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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 (November 15, 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 from the knowledge of such quantities along a limited number of SDs. The task at hand is to determine as many anisotropic components as the number of available sampling directions. Also discussed is a way of dealing with data when the number of anisotropic components is restricted by a non-optimal set of SDs.

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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 (June 1, 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 lattices as a function of spatial dimension, and discuss the results. We finally calculate the electrostatic repulsion of two constant unit charge distributions in the unit cube. This quantity, a six-dimensional integral, can be integrated analytically five times, leaving a simple one-dimensional integral to be done numerically. Key words: ionic crystal, Madelung constant, ionic cluster, electrostatic energy.

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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, and 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, no. 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 between the plane of the water molecule and the M-O bond vector being 1° (M = V) and 35° (M = Rh ). The tilt angle for water coordinated to rhodium in CsRh (SeO4)2.12H2O is inferred from the unit cell dimensions to be similar to that of the corresponding sulfate salt and not that which generally pertains for caesium selenate alums. Significant differences in the H-O-H bond angle are found for trigonal planar and trigonal pyramidal water coordination, suggesting that differences in the metal(III)-water interaction are a determinant of the geometry of the coordinated water molecule in the caesium sulfate/ selenate alum lattices.

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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 reveals the evolution of an exothermic peak at 465oC indicating the rapid decomposition of the hexamine and dissociation of nitrate salts, forming the final compound lithium nickealte. The XRD pattern reveals the rhombohedral structure of LiNiO2with trigonal symmetry comprising of two interpenetrating close packed FCC sub-lattices. The lattice constant values ̒a̓ and ̒c̓ are in good agreement with the reported data. In the FT-IR spectra, vibrational bands are identified in the range of 400-800 cm-1representing the NiO2layer. LiNiO2exhibits a very fine crystalline structure with an irregular morphology. The La substituted LiNiO2powder has shown a smooth-edged polyhedral structure with an average particle size of 5-10 μm.

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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 (March 30, 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 basis of a finer lattice, the digital modeling lattice Λ, which includes the form lattice as a sublattice. This leads to a coarse-grained description of the protein. In the crystallographic point-group case, the planar indices are obtained from a projection of atomic positions along the rotation axis, taken as thezaxis. The planar indices of a Cαare then those of the nearest projected lattice point. In the non-crystallographic case, low indices are an additional requirement. The coarse-grained bead follows from the condition imposed on the residues selected to have azcoordinate within a band of value δ above and below the height of lattice points. The choice of δ permits a variation of the coarse-grained bead model. For example, the value δ = 0.5 leads to a fine-grained indexing of the full set of residues, whereas with δ = 0.25 one gets a coarse-grained model which includes only about half of these residues. Within this procedure, the indexing of the Cαonly depends on the choice of the digital modeling lattice and not on the value of δ. The characteristics which distinguish the present approach from other coarse-grained models of proteins on lattices are summarized at the end.

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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 (March 15, 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 (April 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 (July 11, 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 base of a square pyramid, whereas the acetate oxygen occupies its apex. The O3N2 donor set in 2 defines a polyhedron which more closely resembles a trigonal bipyramid. The packing in the crystal lattices of both compounds is governed by hydrogen-bonds. Complexes 1 and 2 display higher stability than curcumin in buffered media at pH = 7.0, however, the degradation of coordinated cur– is comparable to that of yellow pigment curcumin (curH) when the pH is raised to 7.2. Both complexes 1 and 2 in DMSO exhibit fluorescence with Stokes shifts of 5367 and 4634 cm−1, respectively.

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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 (July 1, 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) could be successfully fitted by distorted cubic lattices (trigonal symmetry). The NMR line shapes observed in these compounds were explained by overall molecular motions with large amplitudes (pseudo-isotropic reorientations). Differential scanning calorimetry (DSC) spectra of NEtyPr(4 − y)BEt4 (y=1–3) showed a low entropy change (ΔSmp) of 6–8 J K−1 mol−1 at the melting point. Ionic diffusion was identified by electrical conductivity measurements of NEtxMe(4 − x)BEt4 and NEtyPr(4–y)BEt4 (x=0–4, y=1–3). In the case of NPr4BEt4 crystals, ionic diffusion was also detected, although complex powder patterns and large ΔSmp values were observed by XRD and DSC measurements, respectively.

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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 dimers , through weak intermolecular Me…S interactions, in their respective crystal lattices. Crystals of β-As(S2COCH3)3 are monoclinic, P21/c, with unit cell parameters a 14.816(4), b 9.641(6), c 21.255(6) �, β 90.18(2)�, Z = 8. The antimony and bismuth compounds are isomorphous, crystallizing in the triclinic space group P1, with cell dimensions (bismuth details given second) a 5.904(1), 5.924(3); b 10.4891(8), 10.499(3); c 12.3635(9), 12.485(4) �; α 95.993(6), 95.99(3); β 100.92(1), 101.76(4); γ 99.04(1), 101.45(4)�; Z = 2, 2. The structures were solved by normal Fourier methods and refined by a full-matrix least-squares procedure in each case on reflections which satisfied the I ≥2.5σ(I) criterion. Final refinement details for the β arsenic (antimony, bismuth) compounds: R 0.034 (0.027, 0.055), Rw 0.034 (0.029, 0.052) for 2777 (2115, 1894) reflections.

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12

Matsutani, Shigeki. "Trigonal Toda Lattice Equation." Journal of Nonlinear Mathematical Physics 27, no. 4 (September 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 (January 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 and those of synthetic compositional variants. In the past five years it has been recognized that the layered copper hydroxyhalides barlowite, Cu4BrF(OH)6, and claringbullite, Cu4FCl(OH)6, are also the parent structures of a family of kagome phases, as they also have triangular magnetic lattices. This paper concerns the structural behavior of claringbullite that is a precursor to the novel frustrated antiferromagnetic states that occur below 30 K in these minerals. The reversible hexagonal (P63/mmc) ↔ orthorhombic (Pnma or Cmcm) structural phase transition in barlowite at 200−270 K has been known for several years, but the details of the structural changes that occur through the transition have been largely unexplored, with the focus instead being on quantifying the low-temperature magnetic behavior of the orthorhombic phase. This paper reports the details of the structural phase transition in natural claringbullite at 100−293 K as studied by single-crystal X-ray diffraction. The transition temperature has been determined to lie between 270 and 293 K. The progressive disordering of Cu at the unusual trigonal prismatic Cu(OH)6 site on heating is quantified through the phase transition for the first time, and a methodology for refining this disorder is presented. Key changes in the behavior of Cu(OH)4Cl2 octahedra in claringbullite have been identified that suggest why the Pnma structure is likely stabilized over an alternative Cmcm structure. It is proposed that the presence of a non-centrosymmetric octahedron in the Pnma structure allows more effective structural relaxation during the phase transition than can be achieved by the Cmcm structure, which has only centrosymmetric octahedra.

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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 distortions (angular decreases) in the impurity-ligand bond angles related to the C3 axis due to the size mismatching substitution. The contributions from the ligand orbital and spin-orbit coupling interactions are important and should be taken into account.

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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 (June 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. Kaskasite and manganokaskasite mainly occur as flakes and their near-parallel ‘stacks’ (kaskasite: up to 0.03 mm × 1 mm × 1.5 mm; manganokaskasite: up to 0.02 mm × 0.5 mm × 1 mm) epitaxially overgrow Ti-bearing pyrrhotite partially replaced by Ti-bearing pyrite. All three new minerals are opaque, ironblack, with metallic lustre. Cleavage is {001} perfect and mica-like. Flakes are very soft, flexible and inelastic. Mohs hardness is ∼1. D(calc.) = 3.63 (ekplexite), 3.83 (kaskasite) and 4.09 (manganokaskasite) g cm−3. In reflected light all these minerals are grey, without internal reflections. Anisotropism and bireflectance are very strong and pleochroism is strong. The presence of OH groups and an absence of H2O molecules are confirmed by the Raman spectroscopy data. Chemical data (wt.%, electron probe) for ekplexite, kaskasite and manganokaskasite, respectively, are: Mg 6.25, 5.94, 0.06; Al 4.31, 3.67, 3.00; Ca 0.00, 0.04, 0.00; V 0.86, 0.16, 0.15; Mn 0.00, 0.23, 11.44; Fe 0.44, 1.44, 2.06; Nb 18.17, 13.39, 14.15; Mo 15.89, 23.18, 20.08; W 8.13, 7.59, 9.12; S 27.68, 27.09, 24.84; O 16.33, 15.66, 13.36; H (calc.) 1.03, 0.99, 0.89; total 99.09, 99.08, 99.15. The empirical formulae calculated on the basis of 2 S a.p.f.u. are: ekplexite: (Nb0.45Mo0.38W0.10V0.04)S0.97S2· (Mg0.60Al0.37Fe0.02)S0.99(OH)2.36; kaskasite: (Mo0.57Nb0.34W0.10V0.01)S1.02S2· (Mg0.58Al0.32Fe0.06Mn0.01)S0.97(OH)2.32; manganokaskasite: (Mo0.54Nb0.39W0.13V0.01)S1.07S2· (Mn0.54Al0.29Fe0.10Mg0.01)S0.94(OH)2.28. All three minerals are trigonal, space groups Pm1, P3m1 or P321, one-layer polytypes (Z = 1). Their structures are non-commensurate and consist of the MeS2-type (Me = Nb, Mo, W) sulfide modules and the brucite-type hydroxide modules. Parameters of the sulfide (main) sub-lattices (a, c in Å, V in Å3) are: 3.262(2), 11.44(2), 105.4(4) (ekplexite); 3.220(2), 11.47(2), 102.8(4) (kaskasite); 3.243(3), 11.61(1), 105.8(3) (manganokaskasite). Parameters of the hydroxide sub-lattices (a, c in Å, V in Å3) are: 3.066(2), 11.52(2), 93.8(4) (ekplexite); 3.073(2), 11.50(2), 94.0(4) (kaskasite); 3.118(3), 11.62(1), 97.9(2) (manganokaskasite). Ekplexite was named from the Greek word έκπληξη meaning surprise, for its exotic combination of major chemical constituents, kaskasite after the discovery locality and manganokaskasite as a Mn analogue of kaskasite.

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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 (August 23, 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 (February 1, 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 s-orbital contributions. The local lattice distortion obtained in this work is discussed.

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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 (August 20, 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 the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

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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 latter occupying the capping positions, while the hmpa ligands are singly O-bound to one trigonal face. Heavier lanthanides (Gd, Lu) and Y have been found to give isomorphous (monoclinic, P21/n, Z 4) species of stoichiometry [Ln(pic)3(hmpa)2], with 8-coordinate Ln of an irregular geometry best considered as close to that of a bicapped trigonal-prism. The picrate ligands chelate in the same manner as in the lighter Ln complexes but with one spanning a trigonal edge, and the hmpa-O donors occuping two apices of the other trigonal face. The ligand ompa has been found to act as a bidentate chelate in all isolated species, displacing one picrate from the metal ion coordination sphere to give ionic complexes. For La, Nd, and Gd, isomorphous (monoclinic, P21/n, Z 4) complexes of stoichiometry [Ln(pic)2(ompa)2(OH2)](pic)·0.5H2O containing 9-coordinate, tricapped trigonal-prismatic Ln with a single aqua ligand have been defined, while for Er, Yb, Lu, and Y, both the coordinated and lattice water molecules are lost in isomorphous (monoclininc, P21/c, Z 8) 8-coordinate, square-antiprismatic species of stoichiometry [Ln(pic)2(ompa)2](pic). For Er, further polymorphs, one monoclinic, P21/c, and the other triclinic, , have also been characterised.

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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, Artem A. Eliseev, Oxana V. Magdysyuk, Robert E. Dinnebier, Reinhard K. Kremer, Claudia Felser, and Martin Jansen. "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, Toetsu Shishido, Tsuguo Fukuda, Masahiko Tanaka, Takeharu Mori, and Satoshi Sasaki. "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 (October 1, 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 with the average ionic radii of R^{3+}, accompanying a structural change from orthorhombic to a trigonal system at around R^{3+}=1.11 Å corresponding to average ionic radii of 0.7{\rm Nd}^{3+}+0.3{\rm Sm}^{3+}. In orthorhombic phases, deformation of the crystal lattice from its ideal cubic lattice is minimized at aroundx = 0.0–0.2 in (Ndx, Sm_{1-x})AlO3and increased with increasing average ionic radii of Nd^{3+} and Sm^{3+}. The structure changes from orthorhombic to trigonal at aroundx = 0.7.

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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 (August 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 (August 3, 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 (March 1, 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 (June 1, 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 (November 6, 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 the second and third domains of this nonmerohedral twin, a trigonal lattice is emulated, although the correct crystal system is orthorhombic.

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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 compared with available experimental values. The second-order elastic constant C11which corresponds to the elastic stiffness along the basal plane of the crystal is less than C33which corresponds to the elastic stiffness tensor component along thec-axis of the crystal. The pressure derivatives, dC'ij/dp obtained in the present work, indicate that trigonal LiNbO3is compressible. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in LiNbO3. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

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30

Wang, Xuefeng, Yurui Gao, Xi Shen, Yejing Li, Qingyu Kong, Sungsik Lee, Zhaoxiang Wang, Richeng Yu, Yong-Sheng Hu, and Liquan Chen. "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_0.5NbO₂composed of NbO₆trigonal prisms and NaO₆octahedra 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 (June 1, 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 (December 1, 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, no. 4 (August 1, 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 pseudomonoclinic C-centered cell.

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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 (September 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 (December 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 (March 1, 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 large temperature range indicates that the structures in solution and in the solid state are virtually identical. The results are discussed in relation to the known structure of the ion in the lattice [vIVdi(amH)sar -2H](S2O6)2, the sites of deprotonation of the coordinated amines and in relation to the trigonal and small rhombic distortions of the complex.

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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 (March 29, 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 ‾ $‾{6}$ 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 were refined from the diffraction data. Decreasing platinum content leads to decreasing a and c lattice parameters. Satellite reflections were observed for the Sc3Pt3–xIn3 crystals with x = 0.31–0.83. These satellite reflections could be described with a modulation vector ( 1 3 , 1 3 , γ ) $\left(\frac{1}{3},\frac{1}{3},\gamma \right)$ ( γ = 1 2 $\gamma =\frac{1}{2}$ c* for all crystals) and are compatible with trigonal symmetry. The interplay of platinum filled vs. empty In6 trigonal prisms is discussed for an approximant structure with space group P3m1.

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39

Lee, Jeong-Eun, Ulrich Burkhardt, and Alexander Christoph Komarek. "Synthesis of a New Ruthenate Ba26Ru12O57." Crystals 10, no. 5 (April 30, 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 Ru ions should be formally close to 5+.

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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 (January 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 NLSB for x = 0 to 1. The concentration dependence of fluorescence lifetime was measured and derived from Dexter's theory of resonant energy transfer.

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41

Geng, Xianguo, and Xin Zeng. "Application of the trigonal curve to the Blaszak–Marciniak lattice hierarchy." Theoretical and Mathematical Physics 190, no. 1 (January 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 (April 2008): 1225–30. http://dx.doi.org/10.12693/aphyspola.113.1225.

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43

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 (June 26, 2003): 317–26. http://dx.doi.org/10.1107/s0108767303008766.

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44

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 (August 1, 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 were reported, possessing a crystal structure, in which the localization and refinement of one boron atom was obviously overlooked. The structure of Pb6B12O21(OH)6 is built up from trigonal planar BO3 and tetrahedral BO4 groups forming complex chains. The Pb2+ cations are located between neighboring polyborate chains. The here reported compound Pb6B12O21(OH)6 and “Pb6B11O18(OH)9” were, however, produced under different synthesis conditions. While “Pb6B11O18(OH)9” was synthesized via a hydrothermal synthesis including ethylenediamine and acetic acid, the here reported lead borate Pb6B12O21(OH)6 could be obtained under moderate hydrothermal conditions (240°C) without the addition of organic reagents.

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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-order elastic constants C11, which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C33, which corresponds to the elastic stiffness tensor component along the c-axis of the crystal. First order pressure derivatives of the second-order elastic constants of calcite are evaluated. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in calcite. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

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46

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 (February 1, 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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47

Shamsuzzoha, M., and B. W. Lucas. "Polymorphs of rubidium nitrate and their crystallographic relationships." Canadian Journal of Chemistry 66, no. 4 (April 1, 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 (forming the Rb atom sublattice) transform to a cell edge of an ideal s.c. lattice of Rb atoms, a = 4.39(1) Å, Z = 1, and space group Pm3m. The orientationally disordered NO3 groups in III form another close to ideal 8-fold anion–cation coordination with the Rb atoms. At III → II, the s.c. lattice of III changes to form a larger b.c.c. lattice, a = 8.84(3) Å, Z = 8, in II. A parallel-axes unit cell relationship, i.e. <100>III//<100>II and 2(a)III = (a)II, exists between III and II. The NO3 group in II is postulated to form a close to ideal 8-fold anion–cation coordination with the surrounding Rb atoms. At II → I, II transforms to a f.c.c. lattice, a = 7.32 Å, Z = 4, and space group Fm3m. The NO3 group in I forms a close to ideal 6-fold anion–cation coordination with the surrounding Rb atoms. It is suggested that [Formula: see text] and related segments in II, which form a trigonal Rb atom sublattice, a = 7.65(3) Å and α = 109.47°, after II → I, transform to orthogonal cell edges of the cubic lattice of I.

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48

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 (August 9, 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 determination of all crystals with trigonal symmetry and is indispensable for structure refinements of such materials from Laue diffraction data.

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49

Frenzel, Nancy, Elisabeth Irran, Martin Lerch, and Alexandra Buchsteiner. "Synthesis and Crystal Structure of Nb0.84N." Zeitschrift für Naturforschung B 66, no. 1 (January 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. The nitrogen positions are fully occupied, the niobium positions only partially. Nb0.84N is part of a family of crystal structures between the anti-NiAs and the NaCl type consisting of close-packed metal layers with varying stacking sequences

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50

Taleb, Nassiba, Victoria J. Richards, Stephen P. Argent, Joris van Slageren, William Lewis, Alexander J. Blake, and Neil R. Champness. "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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