Volume 213, Issue 3

Coordination sequences have been determined for tilings { p , q } of the hyperbolic plane in which q p -gons meet at each vertex. The number of vertices in successive shells is related by a recurrence to the numbers in earlier shells and grows exponentially. General expressions for the recurrences are given and numerical expressions for the growth rate are determined. For p = 3 – 10, 12, 14, 16 and 18 exact expressions, that require finding roots of polynomials of degree ≤4, are given for the coordination sequence. Some differences between hyperbolic tilings and 3-dimensional nets are noted.

Main structural subdivisions of sulphate minerals and synthetic compounds were considered in the frame of a new structural classification of minerals, based on the strength distribution and directional character of the bonds. The specific features of their crystal chemistry were expressed by the corresponding structural formulas. The recommendations expressed by the Subcommittee on the Nomenclature of the Inorganic Structure Types of the IUCr Commission on the Crystallographic Nomenclature were also considered. Consequently the structural systematics of sulphates includes the following five main categories of structures: 1) atomic (or close-packed), 2) group, 3) chain, 4) sheet and 5) framework. Sulphate atomic structures occur mostly when individual atoms form either closest packing or any other close packing. In contrast to the present study this subdivision was not considered in all previous systematics of sulphate minerals. The next categories comprise the structures formed either by isolated SO 4 tetrahedra and MO n polyhedra with the M–O bond strengths comparable with those of the S–O bonds, or by the complex structural units, where SO 4 tetrahedra are linked to MO n polyhedra. The category of the structures, involving different types of structural units, corresponds to the structural unit with the highest dimensionality. Crystal chemical peculiarities of sulphates are revealed as a result of the structural systematics.

The title compound was synthesized from 3 α -acetoxy-12 α -hydroxy-24- nor -5 β -cholan- 23 -oic acid by treating it with dichloroethylphosphate and triethylamine. The crystals are orthorhombic, space group P 2 1 2 1 2 1 , a = 19.166(2) Å, b = 14.109(2) Å, c = 8.246(1) Å, V = 2229.9(6) Å 3 , Z = 4, D c = 1.189 g cm −3 , λ (Cu K α ) = 1.5418 Å, μ = 0.55 mm −1 , F (000) = 880, T = 298 K. The structure was solved by direct methods and refined to R = 0.049 for 894 observed reflections collected on a CAD-4 diffractometer. The molecules in the crystal are in their monolactone form. Energy calculations, based on molecular modeling were carried out for similar molecules containing 6- to 11-membered monolactone and 12- to 22-membered bislactone rings. The relative minimum energy values, obtained by MMX calculations, show a considerable decrease for monolactone rings with less than eight members, and a considerable increase for the bislactones with less than sixteen atoms. The MMX calculations are in agreement with current experimental results which indicate that the monolactonization occurs only in cases where the number of atoms forming the lactone ring is less than eight.

Large single crystals of KN 3 , KHF 2 , NH 4 HF 2 , KSCN and NH 4 SCN, which are structurally related to those of the CsCl type, were grown from aqueous solutions by controlled evaporation. Elastic, thermoelastic and piezoelastic constants were determined from ultrasonic resonance frequencies of thick plane-parallel plates. In addition, the tensors of thermal expansion were measured. Elastic properties and thermal expansion reflect the close relationship to the CsCl-type structure. The anisotropy is mainly caused by the preferential orientation of the long axes of the anionic dumb-bells within one distinct plane. KSCN exhibits weak elastic anomalies approaching the phase transition at 413 K. These effects, which are much smaller than those found in the high-temperature phases of the alkali cyanides, indicate, together with the almost missing hysteresis and the small transition enthalpy, a transition of mainly second order. The variation of the elastic behaviour of KHF 2 and NH 4 SCN passing through the transition at 471 K and 367 K, respectively, express first-order processes.

Large single crystals of optical quality of (±)-tris(ethylenediamine)cobalt(III) nitrate have been grown from aequeous solutions. An X-ray structure analysis yielded space group Pca 2 1 , a 1 = 15.441(3) Å, a 2 = 8.607(2) Å, a 3 = 12.328(2) Å, Z = 4, ϱ calc = 1.724 g cm −3 , ϱ obs = 1.730 g cm −3 . The structure is built up from [Co(H 2 N(CH 2 ) 2 NH 2 )] 3+ cations and nitrate anions which are linked by Coulomb interactions and by a three-dimensional network of hydrogen bonds. Two ligands of the cationic chelate complex are disordered. Its probable conformation is Δδλλ or the enantiomorphic Λδδλ . Pyroelectric, dieletric, piezoelectric and elastic constants have been determined at room temperature. Additionally, we have studied the coefficients of thermal expansion and the thermoelastic constants in the range between 270 K and 350 K. The structure exhibits a nearly trigonal symmetry around the [unk] 2 -axis. The physical properties obey qualitatively this symmetry. The maximum longitudinal piezoelectric effect surmounts d 111 of α -quartz by a factor 10. The largest piezoelectric constant is d 113 ≈ 14 d 111 of α -quartz. Dielectric and elastic constants appear only slightly anisotropic, contrary to a strongly anisotropic thermal expansion.

The structure of a cubic Al 67.4 Pd 11.4 Mn 14.4 Si 6.8 phase, which is referred as an 1/1 rational approximant of an icosahedral phase, was determined by means of single crystal X-ray structural analysis: space group Pm 3 (No. 200), a = 12.281(1) Å, V = 1852.0(3) Å 3 , Mo K α ( λ = 0.71069 Å); refined as Al 66.3 Pd 12.0 Mn 14.7 Si 7.0 , atom/cell = 122.72, F (000) = 2305, μ = 7.54 mm −1 , D calc = 4.47 Mgm −3 , R = 0.0319 for the observed 703 reflections with I > 2.0 σ ( I ). An atom cluster with about 13 Å in diameter is found at the origin of a unit cell and the cubic arrangement of these clusters through the shared edges can reproduce the present 1/1 approximant structure. This atom cluster is ranked into five atomic shells, where the atomic arrangement analogous to the Bergman cluster is clearly identified. The clusters of Bergman's derivation are suggested to be one of the most essential cluster units for the face-centered icosahedral quasicrystals.

Reaction of triphenylmethane with cesium metal in dimethoxyethane (DME) or of phenothiazine in diglyme yields two organometallic cesium compounds as extremly air and moisture sensitive single crystals. In triphenylmethanide cesium · 1.5 DME, the counter cations form two structurally different contact ion pairs to symmetry-related triphenylmethanide anions and are solvated in addition by two crystallographically independent ether solvent molecules, which partly connect the resulting polymeric chains. In phenothiazine cesium diglyme, each counter cation is surrounded by three symmetry-related phenothiazine anions and one diglyme molecule predominantly via their oxygen, nitrogen and sulfur centers and again infinite polymer chains are formed. All structural results are discussed based on literature data of analogous complexes.

The crystallographic characterization of the following three calcium channel antagonists is reported here: 2,6-dimethyl-3,5-dicarbamoyl-4-[2-nitro]-1,4-dihydropyridine ( 1 ), 2,6-dimethyl-3,5-dicarbamoyl-4-[4-methoxy]-1,4-dihydropyridine ( 2 ) and 2,6-dimethyl-3,5-dicarbamoyl-4-[3,4-dichloro]-1,4-dihydropyridine ( 3 ). The dihydropyridine rings are in shallow boat conformation in all the three compounds. The carbamoyl groups at C3 and C5 are oriented anticlinal in 1 and 2 ; but in 3 , they are anticlinal and synperiplanar, respectively. It is possible that intra and intermolecular interactions may be influencing the positioning and orientation of the aryl substituents and the conformation of the novel C3 and C5 carbamoyl group. In addition, it is seen that participation of the molecules of crystallization has significantly changed the hydrogen bonding network.

The title compound [Mn(BPDC)(H 2 O) 4 ] n (BPDC = C 12 H 6 N 2 O 4 2− , the dianion of 2,2′-bipyridine-3,3′-dicarboxylic acid), C 12 H 14 N 2 O 8 Mn, has been prepared and its crystal structure determined by single crystal X-ray diffraction at room temperature. The cell parameters are a = 13.951(2) Å, b = 6.374(1) Å, c = 8.408(1) Å, orthorhombic, P 2 1 2 1 2. The six coordinated Mn(II) complex adopts a distorted octahedron. The Mn atoms are located on the two fold axis and connected by carboxylate ions to form polymeric chains along the b -axis. The carboxylate acts as monodentate, and bipyridine does not coordinate to Mn. In the coordination polyhedron, the Mn…O distances are in the range 2.207(3) Å to 2.215(3) Å. The two pyridine rings are not coplanar [ τ = 63.8°]. The water molecules are involved in three-dimensional hydrogen bond network.