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With only a 2.6 Å resolution laboratory powder diffraction pattern of the θ phase of Pigment Yellow 181 (P.Y. 181) available, crystal-structure solution and Rietveld refinement proved challenging; especially when the crystal structure was shown to be a triclinic dimethylsulfoxide N-methyl-2-pyrrolidone (1:1:1) solvate. The crystal structure, which in principle has 28 possible degrees of freedom, was determined in three stages by a combination of simulated annealing, partial Rietveld refinement with dummy atoms replacing the solvent molecules and further simulated annealing. The θ phase not being of commercial interest, additional experiments were not economically feasible and additional dispersion-corrected density functional theory (DFT-D) calculations were employed to confirm the correctness of the crystal structure. After the correctness of the structure had been ascertained, the bond lengths and valence angles from the DFT-D minimized crystal structure were fed back into the Rietveld refinement as geometrical restraints (‘polymorph-dependent restraints’) to further improve the details of the crystal structure; the positions of the H atoms were also taken from the DFT-D calculations. The final crystal structure is a layered structure with an elaborate network of hydrogen bonds.
Denisovite is a rare mineral occurring as aggregates of fibres typically 200–500 nm diameter. It was confirmed as a new mineral in 1984, but important facts about its chemical formula, lattice parameters, symmetry and structure have remained incompletely known since then. Recently obtained results from studies using microprobe analysis, X-ray powder diffraction (XRPD), electron crystallography, modelling and Rietveld refinement will be reported. The electron crystallography methods include transmission electron microscopy (TEM), selected-area electron diffraction (SAED), high-angle annular dark-field imaging (HAADF), high-resolution transmission electron microscopy (HRTEM), precession electron diffraction (PED) and electron diffraction tomography (EDT). A structural model of denisovite was developed from HAADF images and later completed on the basis of quasi-kinematic EDT data by ab initio structure solution using direct methods and least-squares refinement. The model was confirmed by Rietveld refinement. The lattice parameters are a = 31.024 (1), b = 19.554 (1) and c = 7.1441 (5) Å, β = 95.99 (3)°, V = 4310.1 (5) Å3 and space group P12/a1. The structure consists of three topologically distinct dreier silicate chains, viz. two xonotlite-like dreier double chains, [Si6O17]10−, and a tubular loop-branched dreier triple chain, [Si12O30]12−. The silicate chains occur between three walls of edge-sharing (Ca,Na) octahedra. The chains of silicate tetrahedra and the octahedra walls extend parallel to the z axis and form a layer parallel to (100). Water molecules and K+ cations are located at the centre of the tubular silicate chain. The latter also occupy positions close to the centres of eight-membered rings in the silicate chains. The silicate chains are geometrically constrained by neighbouring octahedra walls and present an ambiguity with respect to their z position along these walls, with displacements between neighbouring layers being either Δz = c/4 or −c/4. Such behaviour is typical for polytypic sequences and leads to disorder along [100]. In fact, the diffraction pattern does not show any sharp reflections with l odd, but continuous diffuse streaks parallel to a* instead. Only reflections with l even are sharp. The diffuse scattering is caused by (100) nanolamellae separated by stacking faults and twin boundaries. The structure can be described according to the order–disorder (OD) theory as a stacking of layers parallel to (100).
Inositol, 1,2,3,4,5,6-hexahydroxycyclohexane, exists in nine stereoisomers with different crystal structures and melting points. In a previous paper on the relationship between the melting points of the inositols and the hydrogen-bonding patterns in their crystal structures [Simperler et al. (2006[Simperler, A., Watt, S. W., Bonnet, P. A., Jones, W. & Motherwell, W. D. S. (2006). CrystEngComm, 8, 589-600.]). CrystEngComm 8, 589], it was noted that although all inositol crystal structures known at that time contained 12 hydrogen bonds per molecule, their melting points span a large range of about 170 °C. Our preliminary investigations suggested that the highest melting point must be corrected for the effect of molecular symmetry, and that the three lowest melting points may need to be revised. This prompted a full investigation, with additional experiments on six of the nine inositols. Thirteen new phases were discovered; for all of these their crystal structures were examined. The crystal structures of eight ordered phases could be determined, of which seven were obtained from laboratory X-ray powder diffraction data. Five additional phases turned out to be rotator phases and only their unit cells could be determined. Two previously unknown melting points were measured, as well as most enthalpies of melting. Several previously reported melting points were shown to be solid-to-solid phase transitions or decomposition points. Our experiments have revealed a complex picture of phases, rotator phases and phase transitions, in which a simple correlation between melting points and hydrogen-bonding patterns is not feasible.