Crystal structure of the 6H BaCrO3 polytype

A product from the reaction between CrO₂ and Ba₂CrO₄ at 900°C under 60–65 kbar was found to be the six-layer polytype of BaCrO₃ from powder diffraction studies. A hexagonal black crystal obtained from this reaction was isolated for single crystal studies and structure determination. The crystal was found to possess a six-layer stacking sequence of BaO₃ layers with space group $\text{P6}{}_3\text{mmc}$ and had unit cell parameters a = 5.629(2), c = 13.698(6)Å, and Z = 6. The structure was determined from 936 independent reflections of which 693 were considered observed. Averaging equivalent reflections yielded 163 unique, observed reflections. Refinement of the structure by least-squares methods gave a conventional R value of 4.8% (R_w = 6.2%). The structure consists of a six-layer stacking sequence of close-packed BaO₃ layers containing tetravalent chromium in all the octahedral oxygen interstices. The compound was found to be isostructural with previously reported BaMO₃ phases.     

Structural evidence that alkoxy substituents adopt electronically preferred pseudoaxial orientations in six-membered ring dioxocarbenium ions

Nucleophilic substitution reactions of monosubstituted tetrahydropyran acetals give opposite selectivities when a remote alkyl or alkoxy substituent is present at C-4. Coupled with earlier computational reports on the intermediates of glycosylation reactions, these results are consistent with the preference for the oxocarbenium ion intermediate derived from alkoxy-substituted tetrahydropyran acetals to occupy a pseudoaxial conformation. Theoretical, spectroscopic, and X-ray crystallographic evidence of this conformational preference in an analogous and more stable dioxocarbenium ion are provided. This contrasteric preference for an axial orientation of an alkoxy substituent likely derives from the electronically favored pseudoaxial orientation of remote electronegative substituents in neutral six-membered rings possessing electron-deficient carbon atoms.     

The preparation and crystal structure of a BaRhO3 polytype

Barium rhodium oxide, BaRhO₃, was prepared at 1175°C and 60–65 kbar by the reaction of BaO₂ and RhO₂. A hexagonal black platelet obtained in the reaction product was found to possess a four-layer stacking sequence in space group $\text{P6}{}_3\text{mmc}$ having hexagonal unit cell parameters a = 5.744(1), c = 9.642(1) Å. The structure was detemined from 707 independent reflections of which 224 were considered observed. Averaging equivalent reflections yielded 132 unique observed reflections. Refinement of the structure by least-squares methods gave a conventional R value of 4.4%. The structure consists of a four-layer stacking sequence of close-packed BaO₃ layers containing tetravalent rhodium in all the octahedral oxygen interstices. The compound was found to be isostructural with previously reported BaMO₃ phases. This is the first single-crystal refinement of the 4H polytype using a four-circle diffractometer.     

Using nucleophilic substitution reactions to understand how a remote alkyl or alkoxy substituent influences the conformation of eight-membered ring oxocarbenium ions

[reaction: see text] A remote alkoxy substituent strongly stabilizes one particular conformer of an eight-membered ring oxocarbenium ion by a through-space electrostatic effect. X-ray crystallographic analysis of a crystalline derivative proves that kinetically controlled nucleophilic substitution favors the 1,4-trans product. Nucleophilic substitution of the corresponding alkyl-substituted acetate, however, is unselective. A computational model has been developed and experimentally validated to predict the low-energy conformers of C3-, C4-, or C5-alkyl- or alkoxy-substituted eight-membered ring oxocarbenium ions.     

A characterization of the disc by sets of uniqueness in tomography

In mathematical tomography, one wishes to reconstruct a density function on a compact set from knowledge of certain integrals. If one knowsa priori that this function is a characteristic function, some reduction in the amount of data needed may be obtained (see Fishburn et al. SIAM J. Appl. Math.50, 288–306, 1990). In such a situation we say the support regionD is a set of uniqueness. We show here that ifD is a smoothly-bounded Jordan domain which is a set of uniqueness for every pair of orthogonal directions, thenD is a disc.G.M.L.G. was supported by a Natural Sciences and Engineering Research Council of Canada grant.     

A high-pressure modification of MgVO3

The preparation of a high-pressure form of MgVO₃ has been accomplished utilizing two independent synthesis methods. The triclinic, ilmenite-type phase has been characterized by its crystallographic, magnetic, and electrical properties. Its structure is believed to be similar to that previously observed for other ilmenite-type AVO₃ derivatives (CoVO₃, NiVO₃, and MnVO₃). The properties of MgVO₃ appear to be intermediate between the localized electron model found in MnVO₃, CoVO₃, and NiVO₃, and the delocalized electron regime observed in CuVO₃.