Volume 212, Issue 10

A Monte Carlo approach to indexing is described in which direct space is randomly sampled in order to obtain the direct space lattice vectors appropriate for indexing a set of reflections in an unbiased fashion. A conjugate gradient approach is used to optimize these vectors once a point in that locality is sampled. Probabilities are assigned to the reflections based on their deviations from integer for each of the three basis vectors and the combined probability provides a basis for downweighting effects due to satellite crystals.

The kinetics of the α -quartz to coesite transition have been studied in the pressure range of 3.2 GPa to 5.2 GPa and in the temperature range 950 K–1175 K by in situ X-ray diffraction using a MAX80 cubic anvil high-pressure apparatus at the Hamburger Synchrotronstrah-lungslabor (HASYLAB). During the phase transition, X-ray diffraction patterns were collected at intervals of 60 s. The transformed volume fraction has been calculated from the diffracted intensities of the respective phases as a function of time. By fitting a fundamental rate equation for grain boundary nucleation and interface-controlled growth to the transformation-time data, rates of nucleation and growth have been calculated. A discrepancy between the experimental determined and theoretical calculated phase boundary is discussed. After quenching the samples, the reaction products could be investigated by TEM images. A specific feature of the synthesised coesite crystals was a concentrated microtwinning. Its influence on the crystal structure and thus on the thermodynamic behaviour of the α -quartz-coesite phase transition is illustrated.

The crystal structure of (NH 4 ) 4 · [Mo 8 O 24+ x (O 2 ) 2− x (H 2 O) 2 ] · 4H 2 O ( x = 0.8) has been determined from single-crystal X-ray diffraction data. The yellow compound crystallizes in the monoclinic space group P 2 1 / n with a = 10.427(3) Å, b = 7.914(5) Å, c = 18.103(3) Å, β = 96.10(2)°, V = 1485.5(9) Å 3 and Z = 2. Full-matrix least-squares refinement of 213 structural parameters gave R ( F ) = 0.034 ( R w ( F ) = 0.042) for 2630 observed [ I > 3 σ ( I )], independent reflections. The formula implies that part of the diaquatetracosaoxodiperoxooctamolybdate(VI) ions have been replaced by diaquahexacosaoxooctamolybdate(VI) ions and/or diaquapentacosaoxomonoperoxooctamolybdate(VI) ions (substitutional solid solution). The centrosymmetric [Mo 8 O 24 (O 2 ) 2 (H 2 O) 2 ] 4− anion consists of six MoO 6 octahedra and two MoO 5 (O 2 ) pentagonal bipyramids, sharing edges. Selected bond distances: Mo–O peroxo 1.940(9) Å–1.964(10) Å, Mo=O terminal 1.681(6) Å–1.719(6) Å, Mo–O bridging 1.751(5) Å–2.429(5) Å and (O–O) peroxo 1.462(13) Å. Mo·· ·Mo edge–sharing is 3.244(1) Å–3.494(1) Å and Mo…Mo corner–sharing is 3.833(1) Å and 4.123(1) Å.

The new mineral gordaite [14] from the Sierra Gorda, Chile, has chemical composition NaZn 4 (SO 4 )(OH) 6 Cl · 6H 2 O and crystallizes trigonal with space group P [unk]. The lattice parameters are a = 8.3556(3) Å and c = 13.025(1) Å. The structure was determined using direct methods and difference Fourier maps. Structure refinement yielded a final R ( F )-value of 8.19%. The structure is characterized by brucite-like sheets of composition [Zn 6 (OH) 12 O 2 ] 4− which are formed by edgeshared Zn(OH) 6 octahedra. One seventh of the octahedral sites in the sheet is vacant. Above and below these sites [Zn(OH) 3 Cl] 2− tetrahedra are located sharing their basal hydroxides with six octahedra. Sulfate groups are connected to the sheets on both sides by corner sharing. The composition for this modified layer is [Zn 6 oct □ oct (OH) 6 Zn 2 tet (OH) 6 Cl 2 (SO 4 ) 2 ] 2− . To compensate for the negative charge Na + ions which are octahedrally coordinated by water molecules are incorporated between the layers. A complex hydrogen bonding system further links subsequent layers. The structure of gordaite is closely related to that of the synthetic material Zn 4 (OH) 6 SO 4 · m H 2 O with m = 3,5 described by Bear et al. in 1986 and presumably the same material as the one investigated by MacEwan, Cruz Cumplido and Cano Ruiz (1966) who state an average chemical composition of Zn 12 (OH) 15 (SO 4 ) 3 Cl 3 · 5H 2 O. A comparison to these materials as well as to Zn 5 (OH) 8 Cl 2 · H 2 O described by Nowacki and Silverman in [12] is drawn.

Electron diffraction patterns of M 56 (O, F) 156 (M = Mg, Nb, W) (along [001]) exhibit eight additional spots arranged on an octagon around every reflection of the tetragonal tungsten bronze-type (TTB) substructure. Four superstructure spots are located between the main reflections along all 〈210〉 TTB directions. Two orientations of the new TTB superstructure ( a = b = 2.73 nm, c [unk] 0.38 nm, α = β = γ = 90°) are present in the investigated crystal regions causing the unique octagonal array of spots. Highly resolved lattice images show that the arrangement of pentagonal tunnels filled with metal-oxygen strings is systematic in small domains. Four distinguishable variants of the superstructure appear. In each case two of them have the same orientation with respect to the TTB sublattice.

The structural changes of stoichiometric LiNbO 3 at temperatures up to 1470 K have been investigated by neutron powder diffraction. At T c ≈ 1460 K, LiNbO 3 transforms from a paraelectric high-temperature ( R [unk] c ) to a ferroelectric low temperature structure ( R 3 c ). The phase transition is of coupled order-disorder and displacive type. In the high-temperature phase, Li is highly disordered over two off-centre positions, whereas Nb takes a centrosymmetric position within O 6 octahedra. An analysis of anisotropic displacement parameters shows that the probability density function of Li is extended along c , that of the oxygens is more or less perpendicular to the Nb–O bonds, and that of Nb is slightly extended in the a – b plane at high temperatures. An increase of the tilt angle of the NbO 6 octahedra away from an h.c.p. arrangement towards a perovskite structure was observed. The octahedra become almost regular at high temperatures. Comparison with an earlier investigation of congruent lithium niobate shows a quite similar behaviour, however, all parameters of the latter are closer to those of the perovskite structure at same temperatures. Anomalies in the behaviour of the order parameters, a more complicated disorder and a high mobility of Li at high temperatures are explained by the competition of the order-disorder and displacive character of the phase transition.

Co 3 (C 2 O 4 )(SeO 3 ) 2 and Zn(C 2 O 4 ) · 2H 2 O were synthesized investigating the reaction products of Fe(C 2 O 4 ) · 2H 2 O and SeO 2 combined with transition metal elements at low-hydrothermal conditions. The crystal structures were determined by direct methods from single-crystal X-ray diffraction data. Co 3 (C 2 O 4 ) (SeO 3 ) 2 : space group C 2/ m , Z = 2, a = 9.163(2) Å, b = 6.513(2) Å, c = 7.806(2) Å, β = 117.14(2)°, V = 414.6(2) Å 3 , R 1 = 0.023. Zn(C 2 O 4 ) · 2H 2 O: space group C 2/ c , Z = 4, a = 11.812(3) Å, b = 5.402(1) Å, c = 9.919(2) Å, β = 127.72(1)°, V = 500.6(1) Å 3 ; R 1 = 0.029. Both compounds consist of MO 6 octahedra (M = Co, Zn), linked via the oxalate groups to chainlike subunits. These are further combined via additional CoO 6 octahedra and the trigonal pyramidal selenite group or via hydrogen bonds, respectively. Mean bond lengths are 2.119 Å and 2.099 Å for Co [6] –O, 1.701 Å for Se(IV) [3] –O and 2.094 Å for Zn [6] –O.

The crystal structure of LiHSeO 3 has been redetermined using synchrotron radiation X-ray diffraction data collected up to sin θ / λ = 0.575 Å −1 at five different wavelengths, four close to the Se K -absorption edge (0.97974 Å), the fifth at 0.560 Å. Each data set was initially refined separately (460–470 unique reflections, 53 parameters), but a joint refinement of all data (2319 reflections, 61 parameters) resulted in substantially decreased standard deviations of atomic parameters and derived quantities. LiHSeO 3 crystallizes in the orthorhombic and non-centrosymmetric space group P 2 1 2 1 2 1 [ Z = 4, a = 5.0551(2) Å, b = 11.1874(6) Å, c = 5.2202(3) Å, V = 295.22(8) Å 3 ]. Its crystal structure consists of pyramidal HSeO 3 − ions with two shorter Se–O [both 1.660(1) Å] and one longer Se–OH [1.782(1) Å]. The HSeO 3 − are linked into spiral chains along [100] by hydrogen bonds [O(3)…O(1) = 2.622(1) Å, O(3)–H = 0.77(2) Å, O(1)…H = 1.87(2) Å]. Each of the Li + is tetrahedrally surrounded by oxygens at distances 1.910(2) Å, 1.943(2) Å, 1.968(3) Å, and 2.021 (3) Å, joining the HSeO 3 − chains into a space-filling three-dimensional network.

The crystal structures of four Cs 3 MI 5 (M = Mn, Cd, Hg) compounds have been determined. Cs 3 MnI 5 ( A ) is tetragonal, I 4/ mcm , with a = 10.187(1) Å and c = 16.574(1) Å. It has the Cs 3 CoCl 5 structure type. At room temperature there are two orthorhombic modifications ( B and C ) of Cs 3 CdI 5 crystals, both grown from water solution of CsI and CdI 2 . In addition a compound with composition Cs 3 (Cd 0.52 Hg 0.48 )I 5 ( D ) was prepared. B crystallizes in Pnma , a = 10.036(1) Å, b = 11.852(1) Å, c = 14.850(1) Å, and C and D in Pbca , with cell dimensions a = 18.893(1) Å, b = 37.015(4) Å, c = 10.085(1) Å, and a = 18.771(2) Å, b = 18.439(3) Å, c = 10.118(2) Å, respectively. The B compound has the (NH 4 ) 3 ZnCl 5 -type structure, while C is very closely related to D and the Cs 3 HgI 5 type. All four structures can be described as built from MI 4 2− tetrahedra and units of Cs 3 I 2+ with I surrounded octahedrally by six Cs. In A there is a rotationally distorted ReO 3 type framework of corner-sharing ICs 6 octahedra. B , C and D have columns of face-sharing ICs 6 octahedra, extending in each case along the 10 Å axis. In this description A is an antitype of perovskite and the B , C and D structures are related to the antitype of BaNiO 3 . The C and D structures can be generated from the B type by glide-reflection twinning in the octahedral planes parallel to (011) of B . D requires twinning in all planes, and C requires that every other plane is a twin plane. The tetrahedral Mn–I distances are 2.690(1) Å and the Cd–I distances are 2.748(1) Å–2.786(1) Å [ B ], 2.725(3) Å–2.785(3) Å [ C ], 2.726(2) Å–2.789(2) Å [ D , average of Cd–I and Hg–I]. The Cs–I distances in the ICs 6 octahedra are in the range 3.848(1) Å–4.143(1) Å [ A ], 3.771(1) Å–4.019(1) Å [ B ], 3.778(3) Å–4.022(3) Å [ C ], and 3.794(2)Å–3.953(2) Å [ D ]. In the alternative, conventional, description the Cs + ions are eight or nine coordinated by I in all four structures, except one of the two independent Cs + in A which is ten coordinated. The origin of the Cs 3 CdI 5 polymorphism is discussed. The cell volume per formula unit of the Cs 3 (Cd, Hg)I 5 obeys Vegard's law.

The crystal and molecular structure of polymeric magnesium bis ( p -nitrophenolate) dihydrate, [Mg(O 2 NC 6 H 4 O) 2 (OH 2 ) 2 ] ∞ , C 12 H 12 MgN 2 O 8 , has been determined at room temperature. The orange crystals are monoclinic, space group C 2 with unit cell dimensions a = 21.183(2) Å, b = 3.667(4) Å, c = 10.357(2) Å, β = 117.227(7)°, Z = 2 and D x = 1.562 Mg m −3 . The structure was solved by direct methods and refined by a full-matrix least-squares procedure on F 2 to final R = 0.062 using 960 reflections. The Mg 2+ cation (which lies on a two-fold axis) exists in a slightly distorted octahedral geometry with the basal plane being defined by four water molecules and the axial positions by two oxygen donor atoms derived from two symmetry related NO 2 groups. Each pair of coordinated water molecules links a neighbouring Mg 2+ centre leading to the formation of columns of edge-shared octahedra. These columns are linked via hydrogen bonding contacts involving the non-coordinating oxygen atoms of the p -nitrophenoxide and the Mg…OH 2 groups.

The crystal structures of [NiCl 2 (PMePh 2 ) · (PNMe 2 )] · 1/2 CH 2 Cl 2 ( 1 ), C 33 H 33 Cl 2 NNiP 2 · ½ CH 2 Cl 2 , and [NiCl(PMePh 2 )(PNMe 2 )][PF 6 ] ( 2 ), C 33 H 34 ClF 6 NNiP 3 , have been determined by X-ray diffraction. Complex 1 crystallises in the monoclinic space group P 2 1 / n , a = 11.305(6) Å, b = 17.620(9) Å, c = 18.061(9) Å, β = 90.48(4)°, V = 3597(3) Å 3 and Z = 4. Refinement of 2508 observed reflections and 275 parameters converges to a conventional R of 0.051. The coordination around the Ni(II) centre is distorted trigonal bipyramidal with the two axial positions occupied by the phosphorus atom of the monodentate phosphine and the tertiary amine nitrogen of the bidentate PNMe 2 chelate. The equatorial sites accommodate the remaining phosphorus of the amino-phosphine and two chlorine donors. Complex 2 crystallites in the orthorhombic space group Pbca , a = 18.61(1) Å, b = 15.42(1) Å, c = 23.25(2) Å, V = 6673(7) Å 3 and Z = 8. Refinement of 2351 observed reflections and 347 parameters yields R = 0.051. A square planar geometry describes the coordination around the metal with the two phosphorus donors located in a mutual cis -arrangement. As expected on the basis of the different coordination number, all of the metal-donor distances decrease on going from 1 to 2 , as evidenced, in particular, by the Ni–N bond which contracts from 2.325(8) Å to 2.056(8) Å.

The crystal and molecular structure of N -tetradecyl-(2,4-dihydroxy)-butanoic acid amide (C 18 H 37 NO 3 ) has been determined by direct methods. The compound crystallizes in the monoclinic space group C 2/ c with a = 96.27(3), b = 4.8135(12) Å, c = 8.701(5) Å 3 , β = 91.84(4)°, V = 4030(3) Å 3 , Z = 8, D x = 1.04 Mg · m −3 . The molecules are packed in the bilayer arrangement as usually observed in amphiphiles. The amide bond and the 2-OH group form intralayer oriented hydrogen bonds of Etter graph sets C(4) and C(5), respectively. In contrast to these, the terminal hydroxyl group which exhibits a two-fold disordered hydrogen atom forms hydrogen bonds with centrosymmetrically related counterparts in the neighbouring bilayer (Etter graph set C(2)). Identical hydrogen bond graph sets were also found in the crystal structures of some further compounds chemically related with the title compound.

The structure of a newly synthesised solvated compound, 1,2,3-tris(4-quinolyl)cyclopropane, C 30 H 21 N 3 , has been analysed by X-ray diffraction (monoclinic, space group C 2/ c , a = 26.194(4) Å, b = 7.912(2) Å, c = 23.830(4) Å, β = 96.11(3)°, Z = 8, V = 4910.6(3) Å 3 ). Its structure was partly solved by direct methods and refined by molecular dynamic and least squares procedures on 2816 reflections to final R = 0.053. The general features of the trans conformation of quinoline rings obtained by molecular modelling is in agreement with the X-ray model. However, it fails to predit the orientations of quinoline planes and the C–C–C angles connecting the quinoline rings to the cyclopropane group. Presence of solvent molecules, still not clearly identified, and others factors inducing these discrepancies are discussed.