Academic literature on the topic 'Octahedral geometry'
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Journal articles on the topic "Octahedral geometry"
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Redhammer, Günther J., Haruo Ohashi, and Georg Roth. "Single-crystal structure refinement of NaTiSi2O6 clinopyroxene at low temperatures (298 < T < 100 K)." Acta Crystallographica Section B Structural Science 59, no. 6 (2003): 730–46. http://dx.doi.org/10.1107/s0108768103022018.
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The alkali-metal clinopyroxene NaTi3+Si2O6, one of the rare compounds with trivalent titanium, was synthesized at high temperature/high pressure and subsequently investigated by single-crystal X-ray diffraction methods between 298 and 100 K. One main difference between the high- and the low-temperature form is the sudden appearance of two different Ti3+—Ti3+ interatomic distances within the infinite chain of the TiO6 octahedra just below 197 K. This change can be seen as direct evidence for the formation of Ti—Ti singlet pairs in the low-temperature phase. Mean Ti—O bond lengths smoothly decrease with decreasing temperature and the phase transition is associated with a slight jump in the Ti—O bond length. The break in symmetry, however, causes distinct variations, especially with respect to the two Ti—Oapex bond lengths, but also with respect to the four Ti—O bonds in the equatorial plane of the octahedron. The TiO6 octahedron appears to be stretched in the chain direction with a slightly larger elongation in the P\bar 1 low-temperature phase compared with the C2/c high-temperature phase. Polyhedral distortion parameters such as bond-length distortion and octahedral angle variance suggest the TiO6 octahedron in P\bar 1 to be closer to the geometry of an ideal octahedron than in C2/c. Mean Na—O bond lengths decrease with decreasing temperature and the variations in individual Na—O bond lengths are the result of variations in the geometry of the octahedral site. The tetrahedral site acts as a rigid unit, which does not show pronounced changes upon cooling and through the phase transitions. There are neither large changes in bond lengths and angles nor in polyhedral distortion parameters, for the tetrahedral site, when they are plotted. In contrast with the C2/c → P21/c phase transition, found especially in LiMSi2O6 clinopyroxenes, no very large variations are found for the tetrahedral bridging angle. Thus, it is concluded that the main factor inducing the phase transition and controlling the structural variations is the M1 octahedral site.
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Sheldrick, W. S., H. J. Häusler, and J. Kaub. "Zur Stereochemie von Iodoarsenaten(III). Darstellung und Kristallstrukturen von [nBU4N]2[AS2I8], [pyH][AsI4] und [Et3NH]4[As8I28] / Concerning the Stereochemistry of Iodoarsenates(III). Preparation and Crystal Structures of [nBu4N]2[As2I8], [pyH][AsI4] and [Et3NH]4[As8I28]." Zeitschrift für Naturforschung B 43, no. 7 (1988): 789–94. http://dx.doi.org/10.1515/znb-1988-0701.
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[nBU4N]2[AS2I8] (1), [pyH][AsI4] (2) and [Et3NH]4[As8I28] (3) have been prepared hy reaction of Asl3 with the iodide of the respective nitrogen base (present in a 1:1 molecular ratio) in acetonitrile and their structures determined by X-ray structural analysis. 1 contains discrete [As2I8]2- anions with Q symmetry; the As atoms display a pseudo-octahedral AX4Y'E geometry with bridging A s - I distances of 2.931(1) and 3.289(1) Å. The iodoarsenate(III) anions in 2 form infinite [Asl4-]∞ chains, in which the individual units are edge-bridged distorted AsI6-octahedra with AX4Y'2E geometry. In contrast, 3 contains discrete centrosymmetric anions [As8I28]4-. in which the individual As atoms all display a distorted octahedral AX,Y,E geometry. The lone pairs are stereochemically inert in 2 and 3. The structures of 1-3 are compared with those of analogous chloro- and bromoarsenate(III) anions.
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Merola, Joseph S., та Arthur W. Grieb. "Crystal structure of chlorido(η2-phenyl isothiocyanate-κ2C,S)-mer-tris(trimethylphosphane-κP)iridium(I)". Acta Crystallographica Section E Structure Reports Online 70, № 11 (2014): 352–54. http://dx.doi.org/10.1107/s160053681402162x.
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The molecule of the title compound, [IrCl(C7H5NS)(C3H9P)3], is a distorted octahedral iridium complex with three PMe3ligands arranged in a meridional geometry, a chloride ioncisto all three PMe3groups and the phenyl isothiocyanate ligand bonded in an η2-fashion through the C and S atoms. The C atom istransto the chloride ion and the S atom is responsible for a significant deviation from an ideal octahedral geometry. The geometric parameters for the metal-complexing phenyl isothiocyanate group are compared with other metal-complexed phenyl isothiocyanates, as well as with examples of uncomplexed aryl isothiocyanates.
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Thomas, Noel W. "Phase transitions and (p–T–X) behaviour of centrosymmetric perovskites: modelling with transformed crystallographic data." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 78, no. 1 (2022): 40–60. http://dx.doi.org/10.1107/s2052520621012713.
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A reversible transformation of the unit-cell parameters and atomic coordinates of centrosymmetric perovskites ABX 3 into a Cartesian space is defined. Analytical expressions for the three vectors for the pseudocubic cell and three vectors for a BX 6 octahedron are derived for space groups Pbmn, Cmcm, Ibmm, P4/mbm, P4/nmc, I4/mcm and R 3 c. The following structural parameters may be derived from these vectors: up to six pseudocubic parameters defining octahedral geometry; length- and angle-based octahedral distortion parameters λ and σ; inclination angles of tilted octahedra, θ1, θ2 and θ3; angles of tilt of octahedra; AX 12:BX 6 polyhedral volume ratio, V A /V B ; parameters η A and η B defining the relative contraction of inner AX 8 polyhedra and expansion of BX 6 octahedra due to octahedral tilting. The application of these parameters is demonstrated by reference to published crystal structures. The variation of η A and η B with temperature in the compositional series Sr x Ba1–x SnO3 and Sr x Ba1–x HfO3, as well as the temperature series of BaPbO3 and CaTiO3, is related to the sequence of phases Pbmn → Ibmm→ Pm 3 m. Stabilization of the Cmcm phase is likewise interpreted in terms of these two parameters for NaTaO3 and NaNbO3. The pressure evolution of the structures of MgSiO3, YAlO3, (La1–x Nd x )GaO3 (0 ≤ x ≤ 1) and YAl0.25Cr0.75O3 is modelled with the appropriate structural parameters, thereby also addressing the characteristics of the Pbmn → R 3 c transition. Simulation of MgSiO3 up to 125 GPa and of YAlO3 up to 52 GPa in space group Pbnm is carried out by using the Birch–Murnaghan equation of state. In both cases, full sets of oxygen coordinates assuming regular octahedra are generated. Octahedral distortion is also modelled in the latter system and predicted to have a key influence on structural evolution and the sequence of phase transitions. The core modelling procedures are made available as a Microsoft Excel file.
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Hunt, K. H., and P. R. McAree. "The Octahedral Manipulator: Geometry and Mobility." International Journal of Robotics Research 17, no. 8 (1998): 868–85. http://dx.doi.org/10.1177/027836499801700805.
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Tamazyan, Rafael, and Sander van Smaalen. "Quantitative description of the tilt of distorted octahedra in ABX 3 structures." Acta Crystallographica Section B Structural Science 63, no. 2 (2007): 190–200. http://dx.doi.org/10.1107/s010876810605244x.
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A description of the tilt of octahedra in ABX 3 perovskite-related structures is proposed that can be used to extract the unique values for the tilt parameters φ, θ and δ of ABX 3 structures with regular and distorted octahedra up to the point symmetry \bar 1, from atomic coordinates and lattice parameters. The geometry of the BX 6 octahedron is described by three B—X bond lengths (r 1, r 2, r 3) and three X—B—X bond angles (ψ12, ψ13 and ψ23) or alternatively by a local strain tensor together with an average B—X bond length. Connections between the proposed method and Glazer's tilt system are discussed. The method is used to analyze structural transformations of I2/c, Pbnm and Immm structures. The proposed description allows the analysis of group–subgroup relations for the ABX 3 structures with distorted octahedra, in terms of octahedral deformations and tilting. The method might also be of interest in the study of the phase transitions in the family of ABX 3 structures.
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Jia, Yong-Yan, Xin-Nian Xie та Huai-Xia Yang. "Poly[[tetraaquabis(μ3-5-carboxybenzene-1,2,4-tricarboxylato)tricadmium] tetrahydrate]". Acta Crystallographica Section E Structure Reports Online 68, № 6 (2012): m801—m802. http://dx.doi.org/10.1107/s1600536812022726.
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There are three independent CdII ions in the title complex, {[Cd3(C10H3O8)2(H2O)4]·4H2O} n , one of which is coordinated by four O atoms from three 5-carboxybenzene-1,2,4-tricarboxylate ligands and by two water molecules in a distorted octahedral geometry. The second CdII ion is coordinated by five O atoms from four 5-carboxybenzene-1,2,4-tricarboxylate ligands and by one water molecule also in a distorted octahedral geometry while the third CdII ion is coordinated by five O atoms from three 5-carboxybenzene-1,2,4-tricarboxylate ligands and by one water molecule in a highly distorted octahedral geometry. The 5-carboxybenzene-1,2,4-tricarboxylate ligands bridge the CdII ions, resulting in the formation of a three-dimensional structure. Intra- and intermolecular O—H...O hydrogen bonds are present throughout the three-dimensional structure.
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Dolai, Malay, Abhishake Mondal, Jun-Liang Liu, and Mahammad Ali. "Three novel mononuclear Mn(iii)-based magnetic materials with square pyramidal versus octahedral geometries." New Journal of Chemistry 41, no. 19 (2017): 10890–98. http://dx.doi.org/10.1039/c7nj02919e.
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Single crystal X-ray diffraction studies reveal that complexes 1 and 2 have square pyramidal geometry and 3 has octahedral geometry, which showed a dependence of negative anisotropy (D) values on the electronic, geometry and packing effects.
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Rastogi, Raj Kamal, Sonu Sharma, Gulshan Rastogi, and Alok K. Singh. "SYNTHESIS AND CHARACTERIZATION OF TI (III), V (III),VO (IV), MOO (V),FE (II) AND FE (III) COMPLEXES OF BENZIL- 2,4-DINITROPHENYL HYDRAZONE P-BROMO ANILINE." Green Chemistry & Technology Letters 2, no. 4 (2016): 177. http://dx.doi.org/10.18510/gctl.2016.242.
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The complexes of Benzil-2, 4-dinitrophenyl hydrazone-p- bromo aniline with Ti(III),V(III), VO(IV),MoO (V), Fe(II), Fe(III) have synthesized and characterized by elemental analysis, magnetic measurement data, molar conductance, TGA,UV-visible and IR spectra data. The complexes of Ti (III), V (III), Fe (II) and Fe (III) have octahedral geometry while VO (IV) and MoO(V) have distorted octahedral geometry due to the presence of M=O moiety.
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Vashi, R. T., C. D. Shelat, and Himanshu Patel. "Synthesis, Spectroscopic Studies and Antifungal Activity of 2-[(4(3-Chlorophenyl) piperazine-1-yl)methyl]-3-[8-hydroxy quinolin-5-yl]-3(H)-quinazolin-4-one Ligand and its Chelates." E-Journal of Chemistry 7, s1 (2010): S163—S168. http://dx.doi.org/10.1155/2010/701409.
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The novel ligand HL6was synthesized using anthranilic acid and it was undergo the chelating reaction with Cu(II), Ni(II), Co(II), Mn(II) and Zn(II) to prepare transition metal chelates. These chelates were characterized by physicochemical methods such as elemental analysis, conductometric studies, magnetic susceptibility, FT-IR, NMR and electronic spectra. The stoichiometry of the complexes has been found to be 1: 2 (Metal: ligand). An octahedral geometry around Co(II), Ni(II) and Mn(II), distorted octahedral geometry around Cu(II) and tetrahedral geometry around Zn(II) have been proposed. The antifungal activity of ligand and its metal chelates were conducted against various fungi.
Dissertations / Theses on the topic "Octahedral geometry"
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Tidwell, Paul H. "Design and construction of a double-octahedral variable geometry truss manipulator." Thesis, Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/74544.
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This thesis deals with the design and construction of a variable geometry truss (VGT) of the double-octahedral (pyramid-pyramid) geometry. The truss is expected to be the focus of several experimental research projects. In this thesis, a kinematic model is formulated, and the forward and inverse kinematic problems are solved. Issues of motor and instrumentation choices are addressed. Dimensional choices and the important problems of joint design are examined. A computer simulation is performed for force and vibration analysis.
A fully collapsible double-octahedral variable geometry truss with three degrees of freedom was built using NC machining technologies. An improved second generation twenty-one degree-of-freedom truss will be built based on this original test article.<br>Master of Science
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Yadav, Priti. "Multiscale Modelling of Proximal Femur Growth : Importance of Geometry and Influence of Load." Doctoral thesis, KTH, Strukturmekanik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-209149.
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Longitudinal growth of long bone occurs at growth plates by a process called endochondral ossification. Endochondral ossification is affected by both biological and mechanical factors. This thesis focuses on the mechanical modulation of femoral bone growth occurring at the proximal growth plate, using mechanobiological theories reported in the literature. Finite element analysis was used to simulate bone growth. The first study analyzed the effect of subject-specific growth plate geometry over simplified growth plate geometry in numerical prediction of bone growth tendency. Subject-specific femur finite element model was constructed from magnetic resonance images of one able- bodied child. Gait kinematics and kinetics were acquired from motion analysis and analyzed further in musculoskeletal modelling to determine muscle and joint contact forces. These were used to determine loading on the femur in finite element analysis. The growth rate was computed based on a mechanobiological theory proposed by Carter and Wong, and a growth model in the principal stress direction was introduced. Our findings support the use of subject- specific geometry and of the principal stress growth direction in prediction of bone growth. The second study aimed to illustrate how different muscle groups’ activation during gait affects proximal femoral growth tendency in able-bodied children. Subject-specific femur models were used. Gait kinematics and kinetics were acquired for 3 able-bodied children, and muscle and joint contact forces were determined, similar to the first study. The contribution of different muscle groups to hip contact force was also determined. Finite element analysis was performed to compute the specific growth rate and growth direction due to individual muscle groups. The simulated growth model indicated that gait loading tends to reduce neck shaft angle and femoral anteversion during growth. The muscle groups that contributes most and least to growth rate were hip abductors and hip adductors, respectively. All muscle groups’ activation tended to reduce the neck shaft and femoral anteversion angles, except hip extensors and adductors which showed a tendency to increase the femoral anteversion. The third study’s aim was to understand the influence of different physical activities on proximal femoral growth tendency. Hip contact force orientation was varied to represent reported forces from a number of physical activities. The findings of this study showed that all studied physical activities tend to reduce the neck shaft angle and anteversion, which corresponds to the femur’s natural course during normal growth. The aim of the fourth study was to study the hypothesis that loading in the absence of physical activity, i.e. static loading, can have an adverse effect on bone growth. A subject-specific model was used and growth plate was modeled as a poroelastic material in finite element analysis. Prendergast’s indicators for bone growth was used to analyse the bone growth behavior. The results showed that tendency of bone growth rate decreases over a long duration of static loading. The study also showed that static sitting is less detrimental than static standing for predicted cartilage-to-bone differentiation likelihood, due to the lower magnitude of hip contact force. The prediction of growth using finite element analysis on experimental gait data and person- specific femur geometry, based on mechanobiological theories of bone growth, offers a biomechanical foundation for better understanding and prediction of bone growth-related deformity problems in growing children. It can ultimately help in treatment planning or physical activity guidelines in children at risk at developing a femur or hip deformity.<br><p>QC 20170616</p>
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Li, Iila Jingjiao. "Flexible polyhedra : exploring finite mechanisms of triangulated polyhedra." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/271806.
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In a quest to design novel deployable structures, flexible polyhedra provide interesting insights. This work follows the discovery of flexible polyhedra and aims to make flexible polyhedra more useful. The dissertation describes how flexible polyhedra can be made. The flexible polyhedra first considered in this dissertation have a rotational degree of freedom. The range of this rotational movement is measured and maximised in this work by numerical maximisation. All polyhedra are established computationally: an iterative solution method is used to find vertex coordinates; several clash detecting methods are described to define whether each rotational position of a flexible polyhedron is physically possible; then a range of motion is defined between occurrences of clashes at the two ends; finally, an optimisation tool is used to maximise the range of motion. By using these tools, the range of motion of two types of simplest flexible polyhedra are maximised. The first type is a series of flexible polyhedra generalised from the Steffen flexible polyhedron. The range of motion of this type is improved to double that of Steffen’s original, from 27° to 59°. Another type of flexible polyhedron is expanded from a model provided by Tachi. Based on the understanding of Steffen’s flexible polyhedron, optimisation parameters are carefully given. This new type has achieved a wider range of motion, so now the range of motion of flexible polyhedron is tripled to 80°. After enlarging the range of motion of the degree of freedom in the 1-dof systems, the dissertation found multiple degrees of freedom in one polyhedron. The multiple mechanisms can be even repetitive, so that an n-dof polyhedron is found. A polyhedron of two degrees of freedom is first presented. Then, a unit cell for any number of mechanisms is found. As a repetitive structure, a 3-dof polyhedron is presented. Finally, this work presents the possibility of configuring a flexible polyhedral torus and a closed polyhedral surface that is able to flex without the need to stop.
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Castle, Toen. "Entangled graphs on surfaces in space." Phd thesis, 2013. http://hdl.handle.net/1885/11978.
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In the chemical world, as well as the physical, strands get tangled. When those strands form loops, the mathematical discipline of ‘knot theory’ can be used to analyse and describe the resultant tangles. However less has been studied about the situation when the strands branch and form entangled loops in either finite structures or infinite periodic structures. The branches and loops within the structure form a ‘graph’, and can be described by mathematical ‘graph theory’, but when graph theory concerns itself with the way that a graph can fit in space, it typically focuses on the simplest ways of doing so. Graph theory thus provides few tools for understanding graphs that are entangled beyond their simplest spatial configurations.
This thesis explores this gap between knot theory and graph theory. It is focussed on the introduction of small amounts of entanglement into finite graphs embedded in space. These graphs are located on surfaces in space, and the surface is chosen to allow a limited amount of complexity. As well as limiting the types of entanglement possible, the surface simplifies the analysis of the problem – reducing a three-dimensional problem to a two-dimensional one.
Through much of this thesis, the embedding surface is a torus (the surface of a doughnut) and the graph embedded on the surface is the graph of a polyhedron. Polyhedral graphs can be embedded on a sphere, but the addition of the central hole of the torus allows a certain amount of freedom for the entanglement of the edges of the graph. Entanglements of the five Platonic polyhedra (tetrahedron, octahedron, cube, dodecahedron, icosahedron) are studied in depth through their embeddings on the torus. The structures that are produced in this way are analysed in terms of their component knots and links, as well as their symmetry and energy.
It is then shown that all toroidally embedded tangled polyhedral graphs are necessarily chiral, which is an important property in biochemical and other systems. These finite tangled structures can also be used to make tangled infinite periodic nets; planar repeating subgraphs within the net can be systematically replaced with a tangled version, introducing a controlled level of entanglement into the net.
Finally, the analysis of entangled structures simply in terms of knots and links is shown to be deficient, as a novel form of tangling can exist which involves neither knots nor links. This new form of entanglement is known as a ravel. Different types of ravels can be localised to the immediate vicinity of a vertex, or can be spread over an arbitrarily large scope within a finite graph or periodic net. These different forms of entanglement are relevant to chemical and biochemical self-assembly, including DNA nanotechnology and metal-ligand complex crystallisation.
Books on the topic "Octahedral geometry"
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Williams, Robert L. Kinematic modeling of a double octahedral variable geometry truss (VGT) as an extensible gimbal. National Aeronautics and Space Administration, Langley Research Center, 1994.
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National Aeronautics and Space Administration (NASA) Staff. Kinematic Modeling of a Double Octahedral Variable Geometry Truss (Vgt) As an Extensible Gimbal. Independently Published, 2018.
Find full textBook chapters on the topic "Octahedral geometry"
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Holzapfel, Rolf-Peter, and Maria Petkova. "An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups." In Arithmetic and Geometry Around Galois Theory. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0487-5_10.
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Bárány, Imre. "Tensors, colours, octahedra." In Geometry, Structure and Randomness in Combinatorics. Scuola Normale Superiore, 2014. http://dx.doi.org/10.1007/978-88-7642-525-7_1.
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Bunker, Bruce C., and William H. Casey. "Aqueous Polymerization of Silicates and Aluminosilicates." In The Aqueous Chemistry of Oxides. Oxford University Press, 2016. http://dx.doi.org/10.1093/oso/9780199384259.003.0022.
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Part Five of this book is devoted to silicates for several important reasons. First, silicates represent critical components of our planet and our lives. Silicon is the second most abundant element in Earth’s crust after oxygen, representing about 28% of the atoms present. As such, transformations of silicate minerals dominate much of the aqueous geochemistry of Earth. Every day, each of us encounters materials and objects the primary constituents of which are silicon oxides and related phases such as aluminosilicates. Granite facings on buildings, bricks, glass, pottery, ceramics, engineered materials used in water purification, catalysis, electronics, and even the optical fibers used in our most advanced communication systems are all silica based. Aluminosilicate minerals are even used as food additives. A key attribute of silicates that distinguishes them from most of the oxides highlighted in Parts One through Four of this book is that the Si(IV) cation is almost always present in a tetrahedral rather than in an octahedral coordination geometry. Exceptions include a few high-pressure phases such as stishovite (see Chapter 2) and a limited number of chelated Si(IV) complexes (see Section 14.3). The authors know of no stable compounds where Si(IV) is coordinated to only three oxygen atoms. The pathways for both forming and destroying silicate bonds are substantially different than for octahedral metal ions. Ligand-exchange pathways for silicate ions are via nucleophilic attack, where the coordination number increases in a transition state from four to five or even six (see Section 14.3 and Chapters 4 and 5). These contrast with pathways for octahedral metal ions, such as Al(III), where it is easier to decrease the coordination number from six to five or four in dissociative ligand exchange reactions. Of course, Si(IV) is not the only common element capable of forming tetrahedral oxide species. As outlined in Chapters 2 and 4, any cation with an ionic radius between roughly 0.03 nm and 0.055 nm can fit within the tetrahedral void between four close-packed oxygen anions, as expressed by Linus Pauling’s First Rule of coordination chemistry (see Chapter 2).
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R. Bond, Marcus. "Structural Diversity in Substituted Pyridinium Halocuprates(II)." In Chemistry with Pyridine Derivatives [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.107124.
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The flexible coordination sphere of the Jahn-Teller active Cu(II) ion provides access to a full spectrum of coordination geometries from 4-coordinate (tetrahedral or square planar) to 6-coordinate elongated octahedral. This is further enhanced in anionic halide complexes by the ability of the halide ligand to bridge between Cu(II) centers to generate extended oligomeric or polymeric complexes. Coordination geometry and extended structure of the anionic complex is very sensitive to the nature of the organic counterion. This is especially true for planar substituted pyridinium cations in which minor changes in the nature or position of the substituted group can generate completely different halocuprate(II) structures. Early work focused on reducing ligand-ligand repulsion through strong hydrogen bonding with the organic cation in order to manipulate the Cu(II) coordination sphere. However, many unique structures have been found in which quaternary pyridinium cations were employed-including the remarkable thermochromic compound (1,2,6-trimethylpyridinium)2CuCl4- in which strong hydrogen bonding is absent. More recently aminopyridinium cations, which further increase structural diversity not only through the possibility of having mono- or di-protonated cations but also the ability of monoprotonated cations to coordinate to the Cu(II) center through the amino group, have been investigated.
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"Chains of Metallic Clusters With Ligands." In Nanotechnologies and Clusters in the Spaces of Higher Dimension. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-3784-8.ch004.
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This chapter geometrically investigated the structure of clusters, the core of which represent the metal chains (linear or curved) of both identical and different elements. It was shown that the dimension of the structures of these clusters is more than three. To create a model of these chains in a higher dimension space, a new geometric approach has been developed that allows us to construct convex, closed polytopes of these chains. It consists of removing part of the octahedron edges necessary for constructing the octahedron and adding the same number of new edges necessary to build a closed polytope chain while maintaining the number of metal atoms and ligands and their valence bonds. As a result, it was found that metal chain polytopes consist of polytopes of higher dimension, adjacent to each other along flat sections.
Conference papers on the topic "Octahedral geometry"
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Azizah, Ninna Arifatun Nurul, Sentot Budi Rahardjo, Witri Wahyu Lestari, and Soerya Dewi Marliyana. "Synthesis and Characterization of Copper Complex Chelated with Phenobarbital Ligand." In 8th International Conference on Advanced Material for Better Future. Trans Tech Publications Ltd, 2025. https://doi.org/10.4028/p-n2rlar.
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The research is intended to synthesize copper(II) with Phenobarbital (PB) complex in 1 : 4 mole ratio. The sole reflux method is designated to synthesize reactant within methanol solvent. Cu(II) complex is characterized using Atomic Absorption Spectrophotometry (AAS), UV-Vis Spectrophotometer, Fourier-transform Infrared Spectroscopy (FTIR), Thermogravimetric Analysis (TGA), Conductivity meter, and Magnetic Susceptibility Balance (MSB). The Cu(II)-PB complex signified 1 absorption peak at 517.5 nm with 2Eg → 2T2g transition. Complex is then composed by 6 electron donors of Cu ion-bound ligand, forming the octahedral geometry. Complex possesses the molecule formula of [Cu(PB)3]Cl2, this signifies only the PB that bound to Cu(II) ion as ligand through Oxygen and Nitrogen atom donors. There is no evidence of H2O molecules coordinated as ligand. Complex is electrolyte along with Cl- as counter ion that neutralized the complex charge. Complex is also being paramagnetic with the value of μeff of 1.74 BM.
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Arun, V., Babu Padmanabhan, Krishnan Kolady, and Charles F. Reinholtz. "Determination of the Workspace of the 3-DOF Double-Octahedral Variable-Geometry-Truss Manipulator." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0250.
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Abstract This paper presents methods to determine the workspace of the 3-DOF double-octahedral variable-geometry-truss manipulator (VGTM). These methods take advantage of some of the geometric properties inherent in octahedral VGT construction and define regions in space whose intersection results in the workspace of the manipulator. This approach of obtaining a ‘common volume’ can be extended to other parallel manipulators.
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Lee, Chung-Ching. "On the Generation Synthesis of Movable Octahedral 6R Mechanisms." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1576.
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Abstract The geometric characteristics of three well-known movable octahedral 6R mechanisms are described and then, by matrix algebra method, we derive their general displacement closed-form solutions for further investigation and analysis. Based on the fundamentals of three dimensional analytical coordinate geometry, a systematic approach is offered to generate the configuration of movable octahedral 6R mechanism with the help of computer graphics. In addition, a user-friendly computer aided program implementing the process of generation synthesis can be developed in Autolisp, a Lisp language interpreter within autoCAD. The numerical results for every generation and their constrained motion are confirmed by the derived analytical solutions. The physical models of these synthesized mechanisms are also built respectively.
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Gattas, Joseph M., and Yan Chen. "Synthesis of Folded Frame Structures From Cube-Type and Eggbox-Type Kirigami Geometry." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46433.
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Rigid-foldable cube-type and eggbox-type kirigami geometries have been of interest for applications including folded-core sandwich panels and deployable structures. Recent studies of these geometry families noticed that their convex pattern vertices enabled several further potential applications that were not otherwise possible with the concave vertices of more common pattern families such as Miura-type patterns. The following paper investigates one such application: the synthesis of folded frame structures from kirigami pattern geometric parametrisations. A new synthesis method is proposed for two geometries: a two-way orthogonal lattice frame generated from a kirigami cube pattern; and a multi-layer octahedral frame generated from a non-developable eggbox pattern. Both frames are developed with initial translation of folded geometries to frame element centre-lines and subsequent generation of integral frame elements with pattern sub-folds. Simple prototypes are manufactured to validate the synthesis method and it is found that the cube-generated frame compares favourable with typical frames with respect to packaging efficiency.
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M. AHMED, Riyadh, Sarah S. ABDUL RAHMAN, Dhefaf H. BADRI, Khawla M. SULTAN, Ismaeel Y. MAJEED, and Ghada M. KAMIL. "SYNTHESIS AND CHARACTERISATION OF NEW Co(II), Zn(II) AND Cd(II) COMPLEXES DERIVED FROM OXADIAZOLE LIGAND AND 1,10-PHENANTHROLINE AS Co-LIGAND." In V. International Scientific Congress of Pure, Applied and Technological Sciences. Rimar Academy, 2022. http://dx.doi.org/10.47832/minarcongress5-5.
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In this work, prepared new ligand namely 5-(2,4—dichloro-phenyl)-1,3,4- oxadiazole-2-(3H)-thion, which was obtained from the 2,4-dichlorobenzoyl chloride with hydrazine, after that reaction with CS2/KOH in methanol. This ligand was reaction with (Co, Zn and Cd) and 1,10-phenanthroline as co-ligand. The ligand and complexes were characterised by IR, UV-Vis, C-H-N, magnetic moment, A.A, Cl content, and m.p.. The data that collected indicate the octahedral geometry around metal ions in all complexes. In IR spectra of complexes, the small shift in ν(C=S), indicating the exocyclic sulfur is not bonding. The ligand is present in thion form, which indicate deprotonated N-H group in complexes and is bonded to Co(II), Zn(II) and Cd(II) through the oxadiazole nitrogen
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Robertson, M. G., J. Haseltine, and S. Tawfick. "Inflatable Octet-Truss Structures." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9090.
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The development of variable-stiffness systems is key to the advance of compact engineering solutions in a number of fields. Rigidizable structures exhibit variable-stiffness based on external stimuli. This function is necessary for deployable structures, such as inflatable space antennas, where the deployed structure is semi-permanent. Rigidization is also useful for a wide range of applications, such as prosthetics and exoskeletons, to help support external loads. In general, variable-stiffness designs suffer from a tradeoff between the magnitude of stiffness change and the ability of the structure to resist mechanical failure at any stiffness state. This paper presents the design, analysis, and fabrication of a rigidizable structure based on inflatable octet-truss cells. An octet-truss is a lattice-like configuration of elements, traditionally beams, arranged in a geometry reminiscent of that of the FCC lattice found in many metals; namely, the truss elements are arranged to form a single interior octahedral cell surrounded by eight tetrahedral cells. The interior octahedral cell is the core of the octet-truss unit cell, and is used as the main structure for examining the mechanics of the unit as a whole. In this work, the elements of the inflatable octet truss are pneumatic air muscles, also called McKibben actuators. Generalized McKibben actuators are a type of tubular pneumatic actuator that possess the ability to either contract or expand axially due to an applied pressure. Their unique kinematics are achieved by using a fiber wrap around an isotropic elastomeric shell. Under normal conditions, pressurizing the isotropic shell causes expansion in all directions, like a balloon. The fiber wrap constrains the ability of the shell to freely expand, due to the fiber stiffness. The wrap geometry thus guides the extensile/contractile motion of the actuator by controlling its kinematics. It is their ability to contract under pressure that makes McKibben actuators unique, and consequently they are of great interest presently to the robotics community due to their similitude to organic muscles. Kinematic analysis from constrained maximization of the shell volume during pressurization is used to obtain relations between the input work due to applied pressure and the resulting shape change due to strain energy. Analytical results are presented to describe the truss stiffness as a function of the McKibben geometry at varying pressures.
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Trzeciak, M., and H. Sone. "Polyaxial Failure Criteria in Borehole Breakout Stress Analysis." In 57th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2023. http://dx.doi.org/10.56952/arma-2023-0074.
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ABSTRACT Analysis of borehole wall failures, breakouts, is the primary method of constraining the maximum horizontal stress in deep wells. To estimate stress using the breakout method, one needs to measure the breakout width from image or caliper logs, and use a failure theory to predict stress that led to the development of the measured breakout. Most commonly, Mohr-Coulomb failure criterion is used which disregards the influence of intermediate stress on strength. Different polyaxial criteria have been proposed to include this effect. Here, we first review selected polyaxial criteria: Drucker-Prager, Mogi and modified Wiebols-Cook, and we conclude that their application in breakout analysis is cumbersome and often unreliable. One reason for these problems is that the criteria are defined using octahedral stresses or invariants, while the breakout analysis is most easily done in the principal stress space. Therefore, the polyaxial criterion can be defined as a simple relation between maximum and intermediate stresses. We propose to define such an empirical criterion as a second order polynomial which fits trends observed in polyaxial laboratory strength data. INTRODUCTION Knowledge of in situ stress is essential for many geological engineering applications including: borehole stability, hydraulic stimulation, induced seismicity, and others (e.g. Zoback, 1992, 2007; Jaeger et al., 2007; Heidbach et al., 2018). Among the three principal stresses, the maximum horizontal stress (σH) is the most challenging to constrain (Zoback et al., 2003). The most commonly used method is based on analysis of borehole wall compressive failures, i.e. breakouts. Breakout analysis requires two components: i) the breakout geometry observed from image or caliper logs, and ii) a failure theory to predict stress that led to the development of a breakout with the measured geometry. Most commonly, the Mohr-Coulomb criterion is used in borehole wall strength analysis and its failure is predicted when the hoop stress reaches a critical value (Barton et al., 1988). However, such approach disregards the influence of the intermediate principal stress (σ2) on rock strength (understood as the maximum principal stress, σ1, at failure) which has been described in numerous experimental studies (e.g. Mogi, 1971; Michelis, 1985, 1987; Haimson and Chang, 2000; Chang and Haimson, 2000; Ingraham et al., 2013; Ma and Haimson, 2016; Lee and Haimson, 2011). Therefore, several polyaxial failure criteria which include the σ2 dependence of strength has been proposed and applied in borehole breakout analyses (Zhou, 1994; Ewy, 1999; Al-Ajmi and Zimmerman, 2005; Chang et al., 2010).
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Arakere, Nagaraj K., and Gregory Swanson. "Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys." In ASME Turbo Expo 2000: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/2000-gt-0334.
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High Cycle Fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Single crystal nickel turbine blades are being utilized in rocket engine turbopumps and jet engines throughout industry because of their superior creep, stress rupture, melt resistance and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal turbine blade superalloys are PWA 1480/1493, PWA 1484, RENE’ N-5 and CMSX-4. These alloys play an important role in commercial, military and space propulsion systems. Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. The failure modes of single crystal turbine blades are complicated to predict due to the material orthotropy and variations in crystal orientations. Fatigue life estimation of single crystal turbine blades represents an important aspect of durability assessment. It is therefore of practical interest to develop effective fatigue failure criteria for single crystal nickel alloys and to investigate the effects of variation of primary and secondary crystal orientation on fatigue life. A fatigue failure criterion based on the maximum shear stress amplitude [Δτmax] on the 24 octahedral and 6 cube slip systems, is presented for single crystal nickel superalloys (FCC crystal). This criterion reduces the scatter in uniaxial LCF test data considerably for PWA 1493 at 1200F in air. Additionally, single crystal turbine blades used in the alternate advanced high-pressure fuel turbopump (AHPFTP/AT) are modeled using a large-scale 3D finite element (FE) model. This FE model is capable of accounting for material orthotrophy and variation in primary and secondary crystal orientation. Effects of variation in crystal orientation on blade stress response are studied based on 297 FE model runs. Fatigue lives at critical points in the blade are computed using FE stress results and the failure criterion developed. Stress analysis results in the blade attachment region are also presented. Results presented demonstrates that control of secondary and primary crystallographic orientation has the potential to significantly increase a component’s resistance to fatigue crack growth without adding additional weight or cost.
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Xu, Li Ju, Yang Duan, and Sui Xian Yang. "Closed-Form Inverse Kinematic Solution of Triple Octahedron Variable Geometry Truss Manipulators." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5955.
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Abstract In this paper the triple-octahedron variable geometry truss manipulator is presented and its inverse displacement analysis in closed form is studied, Input-output displacement equation in one output variable is derived. The solution procedure is given in detail. A numerical example is presented for illustration.
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Abu-Muharib, Andrew, Andrey P. Jivkov, Peter James, and John R. Yates. "Cleavage Fracture Modelling for RPV Steels: Discrete Model for Collective Behaviour of Micro-Cracks." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-97431.
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The ability to predict variations in cleavage fracture toughness behaviour of ferritic RPV steels, accounting for the effects of irradiation and defect geometry, is vital to safety assessment and life extension decisions. Local approaches to cleavage fracture offer a promising methodology to accomplish such calculations. However, the limited progress achieved by improving the local failure probability expression suggests that the methodology for calculating global cleavage might not be adequately representing real material. The basis for the existing methodology is the weakest-link assumption that all individual failure events are independent and non-interacting. Here an approach is considered which utilises a microstructure-informed model incorporating the experimental knowledge needed to postulate deterministic criteria for particle rupture and micro-crack propagation, whilst accounting for the probabilistic distribution of particle sizes. This is then used in a lattice model that can help detail the evolution of the formation of micro-cracks on global failure, therefore inferring the suitability of the weakest-link assumption. Predicting the probability of cleavage fracture requires such models, as the macroscopic cleavage phenomenon is governed by a number of micro-structural features. The material microstructure is represented by a regular lattice of truncated octahedral cells forming a computational site-bond model, with sites located at the cell centres and connected by two distinct sets of bonds. These bonds are modelled with structural beam elements, which represent all the possible relative deformations between coordinated sites. Particles of various sizes are distributed in the bonds, based on an experimentally determined distribution of cleavage initiating particles in RPV steel (Euro Material A). Although only elastic deformations are considered here, the results demonstrate that the interactions between individual failure events could potentially have a strong effect on the way global failure is reached. Nucleation of micro-cracks by rupturing second-phase particles affects their subsequent formation. In particular, it was found that once formed there is a reduced probability of further development of micro-cracks at particles outside the crack planes and an enhanced probability of formation at particles along the crack planes. This will therefore influence the distribution of micro-crack sizes that could in principle be used to calculate the global probability of failure, and could lead to substantially different distributions of particle sizes, then used in the current local approach methods.