Статті в журналах: "Octahedron"

1

Yang, Jian Hui, Rong Ling Sun, Zheng Hao Yang, Xin Yang Lin, and Hai Cheng Niu. "Constitutive Relations of Concrete under Plane Stresses Based on Generalized Octahedral Theory." Applied Mechanics and Materials 71-78 (July 2011): 342–52. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.342.

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Continuous (or generalized) octahedral element bodies can be obtained by intercepting a cube with three groups of failure (or yield) planes successively under true triaxial stress state, on which the stresses are twin stresses. Among the resulting polyhedral characteristic element bodies, isoclinal octahedron and orthogonal octahedron are of particular importance. Strength models of continuous octahedrons are then derived by stress analysis to arbitrary inclined sections in three dimensional stress space, and strain models by the principle of strain analysis, so the plane constitutive relations of concrete can be understood by plane problems transformed by stress-strain space according to the symmetry of an orthogonal octahedral octahedron where an arbitrary oblique plane is parallel to one of three rectangular coordinate axes.

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2

Colombo, F., J. Rius, O. Vallcorba, and E. V. Pannunzio Miner. "The crystal structure of sarmientite, Fe23+ (AsO4)(SO4)(OH)·5H2O, solved ab initio from laboratory powder diffraction data." Mineralogical Magazine 78, no. 2 (April 2014): 347–60. http://dx.doi.org/10.1180/minmag.2014.078.2.08.

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AbstractThe crystal structure of sarmientite, Fe23+ (AsO4)(SO4)(OH)·5H2O, from the type locality (Santa Elena mine, San Juan Province, Argentina), was solved and refined from in-house powder diffraction data (CuKα1,2 radiation). It is monoclinic, space group P21/n, with unit-cell dimensions a = 6.5298(1), b = 18.5228(4), c = 9.6344(3) Å, β = 97.444(2)º, V = 1155.5(5) Å3, and Z = 4. The structure model was derived from cluster-based Patterson-function direct methods and refined by means of the Rietveld method to Rwp = 0.0733 (X2 = 2.20). The structure consists of pairs of octahedral-tetrahedral (Fe−As) chains at (y,z) = (0,0) and (½,½), running along a. There are two symmetry-independent octahedral Fe sites. The Fe1 octahedra share two corners with the neighbouring arsenate groups. Both individual chains are related by a symmetry centre and joined by two symmetry-related Fe2 octahedra. Each Fe2 octahedron shares three corners with double-chain polyhedra (O3, O4 with arsenate groups; the O8 hydroxyl group with the Fe1 octahedron) and one corner (O11) with the monodentate sulfate group. The coordination of the Fe2 octahedron is completed by two H2O molecules (O9 and O10). There is also a complex network of H bonds that connects polyhedra within and among chains. Raman and infrared spectra show that (SO4)2− tetrahedra are strongly distorted.

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3

Sowa, H., and H. Ahsbahs. "Pressure-Induced Octahedron Strain in VF3-Type Compounds." Acta Crystallographica Section B Structural Science 54, no. 5 (October 1, 1998): 578–84. http://dx.doi.org/10.1107/s0108768198001207.

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High-pressure X-ray investigations on crystal powders of the TiF3, titanium trifluoride, and FeF3, iron trifluoride, phases with VF3-type structures were performed up to 7.67 (7) and 9.00 (7) GPa, respectively. Both compounds are highly compressible and show strong anisotropic behavior. While the hexagonal a lattice parameters are shortened under pressure, the c parameters are elongated. These changes are associated with distortions of the TiF6 and FeF6 coordination octahedra, whereby the octahedron strain is stronger in TiF3 than in FeF3. The high-pressure behavior is characterized by cooperative tiltings of the octahedra, while simultaneously repulsive interactions between the cations probably cause the octahedral distortions.

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4

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 (November 25, 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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5

Yang, Juan, Xin Zhang, Biao Liu, Wei Sun, and Ya-Xi Huang. "K2[FeII 3(P2O7)2(H2O)2]." Acta Crystallographica Section E Structure Reports Online 68, no. 6 (May 19, 2012): i47—i48. http://dx.doi.org/10.1107/s1600536812021484.

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The title compound, dipotassium diaquabis(diphosphato)triferrate(II), K2[FeII 3(P2O7)2(H2O)2], was synthesized under solvothermal conditions. The crystal structure is isotypic with its Co analogue. In the structure, there are two crystallographically distinct Fe positions; one lies on an inversion center, the other on a general position. The first Fe2+ cation adopts a regular octahedral coordination with six O atoms, whereas the other is coordinated by five O atoms and a water molecule. The [FeO6] octahedron shares its trans-edges with an adjacent [FeO5(H2O)] octahedron; in turn, the [FeO5(H2O)] octahedron shares skew-edges with a neighbouring [FeO6] octahedron and an [FeO5(H2O)] octahedron, resulting in a zigzag octahedral chain running along [001]. The zigzag chains are linked to each other by the P2O7 diphosphate groups, leading to a corrugated iron diphosphate layer, [Fe3(P2O7)2(H2O)2]2−, parallel to (100). The interlayer space is occupied by K+ cations, which adopt an eight-coordination to seven O atoms and one water molecule from a neighbouring iron diphosphate layer. Thus, the K+ ions not only compensate the negative charge of the layer but also link the layers into a network structure.

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6

Bosi, Ferdinando. "Chemical and structural variability in cubic spinel oxides." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 75, no. 2 (March 28, 2019): 279–85. http://dx.doi.org/10.1107/s2052520619002282.

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The empirical relations between cubic spinel oxides of different compositions were investigated using data from 349 refined crystal structures. The results show that the spinel structure is able to tolerate many constituents (at least 36) by enlarging and decreasing the tetrahedra and octahedra. This is reflected in a large variation in tetrahedral and octahedral bond distances. The oxygen positional parameter (u) may be regarded as a measure of the distortion of the spinel structure from cubic close packing or of the angular distortion of the octahedron. The distortion can best be explained in terms of ionic potential (IP), which merges the size and charge properties of an ion. Sterically induced distortion depends on ion size, whereas electrostatically induced distortion is caused by cation–cation repulsion across faces of tetrahedra and shared edges of octahedra. The strong correlations between the u parameter and the IP at the T and M sites are consistent with the main role played by the both charge and size. Large distortions (u ≫ 0.27) result in oxygen–oxygen distances of the octahedron shorter than 2.50 Å, which would lead to structural instability because of increased non-bonded repulsion forces between the oxygen atoms.

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7

Abdulla-Al-Mamun, Md, Yoshihumi Kusumoto, and Md Shariful Islam. "A new, simple hydrothermal synthesis of magnetic nano-octahedrons — Application to hyperthermia cancer cell killing." Canadian Journal of Chemistry 90, no. 8 (August 2012): 660–65. http://dx.doi.org/10.1139/v2012-046.

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Surfactant-free magnetic nano-octahedrons were successfully synthesized by the alkaline hydrothermal decomposition of ferric nitrate salt (Fe(NO3)3·9H2O) in a water–ethanol mixed solvent with a variety of alkaline concentrations. High-resolution scanning electron microscope (SEM) pictures demonstrated the formation of octahedron-structured magnetic nanoparticles at a 10 mol/L alkaline concentration. A possible synthesis mechanism of the magnetic nano-octahedron was discussed. An alternating current magnetic field to induce hyperthermia cancer cell killing was investigated. Maximum hyperthermia cancer cell killing (~100%) was found with 10 mol/L alkaline-synthesized nano-octahedrons, whereas that with 2 mol/L alkaline gave ~40%.

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8

Panchenko, Tetiana, Maria Evseeva, Anatoliy Ranskiy, Vyacheslav Baumer, and Olga Gordienko. "Synthesis and Crystal Structure of Cadmium(II) Dichloroaquasalicylidenesemicarbazone." Chemistry & Chemical Technology 10, no. 3 (September 15, 2016): 285–90. http://dx.doi.org/10.23939/chcht10.03.285.

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Cadmium(II) complex with salicyl aldehyde semicarbozone (Н2L) has been synthesized. Based on elemental analysis and IR spectroscopy its composition – [Cd∙Н2L∙H2O∙Cl2] – has been established. The complex crystal structure has been examined using XRD analysis. The coordination polyhedron of cadmium atom is a distorted octahedron, where two cis-positions are occupied by oxygen atoms of water molecule and carbamide fragment of H2L molecule, other positions are occupied by chlorine atoms. At the same time two edges of octahedron are combined with adjoined octahedrons and form endless zigzag chains of octahedrons in the structure along the crystallographic axis. H2L molecule is a planar one due to the presence of intramolecular hydrogen bond.

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9

Fernández-Ruiz, Manuel Alejandro, Enrique Hernández-Montes, Juan Francisco Carbonell-Márquez, and Luisa María Gil-Martín. "Octahedron family: The double-expanded octahedron tensegrity." International Journal of Solids and Structures 165 (June 2019): 1–13. http://dx.doi.org/10.1016/j.ijsolstr.2019.01.017.

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10

Qian, Li Min, Jie Zhou, Chu Zheng, Di Chen, Bi Shen, Yong Kun Liu, Li Xiao Wang, and Yan Hua Tong. "Comparative Photocatalytic Properties of Cu₂O from Octahedron to Sphere Structures." Key Engineering Materials 609-610 (April 2014): 45–50. http://dx.doi.org/10.4028/www.scientific.net/kem.609-610.45.

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Cu2O, a p-type semiconductor, has broad potential applications, especially as a visible-light photocatalyst. This paper presents a simple water-bath reflux to prepare Cu2O micro/nanoparticles. The morphology evolution from intact octahedrons to surface-pitted spheres was obtained by adjusting reducing agent and additive. Reflectance spectra show similar photo-absorption intensity and the same range from 250 nm to 650 nm. However, they perform different photocatalytic activity. Intact octahedron has the best photodegradation ability and next is vertex-and edge-damaged octahedron, the lowest for vertex-free polyhedrons and surface-pitted spheres. The enhanced photocatalytic activity for intact octahedrons should to be attributed to its surface characteristics of high index. Our study not only provides a simple method for controllable preparation of Cu2O micro/nanoparticles with different morphologies but also confirms the effect of morphologies on photocatalytic activity.

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11

Hicock, Stephen R. "Glacial Octahedron." Geografiska Annaler. Series A, Physical Geography 75, no. 1/2 (1993): 35. http://dx.doi.org/10.2307/521051.

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12

Hicock, Stephen R. "Glacial Octahedron." Geografiska Annaler: Series A, Physical Geography 75, no. 1-2 (April 1993): 35–39. http://dx.doi.org/10.1080/04353676.1993.11880381.

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13

Palatnikov, M. N., A. V. Kadetova, L. A. Aleshina, and O. V. Sidorova. "Analysis of doping influence on structural defects in LiNbO3." Transaction Kola Science Centre 11, no. 3-2020 (November 25, 2020): 87–92. http://dx.doi.org/10.37614/2307-5252.2020.3.4.019.

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Changes in a structural state of homogeneous doped lithium niobate crystals with magnesium in the region of 5 mol. % were studied by X-ray diffraction methods. It was found that the changes in the structure of LiNbO3: Mg occured not only in the region of the impurity defect, but also in the region of the main motive of the structure. Bond lengths in the octahedra of the main motive and the Nb–Li distance along the polar axis of the crystal changed. The magnesium introduced into the vacant lithium octahedron distorted the shape of the octahedron more strongly than niobium.

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14

Adachi, Sadao. "Luminescence Spectroscopy of 3d³ (Mn⁴⁺, Cr³⁺) Ions in Multiple Octahedral-Site Phosphors." ECS Journal of Solid State Science and Technology 11, no. 4 (April 1, 2022): 046002. http://dx.doi.org/10.1149/2162-8777/ac63e4.

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Investigating spectroscopic properties of luminescent ions in multiple sites of host materials is not only of scientific interest, but also technological importance. The present investigation focuses on this problem and reports the analysis results of the optical properties of 3d 3 ions in the multiple octahedron sites. The phosphor materials considered are double-perovskite La4Ti3O12:Mn4+ and Ca3−x Lu x Hf2Al2+x Si1−x O12:Cr3+ (x = 0−1.0) phosphors. An analysis method is demonstrated for obtaining reliable and site-dependent crystal-field (Dq) and Racah parameters (B and C) based on a ligand field theory with paying an attention to difficulty in the exact estimation of such important crystal-field-related parameters. For example, the difference in the crystal-field splitting energies between the slightly and highly-distorted octahedron sites determined are ΔDq ∼ 1615 and 405 cm−1 (x = 0) for the [MnO6]8− and [CrO6]9− octahedrons, respectively. All results are in satisfactory agreement with the Tanabe−Sugano energy-level diagram plots, promising good understanding of such 3d 3-ion-activated phosphors with multiple octahedron sites.

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15

Lee, Hee Jung, Won Cho, and Moonhyun Oh. "Fluorescent octahedron and rounded-octahedron coordination polymer particles (CPPs)." CrystEngComm 12, no. 11 (2010): 3959. http://dx.doi.org/10.1039/c004214e.

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16

Zhu, Yan Hua, Jing Jing Ma, and Qing Yang. "One-Step Alcohothermal Synthesis and Growth Mechanism of NiSe₂ Porous Octahedron." Applied Mechanics and Materials 37-38 (November 2010): 769–72. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.769.

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Microscale crystalline NiSe2 porous octahedrons have been solvothermally synthesized from reaction of NiCl2∙6H2O with Se powder in ethanol with dodecylbenzene sulfonic acid sodium salt as surfactant at 200°C for 20h. The samples are octahedral crystals with mean size of 2 micron in diameter and the micro-octahedrons present porous morphologies. The octahedral NiSe2 microcrystals exposed with {111} facets are grown under a thermodynamic process and the porous textures within the octahedrons are resulted from the cooperative effects of the oxidation of selenium in HNO3 and the coordination of Ni2+ with Cl– under the alcohothermal process. The surfactant increases the monodispersity of the NiSe2 crystals with octahedral shapes.

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17

Wu, Shao-Yi, Hua-Ming Zhang, Guang-Duo Lu, and Jin-Song Yao. "Theoretical Investigations of the Defect Structure and the g Factors of a Tetragonal Ni3+ Center in PbTiO3." Zeitschrift für Naturforschung A 62, no. 5-6 (June 1, 2007): 338–42. http://dx.doi.org/10.1515/zna-2007-5-616.

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The defect structure and the anisotropic g factors of a tetragonal Ni3+ center in PbTiO3 are theoretically investigated from improved perturbation formulas of the g factors for a 3d7 ion with low spin S = 1/2 in tetragonally elongated octahedra, established in this work. Based on the studies, the distance between the impurity Ni3+ and the center of the oxygen octahedron is found to be about 0.14 Å, which is smaller than that (≈ 0.3 Å) for the host Ti4+ site due to the inward shift (≈ 0.16 Å ) towards the center of the oxygen octahedron. The theoretical g factors based on the above defect structure agree well with the observed values.

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18

Hawthorne, F. C., and M. A. Cooper. "The crystal structure of chalcoalumite: mechanisms of Jahn-Teller-driven distortion in [6]Cu2+-containing oxysalts." Mineralogical Magazine 77, no. 7 (October 2013): 2901–12. http://dx.doi.org/10.1180/minmag.2013.077.7.02.

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AbstractThe crystal structure of chalcoalumite, ideally Cu2+Al4(SO4)(OH)12(H2O)3, monoclinic, P21/n, Z = 4:a 10.228(3), b 8.929(3), c 17.098(6) Å, β 95.800(11)°, V 1553.6(1.5) Å3, has been refined to R1 = 3.08% for 4,022 unique observed (4σ) reflections collected on a Bruker D8 three-circle diffractometer equipped with a rotating-anode generator, multilayer optics and an APEX-II CCD detector. In the structure of chalcoalumite, there is one S site, tetrahedrally coordinated by four O anions, with <S–O> = 1.472 Å. There are four Al sites with site-scattering values in accord with occupancy by Al and <Al–O> distances of 1.898–1.919 Å. There is one Cu site occupied by Cu2+ and coordinated by six anions in the [4 + 2] arrangement typical for octahedrally coordinated Cu2+. The short <Cu–O> distance of 2.086 Å is in accord with the low degree of bond-length distortion of the Cu octahedron. There are 19 anion sites: 4 sites are occupied by O atoms that are bonded to the S cation, 12 sites are occupied by (OH) groups that bond to all octahedrally coordinated cations, and 3 sites are occupied by (H2O) groups that are held in the structure solely by hydrogen bonding. The structure of chalcoalumite consists of interrupted sheets of edge-sharing Al and Cu octahedra of the form [Cu2+Al4(OH)12]2+ that intercalate layers of (SO4) tetrahedra and (H2O) groups. Chalcoalumite is a member of the nickelalumite group.Cu2+ϕ6(ϕ = O2–, (OH)–, (H2O)0) octahedra show a wide range of bond-length distortion away from the holosymmetric arrangement, driven by spontaneous symmetry-breaking of the degenerate electronic ground-state in holosymmetric octahedral coordination. Here, we examine the structural mechanisms that allow large octahedron distortions of this type. There are two mechanisms: (1) coupling of (usually parallel) octahedron distortions to a vibrational phonon, inducing a (often ferroelastic) phase transition in M2+-Cu2+ solid-solutions; (2) cooperative orientational disorder, where bond topology (polyhedron linkage) allows large differences in bond lengths within polyhedra to accord with the valence-sum rule of bond-valence theory.

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19

Li, W. M., J. F. Zhao, L. P. Cao, Z. Hu, Q. Z. Huang, X. C. Wang, Y. Liu, et al. "Superconductivity in a unique type of copper oxide." Proceedings of the National Academy of Sciences 116, no. 25 (May 20, 2019): 12156–60. http://dx.doi.org/10.1073/pnas.1900908116.

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The mechanism of superconductivity in cuprates remains one of the big challenges of condensed matter physics. High-Tc cuprates crystallize into a layered perovskite structure featuring copper oxygen octahedral coordination. Due to the Jahn Teller effect in combination with the strong static Coulomb interaction, the octahedra in high-Tc cuprates are elongated along the c axis, leading to a 3dx2-y2 orbital at the top of the band structure wherein the doped holes reside. This scenario gives rise to 2D characteristics in high-Tc cuprates that favor d-wave pairing symmetry. Here, we report superconductivity in a cuprate Ba2CuO4-y, wherein the local octahedron is in a very exceptional compressed version. The Ba2CuO4-y compound was synthesized at high pressure at high temperatures and shows bulk superconductivity with critical temperature (Tc) above 70 K at ambient conditions. This superconducting transition temperature is more than 30 K higher than the Tc for the isostructural counterparts based on classical La2CuO4. X-ray absorption measurements indicate the heavily doped nature of the Ba2CuO4-y superconductor. In compressed octahedron, the 3d3z2-r2 orbital will be lifted above the 3dx2-y2 orbital, leading to significant 3D nature in addition to the conventional 3dx2-y2 orbital. This work sheds important light on advancing our comprehensive understanding of the superconducting mechanism of high Tc in cuprate materials.

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20

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 (March 16, 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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21

Zhai, Yun, Sibo He, Lei Lei, and Tianmin Guan. "Mechanical property of octahedron Ti6Al4V fabricated by selective laser melting." REVIEWS ON ADVANCED MATERIALS SCIENCE 60, no. 1 (January 1, 2021): 894–911. http://dx.doi.org/10.1515/rams-2021-0080.

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Abstract The stress shielding effect is a critical issue for implanted prosthesis due to the difference in elastic modulus between the implanted material and the human bone. The adjustment of the elastic modulus of implants by modification of the lattice structure is the key to the research in the field of implanted prosthesis. Our work focuses on the basic unit structure of octahedron Ti6Al4V. The equivalent elastic modulus and equivalent density of porous structure are optimized according to the mechanical properties of human bone tissue by adjusting the edge diameter and side length of octahedral lattice. Macroscopic long-range ordered arrangement of lattice structures is fabricated by selective laser melting (SLM) technology. Finite element simulation is performed to calculate the mechanical property of octahedron Ti6Al4V. Scanning electronic microscopy is applied to observe the microstructure of octahedron alloy and its cross section morphology of fracture. Standard compression test is performed for the stress–strain behavior of the specimen. Our results show that the octahedral lattice with the edge diameter of 0.4 mm and unit cell length of 1.5 mm has the best mechanical property which is close to the human bone. The value of equivalent elastic modulus increases with the increase in the edge diameter. The SLM technology proves to be an effective processing way for the fabrication of complex microstructures with porosity. In addition, the specimen exhibits isotropic mechanical performance and homogeneity which significantly meet the requirement of implanted prosthetic medical environment.

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22

Appel, P. W. U., and M. F. Brigatti. "Ludwigite from central Sweden: new data and crystal structure refinement." Mineralogical Magazine 63, no. 4 (August 1999): 511–18. http://dx.doi.org/10.1180/002646199548682.

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AbstractLudwigite from B-bearing iron ores in the Bergslagen area of central Sweden and in the coastal area north of Stockholm has been studied using chemical and single-crystal diffraction techniques. Structure refinements, completed for three crystals showing slightly different Al contents, in the space group Pbam (agreement factor: 2.42 ≤ R ≤ 2.79) indicate that: (1) octahedral M1, M2 and M3 bond distances are similar, although the calculated site population suggests that M1 and M2 are nearly completely occupied by Mg whereas M3 also contains Fe2+ and Fe3+; (2) in the M4 octahedron Fe3+ and Al dominate over Mg (and Fe2+); and (3) the distortion parameter, BLD, indicates that M3 is the most regular, whereas M4 is the most distorted octahedron.

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23

Grangeon, Sylvain, Bruno Lanson, and Martine Lanson. "Solid-state transformation of nanocrystalline phyllomanganate into tectomanganate: influence of initial layer and interlayer structure." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 70, no. 5 (September 18, 2014): 828–38. http://dx.doi.org/10.1107/s2052520614013687.

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In surficial environments, the fate of many elements is influenced by their interactions with the phyllomanganate vernadite, a nano-sized and turbostratic variety of birnessite. To advance our understanding of the surface reactivity of vernadite as a function of pH, synthetic vernadite (δ-MnO2) was equilibrated at pH ranging from 3 to 10 and characterized structurally using chemical methods, thermogravimetry and modelling of powder X-ray diffraction (XRD) patterns. With decreasing pH, the number of vacant layer sites increases in the octahedral layers of δ-MnO2(from 0.14 per layer octahedron at pH 10 to 0.17 at pH 3), whereas the number of layer Mn3+is, within errors, equal to 0.12 per layer octahedron over the whole pH range. Vacant layer sites are capped by interlayer Mn3+sorbed as triple corner-sharing surface complexes (TC sites). The increasing number of interlayer Mn3+with decreasing pH (from 0.075 per layer octahedron at pH 10 to 0.175 at pH 3) results in the decrease of the average Mn oxidation degree (from 3.80 ± 0.01 at pH 10 to 3.70 ± 0.01 at pH 3) and in the lowering of the Na/Mn ratio (from 27.66 ± 0.20 at pH 10 to 6.99 ± 0.16 at pH 3). In addition, in-plane unit-cell parameters are negatively correlated to the number of interlayer Mn at TC sites and decrease with decreasing pH (fromb= 2.842 Å at pH 10 tob= 2.834 Å at pH 3), layer symmetry being systematically hexagonal witha=b× 31/2. Finally, modelling of X-ray diffraction (XRD) patterns indicates that crystallite size in theabplane and along thec* axis decreases with decreasing pH, ranging respectively from 7 nm to 6 nm, and from 1.2 nm to 1.0 nm (pH 10 and 3, respectively). Following their characterization, dry samples were sealed in polystyrene vials, kept in the dark, and re-analysed 4 and 8 years later. With ageing time and despite the dry state, layer Mn3+extensively migrates to the interlayer most likely to minimize steric strains resulting from the Jahn–Teller distortion of Mn3+octahedra. When the number of interlayer Mn3+at TC sites resulting from this migration reaches the maximum value of ∼ 1/3 per layer octahedron, interlayer species from adjacent layers share their coordination sphere, resulting in cryptomelane-like tunnel structure fragments (with a 2 × 2 tunnel size) with a significantly improved layer stacking order.

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24

Starova, G. L., S. K. Filatov, G. L. Matusevich, and V. S. Fundamensky. "The crystal structure of vlodavetsite, AlCa2(SO4)2F2Cl·4H2O." Mineralogical Magazine 59, no. 394 (March 1995): 159–62. http://dx.doi.org/10.1180/minmag.1995.59.394.16.

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AbsractThe crystal structure of vlodavetsite, AlCa2(SO4)2F2Cl·4H2O, has been determined, space group I4/m, a = 6.870(1), c = 13.342(2) Å, Z = 2, Dx = 2.35 g/cm3. The polyhedron cation chains are parallel to [001] and consist of couples of distorted Ca octahedra alternating with one distorted Al octahedron rotated through 24° with respect to the former. The chains are linked by SO4-tetrahedra so that all of the four tetrahedron oxygen atoms take part in coordination of Ca atoms to form a distorted octahedron with Cl and F atoms. The Al coordination polyhedron consists of two F atoms and four oxygen atoms belonging to water molecules. There is a specific interaction via hydrogen bonds between oxygen atoms of SO4-tetrahedra and water molecules.

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25

Bakulin, Alexander, Alexander Latyshev, and Svetlana Kulkova. "Absorption and Diffusion of Oxygen in Ti-Al Bulk Alloys." Solid State Phenomena 258 (December 2016): 408–11. http://dx.doi.org/10.4028/www.scientific.net/ssp.258.408.

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The oxygen absorption and diffusion properties are studied in γ-TiAl and TiAl3 alloys within density functional theory using projector augmented wave method in the plane-wave basis. It is shown that the octahedral site inside the Ti-rich octahedron is preferable for oxygen in case of γ-TiAl alloy whereas the Al-rich octahedron is more favorable environment for oxygen in TiAl3. It is shown that the energy barriers for oxygen jumps between different sites in bulk alloys depend significantly on the local environments of oxygen and increase for its jump from Ti-rich sites. The trajectories with minimum energy barriers are determined for both Ti-Al alloys. It is shown that the increase of Al content in alloy leads to the decrease of barriers for oxygen jumps.

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26

Kong, Yueyue, Ranran Jiao, Suyuan Zeng, Chuansheng Cui, Haibo Li, Shuling Xu, and Lei Wang. "Study on the Synthesis of Mn3O4 Nanooctahedrons and Their Performance for Lithium Ion Batteries." Nanomaterials 10, no. 2 (February 20, 2020): 367. http://dx.doi.org/10.3390/nano10020367.

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Among the transition metal oxides, the Mn3O4 nanostructure possesses high theoretical specific capacity and lower operating voltage. However, the low electrical conductivity of Mn3O4 decreases its specific capacity and restricts its application in the energy conversion and energy storage. In this work, well-shaped, octahedron-like Mn3O4 nanocrystals were prepared by one-step hydrothermal reduction method. Field emission scanning electron microscope, energy dispersive spectrometer, X-ray diffractometer, X-ray photoelectron spectrometer, high resolution transmission electron microscopy, and Fourier transformation infrared spectrometer were applied to characterize the morphology, the structure, and the composition of formed product. The growth mechanism of Mn3O4 nano-octahedron was studied. Cyclic voltammograms, galvanostatic charge–discharge, electrochemical impedance spectroscopy, and rate performance were used to study the electrochemical properties of obtained samples. The experimental results indicate that the component of initial reactants can influence the morphology and composition of the formed manganese oxide. At the current density of 1.0 A g−1, the discharge specific capacity of as-prepared Mn3O4 nano-octahedrons maintains at about 450 mAh g−1 after 300 cycles. This work proves that the formed Mn3O4 nano-octahedrons possess an excellent reversibility and display promising electrochemical properties for the preparation of lithium-ion batteries.

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27

Lee, Jeong-Gon, Young Bae Jun, and Kul Hur. "Octahedron Subgroups and Subrings." Mathematics 8, no. 9 (August 28, 2020): 1444. http://dx.doi.org/10.3390/math8091444.

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In this paper, we define the notions of i-octahedron groupoid and i-OLI [resp., i-ORI and i-OI], and study some of their properties and give some examples. Also we deal with some properties for the image and the preimage of i-octahedron groupoids [resp., i-OLI, i-ORI and i-OI] under a groupoid homomorphism. Next, we introduce the concepts of i-octahedron subgroup and normal subgroup of a group and investigate some of their properties. In particular, we obtain a characterization of an i-octahedron subgroup of a group. Finally, we define an i-octahedron subring [resp., i-OLI, i-ORI and i-OI] of a ring and find some of their properties. In particular, we obtain two characterizations of i-OLI [resp., i-ORI and i-OI] of a ring and a skew field, respectively.

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28

She, XueFeng, Kewei Zhu, JingSong Wang, and QingGuo Xue. "Product control and a study of the structural change process during the recycling of lithium-ion batteries based on the carbothermic reduction method." Journal of Chemical Research 46, no. 1 (January 2022): 174751982110665. http://dx.doi.org/10.1177/17475198211066533.

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Carbothermal reduction to recover lithium-ion batteries is an environmentally friendly recycling method. This work provides a theoretical analysis of the thermodynamics and an experimental verification process for the carbon thermal reduction recovery of lithium cobaltate (LiCoO2), as well as an explanation of the microstructural changes. The reaction conditions are controlled to obtain the ideal recovery product. A thermodynamic graph of the possible reaction between LiCoO2 and graphite (C) and the reduction of cobalt oxide (CoO, Co2O3, Co3O4) by carbon monoxide (CO) is obtained by thermodynamic analysis. The feasibility of the carbothermic reduction reaction of LiCoO2 at high temperature is studied under standard atmospheric pressure. By controlling the reaction temperature (800 °C) and the ratio of the reactants (LiCoO2/C = 4:5), the reduction products cobalt monoxide (CoO) and lithium carbonate (Li2CO3) are obtained, and the recovery rates are 89% and 84%, respectively. From the perspective of the crystal structure, the reduction process of LiCoO2 is analyzed. The Li-O bond in the LiCoO2 crystal structure is destroyed by CO, which promotes destruction of the Li-O octahedral structure and the formation of a Co-O octahedron. The Li-O octahedron is transformed into a tetrahedral structure in Li2O, and Li2O then reacts with CO2 to form Li2CO3; the Co-O octahedrons combine to form a CoO crystal structure. When the temperature continues to rise, CoO is reduced to Co. The carbothermic reduction recovery method does not require any additional hazardous chemicals and can avoid secondary pollution during the recovery process. This research provides theoretical support for the industrial recycling of lithium-ion batteries.

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29

Zeitler, Herbert. "Tetrahedron and octahedron fractals." International Journal of Mathematical Education in Science and Technology 29, no. 3 (May 1998): 329–41. http://dx.doi.org/10.1080/0020739980290303.

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30

Clarisó, Robert, and Jordi Cortadella. "The octahedron abstract domain." Science of Computer Programming 64, no. 1 (January 2007): 115–39. http://dx.doi.org/10.1016/j.scico.2006.03.009.

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31

Klepp, Kurt O. "Darstellung und Kristallstruktur von Tl2TiS4 : Ein Perthiotitanat(IV) mit ∞1-[TiS42-]-Ketten Preparation and Crystal Structure of Tl2TiS4 : A Perthiotitanate(IV) with ∞1-[TiS42-]-Chains." Zeitschrift für Naturforschung B 40, no. 2 (February 1, 1985): 229–34. http://dx.doi.org/10.1515/znb-1985-0214.

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Abstract Tl2TiS4 is orthorhombic, space group Pbca, with a = 22.176(7), b = 9.484(4), c = 6.3977(9) Å, Z = 8. The crystal structure was solved by direct methods and refined to a conventional R of0.058 for 704 reflections with I ≥3σ(I). The crystal structure is characterized by infinite perthioanions, ∞1-[TiS 4/2 (S2)2- ], which are separated by Tl+ -cations. The anion chains are built up by distorted octahedra which share two skew edges to form infinite cis-chains running along [001], The two unshared S-atoms of each octahedron are connected via a S -S-single bond of 2.10 Å length. The crystal structure is described as a mixed packing of TI-and S-atoms, composed of puckered TlS2 -layers, in which the Ti-atoms occupy the octahedral interstices. The relationship of the ∞1-[TiS42- -]-chains to the anionic groups of Cs2TiS3 is discussed.

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32

Zhu, Gang, та Zong-Xun Tang. "Diaquabis(1,10-phenanthroline-κ2 N,N′)manganese(II) pentafluorooxoniobate(V)". Acta Crystallographica Section E Structure Reports Online 62, № 5 (11 квітня 2006): m1018—m1020. http://dx.doi.org/10.1107/s1600536806012591.

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In the title compound, [Mn(C12H8N2)2(H2O)2][NbOF5], each of the MnII and NbV atoms has a distorted octahedral coordination. In the [NbOF5]2− anion, a characteristic short terminal Nb=O bond and a longer Nb—F bond are observed, which result in the out-of-center distortion of the octahedron, a manifestation of the second-order Jahn–Teller effect.

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33

Fan, Wei, Yih Hong Lee, Srikanth Pedireddy, Qi Zhang, Tianxi Liu, and Xing Yi Ling. "Graphene oxide and shape-controlled silver nanoparticle hybrids for ultrasensitive single-particle surface-enhanced Raman scattering (SERS) sensing." Nanoscale 6, no. 9 (2014): 4843–51. http://dx.doi.org/10.1039/c3nr06316j.

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Ag octahedron nanoparticles are assembled with graphene oxide (GO) sheets to form Ag octahedron@GO hybrids. Owing to the excellent chemical enhancement of GO, single particle SERS demonstrates an enhancement factor of 9 × 10⁵, which is twice as large as that of a pure octahedron.

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34

Gatehouse, BM, and SN Platts. "The Structures of Some Zirconium(IV) Chromium(III) Basic Sulfates Containing New Heteropolyanions." Australian Journal of Chemistry 46, no. 1 (1993): 1. http://dx.doi.org/10.1071/ch9930001.

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Three complexes (A)-(C), MI4 [Zr6Cr4O8(OH)8(SO4)8(H2O)4].yH2O, where MI4 is Cs2.78- Na1.22 (A), Na4 (B) or not present (C), in which (A) and (B) contain the same ZrIV-CrIII heteropolyanion and (C) contains a structural isomer of it, have been crystallographically characterized with varying degrees of refinement. A fourth complex (D), [Zr6Cr4O8(OH)8(SO4)5(DL-α-Ala)4(H2O)4]n+ hydrate, in which some of the sulfate groups that form part of the heteropolyanion have been replaced by alanine (Ala) molecules, is also described. The heteropolyanion [it has 4 crystallographic symmetry in (A), no symmetry in (B)] is best described as an octahedron of eight-coordinate ZrIV ions (intermediate between square-antiprismatic and dodecahedral stereochemistry) with CrIII octahedra and sulfate tetrahedra bound to it. In (C), two CrIII octahedra and two sulfate groups have been rotated with respect to the octahedron of zirconium ions leaving an unsymmetrical heteropolyanion, while in (D) the heteropolyanion has twofold symmetry and is similar to that in (A) and (B) except for the presence of alanine in place of some sulfate groups.

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35

Afanasiev, Valentin, Sargylana Ugapeva, Yuri Babich, Valeri Sonin, Alla Logvinova, Alexander Yelisseyev, Sergey Goryainov, Alexey Agashev, and Oksana Ivanova. "Growth Story of One Diamond: A Window to the Lithospheric Mantle." Minerals 12, no. 8 (August 20, 2022): 1048. http://dx.doi.org/10.3390/min12081048.

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A diamond plate cut out of a transparent, colorless octahedral diamond crystal of gem quality, with a small chromite inclusion in the core, sampled from the XXIII CPSU Congress kimberlite (Yakutia, Mirny kimberlite field, vicinities of Mirny city), has been studied by several combined methods: absorption spectroscopy at different wavelengths (UV-visible, near- and mid-IR); photoluminescence, cathodoluminescence, and Raman spectroscopy (local version) and lattice strain mapping; birefringence in cross-polarized light; and etching. The diamond plate demonstrates a complex growth history consisting of four stages: nucleation and growth to an octahedron → habit change to a cuboid → habit change to octahedron-1 → habit change to octahedron-2. The growth history of the diamond records changes in the crystallization conditions at each stage. The revealed heterogeneity of the crystal structure is associated with the distribution and speciation of nitrogen defects. The results of this study have implications for the information value of different techniques as to the diamond structure defects, as well as for the as yet poorly known evolution of the subcontinental lithospheric mantle in the Siberian craton, recorded in the multistage growth of the diamond crystal. At the time of writing, reconstructing the conditions for each stage is difficult. Meanwhile, finding ways for such reconstruction is indispensable for a better understanding of diamond genesis, and details of the lithosphere history.

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36

Şenel, Güzide, Jeong-Gon Lee, and Kul Hur. "Distance and Similarity Measures for Octahedron Sets and Their Application to MCGDM Problems." Mathematics 8, no. 10 (October 1, 2020): 1690. http://dx.doi.org/10.3390/math8101690.

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In this paper, in order to apply the concept of octahedron sets to multi-criteria group decision-making problems, we define several similarity and distance measures for octahedron sets. We present a multi-criteria group decision-making method with linguistic variables in octahedron set environment. We give a numerical example for multi-criteria group decision-making problems.

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37

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 (January 20, 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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38

Reinauer, F., and R. Glaum. "Ideal and Real Structure of Ti5O4(PO4)4: X-ray and HRTEM Investigations." Acta Crystallographica Section B Structural Science 54, no. 6 (December 1, 1998): 722–31. http://dx.doi.org/10.1107/s0108768198003590.

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The crystal structure of pentatitanium tetraoxide tetrakis(phosphate), Ti5O4(PO4)4, has been determined and refined from X-ray diffraction single-crystal data [P212121 (No. 19), Z = 4, a = 12.8417 (12), b = 14.4195 (13), c = 7.4622 (9) Å (from Guinier photographs); conventional residual R 1 = 0.042 for 2556 Fo > 4σ(Fo ), R 1 = 0.057 for all 3276 independent reflections; 282 parameters; 29 atoms in the asymmetric unit of the ideal structure]. The structure is closely related to those of β-Fe2O(PO4)-type phosphates and synthetic lipscombite, Fe3(PO4)4(OH). While these consist of infinite chains of face-sharing MO6 octahedra, in pentatitanium tetraoxide tetrakis(phosphate) only five-eighths of the octahedral voids are occupied according to □3Ti5O4(PO4)4. Four of the five independent Ti4+O6 show high radial distortion [1.72 ≤ d(Ti−O) ≤ 2.39 Å] and a typical 1 + 4 + 1 distance distribution. The fifth Ti4+O6 is an almost regular octahedron [1.91 ≤ d(Ti−O) ≤ 1.98 Å]. Partial disorder of Ti4+ over the available octahedral voids is revealed by the X-ray structure refinement. High-resolution transmission electron microscopy (HRTEM) investigations confirm this result.

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39

Balić-Žunić, Tonči, Martha G. Pamato, and Fabrizio Nestola. "Redetermination and new description of the crystal structure of vanthoffite, Na6Mg(SO4)4." Acta Crystallographica Section E Crystallographic Communications 76, no. 6 (May 1, 2020): 785–89. http://dx.doi.org/10.1107/s2056989020005873.

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The crystal structure of vanthoffite {hexasodium magnesium tetrakis[sulfate(VI)]}, Na6Mg(SO4)4, was solved in the year 1964 on a synthetic sample [Fischer & Hellner (1964). Acta Cryst. 17, 1613]. Here we report a redetermination of its crystal structure on a mineral sample with improved precision. It was refined in the space group P21/c from a crystal originating from Surtsey, Iceland. The unique Mg (site symmetry \overline{1}) and the two S atoms are in usual, only slightly distorted octahedral and tetrahedral coordinations, respectively. The three independent Na atoms are in a distorted octahedral coordination (1×) and distorted 7-coordinations intermediate between a `split octahedron' and a pentagonal bipyramid (2×). [MgO6] coordination polyhedra interchange with one half of the sulfate tetrahedra in <011> chains forming a (100) meshed layer, with dimers formed by edge-sharing [NaO7] polyhedra filling the interchain spaces. The other [NaO7] polyhedra are organized in a parallel layer formed by [010] and [001] chains united through edge sharing and bonds to the remaining half of sulfate groups and to [NaO6] octahedra. The two types of layers interconnect through tight bonding, which explains the lack of morphological characteristics typical of layered structures.

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40

Levin, Igor, and Leonid A. Bendersky. "Symmetry classification of the layered perovskite-derived A n B n X 3n+2 structures." Acta Crystallographica Section B Structural Science 55, no. 6 (December 1, 1999): 853–66. http://dx.doi.org/10.1107/s0108768199005479.

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The effects of combinations of octahedral tilts on the symmetries of layered A n B n X 3n+2 structures were considered. Two complementary approaches were used to deduce the symmetries. The space groups associated with different tilt systems were determined for structures with different layer thicknesses (n values) and for structures with different layer stacking arrangements. For the most symmetrical tilts about the orthorhombic axes of the A n B n X 3n+2 structure, maximal group/subgroup relations were established. Comparison of these results with experimental data available in the literature suggests that the symmetries of most observed A n B n X 3n+2 compounds are fully determined by the tilt systems adopted by rigid BX 6 octahedra. The most common tilt system observed at room temperature is a combination of an in-phase tilt about an orthorhombic axis parallel to the pseudo-fourfold axis of the octahedron with a tilt about an orthorhombic axis perpendicular to the layers.

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41

Hohn, Frauke, Heinrich Billetter, Ingo Pantenburg, and Uwe Ruschewitz. "Ni(C2(COO)2)(H2O)4 · 2 H2O und Ni(C2(COO)2)(H2O)2: zwei Koordinationspolymere mit dem Acetylendicarboxylat-Dianion / Ni(C2(COO)2)(H2O)4 · 2 H2O and Ni(C2 (COO)2)(H2O)2: Two Co-ordination Polymers of the Acetylenedicarboxylate Dianion." Zeitschrift für Naturforschung B 57, no. 12 (December 1, 2002): 1375–81. http://dx.doi.org/10.1515/znb-2002-1206.

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From a solution of Ni(CH3COO)2 ∙ 4 H2O and acetylenedicarboxylic acid in deionized water single crystals of Ni(C2(COO)2)(H2O)4 ∙ 2 H2O(P21/a, Z = 2, isotypic to Co(C2(COO)2)(H2O)4 ∙ 2 H2O) were obtained by slow evaporation of the solvent. In the solid state structure nickel is octahedrally surrounded by four water molecules and two oxygen atoms of the carboxylate anions. These octahedra are connected to chains by the dicarboxylates. Heating the hexahydrate to 100 °C in a stream of argon leads to Ni(C2(COO)2)(H2O)2 (C2/c, Z = 4, isotypic to Mn[C2(COO)2] ∙ 2 H2O). Here, the NiO6 octahedron is built by two water molecules and four oxygen atoms of the dicarboxylate ligands, which connect the Ni octahedra to a three-dimensional network. Thermoanalytical investigations show another mass loss at about 200 °C, which leads to non-crystalline products. Finally, at about 400 °C NiO is formed. Measurements of the magnetic susceptibilities result in the expected behaviour for Ni2+ in an octahedral co-ordination (3A2 ground state). The effective magnetic moment at room temperature is μeff = 3.20 μB.

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42

Chen, Lei, Hui-Yuan Wang, Dan Luo, Hua-Yuan Zhang, Bo Liu, and Qi-Chuan Jiang. "Synthesis of octahedron and truncated octahedron primary Mg2Si by controlling the Sb contents." CrystEngComm 15, no. 9 (2013): 1787. http://dx.doi.org/10.1039/c2ce26649k.

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43

Fernández-Ruiz, Manuel Alejandro, Enrique Hernández-Montes, and Luisa María Gil-Martín. "The Octahedron family as a source of tensegrity families: The X-Octahedron family." International Journal of Solids and Structures 208-209 (January 2021): 1–12. http://dx.doi.org/10.1016/j.ijsolstr.2020.10.019.

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44

Suzuki, K. "Approximate model for the crystal structure of precipitates in NaF doped with AlF3." Acta Crystallographica Section A Foundations of Crystallography 49, no. 6 (November 1, 1993): 846–53. http://dx.doi.org/10.1107/s0108767393004520.

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The crystal structure of precipitates in a mixed crystal of NaF and 1 mol% AlF3 has been studied at room temperature using both stationary-crystal and rotating-crystal X-ray photographic methods. It has been found that almost all the reflections can be assigned to a face-centered-cubic (f.c.c.) lattice with unit-cell parameter 7.77 Å. The main feature of the diffraction pattern is that the 311 reflection is very strong while the 222 reflection is practically zero, in contrast to the case of high-form cryolite, i.e. cubic Na3AlF6. These features are explained by assuming an f.c.c. arrangement of AlF6 octahedra that are rotated around the 〈111〉 axes by about 47° from the highest-symmetry orientation. It has also been shown that the F ions in each octahedron make large overlaps with the Al ion at the center of the octahedron. A random distribution of rotation axes is also proposed to conform to the cubic symmetry of the lattice structure of the precipitate.

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45

Brynda, Jiří, Bohumil Kratochvíl, and Ivana Císařová. "The determination of crystal structure of chromium(II) phosphite dihydrate, CrHPO3 2 H2O." Collection of Czechoslovak Chemical Communications 52, no. 7 (1987): 1742–47. http://dx.doi.org/10.1135/cccc19871742.

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The crystal structure of CrHPO3.2 H2O has been solved by the heavy atom method. The compound crystallizes in the orthorhombic space group P212121 with the unit cell parameters a = 679·25(8), b = 915·61(8), c = 752·2(1) pm, Z = 4. The structure was refined to the final reliability factor R = 0·043 for 1 040 observed reflexions (I > 1·96σ(I)). The structure consists of chains formed by CrO6 octahedra connected each other in vertices. The chains are interconnected by phosphite tetrahedra HPO3. Hydrogen bridges of water-phosphite tetrahedron and water-water types form space cross-linking of the whole structure. Bond distances Cr-O in the tetragonally distorted octahedron range from 201·2 to 304·9 pm. The interatomic distances P-O in phosphite tetrahedron are between 152·1 and 152·7 pm. The degree of the distorsion DISQ of HPO3 tetrahedron and CrO6 octahedron is discussed on the basis of known structures of phosphites and chromium(II) compounds.

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46

Sheldrick, W. S., and J. Kiefer. "Trioktaedrische Halogenoarsenate(III) [As3X12]3− (X = Br, I) mit Ecken- und Flächenverknüpfung. Strukturkorrelation für Iodoarsenate(III) / Trioctahedral Haloarsenates(III) [As3X12]3− (X = Br, I) with Vertex and Face Sharing. Structural Correlation for Iodoarsenates(III)." Zeitschrift für Naturforschung B 47, no. 8 (August 1, 1992): 1079–84. http://dx.doi.org/10.1515/znb-1992-0805.

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The haloarsenates(III) [Et3NH]3[As3Br12] (1) and [Me3NH]3[As3I12] (2) have been prepared and their structures established by X-ray analysis. Both trioctahedral anions display a novel structure in which a central AsX6 octahedron shares two faces with a common vertex with two terminal AsX6 octahedra. The bridging As–X-bonds in the latter building units are markedly longer than the opposite terminal As–X-bonds in both anions. For example, the former As–I-bonds in [As3I12]3− lie in the range 3.154(1)-3.400(1)A, the latter As – I-bonds between 2.581(1) and 2.656(1)A. The distortion of the central AsX6 octahedron is less marked for both anions, e.g. the As–I distances in [As3I12]3− lie in this central polyhedron between 2.706(1) and 3.048(1) A. Using the results for (2) and for other characterised anions, a structural correlation is presented for 28 trans-sited As–I bond distances in iodoarsenates(III).

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47

WU, S. Y., J. S. YAO, H. M. ZHANG, and G. D. LU. "INVESTIGATIONS ON THE EPR g FACTORS FOR THE SIX-COORDIANTED Cu2+(1) SITE IN YBa2Cu3O6+x." International Journal of Modern Physics B 21, no. 18n19 (July 30, 2007): 3250–53. http://dx.doi.org/10.1142/s0217979207044305.

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The EPR g factors g // and g ⊥ for the six-coordinated Cu 2+(1) site in YBa 2 Cu 3 O 6+x are theoretically investigated from the perturbation formulas for a 3 d 9 ion in tetragonally elongated octahedra. The related tetragonal crystal-field parameters Ds and Dt are determined from the superposition model and the structural data for the Cu 2+(1) site, by considering the effective elongation of the oxygen octahedron due to the Jahn-Teller effect of the Cu 2+ cluster. Based on the calculations, the effective elongation (≈ 15%) of the ligand octahedron is obtained for the signals at 100K. As for the EPR signals at room temperature, the elongation declines to merely 4%, corresponding to the smaller anisotropy Δ g (= g // - g ⊥). The theoretical results for the g factors are in good agreement with the observed values, and the local tetragonal distortion due to the Jahn-Teller effect is discussed.

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48

Cui, Zixiang, Yidi Xue, Yongqiang Xue, Mengying Wang, Jiaojiao Chen, Bo Teng Ji, Chenyu Wang, and Lu Zhang. "Shape- and size-dependent desorption kinetics and surface acidity of nano-SnO₂." New Journal of Chemistry 46, no. 4 (2022): 1608–20. http://dx.doi.org/10.1039/d1nj05540b.

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49

Shu, Zhengxiang, Can Shen, Anhuai Lu, and Xiangping Gu. "Chemical Composition and Crystal Structure of Kenoargentotetrahedrite-(Fe), Ag6Cu4Fe2Sb4S12, from the Bajiazi Pb-Zn Deposit, Liaoning, China." Crystals 12, no. 4 (March 27, 2022): 467. http://dx.doi.org/10.3390/cryst12040467.

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Kenoargentotetrahedrite-(Fe) is observed as greenish-grey anhedral grains, 50–150 μm in size, in association with galena, sphalerite and chalcopyrite in the Bajiazi Pb-Zn deposit of magmatic-hydrothermal type, Liaoning, China. The empirical formula from electron microprobe analyses is Ag5.50Cu4.17Fe1.75Zn0.31Sb3.96As0.04S12.08, corresponding to the ideal formula Ag6Cu4Fe2Sb4S12. The crystal structure of kenoargentotetrahedrite-(Fe) has been determined and refined by single-crystal X-ray diffraction with R1 = 0.0192 for 1866 (404 unique) reflections. It is cubic, space group I4¯3m with unit cell parameters a = 10.4928(2) Å, V = 1155.26(7) Å3 and Z = 2. The structure of kenoargentotetrahedrite-(Fe) is characterized by a poor occupancy of 0.05 of the octahedral S(2) site with the S(2)-M(2) bonding length of 1.9994(8) Å. The six Ag atoms at M(2) around S(2) form an octahedron cluster (Ag6)4+ with the valence state of +4 and Ag-Ag distance of 2.8276(1) Å. The structure is identical to that by Rozhdestvenskaya et al., being composed of a collapsed sodalite-like framework of corner-connected M(1)S4 tetrahedron forming cages containing M(2)6-octahedron cluster, encircled by four SbS3 trigonal pyramids. It is related to the tetrahedrite group minerals with the existence of the (Ag6)4+ cluster replacing the S(2)-centered Ag6 octahedron according to the substitution mechanism 6M(2)Ag+ + S(2)S2−=M(2)(Ag6)4+ + S(2) S.

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50

Kampf, A. R., F. Colombo, and J. González del Tánago. "Carlhintzeite, Ca2AlF7·H2O, from the Gigante granitic pegmatite, Córdoba province, Argentina: description and crystal structure." Mineralogical Magazine 74, no. 4 (August 2010): 623–32. http://dx.doi.org/10.1180/minmag.2010.074.4.623.

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AbstractCarlhintzeite, Ca2AlF7·H2O, has been found at the Gigante pegmatite, Punilla Department, Córdoba Province, Argentina. It occurs as colourless prismatic crystals up to 0.8 mm long, ubiquitously twinned on {001}. Electron microprobe analyses provided the empirical formula Ca1.98Al1.02F6.24(OH)0.76·H1.62O. A crystal fragment used for the collection of structure data provided the triclinic, C1̄ cell: a = 9.4227(4), b = 6.9670(5), c = 9.2671(7) Å, α = 90.974(6), β = 104.802(5), γ = 90.026(6)°, V = 558.08(7) Å3 and Z = 4. The crystal structure, solved by direct methods and refined to R1 = 0.0322 for 723 Fo > 4σF reflections, is made up of linkages of AlF6 octahedra, CaF8 polyhedra and CaF6(H2O)2 polyhedra. The AlF6 octahedra are isolated from one another, but share polyhedral elements with Ca polyhedra. Most notably, the Al1 octahedron shares trans faces with two CaF8 polyhedra and the Al2 octahedron shares trans edges with two CaF6(H2O)2 polyhedra. The linkage of the Ca polyhedra alone can be described as a framework in which edge-sharing chains along b are cross-linked by edge-sharing. Edge-sharing chains of Ca polyhedra along b in the carlhintzeite structure are similar to those along c in the structures of gearksutite, CaAlF4(OH)·(H2O), and prosopite, CaAl2F4(OH)4.

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