Cooperative Jahn–Teller distortion leading to the spin-1/2 uniform antiferromagnetic chains in triclinic perovskites AgCuF3 and NaCuF3

Polycrystalline samples of AgCuF₃, isostructural with NaCuF₃, were synthesized by solid state reaction and characterized by powder X-ray diffraction. The magnetic properties of AgCuF₃ and NaCuF₃ were examined by measuring their magnetic susceptibilities and evaluating their spin exchange interactions. The three-dimensional CuF₃ network of corner-sharing CuF₆ octahedra present in AgCuF₃ and NaCuF₃ shows a cooperative Jahn–Teller distortion such that their magnetic susceptibilities above 50 K are well described by an S = 1/2 Heisenberg uniform antiferromagnetic chain model with average spin exchange of J/k_B ≈ ?300 and ?180 K, respectively. The relative strengths of these interactions are well reproduced by spin dimer analysis based on tight-binding calculations, but not by mapping analysis based on first principles density functional calculations.     

X-Ray Crystallographic Structure of the Cyclic Di-amino Acid Peptide: <Emphasis Type="Italic">N,N</Emphasis>′-Diacetyl-cyclo(Gly-Gly)

Abstract  

The cyclic di-amino acid peptide N,N′-diacetyl-cyclo(Gly-Gly), C₈H₁₀N₂O₄, crystallizes in the triclinic space group P[`1] P\bar{1} with unit cell parameters a = 9.4855(4) ?, b = 10.0250(3) ?, c = 10.0763(4) ?, α = 73.682(2)°, β = 82.816(2)°, γ = 81.733(2)°, V = 906.40(6) ?<sup>3</sup>, Z = 4 (2 molecules, A and B, per asymmetric unit), D<sub>c</sub> = 1.452 g cm<sup>−3</sup> and linear absorption coefficient 0.118 mm<sup>−1</sup>. The crystal structure determination was carried out with MoKα X-ray data measured at 120(2) K. In the final refinement cycle the data/restraints/parameter ratios were 4124/0/258 and goodness-of-fit on F<sup>2</sup> = 1.0008. Final R indices for [I > 2σ(I)] were R<sub>1</sub> = 0.0501, wR<sub>2</sub> = 0.1007 and R indices (all data) R<sub>1</sub> = 0.0864, wR<sub>2</sub> = 0.11180. The largest electron density difference peak and hole were 0.241 and −0.232 e ?<sup>−3</sup>, respectively. The DKP rings in both molecules A and B have boat conformations with pseudo mm2 (C<sub>2v</sub>) symmetry if the N atoms and CH<sub>2</sub> groups are considered identical. In each case, the prow and stern of the boat are the α-carbons C(3) and C(6). The overall molecular symmetry of molecules A and B is approximately C<sub>2</sub> with the twofold symmetry axis of the DKP boat being maintained through the centre of the DKP ring. Details of the molecular geometry are compared with that of the parent compound cyclo(Gly-Gly) in which the DKP ring is planar with exact symmetry [`1] \bar{1} (C_i).     

Loss of convexity and embeddedness for geometric evolution equations of higher order

We show that for a large class of geometric evolution equations of immersed surfaces in the Euclidean space, there are compact embedded surfaces that lose their embeddedness and compact strictly convex surfaces that lose their convexity under these evolution equations.     

Über den Zusammenhang zwischen Volumänderung und dem specifischen Drehungsvermögen activer Lösungen

Ohne Zusammenfassung     

Determination of the chemical diffusion coefficient of lithium in multiwall carbon nanotubes

Electrochemical intercalation of lithium into multiwall carbon nanotubes produced by the arc-electric technique has been carried out in button cells to estimate the solid state diffusion coefficients of lithium. An extension of the Galvanostatic Intermittent Titration Technique (G.I.T.T.) of Weppner and Huggins and further developed by Honders is employed. The results are interpreted providing that the lithium species enter the nanotubes perpendicularly to their walls and thus give rise to a necklace structure as observed by Transmission Electron Microscopy (TEM). Finally, the results are compared with the data obtained for different kinds of carbon: carbon fiber, petroleum coke and graphite. Paper presented at the 6th Euroconference on Solid State Ionics, Cetraro, Calabria, Italy, Sept. 12–19, 1999.     

An optimization-based numerical method for diffusion problems with sign-changing coefficients

A new optimization-based numerical method is proposed for the solution to diffusion problems with sign-changing conductivity coefficients. In contrast to existing approaches, our method does not rely on the discretization of a stabilized equation, and the convergence of the scheme can be proved without any symmetry assumption on the mesh near the interface where the conductivity sign changes.