Volume 224, Issue 7

For a centric crystal structure represented by m equal point scatterers at rest, absolute scaling of a small number n of reflection data reduced to relative geometrical structure amplitudes g ′( h ) = K · |∑ cos (2π i hr j )|, j = 1, …, m ; K = scaling factor) is obtained by dividing each amplitude through the r.m.s. average of the amplitudes to be considered. For the same batch of reflections, the resulting values e ( h , n ) are proportional to the well known normalized structure amplitudes | E ( h )| in Direct Methods. Choosing a set of n harmonic reflections of a central reciprocal lattice row, the e ( h , n ) serve to determine the m independent coordinates of the point scatterers projected onto the corresponding direct space direction, e.g . h 00-reflections for coordinates x j , hh 0-reflections for ( x + y ) j ( j = 1, …, m ), etc . This is achieved by applying the concept of an m -dimensional parameter space P m with asymmetric part A m containing ( m – 1)-dimensional iso-surfaces E ( h , n ; e ) determined by the values e ( h , n ), which define boundaries between forbidden and permitted solution regions (the latter containing test structure vectors Xt ) based on observed inequalities, e.g. e ( h , n ) < e ( k , n ). Due to the spatial resolution potential of the concept even less than m data suffice to yield in A m tractable amounts of such test structure vectors ready for conventional least-squares refinement based on n > m data in order to obtain the “best” solution of the considered one-dimensional structure projection. The refined coordinates of various different projections can then be combined for reconstructing the three-dimensional structure. Properties of the e ( h , n ) and their iso-surfaces E ( h , n ; e ) are discussed and determinations of two very small structures (centric and acentric) as well as of a centric 15-atom structure are presented as examples for the applicability of the method.

It is shown that the coincidence isometries of certain modules in Euclidean n -space can be decomposed into a product of at most n coincidence reflections defined by non-zero module elements. This generalizes previous results obtained for lattices to situations that are relevant in quasicrystallography.

The structure of CaIrO 3 post-perovskite has been determined using CAD4 and Bruker SMART diffractometers for two different crystals. In both cases the structure was solved by Direct Methods which revealed all four atoms in the asymmetric unit. Anisotropic refinement of all atoms gave (CAD4/SMART): R 1 = 0.016/0.008, wR 2 = 0.032/0.009. There is excellent agreement between the structure models of the two studies. However, some notable differences were found between the structures determined here and that reported by Sugahara et al. , (2008): most obviously, we observe no significant anisotropic displacements for any of the atoms. Anisotropic displacement parameters for Ca, Ir and O atoms are very similar to those of their counterparts in MgSiO 3 perovskite. The close similarity of the structures of the two crystals determined here using two very different diffractometers suggests that the derived model structure reported here is better-constrained and more representative of the characteristic features of CaIrO 3 post-perovskite than that obtained by Sugahara et al. , (2008).

The new stannide Eu 2 Pt 3 Sn 5 was synthesized by induction melting of the elements in a sealed tantalum tube in a water-cooled silica sample chamber. The structure was refined on the basis of single crystal X-ray diffractometer data: Y 2 Rh 3 Sn 5 type, Cmc 2 1 , a = 453.30(9), b = 2662.9(8), c = 731.8(2) pm, wR 2 = 0.0472, 1493 F 2 values and 62 variables). The platinum and tin atoms build up a complex three-dimensional [Pt 3 Sn 5 ] network with a broad range of Pt—Sn (264–293 pm) and Sn—Sn (308–373 pm) distances. The two crystallographically independent europium sites occupy large voids of coordination numbers 20 (Eu1) and 18 (Eu2) within the [Pt 3 Sn 5 ] network. Eu 2 Pt 3 Sn 5 shows Curie-Weiss behaviour in the temperature range 50–305 K with an experimental magnetic moment of 7.82(1) μ B per Eu atom indicating purely divalent europium. C p measurements show a broad anomaly with two maxima at 4.9(2) and 6.1(2) K. 151 Eu Mössbauer spectra revealed both crystallographically independent europium sites to be divalent. At 4.2 K two rather different sizes of magnetic hyperfine field splittings are observed due to separate ordering of the two sites. The 119 Sn Mössbauer spectrum shows complex superposition of the five signals in the paramagnetic range.

Despite the fact that both nitrosonium salts NO[SbCl 6 ] and NO[TaCl 6 ] crystallize in the same space group C 2/ c with Z = 4, their disorder behaviour is different. While in the antimony compound the reorientation jumps of the NO + ions are restricted to two alignments of equal weight, the NO + disorder of NO[TaCl 6 ] is in principle six fold, but with two of the alignments underrepresented. NO[SbCl 6 ] undergoes a phase transformation to C -1 at T c = 104 K. NO[TaCl 6 ] stays monoclinic down to 10 K. An extrapolation of the isotropic displacements against abso lute zero reveals permanent components due to genuine dis order. A computer simulation is used to investigate the unusual population of the NO + sites.

Crystallography shows the hexagonal form of Sb(S 2 COEt) 3 to have three-fold symmetry in which the antimony atom is chelated by asymmetrically coordinating xanthate ligands, Sb—S = 2.5204(8) and 3.0603(11) Å. The lone pair of electrons projects out of the triangular face defined by the three weakly coordinating sulfur atoms. The crystal structure comprises layers that stack in an ... ABAB ... fashion in contrast to the previously determined trigonal form. A similar coordination geometry is found in the structure of Sb(S 2 CO—nPr) 3 . Molecules aggregate into a supramolecular helical chain via secondary Sb ... S interactions. Crystal data for C 9 H 15 O 3 S 6 Sb, hexagonal, P 6 3 , a = 14.642(4), c = 4.6674(10) Å, V = 866.6(4) Å 3 , Z = 2, R = 0.021; C 12 H 21 O 3 S 6 Sb, monoclinic, P 2 1 / c, a = 14.671(5), b = 8.898(3), c = 17.185(6) Åb = 111.288(4)°, V = 2090.3(12) Å 3 , Z = 4, R = 0.042. An analysis of all available Sb(S 2 COR) 3 structures shows the adoption of molecules with C 3 or C s symmetry. In the case of the latter, well defined intermolecular Sb ... S contacts lead to supramolecular double chains. For the structures with C 3 symmetry, supramolecular aggregation patterns are more varied and less dependent on Sb ... S contacts.