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Journal articles on the topic 'TRIGONAL LATTICES'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Kontrym-Sznajd, G., and M. Samsel-Czekała. "Special directions in momentum space. II. Hexagonal, tetragonal and trigonal symmetries." Journal of Applied Crystallography 45, no. 6 (2012): 1254–60. http://dx.doi.org/10.1107/s0021889812041283.

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This paper is a continuation of a previous one,Special directions in momentum space. I. Cubic symmetries[Kontrym-Sznajd & Samsel-Czekała (2011).J. Appl. Cryst.44, 1246–1254], where new sets of special directions (SDs), having the full symmetry of the Brillouin zone, were proposed for cubic lattices. In the present paper, such directions are derived for structures with unique six-, four- and threefold axes,i.e.hexagonal, tetragonal and trigonal lattices, for both two- and three-dimensional space. The SDs presented here allow for construction, in the whole space, of anisotropic quantities fr

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2

Essén, Hanno, and Arne Nordmark. "Some results on the electrostatic energy of ionic crystals." Canadian Journal of Chemistry 74, no. 6 (1996): 885–91. http://dx.doi.org/10.1139/v96-097.

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We define a class of ionic cyrstals, the alternating Bravais lattice ionic crystals, which has the NaCl and CsCl structures as members. We calculate the electrostatic energy of finite pieces and study the convergence to the macroscopic Madelung limit. For the one-parameter family of trigonal lattices we calculate the dependence of the electrostatic energy on the parameter. The NaCl and CsCl structures correspond to minima, the CsCl minimum being deeper. This is due to long-range effects; for small clusters the NaCl structure is favored. We also study the Madelung constant of simple cubic latti

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3

Takeshita, T., C. Tomé, H. R. Wenk, and U. F. Kocks. "Single-crystal yield surface for trigonal lattices: Application to texture transitions in calcite polycrystals." Journal of Geophysical Research 92, B12 (1987): 12917. http://dx.doi.org/10.1029/jb092ib12p12917.

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4

Beattie, JK, SP Best, FH Moore, BW Skelton та AH White. "Water Molecule Dispositions in the Cesium Sulfate α- and β-Alums: Single-Crystal Neutron Diffraction Studies of CsM(SO4)2.12H2O (M=V, Rh)". Australian Journal of Chemistry 46, № 9 (1993): 1337. http://dx.doi.org/10.1071/ch9931337.

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Room-temperature single-crystal neutron diffraction studies are recorded for two alums, Cs( Rh /V)(SO4)2.12H2O [cubic, Pa3, a 12.357(5) ( Rh ), 12.434(1)Ǻ (V)], residuals 0.037 and 0.068 for 328 and 164 'observed' reflections, with the intention of defining water molecule hydrogen atom orientations. Whereas the two tervalent hexaaqua cations are similar in size [ rM -O = 2.010(6)Ǻ (M = V) and 2.006(2)Ǻ (M = Rh )] the vanadium salt adopts the β alum modification while rhodium gives an α alum. Significantly, the water coordination geometry is different in the two cases with the tilt angle betwee

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5

Kayalvizhi, M., and L. John Berchmans. "Combustion Synthesis of Lanthanum Substituted LiNiO2Using Hexamine as a Fuel." E-Journal of Chemistry 7, s1 (2010): S137—S142. http://dx.doi.org/10.1155/2010/467818.

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Lithium nickelate and its lanthanum substituted compound have been successfully prepared by combustion synthesis process using LiNO3, Ni(NO3)2.6H2O and La(NO3)3.6H2O. Hexamine is used as fuel. The physicochemical properties of the powders were investigated by thermal analysis (TGA/DTA). The crystalline powders were characterized for their phase identification using x-ray diffraction analysis (XRD). FT-IR spectroscopy was used to study the local structure of the oxide environment. The morphological features of the powders were characterized by scanning electron microscopy (SEM). DTA analysis re

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6

Janner, A. "Symmetry-adapted digital modeling I. Axial symmetric proteins." Acta Crystallographica Section A Foundations and Advances 72, no. 3 (2016): 298–311. http://dx.doi.org/10.1107/s2053273316002746.

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Considered are axial symmetric proteins exemplified by the octameric mitochondrial creatine kinase, the Pyr RNA-binding attenuation protein, the D-aminopeptidase and the cyclophilin A–cyclosporin complex, with tetragonal (422), trigonal (32), pentagonal (52) and pentagonal (52) point-group symmetry, respectively. One starts from the protein enclosing form, which is characterized by vertices at points of a lattice (the form lattice) whose dimension depends on the point group. This allows the indexing of Cα's at extreme radial positions. The indexing is extended to additional residues on the bas

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7

Yang, X. L., L. Z. Cai, Y. R. Wang, and Q. Liu. "Interference of four umbrellalike beams by a diffractive beam splitter for fabrication of two-dimensional square and trigonal lattices." Optics Letters 28, no. 6 (2003): 453. http://dx.doi.org/10.1364/ol.28.000453.

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8

Yang, X. L., L. Z. Cai, Y. R. Wang, and Q. Liu. "Interference technique by three equal-intensity umbrellalike beams with a diffractive beam splitter for fabrication of two-dimensional trigonal and square lattices." Optics Communications 218, no. 4-6 (2003): 325–32. http://dx.doi.org/10.1016/s0030-4018(03)01231-8.

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9

Grabner and Modec. "Zn(II) Curcuminate Complexes with 2,2’-bipyridine and Carboxylates." Molecules 24, no. 14 (2019): 2540. http://dx.doi.org/10.3390/molecules24142540.

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Two novel zinc(II) compounds with curcuminate (abbreviated as cur–), [Zn(CH3COO)(cur)(bpy)](1)·CH3OH·2H2O (bpy = 2,2’-bipyridine) and [Zn(PhCOO)(cur)(bpy)] (2)·CH3OH, have been synthesized and characterized. Their composition has been determined by single-crystal X-ray structure analysis. Complexes 1 and 2 are similar: in both a five-fold coordination environment of zinc(II) consists of a monodentate carboxylate, a chelating bidentate 2,2’-bipyridine, and curcuminate, which is bound via a deprotonated 1,3-dione moiety. In 1, 2,2’-bipyridine nitrogen atoms and curcuminate oxygen atoms form the

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10

Hirakawa, Satoru, and Hisashi Honda. "1H and 13C NMR and Electrical Conductivity Studies on New Ionic Plastic Crystals of Tetraalkylammonium Tetraethylborate." Zeitschrift für Naturforschung A 70, no. 7 (2015): 521–28. http://dx.doi.org/10.1515/zna-2015-0105.

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AbstractEight plastic crystals of the types NEtxMe(4 − x)BEt4 and NEtyPr(4 − y)BEt4 (x=0–4, y=1–3) were found in a new region of ionic plastic crystals. In this area, globular cations and anions are assembled by weak interactions. Based on the results of solid-state 1H and 13C nuclear magnetic resonance (NMR) measurements, it was revealed that the ions performed isotropic reorientations in the NEtxMe(4–x)BEt4 crystals (x=0–4). Additionally, X-ray diffraction (XRD) of these compounds was able to identify the CsCl-type cubic structure. In contrast, the XRD reflections of NEtyPr(4−y)BEt4 (y=1–3)

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11

Snow, MR, and ERT Tiekink. "An X-Ray Crystallographic Study of Tris(O-Methyl Dithiocarbonato)-Arsenic(III), Tris(O-Methyl Dithiocarbonato)-Antimony(III) and Tris(O-Methyl Dithiocarbonato)-Bismuth(III)." Australian Journal of Chemistry 40, no. 4 (1987): 743. http://dx.doi.org/10.1071/ch9870743.

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The crystal structures of the methylxanthates of AsIII (two polymorphs), sbIII and BiIII are reported. In the monoclinic form of As(S2COCH3)3 the molecular threefold symmetry, as found in the previously reported trigonal As(S2COCH3)3, is not crystallographically imposed. The distorted octahedral environments about each of the ASIII centres is defined by three asymmetrically chelating xanthate ligands. In contrast, the sbIIIand BiIII analogues adopt different stereochemistries based on pseudo-m symmetry. In addition, the Sb (S2COCH3)3 and Bi(S2COCH3)3 molecules associate to form loosely held di

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12

Matsutani, Shigeki. "Trigonal Toda Lattice Equation." Journal of Nonlinear Mathematical Physics 27, no. 4 (2020): 697–704. http://dx.doi.org/10.1080/14029251.2020.1819622.

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13

Welch, Mark D., Jens Najorka, Michael S. Rumsey, and John Spratt. "The Hexagonal ↔ Orthorhombic Structural Phase Transition in Claringbullite, Cu4FCl(OH)6." Canadian Mineralogist 59, no. 1 (2021): 265–85. http://dx.doi.org/10.3749/canmin.2000041.

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ABSTRACT Frustrated magnetic phases have been a perennial interest to theoreticians wishing to understand the energetics and behavior of quasi-chaotic systems at the quantum level. This behavior also has potentially wide applications to developing quantum data-storage devices. Several minerals are examples of such phases. Since the definition of herbertsmithite, Cu3ZnCl2(OH)6, as a new mineral in 2004 and the rapid realization of the significance of its structure as a frustrated antiferromagnetic phase with a triangular magnetic lattice, there has been intense study of its magnetic properties

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14

Zhang, Zhi Hong, Shao Yi Wu, Xue Feng Wang, and Yue Xia Hu. "Studies of the Spin Hamiltonian Parameters for NiX₂ and CdX₂:Ni²⁺ (X=Cl, Br)." Defect and Diffusion Forum 282 (January 2009): 25–30. http://dx.doi.org/10.4028/www.scientific.net/ddf.282.25.

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The spin Hamiltonian parameters (zero-field splitting D and the g factors) for NiX2 and CdX2:Ni2+ (X=Cl, Br) are quantitatively investigated from the perturbation formulas of these parameters for a 3d8 ion in trigonally distorted octahedra based on the cluster approach. In the calculations, the trigonal field parameters  and ′ are determined from the superposition model and the local structures of Ni2+ in the halides. The theoretical g factors show reasonable agreement with the observed values, and the experimental D for CdX2:Ni2+ are also interpreted by considering suitable lattice distort

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15

Pekov, I. V., V. O. Yapaskurt, Y. S. Polekhovsky, M. F. Vigasina, and O. I. Siidra. "Ekplexite (Nb,Mo)S2·(Mg1−xAlx)(OH)2+x, kaskasite (Mo,Nb)S2·(Mg1−xAlx)(OH)2+x and manganokaskasite (Mo,Nb)S2·(Mn1−xAlx)(OH)2+x, three new valleriite-group mineral species from the Khibiny alkaline complex, Kola peninsula, Russia." Mineralogical Magazine 78, no. 3 (2014): 663–79. http://dx.doi.org/10.1180/minmag.2014.078.3.14.

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AbstractThree new valleriite-group minerals, ekplexite (Nb,Mo)S2·(Mg1−xAlx)(OH)2+x, kaskasite (Mo,Nb)S2·(Mg1−xAlx)(OH)2+x and manganokaskasite (Mo,Nb)S2·(Mn1−xAlx)(OH)2+x are found at Mt Kaskasnyunchorr, Khibiny alkaline complex, Kola Peninsula, Russia. They occur in fenite consisting of orthoclase−anorthoclase and nepheline with fluorophlogopite, corundum, pyrrhotite, pyrite, rutile, monazite-(Ce), graphite, edgarite, molybdenite, tungstenite, alabandite, etc. Ekplexite forms lenticular nests up to 0.2 mm × 1 mm × 1 mm consisting of near-parallel, radiating or chaotic aggregates of flakes. Ka

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16

Sowa, Heidrun, and Elke Koch. "Hexagonal and trigonal sphere packings. IV. Trivariant lattice complexes of trigonal space groups." Acta Crystallographica Section A Foundations of Crystallography 62, no. 5 (2006): 379–99. http://dx.doi.org/10.1107/s0108767306024159.

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17

Wu, Shao-Yi, Xiu-Ying Gao, and Hui-Ning Dong. "Theoretical Study of the Local Lattice Distortion at the Trigonal Cr3+ Center in BiI3." Zeitschrift für Naturforschung A 61, no. 1-2 (2006): 78–82. http://dx.doi.org/10.1515/zna-2006-1-212.

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The local lattice distortion at the trigonal Cr3+ center in BiI3 is theoretically studied by the perturbation formulas of the EPR parameters for a 3d3 ion in trigonal symmetry, based on the cluster approach. In these formulas the contributions from the s-orbitals of the ligands, which were often ignored, are taken into account. It is found that the local angle β (between the direction of the impurityligand bonding R and the C3 axis) in the impurity center is smaller than the host angle βH in the pure crystal. The calculated EPR parameters are improved compared to those in absence of the ligand

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18

Geng, Xianguo, and Xin Zeng. "Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy." Reviews in Mathematical Physics 29, no. 08 (2017): 1750025. http://dx.doi.org/10.1142/s0129055x17500258.

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Utilizing the characteristic polynomial of Lax matrix for the Belov–Chaltikian (BC) lattice hierarchy associated with a [Formula: see text] discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker–Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and th

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19

Chan, Eric J., Jack M. Harrowfield, Brian W. Skelton, Alexandre N. Sobolev, and Allan H. White. "Structural Systematics of Lanthanide(III) Picrate Solvates: Hexamethylphosphoramide and Octamethylpyrophosphoramide Adducts." Australian Journal of Chemistry 73, no. 6 (2020): 477. http://dx.doi.org/10.1071/ch19251.

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Crystalline products of the reactions of lanthanide picrates, Ln(pic)3 (pic=2,4,6-trinitrophenoxide), with hexamethylphosphoramide (hmpa) and octamethylpyrophosphoramide (ompa) have been characterised by single-crystal X-ray diffraction studies. With hmpa and lighter lanthanides (La, Sm, Eu), isomorphous species (monoclinic, P21/c, Z 4) of stoichiometry [Ln(pic)3(hmpa)3]·0.5H2O, have been defined where the molecular units in the lattice contain 9-coordinate Ln with tricapped trigonal-prismatic coordination geometry. The picrate ligands are bidentate through phenoxide-O and 2-nitro-O, with the

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20

Li, Chong, Kyung-Hwan Jin, Shuai Zhang, Fei Wang, Yu Jia, and Feng Liu. "Formation of a large gap quantum spin Hall phase in a 2D trigonal lattice with three p-orbitals." Nanoscale 10, no. 12 (2018): 5496–502. http://dx.doi.org/10.1039/c7nr09067f.

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21

Kazin, Pavel E., Mikhail A. Zykin, Lev A. Trusov, et al. "A Co-based single-molecule magnet confined in a barium phosphate apatite matrix with a high energy barrier for magnetization relaxation." Chemical Communications 53, no. 39 (2017): 5416–19. http://dx.doi.org/10.1039/c7cc02453c.

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22

Du, Shaowu, Meiyan Cui, and Zhangzhen He. "A pentanuclear {Co5} cluster motif forming a capped breathing kagomé lattice." Chemical Communications 57, no. 54 (2021): 6616–19. http://dx.doi.org/10.1039/d1cc01987b.

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23

Saitow, Akihiro, Akira Yoshikawa, Hiroyuki Horiuchi, et al. "Structural Change Caused by Substitution of Nd for Sm in (Nd, Sm)AlO3: Application of Synchrotron High-Resolution Powder X-ray Diffraction." Journal of Applied Crystallography 31, no. 5 (1998): 663–71. http://dx.doi.org/10.1107/s0021889898001629.

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Structural change caused by substitution of Nd for Sm in perovskite (Nd, Sm)AlO3was analysed by application of high-resolution powder X-ray diffraction using synchrotron radiation. The parallel, well monochromated and bright incident X-rays improved the full width at half-maximum (FWHM) to 0.027° in a wide 2θ range for the standard Si powder. Applying this high-resolution optical system, the lattice parameters of the solid solution (Ndx, Sm_{1-x})AlO3were precisely analysed for the phases fromx = 0.0 to 1.0 with an interval of 0.2. The lattice parameters of a series ofRAlO3vary systematically

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24

Choy, Jin-Ho, Young-Il Kim, Seong-Ju Hwang, and Pham V. Huong. "Trigonal Planar (D3h) AuI3Complex Stabilized in a Solid Lattice." Journal of Physical Chemistry B 104, no. 31 (2000): 7273–77. http://dx.doi.org/10.1021/jp000490h.

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25

Moorthy, Jarugu Narasimha, Palani Natarajan, Alankriti Bajpai, and Paloth Venugopalan. "Trigonal Rigid Triphenols: Self-Assembly and Multicomponent Lattice Inclusion." Crystal Growth & Design 11, no. 8 (2011): 3406–17. http://dx.doi.org/10.1021/cg200074z.

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26

Sowa, H., and E. Koch. "Hexagonal and trigonal sphere packings. II. Bivariant lattice complexes." Acta Crystallographica Section A Foundations of Crystallography 60, no. 2 (2004): 158–66. http://dx.doi.org/10.1107/s010876730400162x.

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27

Zheng, Wen-Chen, Qing Zhou, Xiao-Xuan Wu, and Yang Mei. "Theoretical Investigations of the EPR Parameters of Ti3+ in Beryl Crystal." Zeitschrift für Naturforschung A 61, no. 5-6 (2006): 286–88. http://dx.doi.org/10.1515/zna-2006-5-612.

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The EPR parameters (g factors gII, g⊥ and hyperfine structure constants AII, A⊥) of Ti3+ ion at the sixfold coordinated Al3+ site with trigonal symmetry in beryl crystal are calculated by the thirdorder perturbation formulas of 3d1 ions in a trigonal octahedron. In the calculations, the crystal-field parameters are obtained by the superposition model, and the impurity-induced local lattice relaxation (which is similar to that found for Fe3+ in beryl) is considered. The calculated EPR parameters (and also the optical spectra) are in reasonable agreement with the experimental values

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28

Tillmann, Jan, Hans-Wolfram Lerner, and Michael Bolte. "Two ammonium tetrachloridoaluminate salts: how a twinned orthorhombic structure emulates a trigonal crystal system." Acta Crystallographica Section C Structural Chemistry 70, no. 12 (2014): 1092–95. http://dx.doi.org/10.1107/s2053229614022621.

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We have determined the crystal structures of two tetrachloridoaluminate salts. Tetrabutylammonium tetrachloridoaluminate benzene hemisolvate, (C16H36N)[AlCl4]·0.5C6H6, (I), crystallizes with discrete cations, anions and solvent molecules. The benzene molecule is located on a centre of inversion. The structure of the benzene-free polymorph has been determined previously. Tetraethylammonium tetrachloridoaluminate, (C8H20N)[AlCl4], (II), also crystallizes with discrete cations and anions, and forms crystals which appear trigonal but are actually orthorhombic. With the additional reflections of th

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29

Philip, Thresiamma, C. S. Menon, and K. Indulekha. "Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Lithium Niobate." E-Journal of Chemistry 3, no. 3 (2006): 122–33. http://dx.doi.org/10.1155/2006/842320.

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The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3(lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO3are obtained in the present work. The second and third-order elastic constants are c

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30

Wang, Xuefeng, Yurui Gao, Xi Shen, et al. "Anti-P2 structured Na0.5NbO2and its negative strain effect." Energy & Environmental Science 8, no. 9 (2015): 2753–59. http://dx.doi.org/10.1039/c5ee01745a.

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Layer-structured anti-P2 Na<sub>0.5</sub>NbO<sub>2</sub>composed of NbO<sub>6</sub>trigonal prisms and NaO<sub>6</sub>octahedra shows a negative strain effect: its lattice shrinks upon Na-ion intercalation and expands upon deintercalation.

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31

Haberer, Almut, and Hubert Huppertz. "High-pressure Synthesis and Crystal Structure of the Vanadium Orthoborate VBO3." Zeitschrift für Naturforschung B 63, no. 6 (2008): 713–17. http://dx.doi.org/10.1515/znb-2008-0618.

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The vanadium orthoborate VBO3 was synthesized under high-pressure / high-temperature conditions of 7.5 GPa and 1250 °C in a Walker-type multianvil apparatus. The crystal structure was determined on the basis of single crystal X-ray diffraction data, collected at r. t. The title compound crystallizes in the trigonal calcite structure, space group R3̄c, with the lattice parameters a = 462.0(1) and c = 1450.9(3) pm. Within the trigonal planar BO3 groups, the B-O distance is 138.8(3) pm. The vanadium atoms have a slightly distorted octahedral oxygen coordination (V-O: 202.3(2) pm).

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32

He, Lv, Xiao-Xuan Wu, Wen-Chen Zheng, and Yang Mei. "Investigations of the EPR Parameters and Defect Structures of Two Types of Trigonal Cr3+ Centers in CsMgCl3, CsMgBr3 and CsCdBr3 Crystals." Zeitschrift für Naturforschung A 60, no. 11-12 (2005): 823–26. http://dx.doi.org/10.1515/zna-2005-11-1210.

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The EPR g factors g||, g⊥ and zero-field splitting D of trigonal Cr3+-M+ (M+ = Li+, Cu+, Na+) and Cr3+-VB-M3+ (M3+ = Cr3+, In3+, Sc3+, Y3+, Lu3+; VB denotes the B2+ vacancy) centers in some CsBX3 (B = Mg, Cd; X = Cl, Br) crystals are calculated from high-order perturbation formulas based on the two-spin-orbit coupling parameter model of the 3d3 ion in trigonal symmetry. From the calculations, these EPR parameters are reasonably explained and the local lattice distortions caused by the charge compensators M+ or VB are estimated. The results are discussed.

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33

Ruck, M. "Kristallstruktur und zwillingsbildung der intermetallischen phase β-Bi2Rh". Acta Crystallographica Section B Structural Science 52, № 4 (1996): 605–9. http://dx.doi.org/10.1107/s0108768196003400.

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β-Bi2Rh was prepared from the elements in the presence of iodine. At room temperature the lattice constants of the triclinic centrosymmetric structure are a = 6.743 (1), b = 7.030 (1), c = 7.067 (1) Å, α = 104.76 (1), β = 100.73 (1), γ = 105.79 (I)°. X-ray investigations on a single crystal revealed that each Rh atom is surrounded by seven Bi atoms in a monocapped trigonal prism. The prisms share common rectangular and trigonal faces to build infinite rows of double prisms, which are finally connected into parallel (100) layers. Twinning along [010] is commonly observed, indicating a pseudomon

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34

Clayton, J. D. "Modeling finite deformations in trigonal ceramic crystals with lattice defects." International Journal of Plasticity 26, no. 9 (2010): 1357–86. http://dx.doi.org/10.1016/j.ijplas.2010.01.014.

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35

Rodriguez, Mark A., and David P. Adams. "X-ray powder diffraction data for rhombohedral AlPt." Powder Diffraction 21, no. 4 (2006): 318–19. http://dx.doi.org/10.1154/1.2362854.

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X-ray powder diffraction data for a rhombohedral AlPt phase formed by self-propagating, high-temperature reactions of Al∕Pt bi-layer films are reported. Multilayer Al∕Pt thin film samples, reacted in air or vacuum, transformed into rhombohedral AlPt with space group R-3(148). Indexing and lattice parameter refinement of AlPt powders (generated from thin-film samples) yielded trigonal/hexagonal unit-cell lattice parameters of a=15.623(6) Å and c=5.305(2) Å, Z=39, and V=1121.5 Å3.

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36

Wulff, L., and Hk Müller-Buschbaum. "Isolierte trigonale SrO6 – Prismen verknüpfen Kagome-Netze im Strontium-Manganat(IV)-Tellurat(VI): SrMnTeO6 / Kagomé Layers Connected by Isolated Trigonal SrO6 Prisms in the Strontium Manganate(IV) Tellurate(VI): SrMnTeO6 L." Zeitschrift für Naturforschung B 53, no. 3 (1998): 283–86. http://dx.doi.org/10.1515/znb-1998-0305.

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Abstract Single crystals of the hitherto unknown compound SrMnTeO6 have been prepared from Sr(OH)2 ·8H2O , MnCO3(aq) and TeO2 in air by crystallization below the melt range. X-ray investigations showed hexagonal symmetry, space group D33h -P6̅2m, lattice constants a = 5.143( 1), c = 5.384(2) A, Z = 1. SrMnTeO6 is characterized by staggered [(Mn/Te)6O18] Kagome layers along [001]. These layers are connected by Sr2+ ions, resulting in SrO6 prisms isolated from each other. The structure is discussed with respect to the connection of Kagome nets in the quaternary oxides of the Ba3Ln4O9 type.

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37

Comba, P., and AM Sargeson. "Electron-Paramagnetic-Res Spectroscopy of a Trigonal Prismatic Vanadium Cage Complex - [1,8-Diammonio-3,6,10,13,16,19-hexaazabicyclo-[6.6.6]icosanato(3,6)vanadium(IV)](4+)." Australian Journal of Chemistry 39, no. 7 (1986): 1029. http://dx.doi.org/10.1071/ch9861029.

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An e.p.r . study of the cage complex [VIVdi(amH)sar-2H]4+ gives spin Hamiltonian parameters gX 1.974, gy 1.967, gZ 1.991, giso 1.977, AX 92×10-4 cm-1, Ay 100×10-4 cm-1, AZ 13×10-4 cm-1, Aiso 68×10-4 cm-1, viz. gX ≈ gy < gZ ≈ 2.0 and AX ≈ Ay > AZ. This is consistent with the metal centre approaching a trigonal prismatic environment and a 2A1 (D3) ground state, viz. ...d1/z2. Comparison of the spin Hamiltonian parameters from measurements in frozen and fluid solution, poly(vinyl alcohol) films and dilute powder [VIVdi(amH)sar-2H]4+ doped into the lattice of the protonated ZnII salt over a

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38

Gulay, Nataliya L., Rolf-Dieter Hoffmann, Jutta Kösters, Yaroslav M. Kalychak, Stefan Seidel, and Rainer Pöttgen. "Superstructure formation in the solid solution Sc3Pt3−xIn3 (x = 0–0.93)." Zeitschrift für Kristallographie - Crystalline Materials 236, no. 3-4 (2021): 81–91. http://dx.doi.org/10.1515/zkri-2021-2007.

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Abstract The equiatomic indide ScPtIn (ZrNiAl type, space group P 6 ‾ $&#x203e;{6}$ 2m) shows an extended solid solution Sc3Pt3–xIn3. Several samples of the Sc3Pt3–xIn3 series were synthesized from the elements by arc-melting and subsequent annealing, or directly in a high frequency furnace. The lowest platinum content was observed for Sc3Pt2.072(3)In3. All samples were characterized by powder X-ray diffraction and their lattice parameters and several single crystals were studied on the basis of precise single crystal X-ray diffractometer data. The correct platinum occupancy parameters wer

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Lee, Jeong-Eun, Ulrich Burkhardt, and Alexander Christoph Komarek. "Synthesis of a New Ruthenate Ba26Ru12O57." Crystals 10, no. 5 (2020): 355. http://dx.doi.org/10.3390/cryst10050355.

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Single crystals of Ba 26 Ru 12 O 57 were grown by the floating zone method. The crystal structure is formed by an alternating stacking of pseudo-hexagonal Ru single layers and double layers. The Ru ions within the double layers are dimerized (Ru 2 O 9 ) whereas the Ru ions within the single layers arrange in a distorted Kagome lattice of trigonal bipyramidally coordinated RuO 5 polyhedra. Additionally, this Kagome lattice is “decorated” with RuO 6 octahedra that are situated in the central free spaces within this Kagome lattice. According to the composition, the oxidation state of most of the

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40

Li, Yunkui, G. Aka, A. Kahn-Harari, and D. Vivien. "Phase transition, growth, and optical properties of NdxLa1−xSc3(BO3)4 crystals." Journal of Materials Research 16, no. 1 (2001): 38–44. http://dx.doi.org/10.1557/jmr.2001.0011.

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The low-temperature phase, trigonal phase, of space group R32 was discovered in the compound LaSc3(BO3)4 (LSB) doped with arbitrary concentration of Nd3+ ions (NLSB). For LSB, the lattice constants are a = 9.820 ± 0.003 Å, c = 7.975 ± 0.003 Å. The decomposition of NLSB phase was observed in two regions of temperature below and above the congruent melting point by differential thermal analysis and x-ray powder diffraction methods. The single crystals of 2 × 2 × 3mm3 of dominant trigonal phase for x = 0.5 were grown by the flux method (LiBO2). Second harmonic generation effect was observed in NL

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Geng, Xianguo, and Xin Zeng. "Application of the trigonal curve to the Blaszak–Marciniak lattice hierarchy." Theoretical and Mathematical Physics 190, no. 1 (2017): 18–42. http://dx.doi.org/10.1134/s0040577917010020.

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42

Sławiński, W., R. Przeniosło, I. Sosnowska, M. Bieringer, and I. Margiolaki. "Thermal Lattice Parameters Variation of CaCuxMn7-xO12Compounds with Trigonal Crystal Structure." Acta Physica Polonica A 113, no. 4 (2008): 1225–30. http://dx.doi.org/10.12693/aphyspola.113.1225.

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Sowa, H., E. Koch, and W. Fischer. "Hexagonal and trigonal sphere packings. I. Invariant and univariant lattice complexes." Acta Crystallographica Section A Foundations of Crystallography 59, no. 4 (2003): 317–26. http://dx.doi.org/10.1107/s0108767303008766.

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Schönegger, Sandra, Teresa S. Ortner, Klaus Wurst, Gunter Heymann, and Hubert Huppertz. "Synthesis and characterization of the lead borate Pb6B12O21(OH)6." Zeitschrift für Naturforschung B 71, no. 8 (2016): 925–33. http://dx.doi.org/10.1515/znb-2016-0105.

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AbstractA lead borate with the composition Pb6B12O21(OH)6 was synthesized through a hydrothermal synthesis, using lead metaborate in combination with sodium nitrate and potassium nitrate. The compound crystallizes in the trigonal, non-centrosymmetric space group P32 (no. 145) with the lattice parameters a = 1176.0(4), c = 1333.0(4) pm, and V = 0.1596(2) nm3. Interestingly, the data of Pb6B12O21(OH)6 correct the structure of a literature known lead borate with the composition “Pb6B11O18(OH)9”. For the latter compound, nearly identical lattice parameters of a = 1176.91(7) and c = 1333.62(12) pm

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45

Phlip, Thresiamma, C. S. Menon, and K. Indulekha. "Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Trigonal Calcite." E-Journal of Chemistry 2, no. 4 (2005): 207–17. http://dx.doi.org/10.1155/2005/913794.

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The second- and third-order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second-order elastic constants and the fourteen non-vanishing third-order elastic constants of trigonal calcite are obtained. The second-orde

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Grin, Y., Hk Müller-Buschbaum, and H. G. von Schnering. "„BaNb3O6“ ist ein Perowskit BaNbO3, eine Korrektur und ein Beitrag zu BaxNbO3/“BaNb3O6“ is a Perovskite BaNbO3, a Correction and a Contribution to BaxNbO3." Zeitschrift für Naturforschung B 52, no. 2 (1997): 153–56. http://dx.doi.org/10.1515/znb-1997-0201.

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Abstract It is shown that the trigonal compound “BaNb3O6” described earlier actually is the cubic perovskite BaNbO3 with an unusually small lattice constant of 4.039 A. Furthermore, the refinement of the single crystal data prepared by CO2-LASER techniques did not reveal defects at the Ba position, but defects at the positions of niobium and oxygen, corresponding to the composition Ba(NbO3)0.9 or Ba1.08NbO3.

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Shamsuzzoha, M., and B. W. Lucas. "Polymorphs of rubidium nitrate and their crystallographic relationships." Canadian Journal of Chemistry 66, no. 4 (1988): 819–23. http://dx.doi.org/10.1139/v88-142.

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The crystal structure relationships between the four thermal polymorphs (IV – 437 K – III – 492 K – II – 564 K – I) of RbNO3 are discussed. Trigonal IV, a = 10.55(2), c = 7.47(2) Å at 298 K, Z = 9, and space group P31 (or its enantiomorph P32) has Rb atoms arranged on a pseudocubic sublattice defined by [Formula: see text] and related segments. The ordered NO3 groups are enclosed within respective pseudocubes and form close to ideal 8-fold anion–cation coordination with the surrounding Rb atoms. At IV → III, each of the appropriate (1/3) <10.1> and (1/3) <11.1> segments of IV (form

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Chen, Kai, Catherine Dejoie, and Hans-Rudolf Wenk. "Unambiguous indexing of trigonal crystals from white-beam Laue diffraction patterns: application to Dauphiné twinning and lattice stress mapping in deformed quartz." Journal of Applied Crystallography 45, no. 5 (2012): 982–89. http://dx.doi.org/10.1107/s0021889812031287.

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Synchrotron X-ray Laue microdiffraction is used to investigate the microstructure of deformed quartz, which has trigonal symmetry. The unambiguous indexing of a Laue diffraction pattern can only be achieved by taking the intensities of the diffraction peaks into account. The intensities are compared with theoretical structure factors after correction for the incident X-ray beam flux, X-ray beam polarization, air absorption, detector response and Lorentz factor. This allows mapping of not only the grain orientation but also the stress tensor. The method is applicable for correct orientation det

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Frenzel, Nancy, Elisabeth Irran, Martin Lerch, and Alexandra Buchsteiner. "Synthesis and Crystal Structure of Nb0.84N." Zeitschrift für Naturforschung B 66, no. 1 (2011): 1–6. http://dx.doi.org/10.1515/znb-2011-0101.

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A new compound of the composition Nb0.84N was prepared by ammonolysis of NbO2 at 1100 °C. The crystal structure refinement was performed by the Rietveld method using X-ray and neutron powder diffraction data. Nb0.84N crystallizes in the trigonal space group R3m (no. 166) with the lattice parameters a = 298.5(2) and c = 2384.3(4) pm. The niobium atoms form a close packing with a layer sequence which can be described by the Jagodzinski symbol hhc. The nitrogen atoms fill all octahedral voids. Along [001] a sequence of two layers of trigonal NbN6 prisms and one layer of NbN6 octahedra is formed.

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Taleb, Nassiba, Victoria J. Richards, Stephen P. Argent, et al. "A mixed valence manganese triangle in a trigonal lattice: structure and magnetism." Dalton Transactions 40, no. 22 (2011): 5891. http://dx.doi.org/10.1039/c1dt10057b.

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