with narrowed band gap, lowered surface energy and work function and a negative energy shift of the N 1s level from 404 to 396 eV. Results evidence consistently the presence of the nonbonding lone pairs and the lone pair induced antibonding dipoles upon tetrahedron formation which is responsible for the observations. At PN below and above the optimal value physisorption and hydrogen bond likes formation like to occur.

Active Control Schemes to Satisfy Separation Distance Constraints

T HE proposed NASA benchmark tetrahedron constellation is a complex formation to be maintained at every apogee point. In previous papers, the authors developed a strategy and determined the initial conditions to maintain the tetrahedron formation [1,2]. With this strategy, the constellation maintains the separation distance constraints for a limited number of orbits, depending on the specific size of the NASA benchmark problem [3]. After a pair of satellites violates the separation distance constraints [1,2], a control strategy is needed to maintain the separation distance conditions [3]. The NASA benchmark problem [3] establishes that the nominal separation distance between any pair of satellites within the constellation is 10 km at the apogee point, and, at any other point in the orbit, the separation distance cannot be less than 1 km. To explain the dynamics of a pair of satellites in an elliptical orbit, the linearized Tschauner–Hempel (TH) equations are used. In the TH equations, the coefficient term that varieswith the true anomaly angle will affect the control scheme that is used to maintain the separation distance between a pair of satellites. The control strategy is based on the linear quadratic regulator (LQR) which was used by Bainum, Strong, and Tan (BST) [4–6]. These authors used the LQR control scheme to maintain the separation between a pair of satellites in an along-track formation (string of pearls), and the varying coefficient was adapted in a piecewisemanner. Instead, Carter–Humi (CH) [7,8] used a different approach in which the cost function is defined in terms of the true anomaly angle, and this control scheme will be adapted here to the LQR strategy. These two control schemes will be compared to determine the best response from the BST and CH control approaches. After the constellation is corrected, the Satellite Tool Kit (STK) [9] software is used to propagate the constellation motion and determine when the constellation will again violate the separation distance constraints. Hence, the main objective of this engineering note is to compare and apply these two techniques for the first time to the NASA Benchmark Tetrahedron Constellation to correct the violation of the separation distance constraints [3]. II. Definition of the Specific Sizes (or Phases)

Use of solar radiation pressure to maintain a spatial satellite formation

We discuss the possibility to create and maintain a tetrahedron satellite formation using solar radiation pressure. The problem admits a complete solution in the case of a heliocentric orbit and a partial solution for a high geocentric orbit.

Study of the terrestrial magnetosphere by multipoint data analysis with the CLUSTER mission. Contributions to the characterization of boundary layers and of the inner magnetosphere

A thesis studying the plasma structures encountered by the CLUSTER spacecraft along its orbit during 2001-2004 is presented. CLUSTER is the first space mission dedicated to the three-dimensional study of the terrestrial magnetosphere and its polar orbit and four spacecraft tetrahedron formation enables in situ measurements in various regions. The first part of the thesis describes and tests, two multipoint analysis tools, which include the spatial gradient and the time delay, using synthetic datasets. These analyses reveal the boundary motion and orientation, and the dimensions of the structures encountered, which are unable to be determined with a single satellite mission. The other part of the thesis deals with the plasmasphere, focusing particularly on the topology and dynamics of small- and large-scale density structures. The study also presents and discusses datasets from other CLUSTER instruments, and global images of plasmasphere.

Age and skin structure and function, a quantitative approach (II): protein, glycosaminoglycan, water, and lipid content and structure

The aging process has been studied with fervor recently, given our shifting demographics. As age's effects are so manifest in the skin's appearance, structure, mechanics, and barrier function, it is not surprising that much effort has been made in research to better understand them. Quantitative measurements permitted by bioengineering have allowed us to objectively and precisely study aging skin. These overviews piece together the immense amounts of information that have emerged from recent technological advances in dermatological research in order to develop a unified understanding of the quantitative effects of age on skin. We performed a literature search on age-related changes in protein, glycosaminoglycan (GAG), water, and lipid content and structure, searching Pub-med, Em-Base, Science Citation Index, and the UCSF dermatological library's collection of books on the topic of aging skin. Collagen becomes sparser and less soluble in intrinsically aged skin, but is thickened and more soluble in extrinsically aged areas. Elastin is degraded slowly and accumulates damage with intrinsic aging; also, increased synthesis of abnormally structured elastin occurs in photoexposed areas. This leads to an age-related accumulation of aberrant elastoic material, clumped in the papillary dermis. Generally, age leads to increased folding and decreased interaction of proteins with water. Also, despite increased GAGs in aged skin, these are abnormally deposited on the elastoic material and cannot interact properly with water. Hence, in aged skin, water is found in the tetrahedron form, bound to itself rather than other molecules. Lipid content appears to decrease with age, although the proportion of different lipid classes seems to remain fairly constant. Much work remains to be carried out to reach a consensus on the effects of age on skin structure and function. Future studies would be benefited by increased standardization of skin sites tested, methodology, and increased sample sizes.

Optimal Planner for Spacecraft Formations in Elliptical Orbits

An optimal planner for spacecraft formations in elliptical reference orbits is presented. A fast solution to an individual spacecraft minimum time or fuel maneuver using the Hamilton-Jacobi-Bellman formulation is developed using spline approximations to evaluate thrust effect integrals. The individual optimal spacecraft maneuvers use realistic low-thrust, bounded inputs similar to future electric propulsion systems. A formation optimal planner is then formulated using the individual spacecraft maneuvers as a basis. The formulation is easily scalable to larger clusters, provably optimal over the formation, and numerically robust; it also requires minimal communication between fleet members. An example is presented of a tetrahedron formation in a highly elliptical reference orbit (e = 0.8), with solutions to both formation minimum-time and minimum-fuel problems given. Comparison with linear programming techniques show a distinct savings in fuel usage for high-eccentricity examples.

The disordered cubic structure of Ca 7Co 3Ga 5O 18

The new mixed oxide having composition close to Ca 7Co 3Ga 5O 18 was synthesized from CaCO 3, Co 3O 4 and Ga 2O 3 at 1150 °C in air and studied by neutron and synchrotron X-ray powder diffraction, selected-area electron diffraction and high-resolution electron microscopy. The structure was refined, using time-of-flight (TOF) neutron powder diffraction data, in space group F432, with a = 15.0487 ( 4 ) Å and Z = 8 , to R F = 0.7 % . It is considerably disordered, with four different tetrahedral sites randomly occupied by Co and Ga atoms at a ratio of 1:2. The tetrahedra form a disordered (Co 1/3Ga 2/3)O 2 3D-framework inside which isolated CoO 6 octahedra, surrounded by 8 Ca atoms, are located. The structure is related to the ordered structure of Ca 14Al 10Zn 6O 35. Electron diffraction patterns confirmed the symmetry and unit cell and revealed no diffuse scattering. High-resolution electron microscopy images showed the absence of extended structural defects.

A New Three-Dimensional Method of Assessing Facial Volumetric Changes after Orthognathic Treatment

To validate a new method of facial volumetric assessment that is dependent on the use of stereophotogrammetric models and a software-based Facial Analysis Tool. The method was validated in vitro with three-dimensional (3D) models of a lifelike plastic female dummy head and in vivo with a male-subject head. Thirty facial silicone explants were added in the nasal and perioral regions of each head, and their volumes were obtained by three different algorithms. These were compared with the actual values obtained by a "water displacement" method. The least mean error was found with the "tetrahedron formation" method followed by the "projection" method and the "back-plane construction" method. The error with the tetrahedron formation method was 0.071 cm(3) (95% confidence interval [CI]: -0.074 to 0.2161 cm3) with the in vitro models and 0.314 cm3 (95% CI: -0.080 to 0.708 cm3) with the in vivo models. The increased volumetric assessment error observed in vivo was attributed to the registration procedure and possible changes in facial expression. These results encourage the use of this method in the 3D assessment of orthognathic surgical outcome, provided a standardized facial expression is used for image acquisition.

Dependence of silica sol properties on synthesis situation studied by SAXS

The properties of silica sol, such as the interface characteristics and microstr ucture, were comparatively studied by small angle x-ray scattering (SAXS) assis ted by dynamic light scattering. Four synthesis routes were adopted to relate th e properties of silica sol with the synthesis situation. Very big difference of SAXS results was found between the base-catalyzed and the acid-catalyzed silic a sols with ethanol used as solvent. Under the acid-catalysis of low molecule-w eight organic acid, not only were polysiloxane macromolecules obtained, particle suspension of silica was also produced with complicated inner structures of pa rticles. With ethanol or water as solvent, it was found that the silica particl e would become more irregular in morphology with more polarity of solvent. The formation of Si-O tetrahedron was more difficult in the acidolysis of tetraetho xysilane by formic acid than in the other hydrolysis routes. An interesting co- existing of positive deviation and negative deviation from Porod’s law was foun d in the silica sol with water solvent, and a detailed explanation has been giv en.Many nano-scaled structural difference among these different synthesis situa tions were revealed, which was difficult to be recognized by the experimental m ethods other than SAXS.

Synthesis and crystal structure of tetranuclear zinc benzoate

A tetranuclear zinc benzoate Zn4O(C6H5CO2)6 was synthesized and characterized by X-ray single crystal determination. It crystallizes in cubic, space groupIa-3d. Its crystal cell is very large,a=4. 100 63 (18) nm, V=68.953(5) nm3 and Z=48. The structure is composed of discrete Zn4O(C6H5CO2)6 molecules. In each molecule, four zinc atoms are held together by a central oxygen atom, which results in the formation of a regular tetrahedron. All benzoate ligands coordinate to zinc atoms in a bidentate bridging mode. Each zinc atom is in a slightly distorted tetrahedral geometry, coordinated by three benzoate oxygen atoms and the central oxygen atom. The intermolecular interactions result in the formation of a three-dimensional supramolecular framework, with non-intersecting parallel channels.