Volume 199, Issue 1-2

Probability methods are used to investigate the influence of twinning by merohedry on intensity statistics in case the twin-related reflections are not independent. The correlation of intensities from pairs of structures with the same lattice dimensions and number of atoms were used to derive the probability distributions for the centrosymmetric and non-centrosymmetric case. The examples show that the distributions are also applicable to structures showing superstructure effects due to pseudotranslations provided that different classes of reflections are treated separately.

X-ray (293 K) and neutron diffraction (15 K, 67 K, 120 K, 293 K) intensities have been measured from natural single crystals of MnS 2 . The lattice parameter, interatomic distances and thermal parameters of Mn and S atoms vary approximately linearly in the temperature range from 15 K to 540 K. The mean volume thermal expansion coefficient is found to be β̄ = 3.70 × 10 −5 K −1 . The vibrational amplitudes of the Mn and S atoms are practically the same at 15 K but at 293 K the vibrational amplitude of the Mn atom becomes 25% larger than that of sulfur. The interatomic distances of MnS 2 have been compared with those of other pyrite-structure transition metal dichalcogenides and the nature of chemical bonding in these compounds has been discussed.

Rhodesite from Zeilberg, Unterfranken, Germany ( Z ), from Trinity County, California, USA ( TC ), and from San Venanzo, Rieti, Italy ( SV ), is orthorhombic with space group Pmam . Crystallographic data, given in the order ( Z ), ( TC ), ( SV ), are: a 0 = 23.416(5)/23.444(5)/23.428(20) Å, b 0 = 6.555(1)/6.553(1)/6.557(8) Å, c 0 = 7.050(1)/7.055(1)/7.064(8) Å, Z = 2, D x = 2.268(1)/2.264(1)/2.261(4) g · cm −3 calculated for HKCa 2 Si 8 O 19 · 5H 2 O. The crystal structure was refined to R (unweighted) = 0.044/0.079/0.044 and R (weighted) = 0.036/0.055/0.045 using 939/898/536 non-equivalent reflections. The structure contains loop-branched dreier double layers of corner-sharing [SiO 4 ] tetrahedra. Channel-like pores running parallel to [010] and [001] between the two sublayers of a double layer are occupied by potassium ions and water molecules. Adjacent double layers are held together by rather strong hydrogen bonds (ca. 2.60 Å) and by two sets of calcium ions which are octahedrally coordinated by six terminal oxygen atoms from the silicate layers, and by four terminal oxygen atoms plus two water molecules, respectively. Although no sodium has been found during refinement of the site occupation factors it is concluded from comparison with the closely related crystal structures of delhayelite, hydrodelhayelite, macdonaldite and monteregianite that stoichiometric rhodesite is the sodium-free endmember of a solid solution HK 1 − x Na x + 2 y Ca 2 − y { lB ,3,2 ∞ 2 }[Si 8 O 19 ] · (6 – z ) H 2 O. Conditions for the formation of double-layer silicates of the rhodesite family in nature and for their synthesis are discussed.

The distance-least-squares (DLS) method and the valence-rule (VR) method are combined into a single computer program to predict bond lengths and bond angles in inorganic (static) crystal structures. The strength of the DLS method which allows refinement of the coordinates of all atoms in the asymmetric unit is preserved. Its weaknesses in positioning light atoms (H, Li) and in estimating polyhedral distortion are eliminated by introducing the valence rule condition: the sum of bond strengths around each atom has to agree with its formal valence. Consequently, the objective function to be minimized consists of three terms: the d istance-, angle-, and v alence- l east- s quares terms (DVLS method). Examples of structure simulations using the DVLS program are given and are compared with results based on the VR method as given in the literature.

The crystal structure of cerussite, PbCO 3 , was refined with 669 merged single-crystal neutron data [ F 0 > 3σ( F 0 )] to R = 0.032, R w = 0.025 (space group Pmcn ; a = 5.179(1), b = 8.492(3), c = 6.141(2); Z = 4). – Cerussite belongs to the aragonite-type compounds. The weak aplanarity of the carbonate group, d = 0.026(1) Å, is of the same order of magnitude as in aragonite, CaCO 3 , and strontianite, SrCO 3 , and the direction of the deviation from planarity is the same. The minor details of the stereochemistry differ slightly from the expectations to be drawn from the structures of the alkaline earth carbonates on the basis of the effective ionic radii of the twovalent metals.

Structural distortions which result in symmetry reduction in the sodalite family are discussed. Several observed symmetry reduction pathways are presented in terms of group-subgroup relationships, as well as with the help of irreducible representations. Emphasis is given to aluminate sodalites, which are characterized by a number of active phase transitions. The cubic-to-noncubic transitions result in short-period superstructures. In one example the superstructure could be described and refined as a modulated structure. The superspace approach was employed.

Single crystal X-ray studies on bis[3,4,5,6-tetrabromo-1,2-benzenediolato(2−)](pyrrolidiniomethyl)silicate acetonitrile solvate [(C 6 Br 4 O 2 ) 2 SiCH 2 (H)NC 4 H 8 · CH 3 CN; monoclinic, P 2 1 / c , a = 808.5(4), b = 1533.0(8), c = 2212.6(1) pm, β = 97.67(2)°, Z = 4] revealed a zwitterionic structure with a pentacoordinate, formally negatively charged silicon atom and a positively charged ammonium moiety. The silicon atom is surrounded by four oxygen atoms and one carbon atom in a trigonal-bipyramidal fashion, with the carbon atom in an equatorial position. The structure is displaced by 7.0% from the trigonal bipyramid towards the square pyramid. The zwitterion and the CH 3 CN molecule form intermolecular N – H⋯N hydrogen bonds.

Coarse-grained sapphirines in a high-grade metamorphic basic rock from the Eastern Ghats, India, contain in their cores fine, coherent exsolution lamellae of aluminous orthopyroxene. The interface is formed by the (010) plane of both structures and, in addition, (001) opx and ([unk]03) sapphirine are also subparallel. Therefore, both the chain direction and that of the octahedral strips are the same in both structures. In places, the orthopyroxene lamellae widen and become incoherent. The exsolution process started at high temperatures close to 900°C due to an increase of oxygen fugacity.

The crystal structure of 2,2-diphenyl-1,3,2-oxathiastannolane, (C 6 H 5 ) 2 Sn(OCH 2 CH 2 S), has been determined by means of X-ray diffraction. The space group is P 2 1 / c , M r = 349.04, a = 8.807(4) Å, b = 13.867(4) Å, c = 11.645(5) Å, β = 104.73(3)°, V = 1375.43 Å 3 , Z = 4, D x = 1.685 g cm −3 , λ (Mo Kα ) = 0.71069 Å, μ = 19.91 cm −1 , F (000) = 687.93, T = 213(5) K. The least-squares refinement was based on 4224 independent reflections with I > 3 σ ( I ) and R -factors in the last refinement were R = 0.0279 and wR = 0.0295. Two molecules of the formula unit are dimerized by a Sn – O′ and a Sn′ – O bond. Because of the dimerization the coordination number of tin becomes 5. The strongly distorted coordination polyhedron of tin can be described as intermediate between a trigonal bipyramid, with S and O′ on the axial positions and a square pyramid, with the atom C(1) of the first phenyl ring at the apex. The distortion seems to be due to the constraints, which are imposed by the tricyclic ring system of the dimeric molecule.

Four mineral apatites (three samples of Totenkopf-hydroxyapatite, one sample of Durango-fluorapatite) and a synthetic fluorapatite were analysed as a function of temperature by X-ray and neutron single crystal diffraction mainly to quantify the disorder contribution to the atomic Debye Waller factor (DWF). The anisotropic displacement parameters (ADP's) obtained at RT for hydroxyapatites with different temperature treatment exhibit marked differences up to 75%. The ADP's of all atoms decrease systematically with increasing temperature treatment. Possible processes for such a global structure change are discussed. The anharmonic terms of the atomic DWF are not influenced by the temperature treatments. Especially the oxygen atoms of the PO 4 -groups show highly remarkable anharmonic contributions indicating preferred directions of displacements caused by the disorder of the channel ions. The resulting perturbation of local symmetry suggests that P6 3 /m describes only a time/space average. As expected the fluorapatites with their ordered F arrangement show appreciable lower third and fourth order terms. The dichroitic behaviour of the OH-ions was determined up to the temperature of 500°C by single crystal IR-spectroscopy on Totenkopf-hydroxyapatite. In the studied temperature range the two IR-spectroscopically different OH-ions both maintain their orientation parallel to the channel axis. Neutron diffraction studies were performed on the mineral hydroxyapatite at several temperatures (25°C, 400°C and 800°C) to determine precisely the location of the OH-ion. At 800°C the position of the OH-ion along the channel is no longer well defined. The temperature dependency of the fourth order terms in the atomic DWF of the framework oxygens points to a subtle structural phase transition below 400°C.

The crystal structure of the title compound (C 9 H 15 NO 4 , M w = 201.2) has been determined by X-ray diffraction. Crystals are monoclinic, space group P 2 1 , with a = 6.2465(8), b = 18.3776(34), c = 9.2724(11) Å, β = 92.699(13)°, V = 1063.2(7) Å 3 , Z = 4, D x = 1.25 gcm −3 , λ (Cu Kα ) = 1.5418 Å, 1130 observed reflections. Diffractometric measurements revealed a twinning on all crystals examined. There are two crystallographically independent molecules in the asymmetric unit and their conformations are similar. The molecules are linked by O – H…O hydrogen bonds into chains oriented in the direction of c axis. The urethane amide bond adopts the trans conformation in both independent molecules. The ring is slightly puckered with dihedral angles of 4.4° and 6.8° between the C – C – C and C – N – C planes for the two molecules. The three bonds at the middle N atom form a flattened pyramid with N as apex; the displacement of the N atom from the plane through its bond atoms is 0.15 Å and 0.07 Å for the two molecules respectively.