Volume 216, Issue 1

The space group of a cubic phase of Zn 63 Mg 23 Er 14 has been determined to be F 4̅3 m by convergent-beam electron diffraction (CBED). This space group is in agreement with that assumed by X-ray structure analysis (Sterzel et al. , Philos. Mag. Lett. 80 (2000) 239-247). A rhombohedral phase, which is considered as a superlattice ordered phase of the cubic phase, was found. The space group of the rhombohedral phase has been determined to be R 3 m by the CBED method.

Simulated annealing approach was successfully applied to solve three unknown molecular structures from X-ray laboratory powder data using a priory known structural fragments. Some possible developments of the method are discussed.

The simple rules, based on the bond-valence matching and coordination numbers balance, are extended to minimum-size polyhedral cluster in order to describe all probable bonding topologies for a given inorganic substance. This approach, referred to as the Extended Bond-Valence Model (EBVM), allows one to construct the corresponding connectivity matrices and then to calculate predicted bond valences and bond lengths. The subsequent estimates of individual and average bond distortion indices make it possible to select most probable bonding geometry and compare it with experimental data, whenever feasible. The EBVM approach is applied to predict the bonding topologies of Al 2 SiO 5 polymorphs and hypothetical structures for all allowable coordination environments of cations and anions.

The parameters of the interatomic one-particle potentials of cubic ZnSe were determined experimentally unsing X-ray diffraction methods. The harmonic force constants α of zinc and selenium were obtained from the temperature dependence of mean square displacements evaluated from the intergrated intensities of selected reflections between 50 K and 300 K at a wavelength of λ = 0.806 Å. Least squares analysis of the experimental data yields the room temperature mean square displacements 〈 u 2 Zn 〉 = 0.0129(10)Å 2 and 〈u 2 Se 〉 = 0.0115(10)Å 2 i.e. harmonic force constants α Zn = 3.21(1) · 10 -19 J Å -2 and α Se = 3.60(1) · 10 -19 J Å -2 , respectively. The third order anharmonicity constant β was determined exploiting the energy dependence of the Bijvoet ratio between the reflections 666 and 6̅6̅6̅ near the K-absorption edge of Se. It amounts to β Zn = 1.48(15) · 10 -19 J Å -3 assuming β Zn = - β Se . The coefficients of the one-particle potentials of the series Ge, GaAs and ZnSe α and β decreases with rising ionicity.

A reinvestigation of the Na 3 PO 4 -Mg 3 (PO 4 ) 2 binary at 1000 °C has identified two new ternary oxide phases and confirmed the existence of an orthorhombic solid solution phase in the vicinity of NaMg 4 (PO 4 ) 3 . Cubic γ -Na 3 PO 4 shows a solid solution up to ~20 mol. % Mg 3 (PO 4 ) 2 . Between ~24 and ~29 mol. % a new γ -Na 3 PO 4 -related rhombohedral superstructure phase is observed. At ~44 mol. % Mg 3 (PO 4 ) 2 a new phase with a cristobalite-related structure is observed, which on cooling rapidly to room-temperature transforms to KGaO 2 -type ( Pbca: a = 10.409(2) Å, b = 14.492(2) Å, c = 5.211(1) Å). The NaMg 4 (PO 4 ) 3 solid-solution phase extends between ~72 and 80 mol. % Mg 3 (PO 4 ) 2 . Surprisingly, and contrary to previous investigations, there is no phase at 50 mol. %, i.e. with stoichiometry NaMgPO 4 . All high-temperature annealing was performed in sealed Pt tubes to prevent loss of components to the atmosphere, which is suspected as the reason for the quite different results reported by some previous workers.

The crystal structure of the air sensitive argyrodite Ag 9 AlSe 6 is determined by single-crystal X-ray diffraction at room temperature. Above the phase transition at 287 K γ -Ag 9 AlSe 6 crystallizes with cubic symmetry, space group F4̅3m, with a = 11.0947(2) Å, V = 1365.68 (9) Å 3 and Z = 4. The structure refinement leads to a reliability factor of R = 0.0298 for 271 independent reflections and 45 variables. The selenium substructure of the non-metallic γ -Ag 9 AlSe 6 is topologically equivalent to the arrangement of the Mg and Cu atoms in the tetrahedrally close packed intermetallic compound MgCu 2 , a cubic Laves phase. The selenium atoms form a 3D network of tetrahedra partially occupied by Al atoms in an ordered way. The electron density of silver was described by means of a split model and a Gram-Charlier development of the atomic displacement factor for one silver position. This approach gives evidence for the diffusion pathways of silver atoms in the [AlSe 6 ] 9- framework through tetrahedral holes.

The 13 1/2 a 0 x 13 1/2 a 0 superstructure of 1T-TaSe 2 at room temperature has been studied by singel-crystal X-ray diffraction. The basic structure has symmetry P 3̅ m 1 with a 0 = 3.4733 Å and c 0 = 6.2715 Å. The superstructure has a pseudo hexagonal lattice, but it is triclinic with a 169-fold, 13 1/2 a 0 x 13 1/2 a 0 x 13 c 0 hexagonal supercell with 13 centering vectors. Structure refinements have been performed using space group P 1̅ and the primitive unit cell with a basal plane 13 1/2 a 0 x 13 1/2 a 0 supercell, and with C = 2 a 0 + c 0 . Refinements converged to R F = 0.086 for 2327 observed reflections. Hexagram shaped clusters of 13 Ta atoms are the principle feature of this 13-fold superstructure, in accordance with the study of Brouwer and Jellinek (Physica B 99 (1980) 51). In the present refinement, significant deviations are found from local 6/ m symmetry as it was assumed by Brouwer and Jellinek. The relative phase of the superstructure on neighbouring layers represents the most favourable packing of the buckled planes of Se atoms, and elastic coupling between Se atoms of consecutive layers is identified as the driving force for the observed inter-layer shift vector 2 a 0 . The small deviations from trigonal symmetry of the clusters are responsible for the observation of an ordered superstructure, as it is opposed to a stacking of layers according a random selection of shift vectors (2 a 0 , 2 a 0 + b 0 , and - a 0 - 3 b 0 ) that are equivalent by the trigonal symmetry of the basic structure.

The ordered, low-temperature phase of the globular organic molecule norbornene, (bicyclo[2.2.1]hept-2-ene, C 7 H 10 ), has been determined by high resolution powder X-ray diffraction using synchrotron radiation, by auto-indexing, then by intensity extraction and direct methods using the EXPO package. The structure is monoclinic, space group P 2 1 / c , Z = 4, with a = 7.6063(9) Å, b = 8.6220(1) Å, c = 8.749(1) Å, β = 97.24(1)° at 85 K. The structure was refined whilst restraining the molecule to m (C s ) symmetry as found in the gas phase. The molecular structure agrees with that obtained from ab-initio molecular orbital calculations, and is less distorted than that obtained from a previous solution of the structure involving an unrestrained refinement from conventional powder X-ray diffraction data (Min, Benet-Buchholz and Boese, 1998). Norbornene starts to transform to the hexagonal close-packed, orientationally-disordered, room-temperature form at around 116 K on warming.

The crystal structure of dimethyltin dichloride, Me 2 SnCl 2 , known for a long time, has been corrected by means of four-circle diffractometer data, because in comparison to other diorganotin dichlorides serious doubts about the molecular geometry came up. The new, corrected values confirm the old structure model but supply more reliable data in view of the molecular parameters. In particular, the following values have been found for distances and angles: d (Sn-C) = 212.0(7) pm, d (Sn-Cl) = 238.9(2) pm, ∠(Cl-Sn-Cl) = 98.60(9)°, ∠(C-Sn-C) = 142.2(4)°. The length of the intermolecular tin···chlorine bridge was determined to 343.3 pm. This value shows that dimethyltin dichloride has a strong intermolecular association due to small sterical shielding of the tin atom by the methyl groups.

2,3-Bis[3-(2-pyridyl)pyrazol-1-yl]hydroquinone dihydrate crystallises in the space group C 2/ c with half a molecule of the title compound and a water molecule in the asymmetric unit. A two-fold rotation axis relates the two 3-(2-pyridyl)pyrazol-1-yl substituents. The pyridine and pyrazole rings are approximately coplanar while the pyrazole ring is orthogonal to the benzene ring. Each water molecule is hydrogen bonded to the hydroxyl group and also to nitrogen atoms of two adjacent molecules; these hydrogen bonding interactions give rise to a two-dimensional network architecture.

The structure of decafluoroquarterphenyl has been solved and refined from laboratory X-ray powder data. Structure analysis and ab initio Hartree-Fock calculation showed that the molecules are held by electrostatic interactions and weak hydrogen bonds. A Rietveld refinement supported by slack constraints gave dihedral angles which agreed with those found in similar compounds. In molecules such as these, where the planarity of the rings is known a-priori, and there is little improvement in the fit to the diffraction data at the expense of distorting the structure, conventional slack constrained Rietveld refinement may not bring much additional information and therefore may not be worth the additional effort at the end of the structure solution process.