Refinement of the crystal structures of synthetic nickel- and cobalt-bearing tourmalines

The crystal structures of synthetic tourmalines with a unique composition containing 3d elements (Ni, Fe, and Co) have been refined: (Ca_0.12?_0.88)(Al_1.69Ni _0.81 ²⁺ Fe _0.50 ²⁺ )(Al_5.40Fe _0.60 ³⁺ )(Si_5.82Al_0.18O₁₈)(BO₃)₃(OH)_3.25O_0.75 I, a = 15.897(5), c = 7.145(2) Å, V = 1564(1) Å; Na_0.91(Ni _1.20 ²⁺ Cr _0.96 ³⁺ Al_0.63Fe _0.18 ²⁺ Mg_0.03)(Al_4.26Ni _1.20 ²⁺ Cr _0.48 ³⁺ Ti_0.06)(Si_5.82Al_0.18)O₁₈(BO₃)₃(OH)_3.73O_0.27 II, a = 15.945(5), c = 7.208(2) Å, V = 1587(1) ų and Na_0.35(Al_1.80Co _1.20 ²⁺ )(Al_5.28Co _0.66 ²⁺ Ti_0.06)(Si_5.64B_0.36)O₁₈(BO₃)₃(OH)_3.81O_0.19 III, a = 15.753(8), c = 7.053(3) Å, V = 1516(2) ų. The reliability factors are R ₁ = 0.038?0.057 and wR ₂ = 0.041–0.060. It is found that 3d elements occupy both Y- and Z positions in all structures. The excess positive charge is compensated for due to the incorporation of divalent oxygen anions into the O3(V)+O1(W) positions.     

Refinement of the crystal structures of biomimetic weddellites produced by microscopic fungus Aspergillus niger

The single-crystal structures of four biomimetic weddellites CaC₂O₄ · (2 + x)H₂O with different contents of zeolitic water (x = 0.10–0.24 formula units) produced by the microscopic fungus Aspergillus niger were refined from X-ray diffraction data (R = 0.029–0.038). The effect of zeolitic water content on the structural stability of weddellite was analyzed. The parameter a was shown to increase with increasing x due to the increase in the distance between water molecules along this direction. The water content and structural parameters of the synthesized weddellites are similar to those of weddellites from biofilms and kidney stones.     

Refinement of the crystal structure of Zn-containing greifensteinite

The crystal structure of Zn-containing greifensteinite from the Pirineus Mine (Minas Gerais, Brazil) was refined (R = 0.045, 562 reflections with |F| > 2σ(F)). The unit-cell parameters are a = 15.941(3) Å, b = 11.877(3) Å, c = 6.625(2) Å, β = 95.09(2)°; V = 1249.4 ų; sp. gr. C2/c; and Z = 2. The idealized formula is [Mn(Fe²⁺, Zn)₄]Ca₂Be₄(PO₄)₆(OH)₄ · 6H₂O. The mineral is isostructural with the previously studied monoclinic representatives of the roscherite group from different deposits and differs from these representatives in that it contains Zn in one of two octahedral positions.     

Refinement of the crystal structure of sanidine-like feldspar

The crystal structure of sanidine-like feldspar of the composition KAlSi₃O₈ from the Khibiny alkaline massif (the Kola Peninsula) has been refined (X-ray diffraction analysis; automated Syntex $P\bar 1$ diffractometer; 2θ: θ scanning technique; 2320 reflections; R _(hkl) = 0.0409; anisotropic refinement; AREN program package). The data obtained for KAlSi₃O₈ are: a = 8.615(9), b = 13.030(7), c = 7.200(5) Å, α = 89.99(5)°, β = 116.01(6)°, γ = 89.98(7)°, Z = 4, sp. gr. $C\bar 1$ . Microtwinning revealed in the crystal structure of the mineral explains the simultaneous existence of two structural-optical types in one sample—“high” and “low” sanidines.     

Refinement of the crystal structure of lithium-bearing uvite

The crystal structure of a natural calcium tourmaline, i.e., uvite with a high lithium content (0.51 au per formula (aupf) at the Y site, is refined to R = 0.019, R _w = 0.020, and S = 1.11. It is shown that, in nature, there exist uvites in which the charge balance in the case where the Z site is occupied by trivalent cations is provided by the replacement of part of the divalent magnesium cations at the Y site by univalent cations, divalent calcium cations at the X site by sodium cations, and univalent anions at the W site by oxygen anions. The W site is found to be split into two sites, namely, the W1 and W11 sites (the W1–W11 distance is 0.14 Å), which are partially occupied by the fluorine and oxygen anions, respectively. An analysis of the results obtained in this study and the data available in the literature on the crystal structure of uvites allows the conclusion that uvite can be considered a superspecies and that the nomenclature of this mineral group needs refinement with the use of structural data.     

Refinement of the crystal structure of acetylacetonatodicarbonylrhodium(I)

The structure of acetylacetonatodicarbonylrhodium(I), Rh(acac)(CO)₂, has been refined from three-dimensional X-ray diffractometer data. The complex crystallises in the triclinic space groupP¯1 with two molecules in a unit cell of dimensionsa = 6.5189(5),b = 7.7614(8),c = 9.2049(12)Å, = 106.04(1), = 91.15(1), = 100.21(1) °. Full-matrix least-squares refinement, using 1456 independent reflections, has reachedR = 0.038.The rhodium atom has a square-planar coordination with two Rh-O(acac) distances of 2.040 and 2.044Å, and two Rh-C(carbonyl) distances both equal to 1.831Å, the O-Rh-O angle is 90.8 ° and the C-Rh-C angle is 88.9 °. All twelve non-hydrogen atoms are closely planar, with an average deviation of 0.003Å, and a maximum deviation of 0.006Å, from the least-squares plane through the molecule. A second non-crystallographic plane of symmetry bisects the molecule, which therefore has essentiallymm2 (C _2v ) point symmetry. The molecules stack in such a way that the rhodium atoms of neighbouring molecules occupy the two remaining pseudo-octahedral positions, with Rh...Rh distances of 3.253 and 3.271Å.     

Refinement of the crystal structure of Na2Ti3O7

The crystals of Na₂Ti₃O₇ were obtained by crystallization from flux. The structure of the compound was refined from X-ray diffraction data collected on a four-circle diffractometer (2θ/θ scanning technique, λMoK _α radiation, graphite monochromator, θ_max = 40°). The crystals are monoclinic a = 9.133(2) Å, b = 3.806(1) Å, c = 8.566(2) Å, β = 101.57(3)°, sp. gr. P2₁/m, Z = 2, ρ_calcd = 3.435 g/cm³, R = 0.035, 1241 reflections with I ≥ 2σ(I). The geometric characteristics of the Ti-polyhedra are analyzed as to their positions in the trioctahedral ribbon. The polymorphism of the {Ti₃O₇}^2? anionic radical in the structures of Na₂Ti₃O₇ and PbTi₃O₇ is described. The topology and dimensionality of the { Ti₃O₇}^2? anionic radical are demonstrated to depend on the type of the large cations located at the lattice points of the hexagonal close packing characteristic of both structures.     

Refinement of the crystal and molecular structure of tetraacetylethane by neutron diffraction

The structure of tetraacetylethane has been determined by neutron diffraction. The compound exists in the dienolic form, the enolic hydrogen being intramolecularly bonded to a neighbouring oxygen in a clearly asymmetric mode. The acetylacetonate residues are essentially planar.     

The X-ray crystal structures of three bis(cyclopentadienyl)titanium(IV) derivatives

The X-ray crystal structures of (aqua)bis(cyclopentadienyl)chlorotitanium(IV) trifluoromethanesulfonate, bis(aqua)bis(cyclopentadienyl)titanium(IV) bis(trifluoromethanesul-fonate) and bis(cyclopentadienyl)bis(trifluoromethanesulfonato)titanium(IV) show a pseudo-tetrahedral array of Cp ring centroids and oxygen or oxygen and chloride donors around titanium, and varied long-range packing motifs dependent on the availability of hydrogen bond acceptors within the lattice.     

Refinement of the crystal structure of calcioancylite-(Ce) by the Rietveld method

The crystal structure of calcioancylite-(Ce) of the (Ca_0.30Sr_0.22)_Σ0.52(Ce_0.78La_0.47Nd_0.16Pr_0.05Sm_0.02)_Σ1.48(CO₃)₂((OH)_1.20F_0.28)_Σ1.48 · 1.97H₂O composition from alkali hydrothermalites of Mont Saint-Hilaire, Canada, has been refined by the Rietveld method. The refinement details are as follows: ADP-2 diffractometer, λCuK _α radiation, Ni filter, 10.50° < 2θ < 140.00°, and the number of reflections (α₁ + α₂) 652. All calculations have been performed within the sp. gr. Pmcn (a = 5.0095(1) Å, b = 8.5006(1) Å, c = 7.2670(1) Å, V = 309.46(1) ų, R _wp = 3.45) in the anisotropic approximation of thermal vibrations for cations.     

On the mechanisms of modulation of crystal structures

Based on the assumption that crystal structures of a number of sulfides are the result of modulation of cationic lattices by anionic lattices, the versions of their conjugation in direct and reciprocal spaces have been analyzed using common translational lattices. The concept of this phenomenon, developed within the superspace formalism, is supplemented by a proposed interpretation of the real modulation of the structures.     

New data on vlasovite: Refinement of the crystal structure and the radiation damage of the crystal during the x-ray diffraction experiment

The crystal structure of vlasovite obtained from the Kipawa alkaline complex in Quebec is refined to R _F = 0.053 for 1515 unique reflections with |F| > 4σ(F). The parameters of the monoclinic unit are as follows: a = 11.063(8) Å, b = 10.15(1) Å, c = 8.60(1) Å, β = 100.3(1)°, space group C2/c, and Z = 4. The X-ray diffraction, electron microprobe, and IR spectroscopic data indicate that, under X-ray radiation, the specimen suffers radiation damage, which is accompanied by a partial removal of Na atoms, incorporation of H₂O molecules into the structure, and, possibly, a change in the configuration of the (Si,O) framework.     

Etch figures and crystal structures

The etch figures on some of the naturally occurring faces of crystals of sodium chloride, cuprite, alpha-quartz, tourmaline and topaz are compared with the atomic arrangements on the etched surfaces. The etch figures are influenced in their shape and orientation relative to the natural faces by a number of factors. One of these factors is the crystal structure. In every example of an etched pit bounded by straight edges, it was found that there exists in the crystal structure a continuous chain of relatively strong inter-atomic bonds, running parallel to the straight edge. The study of tourmaline indicates the direction in which all the SiO₄ tetrahedra are pointing relative to the external form.     

Refinement of the crystal structure of malonic acid,C3H4O4

A reinvestigation of the X-ray crystal structure of malonic acid (C₃H₄O₄) has been made in the light of some observations arising from solid-state¹³C NMR studies on this compound. The unit cell parameters are:a=5.156(1),b=5.341(1),c=8.407(1) Å, =71.48^o (2), =76.12^o (2), =85.09^o (2), space group ,Z=2. The structure was solved by direct methods and refined by full-matrix least-squares refinement to a finalR value of 0.038 for 711 unique reflections withl>3. The packing of the molecules involves dimeric hydrogen bonded association of each carboxyl group with a centrosymmetrically related neighbor. The angles O–C–O (123.3^o and 124.8^o, respectively) for the two carboxyl groups agree qualitatively with the values predicted from a linear relationship relating the observed ₂₂ component of the Carbon-13 NMR chemical shielding tensor for the carboxyl carbon atom to the bond angle O–C–O at the carbon atom.Contribution No. 825.     

Molecular and crystal structures of 2,4,6-trinitro-N-methyl-N-nitroaniline

The structure of single crystals of 2,4,6-trinitro-N-methyl-N-nitroaniline C₇H₅N₅O₈ (I) is determined by X-ray diffraction analysis. The unit cell parameters are a = 14.137(3) Å, b = 10.621(2) Å, c = 7.376(2) Å, γ = 95.19 (5)°, space group P2₁/b, and Z = 4. The structure is solved by the direct method and refined in the anisotropic approximation to R = 0.051 for 1917 reflections with I > 2σ(I). All hydrogen atoms are located and refined in the isotropic approximation. The carbon skeleton of the aromatic nucleus of the molecule tends to adopt the C(2),C(5)-boat conformation. The angle of rotation of the planar NNO₂ group with respect to the plane of the six-membered ring is 123.1(2)°. The NO₂groups that are bonded to the aromatic nucleus of the molecule are also rotated relative to this plane.     

Morphogenesis of crystal structures in the discrete modeling of packings

Within the framework of the discrete modeling of molecular packings, a metric approach to the investigation of the mechanisms of crystal formation is proposed. This method is based on the construction of a combination of polyhedra in a space in which the space division into polyhedra (or the periodic packing of polyhedra) is specified by the multistage addition to the initial “seeding” polyhedron set of this division (packing) of the adjacent polyhedra. Crystal growth is modeled using the constructions of bounding boxes in the division of the plane into polyominoes and the three-dimensional space, into polycubes. The formation of phenomenological polygons (polyhedra) in the growth of periodic structures is revealed and theoretically grounded.     

On the modeling of crystal structures and the growth of crystals

It is demonstrated that the universal laws of system organization govern the growth of crystals and the construction of models of crystal structures. It is established that there is an interrelation between the growth of crystals of chemical compounds and the modeling of their crystal structures.     

Pseudosymmetry software for studying the pseudosymmetry of crystal atomic structures

Possibilities for studying the pseudosymmetric features of crystal atomic structures in Pseudo-Symmetry software are described.