Band 220, Heft 7

From studies of the influence of polyhedron distortions on bond valence sums (BVS), it is concluded that larger deviations of the BVS values from corresponding values of their classical valence are due to the fact that so far no distinction has been made between the stoichiometric valence derived from chemical analysis and the structural valence derived from structure data.

Alternative formulas are given to compute the number of crystallographically nonequivalent monoatomic close packed polytypes of length N : Γ ( N ). A formula giving the number of sequence, Ω ( N ), of length N which complies with the neutrality condition (# 1  – # 0  = 0  mod  3) is deduced. The asymptotic behavior of both Γ ( N ) and Ω ( N ) are given.

An equation is derived to calculate the BO 3 triangle to BO 4 (PO 4 ) tetrahedron ratios in the anion complexes of borates and borophosphates from the fractions of O atoms with 1, 2, 3 and 4 single bonds to central atoms, respectively. The validity of this formula is verified on a great number of examples including hydrous and anhydrous phases and also high-pressure modifications. The equation can serve to check the agreement between structural features and reported composition of borate or borophosphate. The fractions of the different O atoms needed for the calculation are accessible from lists of interatomic distances. But for 250 borates with only half-shared O atoms and/or OH groups — a quarter of the known borates — the fractions of O atoms with one and two bonds to central atoms can be read from the chemical formula and the triangle-to-tetrahedron ratio thus be calculated directly in simple fashion.

The crystal structure of the incommensurate modification of SiO 2 tridymite existing between 150 and 200 °C was refined in the 3 + 1 dimensional superspace group P 2 1 ( α β 0) from synchrotron powder diffraction data. The modulation consists of rotations and tiltings of rigid SiO 4/2 tetrahedra with mainly transversal displacements of the atoms. At 165 °C the wave vector is r = 0.054 a ∗ + 0.004 b ∗. The largest amplitude is ca. 0.4 Å for oxygen and ca. 0.2 Å for silicon. Si—O—Si intertetrahedral and O—Si…Si—O torsion angles vary by more than 10°. The torsion rotations are larger for pairs of adjacent tetrahedra in trans-configuration than for those in cis-configuration. The shape of six-membered rings of tetrahedra change from almost hexagonal to ditrigonal along the modulation vector.

The pyrochlore derived fluoride structures with general composition AM 2+ M 3+ F 6 crystallize in space groups which are in group-subgroup relationship to Fd -3 m , the space group of the archetype pyrochlore structure. All orthorhombic representatives investigated so far show an ordered M 2+ /M 3+ distribution over two symmetrically independent octahedral sites. CsMgInF 6 crystallizes in space group Pnma with lattice parameters a = 7.5285(1), b = 7.5285(1) and c = 10.6459(1) Å. The investigated crystal was a second degree twin, where the independent twin elements are a combination of the three- and fourfold rotation axes of the archetype cubic lattice. The pseudosymmetry of the compound with respect to space group Imma is extremely high and a reliable decision about the correct symmetry was only possible when inspecting partial agreement factors for the weak reflections h + k + l = 2 n + 1 only. With respect to the other orthorhombic pyrochlore derived ter nary fluorides, the present compound differs in the fact that the M 2+ /M 3+ ions are completely disordered in CsMgInF 6 .

The synthesis, molecular and crystal structure of ( n BuSn) 9 (V V O) 3 O 14 (OH) 6 Cl 2 (dmso) 2 · 3 DMSO ( 1 ) are described. The yellow compound crystallizes in the monoclinic space group P 2(1)/ n (No. 14) with a = 17.961(5) Å, b = 19.222(4) Å, c = 26.748(6) Å, β = 106.776(2)°, V = 8842(4) Å 3 , Z = 4. The neutral monoorganotin-polyoxo-vanadium molecule ( n BuSn) 9 (V V O) 3 O 14 (OH) 6 Cl 2 × (dmso) 2 ( 1a ) shows the same distorted icosahedral arrangement of the metal atoms and a very similar metal-oxygen framework as the well known [( i PrSn) 12 O 14 (OH) 6 ] 2+ ion ( 2 ) from which it can be derived formally by substitution of three square pyramidally coordinated {RSnO 4 } groups by three {OVO 4 } groups of the same geometry. In addition, two further {RSnO 4 } groups are replaced by two octahedral {RSnO 3 Cl(dmso)} units.

2,3-Diphenyl maleic acid anhydride (DPMA), (C 6 H 5 ) 2 C 4 O 3 , is a “historical” compound for which polymorphism, crystal morphology and fluorescence were first reported by Drugman in 1912. For 2,3-diphenyl maleic imide (DPMI), (C 6 H 5 ) 2 C 4 O 2 NH, crystallographic data have not been reported previously. In this work the polymorphs of DPMA have been crystallised from various solvents, from the supercooled melt and from the vapour phase. Small single crystals of the stable, orthorhombic α -phase (m.p. = 156 °C, ρ = 1.334 g/cm 3 ) and of the metastable, monoclinic β -phase (m.p. = 146 °C, ρ = 1.350 g/cm 3 ) were obtained, as described by Drugman. In addition, a fine powder of a previously unknown second metastable phase γ (m.p. = 149 °C) was crystallised. For DPMI, a stable, triclinic α -phase (m.p. = 216 °C, ρ = 1.307 g/cm 3 ) and a metastable, monoclinic β -phase (m.p. = 212 °C, ρ = 1.296 g/cm 3 ) were observed. The structures of the α - and β -polymorphs of DPMA and DPMI were determined by single-crystal X-ray diffraction. Space groups are Pbca for α -DPMA, P 2 1 / c for β -DPMA, P -1 for α -DPMI and C 2/ c for β -DPMI. In both DPMA polymorphs van der Waals interactions dominate. In both phases of DPMI, pairs of molecules form centrosymmetric dimers via H—N…O hydrogen bonds. Between the dimers significant van der Waals interactions exist. Lattice energy calculations based upon the Dreiding force-field using individual molecules as the building blocks for the crystal lattice yield reasonable energy values for DPMI. For DPMA, however, the calculated lattice energy is significantly higher for the stable phase than for the metastable phase. This observation correlates with the observed violation of the density rule for polymorphs, with ρ α < ρ β , and is discussed here in terms of the different conformational energies of the molecules. The results of fluorescence and Raman spectroscopic measurements on the α - and β -polymorphs of both DPMA and DPMI are reported.

Four water soluble Schiff bases were prepared from the reaction of salicylaldehyde and 2-hydroxy-1-naphtaldehyde with 2-amino-2-methyl-1,3-dihydroxy propane and 2-amino-2-methoxy-1,3-dihydroxy propane. Two of the Schiff bases were characterized using elemental analysis, IR spectroscopy and single crystal X-ray diffraction. In addition cyclic voltammetric studies were performed. The Schiff bases C 11 H 5 NO 4 ( II ) and C 15 H 17 NO 3 ( III ) crystalize in monoclinic space group P 2 1 / c with unit cell dimensions a = 10.499(2), b = 8.725(2), c = 12.635(10) Å, β = 101.649(11); a = 14.579(8), b = 9.834(13), c = 9.542(5) Å, β = 107.559(5) respectively.

A concept is presented for determining a one-dimensional structure of m independent point scatterers by mapping into an m -dimensional space P m at least m observations as ( m – 1)-dimensional so-called “isosurfaces” defined by s ( h ) · g ( h ) or g ( h ) alone, where s ( h ) and g ( h ) are sign and modulus, respectively, of the geometrical structure factor. Values of g ( h ) are derived from the observed | F ( h )|. The “solution vector(s)”, ( x 1 , …, x m ), representing the coordinates x j of the point scatterers is (are) found from the “common” intersection(s) of n ≥ m different isosurfaces. Homometric and quasi-homometric structures can thus safely be detected from multiple solutions, the latter mainly arising from the experimental uncertainties of the g ( h ). Spatial resolution is by far higher than that offered by a corresponding Fourier transform. Computer time can be drastically reduced upon consideration of both the symmetry of P m and the anti-symmetry and self-similarity properties of the isosurfaces, which allow for tayloring of the intersection search routines and/or applying linear approximations. The basic principles of the method are illustrated by various two- and three-atom structure examples and discussed in view of the application potential to real structure problems.

The search for a least dense packing of spheres (circles) makes sense only under suitable restrictions because otherwise sphere packings of arbitrarily low density may be constructed. An effective restriction is that all spheres have to be symmetrically equivalent. It has been tried to weaken this condition such that the spheres (circles) have only to be equal in size as well as in their number of contacts. It turned out, however, that even then series of packings may be derived within which the density approaches zero. Examples for such series are presented.