A single crystal study of eight-layer barium managanese oxide,BaMnO3

A single crystal study of hydrothermally prepared eight-layer BaMnO₃ has been carried out which confirms the (Zhdanov notation) 121121 layer stacking scheme for the BaO₃ layers. The MnO₆ octahedra share faces in strings of four, and these strings are connected to each other by corner sharing. The compound has an hexagonal unit cell of dimensions a = 5.667 ± 0.003 and c = 18.738 ± 0.009 Å, probable space group $\text{P6}{}_3\text{mmc}\text{, Z = 8}$. Its structure has been determined from 352 independent reflections, of which 242 were considered observed, collected manually by a counter technique and refined to a conventional R value of 0.079.     

Magnetic behavior of tetrahedral Cr4+ compounds: Sr2CrO4, Ba2CrO4, and Ba3CrO5

The preparation of the compounds Sr₂CrO₄, Ba₂CrO₄, and Ba₃CrO₅ is described. The characterization of these three Cr⁴⁺ compounds by X-ray and magnetic susceptibility experiments has been conducted. The magnetic moments for Sr₂CrO₄, Ba₂CrO₄, and Ba₃CrO₅ were determined to be in good agreement with the calculated value expected for a tetrahedral Cr⁴⁺ ion. Weak antiferromagnetic ordering for all three compounds is indicated from the small paramagnetic Weiss constants determined from the susceptibility data in the temperature region 80–300 K. Distortions of the tetrahedra from ideality, as determined from the structural features, further cause a reduction in the magnetic moments from the theoretical values.     

Divisibility properties of a class of binomial sums

We study congruence and divisibility properties of a class of combinatorial sums that involve products of powers of two binomial coefficients, and show that there is a close relationship between these sums and the theorem of Wolstenholme. We also establish congruences involving Bernoulli numbers, and finally we prove that under certain conditions the sums are divisible by all primes in specific intervals.     

Magnetic and structural studies of Cr2O5 and Cr3O8

The infrared spectra, indexed X-ray powder diffraction patterns, magnetic susceptibilities between 80 and 300 K, and electron paramagnetic resonance spectra at 80 and 300 K are reported for Cr₂O₅ and Cr₃O₈. The results indicate that both oxides are Cr³⁺/Cr⁶⁺ mixed-valence compounds which contain CrO₆ octahedra and CrO₄ tetrahedra in different ratios. The valence formula for Cr₂O₅ is Cr³⁺₂Cr⁶⁺₄O₁₅ and that of Cr₃O₈ is Cr³⁺₂Cr⁶⁺₇O₂₄. The X-ray powder data for Cr₂O₅ and Cr₃O₈ could be indexed on the basis of a monoclinic unit cell $\text{(a = 12.01(2), b = 8.52(1), c = 9.39(1)}\text{A}\text{?}\text{β = 92.0(1)°)}$ and an orthorhombic unit cell $\text{(a = 12.01(7), b = 36.60(7) and c = 3.82(1)}\text{A}\text{?}\text{)}$, respectively.     

The characterization of calcium iridium oxides

Several calcium iridium oxides were prepared by solid state reactions and by a hydroxide precipitation technique. These phases were characterized by X-ray powder diffraction data, electrical and magnetic properties. The calcium-rich phase, Ca₄IrO₆, was an insulator exhibiting Curie-Weiss behavior above 77°K with a Weiss constant of ?47°K and a magnetic moment of 1.76 μ_B.Ca₂IrO₄ is a semiconductor and the temperature-dependent susceptibility above 77°K was analyzed in terms of one-dimensional linear chains of octahedrally coordinated Ir⁴⁺ ions.Two CaIrO₃ phases were isolated, but only the orthorhombic perovskite modification was sufficiently pure for magnetic studies. It was Pauli paramagnetic with metallic conductivity.