Band 191, Heft 1-2

An X-ray structural study ( R = 0.040 for 1871 reflections) of the title compound has been carried out. Molecules in crystal are pseudocentrosymmetric, the piperidine cycle is in a chair conformation. The N atoms of both paramagnetic centers exhibit, in fact, the same degree of pyramidalization, their displacements from the planes of their bonded atoms being 0.111 and 0.119(2) Å. In crystal the molecules form two sets of infinite ribbons (along the [112] and [[unk]12] directions), which are linked with each other via the O – H … O hydrogen bonds along the [001] direction. Although the packing of diacetylene rod-like groups does not correspond to the conditions of topochemical polymerization of diacetylenes, compound I polymerizes in crystal.

An X-ray structural study ( R = 0.049 for 1254 reflections) of C 22 H 24 N 2 O 2 was carried out. The molecule occupies an inversion center, the six-membered unsaturated heterocycle is in the distorted boat conformation. The N atoms have pyramidal geometry, their displacement from the plane of their bonded atoms being 0.131(2) Å. No indication of conjugation of the double bond in the heterocycle with the diacetylene system is observed. The relative arrangement of the rod-like diacetylene groups of adjacent molecules does not satisfy the conditions of topochemical interaction in diacetylene crystals. Nevertheless the compound studied undergoes polymerization in crystals.

An X-ray structural study ( R = 0.043 for 2704 reflections) of C 24 H 30 N 2 O 4 was carried out. The molecule has a skewed conformation, the piperidine cycles are in a chair conformation. The N atoms of paramagnetic groups exhibit different degrees of pyramidalization, due to crystal packing effects, their displacements from the planes of three bonded atoms being 0.111 and 0.042(2) Å. The H-bonds of the O – H … O type link the molecules into layers parallel to the ac -plane. The molecules do not form characteristic stacking necessary for the topochemical solid state polymerization. This fact is in good agreement with the observed inertness of the crystals with respect to the solid state polymerization.

Lattice similarity operators are transformation matrices which describe a linear mapping of two crystal lattices on to each other such that: (i) points of a common derivative lattice of reasonably low index in both lattices form a coincidence site lattice ; (ii) the deformation occurring with the mapping is tolerably small; (iii) the determinant of the transformation matrix is fixed by the ratio of the formula units in the unit cells of both crystals. These conditions are formulated in terms of matrix algebra. To tackle the discrete optimization problem of searching for lattice similarity operators between two given arbitrary lattices, a search tree algorithm is proposed. It minimizes the number of trial matrices to be investigated by systematic use of geometrical criteria which are derived from the above conditions. The search is based on the identification of triplets of lattice vectors of one lattice in the other. The triplets are limited to those uniquely defining all derivative lattices of interest. Applications of the method are envisaged in all situations where geometrical relationships between lattices or crystal structures have to be described, in particular for the real space description of structural transitions if the transformation matrix cannot be deduced clearly from experimental observations. The method is demonstrated using the martensitic transformation in zirconia and the reconstructive transformation between the (Mn, …)SiO 3 polymorphs Rhodonite and Pyroxmangite as examples.

For cations showing different co-ordination numbers (CN) a curve for bond valence s vs bond length R can be calculated by requiring that for regular co-ordination polyhedra ( R = const. = R ′) the value of s for R ′ coincides with Pauling's bond strength p . The method is applied to the Ca – O bond taking as R ′ the average Ca – O distance in selected polyhedra with CN = 6, 7, 8 and 9. The relationship s = ( R /2.004) −6.41 – 0.008 is proposed.

Most BO 4 -groups deviate significantly from a regular tetrahedron with symmetry [unk]3 m - T d . The geometry of these deviations and the extent of the distortions are the main topics of this study. The shapes of 256 borate groups in 128 compounds have been investigated. In BO 3 -groups with O … BO 3 distances shorter than 3 Å the boron atom is displaced from the plane of the BO 3 -group towards the fourth oxygen atom. The displacement increases as the O … B distance decreases. Borate groups in orthorhombic and cubic boracites seem to represent the extreme distortions of OB [3+1] O 3 - and B [4] O 4 -groups, respectively. Mean B—O distances of the 242 B [4] O 4 -groups vary from 1.444 to 1.534 Å, individual B—O distances from 1.373 to 1.699 Å [mean value = 1.476(35) Å], individual O—B—O angles from 95.72 to 119.43° [mean value = 109.44(2.78)°]. Two simple models, e.g. a variant of a hybrid orbital model and a ligand repulsion model, have been used to calculate the shape of BO 4 -groups with trigonal symmetry, which are in good agreement with those experimentally determined.

The crystal structure of 1-methyltriphenylene, C 19 H 14 , has been determined by application of direct methods to single-crystal X-ray diffractometric data, with refinement by least-squares to R = 0.087 over 987 independent reflections to give apparent estimated standard deviations of 0.01 Å in C – C bond lengths and 0.6° in C – C – C angles. In the methyl-substituted bay region, molecular overcrowding is relieved by a long beach bond C13 – C14 = 1.50(1) Å and a C14 – C1 – C19 bond angle of 126° to the methyl group, with the beach-arm bond angles C12 – C13 – C14 = 122° and C13 – C14 – C1 = 124° compared with about 121° in the unsubstituted bay regions. Substitution of the methyl group into nearly planar triphenylene also causes ring-carbon atoms in all three peripheral rings to deviate by as much as ± 0.3 Å from the mean molecular plane; the methyl-carbon atom is 0.8 Å below this plane. The ring-methyl C1 – C19 bond is long [1.53(1) Å]; and, in the unsubstituted rings, the peripheral bonds C6 – C7 and C10 – C11 at 1.35(1) Å and 1.36(1) Å, respectively, are slightly shorter than in triphenylene.

C 23 H 26 O is monoclinic, space group P 2 1 with a = 9.368(1), b = 17.121(6), c = 11.629(5) Å, β = 91.39(1)°, V = 1864.6 Å 3 , Z = 4, D c = 1.134 Mg m −3 , F (000) = 688, μ = 0.444 mm −1 , λ (Cu Kα ) = 1.5418 Å, T = 293 K. The final R is 0.063 for 2121 observed reflections. The results of the structure determination agree with the circular dichroism analysis through the octant rule. Besides, circular dichroism and configuration of 3,3-dimethyl, 3,3-di(p-chlorobenzyl) nopinones and 3-nopinone-spirocyclopentane are discussed.

CuI is known to undergo two phase transitions at T 1 = 367°C and T 2 = 407°C. The structural changes involve a rearrangement of the anions and disordered distributions of the cations. The low temperature γ -phase has zincblende structure, space group F [unk]3 m [ a = 6.0337(3) Å, Z = 4]. The intermediate β -phase belongs to the hexagonal system with a hcp anion lattice [ a = 4.289(9) Å), c = 7.189(5) Å, Z = 2], space group P [unk] m 2 (coexisting with γ - or α -phase). The high temperature α -phase is cubic again, the anions form a fcc lattice and the cations are randomly distributed over all tetrahedral sites, space group Fm [unk] m [ a = 6.148(1) Å, Z = 4]. A modified powder profile refinement program, which includes anharmonic temperature factors, was used for the refinement of CuI at different temperatures and probability density functions were calculated to elucidate the diffusion paths of this high temperature superionic conductor. Different models were tried with anharmonic coefficients upto the fourth order and split models with anisotropic temperature factors. With increasing temperature the density of Cu cations begins to spread from the center of the tetrahedra towards the vacant octahedral interstices. Aproaching the α-β transition from above the lobes near the tetrahedral faces become more pronounced indicating a transition from a diffusion to a more static (jump) behaviour near the phase transition.

Single crystals of ZnGeO 3 ilmenite have been synthesized at 180 kbar and 1500°C using a uniaxial split-sphere apparatus. The crystal structure of ZnGeO 3 ilmenite has been determined with 588 counter-measured intensities refined by the least-squares method to R = 0.020 and R w = 0.021. ZnGeO 3 ilmenite is trigonal with a = 4.9568(8) Å, c = 13.860(2) Å, V = 294.91(11) Å 3 , space group R [unk] and Z = 6. Zinc and germanium atoms are completely ordered in the structure; the average Zn—O and Ge—O distances are 2.144 Å and 1.898 Å, respectively. The ZnO 6 octahedra in ZnGeO 3 ilmenite display one of the largest quadratic elongation and bond angle variance values among compounds with the ilmenite structure. The distortion and height of the GeO 6 octahedra in ZnGeO 3 ilmenite are comparable with those observed in other germanate ilmenites, consistent with the trend that distortion of the B 4+ O 6 octahedra changes little upon substitution of different A 2+ cations in the structure. Analysis of c / a systematics shows that c / a increases linearly among the germanate and titanate ilmenites as the ‘size mismatch’ (i.e. difference in ionic radii) between the A 2+ and B 4+ cations increases. The different slopes of the two different groups shows that c / a is less affected by substitution of larger A 2+ cations in titanate ilmenites than germanate ilmenites where the ‘size mismatch’ is greater.

The structure of an antimony-rich pinakiolite from the Långban mine in Sweden has been investigated by single crystal X-ray diffraction techniques. The space group symmetry used to describe the structure is C 2/ m , Z = 8, with the unit cell dimensions a = 21.773(4), b = 6.153(2), c = 5.327(2) and β = 94.38(2)°. The derived structural model has been refined versus the 553 most significant reflections with I > 3 · σ ( I ) and sin( θ )/ λ ≤ 0.8 Å −1 to an R -value of 0.047. The results yield the composition Mg 1.90(1) Mn 0.91(1) Sb 0.19(1) O 2 BO 3 in reasonable agreement with the composition Mg 1.83 Mn 0.91 Sb 0.26 O 2 BO 3 found by EDS analysis on the same crystal as was used for the X-ray data collection. The X-ray diffraction studies indicate some disorder in the crystals. The present study, which is based on the non-diffuse X-ray diffraction intensities, only gives a slightly idealized structural model. The results indicate metal ion distributions largely in agreement with those found in other members of the pinakiolite family. The presence of infinite rows of heavily distorted edgesharing coordination octahedra around the Mn 3+ ions is a relevant factor for the occurrence of extended metal position disorder in adjacent rows of octahedra.

The single crystal structure of the high temperature phase, δ -Y 2 Si 2 O 7 , has been established by X-ray diffraction. Crystal data: Y 2 Si 2 O 7 , M = 346.0; orthorhombic, Pnam , a = 13.655(5), b = 5.016(3), c = 8.139(3) Å; V = 557.5 Å 3 , D x = 4.121 g cm −3 , Z = 4. λ (Mo – Kα ) = 0.71069 Å, μ (Mo – Kα ) = 21.2 mm −1 , F (000) = 648 electrons, room temperature; R = 0.077 for 294 reflections. The structure proves to be similar to that proposed in the space group Pna 2, for Gd 2 Si 2 O 7 by Smolin and Shepelev (Acta Crystallogr. 26B (1970) 484 – 492). The present work suggests that the space group Pnam provides an adequate representation of this structure type in the case of Y 2 Si 2 O 7 .

Mimetite Pb 5 (AsO 4 ) 3 Cl, M = 1488.21 Daltons, space group P 6 3 / m , a = 10.250(2), c = 7.454(1) Å, U = 678.214(2) Å 3 , Z = 2, D calc = 7.26 g cm −3 , λ = 1.237 Å, μ (neutron) = 2.85 cm −1 . The structure of the lead chloroarsenate mineral, mimetite, an isomorph of apatite, was refined using single crystal neutron diffractometry [ R (189 hkl ) = 0.057].