Volume 153, Issue 1-2

The crystal structures of the three synthetic title compounds have been refined with three-dimensional Mo Kα X-ray intensities. For each compound results are given in the order a , b , c , β , Z , space group, number of independent reflections, R (unweighted), R (weighted): Ba 4 [Si 6 O 16 ]: 12.477(2) Å, 4.685(1) Å, 13.944(3) Å, 93.54(2)°, 2, P 2 1 / c , 1249, 0.051, 0.046. Ba 5 [Si 8 O 21 ]: 32.675(7) Å, 4.695(1) Å, 13.894(3) Å, 98.10(2)°, 4, C 2/ c , 915, 0.053, 0.044. Ba 6 [Si 10 O 26 ]: 20.196(4) Å, 4.707(1) Å, 13.842(3) Å, 98.61(2)°, 2, P 2 1 / c , 1529, 0.058, 0.048. In the three silicates corner-sharing [SiO 4 ] tetrahedra form chains with two tetrahedra in the repeat unit parallel [010] ( zweier single chains). In Ba 4 [Si 6 O 16 ] three such single chains are linked into a zweier triple chain, in Ba 5 [Si 8 O 21 ] four chains make a zweier quadruple chain and in Ba 6 [Si 10 O 26 ] five chains make a zweier quintuple chain. Each barium ion is coordinated by eight oxygen atoms forming distorted square antiprisms.

The phases containing multiple chains in the series Ba m + 1 [Si 2 m O 5 m +1 ] – those with triple ( m = 3), quadruple ( m = 4) and quintuple ( m = 5) tetrahedral chains – were investigated by high resolution transmission electron microscopy. The resulting images could be correlated with the structures. Variations of the chain multiplicity ( m ) within single crystals were observed as well as faults in the packing of the multiple chains. The occurrence of sextuple ( m = 6) chains suggests, that stable phases with m > 5 could also exist.

The crystal structures of the two title compounds have been refined with three-dimensional Mo Kα X-ray intensities. Results for both are given in the order a , b , c , β , Z , space group, number of independent reflections, R (unweighted), R (weighted): Ba 2 [Si 4 O 10 ](l): 7.688(1) Å, 4.629(1) Å, 13.523(1) Å, 90°, 2, Pmcn , 611, 0.041, 0.045. Ba 2 [Si 4 O 10 ](h): 23.195(2) Å, 4.658(1) Å, 13.613(1) Å, 97.57(1)°, 6, C 2/ c , 1579, 0.033, 0.034. Both polymorphs contain chains with two [SiO 4 ] tetrahedra in the repeat unit of approximately 4.6 Å ( zweier single chains). These chains are linked via every second tetrahedron to zweier single layers parallel (001). The higher degree of corrugation of the layers in the low-temperature phase compared to those of the high-temperature phase is explained by the smaller effective radius of the barium ions at lower temperature. Barium ion coordination number is 9 in the low-temperature and both 9 and 8 + 2 in the high-temperature form respectively. The barium oxygen polyhedra share edges to form layers parallel (001).

The compound crystallizes in the monoclinic space group P 2 1 with 2 molecules in the cell. The relative and absolute configuration was determined. The absolute configuration of Forskolin itself is now also known.

In the first part of the paper a new method of description of polytypic structures of MX 2 type compounds is discussed in detail. In the proposed xyz notation we assume the triple layers x , x̄ , y , ȳ , z , and z̄ to consist of two layers of iodine ions and one layer of cadmium ions sandwiched between them, as basic structural units. The principles of the use of this form of description, particularly in the structural analysis of polytypes, are discussed. Using the xyz notation the regularities in the stacking of xyz layers for polytypes belonging to four groups of X-ray pattern symmetry are derived. The principles presented in the paper allow a reduction in the number of sequences which must be taken into account for identification of a polytype. In the second part of the paper the different known methods of description of structures with stacking faults are discussed. A new method for description of disorder structures of the MX 2 type is presented. In the proposed t – o – f notation the 10 types of layers correspond to 10 different ion arrangements possible for 3 successive layers in the xyz notation.

(Xanthotoxin) 2 · KI 3 is triclinic, a = 9.59(1), b = 11.09(1), c = 7.96(1) Å, α = 118.1(1), β = 86.7(1), γ = 114.5(1)°, Z = 1, P 1̄. The structure determination is based on about 1900 reflection intensities (graphite-monochromated Mo Kα , Stoe two-circle diffractometer). The crystal contains columns of alternating K + and [unk] ions, both located at crystallographic centres of symmetry. These columns (axes along [001]) are surrounded by stacks of xanthotoxin molecules, successive xanthotoxins within a stack being antiparallel. There are no direct iodine–iodine interactions and (xanthotoxin) 2 · KI 3 has a structure typical of complexes formed by inorganic salts and organic molecules. (Glycine) 4 · KI 3 is monoclinic, a = 22.946(6), b = 10.672(3), c = 8.230(3) Å, β = 91.54(8)°, Z = 4, C 2/ c . The glycine molecules are in the zwitterionic form and are arranged in sheets parallel to (100) in which the primary interactions are N-H–O hydrogen bonds and K + –O electrostatic interactions. The K + ions are enclosed in distorted Archimedean antiprisms of oxygens. The triiodide ions are in sheets parallel to and interleaving the glycine-K + sheets and thus the overall structure is similar to the alternating arrangement of positively and negatively charged sheets found in some other polyiodide (and other types of) salts. There are weak I–I interactions within the triiodide sheets [ d (I–I) = 3.982(0) Å].

The crystal structure of β -SnF 2 was refined from single crystal neutron diffraction data: Space group C 2/ c (monoclinic), a = 13.359(3) Å, b = 4.9099(6), c = 13.790(3) Å, β = 109.11(0.02)°. The structure consists of four Sn 4 F 8 tetrameres per unit cell held together by Van der Waals forces. Within the tetrameres we have covalent bonding, in agreement with measurements of the elastic and thermoealstic properties. The coordination of the tin atoms is a SnF 3 trigonal pyramid. Average Sn–F distances in the pyramid are 2.105 + 0.05 Å and 2.170 ± 0.13Å. The average F–Sn–F angle is 83 ± 3°.

A programmable graph-theoretic method has been developed to determine, on the basis of the strong bonds, all the periodic bond chains as well as their directions for any crystal type. The chains are constructed irrespective of whether they satisfy the usually imposed conditions of stoichiometry, and sometimes in addition, zero dipole moment perpendicular to the chain direction. Thus the task of finding periodic bond chains in a given structure is ultimately reduced to rejecting those constructed chains which violate the above conditions. The present paper, I, considers the general case of crystals with covalent, ionic or mixed type bonding. The special case of ionic crystals is treated in the following paper, II, (Strom, 1980), and illustrated by an application on trirutile.

A topological approach to the study of ( n -1)-dimensional lattice hyperplanes in an n -dimensional lattice T is discussed. This considers the stability of their symmetry under symmetry preserving perturbations of T. Full results are given for the case n = 3, which may be of interest to practising crystallographers.

The crystal structures of the isomorphous compounds CdSO 4 and HgSO 4 have been refined from diffractometer data to R = 0.013 (791 reflections) and R = 0.033 (1092 reflections). The crystals are orthorhombic, space group Pn 2 1 m (No 31) with Z = 2 and a = 4.6982(2), b = 4.7191(2), c = 6.5578(4) Å for CdSO 4 and a = 4.7779(2), b = 4.8119(2), c = 6.5720(3) Å for HgSO 4 . The metal atoms are coordinated to four oxygen atoms of different sulphate groups forming very distorted MeO 4 tetrahedra. The angles O – Me – O vary for Cd from 88.1 to 142.7° and for Hg from 84.4 to 143.4°. The bond distances Me – O are for Cd 2.23 (3 ×) and 2.29 Å and for Hg 2.22 (2 ×), 2.29 and 2.42 Å. For Hg there is a tendeny to the usual 2 or possibly a (3 + 1) coordination. Next nearest neighbours are four O atoms; for Cd at 2.58 – 2.92 Å and for Hg at 2.70 – 2.89 Å. The sulphate tetrahedron is very regular for CdSO 4 and somewhat distorted for HgSO 4 . The structures are built up of three-dimensional networks of MeO 4 and SO 4 tetrahedra sharing corners. The absolute atomic configuration was determined for both crystals used by refinements including anomalous dispersion corrections for the metal and sulphur atoms.

The structure of Li 6 Ge 2 O 7 has been determined by single-crystal data and refined to R = 0.037 for 2108 reflections. The crystallographic data are: Monoclinic, P 2 1 / n , a = 8.071(3), b = 5.304(2), c = 14.223(5)Å, β = 92.90(3) °, Z = 4. The structure is based on a hexagonal closest packing of oxygen atoms with Ge and Li occupying tetrahedral and octahedral holes. The mean interatomic distances for the (Ge 2 O 7 ) group are: Ge–O (bridging) = 1.823 Å and Ge–O (non-bridging) = 1.742 Å. The structural relation of Li 6 Ge 2 O 7 to the neighbouring phases Li 4 GeO 4 and Li 2 GeO 3 is discussed.

The cation distribution in the two solid solutions Co 2 Mg(PO 4 ) 2 and Co 1.5 Mg 1.5 (PO 4 ) 2 , prepared at about 1073 K, has been determined by profile-fitting refinements based on X-ray powder diffraction photographs ( R F is 0.089 and 0.108, respectively). The structures are isotypic with Ƴ Zn 3 (PO 4 ) 2 . The cation distribution among the five- and six-coordinated sites shows a slight predominance of Co 2+ at the former sites ( K D ≈ 2). The (Co,Mg)O 5 polyhedra are distorted trigonal bipyramids.