Band 221, Heft 4

The problem of enumerating the possible closest-packings of equal spheres having a period P for each of the possible space groups is solved by systematic exploitation of the properties of the two-color symmetry group of the cyclotomic representation of the Zhdanov symbol. No sophisticated combinatorial or group-theoretical techniques are required, and for some space groups, non-recursive, simple analytical expressions are obtained through the use of Möbius Inversion Formula. A corollary to Möbius theorem, used in the derivation, has been proved.

In this work, a complete crystallochemical characterization of two solid solutions, which were founded in the binary end members system La 2 BaZnO 5 —Eu 2 BaZnO 5 , is reported. Both compounds belong to the family of mixed oxides with formula Ln 2 BaMO 5 which presents interesting magnetic, electric and optical properties. Several works have been reported about this family of compounds with the same stoichiometry but with different structures depending on the M 2+ coordination and rare earth content. Two solid solutions were obtained and characterized. Cell parameters, density measurements and solubility limits were determined for both solid solutions. Structure refinements of Eu 2 BaZnO 5 , La 2 BaZnO 5 and the two solid solution series were carried out by the Rietveld method. Both structures and their relationship were discussed.

The novel compound (UO 2 ) 2 C 2 O 4 (OH) 2 (H 2 O) 2 (UrOx2A) and the previously studied compound UO 2 C 2 O 4 (H 2 O) 3 (UrOx3) have been synthesized by mild hydrothermal methods. Single crystal diffraction data collected at 125 K using Mo K α radiation and a CCD-based area detector were used to solve and refine the crystal structures by full-matrix least-squares techniques to agreement indices (UrOx2A, UrOx3) wR 2 = 0.037, 0.049 for all data, and R 1 = 0.015, 0.024 calculated for 1285, 2194 unique reflections respectively. The compound UrOx2A is triclinic, space group P -1, Z = 1, a = 5.5353(4), b = 6.0866(4), c = 7.7686(6) Å, α = 85.6410(10)°, β = 89.7740(10)°, γ = 82.5090(10)°, V = 258.74(3) Å 3 . The compound UrOx3 is monoclinic, space group P 2 1 / c , Z = 4, a = 5.5921(4), b = 16.9931(13), c = 9.3594(7) Å, β = 99.5330(10)°, V = 877.11(11) Å 3 . The structures consist of chains of uranyl pentagonal bipyramids connected by oxalate groups and, in UrOx2A, hydroxyl groups; UrOx2A is also notable for its high (2 : 1) ratio of uranyl to oxalate groups, higher than any observed in other published structures of uranyl oxalates. The structure determined for UrOx3, previously studied by Jayadevan and Chackraburtty (1972); Mikhailov et al. (1999) is in agreement with the previous results; however, the increased precision of the present low-temperature structure refinement allows for the assignment of H atom positions based on the difference Fourier map of electron density. The infrared spectra of these two materials collected at room temperature are also presented and compared with previous work on uranyl oxalate systems.

The crystal structure of the aluminosilicate, ZSM-10 (T 108 O 216 , where T = Si, Al), has been determined from electron diffraction and powder X-ray diffraction data. The material crystallizes in space group P 6/ mmm , where a = 31.390(2), c = 7.5147(8) Å. The framework [001] projection was determined independently with 300 kV precession electron diffraction amplitudes by direct methods. T-site positions in this projection were consistent with two models proposed in 1996 by Higgins and Schmitt. Subsequent Rietveld refinement favors their model A, comprising stacked cancrinite cages and hexagonal prisms. The framework density is 16.6 T sites/1000 Å 3 , similar to zeolite framework LTL . However, the refinement against synchrotron data from a dehydrated sample ( R wp = 0.1600, R ( F 2 ) = 0.1418) finds no extra-framework species, despite the detection of some K + in the material.

The crystal and molecular structure of the red brown form of [Fe 2 (η 5 -C 5 H 4 Me) 2 (CO)(CN)(μ-CO) · (μ-CNMe 2 )] has been determined by X-ray crystallography. It crystallises with one molecule per asymmetric unit ( P 2 1 / c ) and CO/CN disorder among the terminal ligands. It is a cis isomer with a non-planar Fe 2 (μ-C) 2 bridge having a dihedral angle of 154° between the two Fe 2 C planes. The Fe—C distances to the 2-electron donor ligands (CO, CN, μ-CO and μ-CNMe 2 + ) can be rationalised on the basis of their σ donor and π acceptor abilities.

The crystal structure of silver salicylate C 7 H 5 AgO 3 has been solved originally on powder sample by molecular modeling and reverse Monte-Carlo (RMC) algorithm and then confirmed by X-ray diffraction single crystal structure solution and refinement. C 7 H 5 AgO 3 crystallizes in the monoclinic symmetry (space group P 2 1 / n ) with the lattice parameters: a = 10.9868(15) Å, b = 8.8190(18) Å, c = 7.398(2) Å, β = 112.27(3)° (data from single crystal). The structure consists of [C 6 H 4 (OH)COOAg— AgOOCC 6 H 4 (OH)] dimers and is stabilized by weak intermolecular interactions of the C—H···O type. The comparison of the two independent structure solutions confirmed the effectiveness of the RMC procedure based on powder data to solve the unknown organic structures of the mediocre complexity even using the laboratory X-ray sources.

A complex from Fe(II) and a hexa-dentate linear ligand containing O 2 N 4 donor atoms were prepared and the structure enlightened with X-ray diffraction. The Fe(II) ion in the complex was seen to be oxidized to form a Fe(III) complex, [C 20 H 24 Cl 3 N 4 O 2 ]Fe and the three chloride ions were situated at a distance of Fe…Cl(1) 3.976(5), Fe…Cl(2) 4.479(3) and Fe…Cl(3) 7.509(4) Å outside the coordination sphere. The Fe(III) ion has an octahedral coordination sphere and as expected the two oxygen donor atoms are coordinated in a - cis position. The Fe—O, Fe—N imin and Fe—N amine distances are 1.880(3) Å, 1.931(4) Å and 2.004(4) Å, respectively.

Molecular crystals of 2-phenylbenzimidazole, C 13 H 10 N 2 , exhibit a one-dimensional incommensurate structure. The structure has been solved by charge flipping and refined using the superspace formalism in the (3 + 1) D superspace group C 2/ c (0 b 0) s 0 with modulation wave-vector q = 0.368 b *. The unit cell contains 8 molecules, each one disorderly occupying two configurations related by inversion center. The refinement based on a molecular model with two rigid-body parts per molecule includes up to second order Fourier amplitudes for the modulation. The displacive modulation involves a significant intra-molecular twist between the phenyl and the benzimidazole parts.

A series of crystal structures of adducts formed between cadmium dithiophosphate, Cd(S 2 P(O i Pr) 2 ) 2 , and the isomeric n -pyridinealdazine ligands, n = 2, 3, and 4, are described. A centrosymmetric dimer is found in the 2 : 1 adduct with the 2-isomer, i.e . [Cd(S 2 P(O i Pr) 2 ) 2 (2-NC 5 H 4 C(H) = C(H)C 5 H 4 N-2) 0.5 ] 2 , in which the cadmium atom exists within a cis -N 2 S 4 donor set and the di-pyridyl-type ligand is tetradentate. By contrast, trans -N 2 S 4 donor sets for cadmium and regular bridging modes of coordination lead to polymers with a step-ladder topology are found in the 1:1 adducts with the 3- and 4-isomeric ligands, i.e . [Cd(S 2 P(O i Pr) 2 ) 2 ( n -NC 5 H 4 C(H) = C(H)C 5 H 4 N- n )] ∞ , for n = 3 and 4. Differences in aggregation behaviour are related to the binding requirements of the n -pyridinealdazine ligands.

Metastable 4-methyl benzophenone (4-MBP, C 14 H 12 O) crystallizes in the polar (pyroelectric) and enantiomorphic space groups (SG) P 3 1 and P 3 2 . The optical rotation tensor has been measured for 670 nm and the material was tested for evidence of phase-matchability. The absolute structure was determined via three-beam diffraction, showing that the structural right-hand screw 3 1 is combined with positive (right-handed, i.e. clockwise when looking towards the light source) optical rotation, for both tensor components ρ 11 = ρ 22 = 26(5)°/mm, ρ 33 = 8.3(5)°/mm (contrary to low-quartz which shows negative optical rotation for ρ 33 and positive rotation for ρ 11 in right-hand SG P 3 1 2). The non-linear optical tensors for optical rotation, d -coefficients, electro-optic effect and electrogyration have been calculated using a set of electronic polarizabilities as input parameters for a dipole-dipole interaction model that reproduces the experimental refractive indices and optical rotation. Unusually high polarizability volumes are needed for hydrogen atom bonding to aromatic carbons in order to model the optical tensors. The non-linear optical coefficients are of medium size.