The s-p bonded representatives of the prominent BaAl4 structure type: a case study on structural stability of polar intermetallic network structures

This work presents a detailed, combined experimental and theoretical study on the structural stability of s-p bonded compounds with the BaAl4 structure type (space group I4/mmm, Z = 2) as part of a broad program to investigate the complex questions of structure formation and atomic arrangements in polar intermetallics. From ab initio calculations employing pseudopotentials and a plane wave basis set, we extracted optimized structural parameters, binding energies, and the electronic structure of the systems AeX(III)4, AeX(II)2X(IV)2, AeX(II)2X(III)2 (Ae = Ca, Sr, Ba; X(II) = Mg, Zn; X(III) = Al, Ga; X(IV) = Si, Ge). For all systems we found a pronounced pseudo-gap in the density of states separating network X42- bonding from antibonding electronic states that coincides with the Fermi level for an electron count of 14 electrons per formula unit, the optimum value for stable BaAl4-type polar intermetallics. However, the synthesis and structural characterization (from X-ray single crystal and powder diffraction data) of the new compounds AeZn2-Al2+, AeZn2-deltaGa2+delta (Ae = Ca, Sr, Ba; delta = 0-0.2) and AeMg0.9Al3.1, AeMg1.7Ga2.3 (Ae = Sr, Ba) manifested that electron deficiency is rather frequent for BaAl4-type polar intermetallics. The site preference for different "X" elements in the ternary systems was quantified by calculating "coloring energies", which, for some systems, was strongly dependent on the size of the electropositive Ae component. The Ae2+ cations decisively influence the nearest neighbor distances in the encapsulating polyanionic networks X4(2-) and the structures of these networks are surprisingly flexible to the size of the Ae component without changing the overall bonding picture. A monoclinically distorted variant of the BaAl4 structure occurs when the cations become too small for matching the size of encapsulating X4(2-) cages. An even larger size mismatch leads to the formation of the EuIn4 structure type.     

Tris(2,2''''-bipyridyl)ruthenium(Ⅱ) electrochemiluminescence (ECL) enhanced by rutin on platinum electrode

Ru(bpy)_(3~(2 )) electrochemiluminescence (ECL) was applied to determination of rutin. ECL intensity of Ru(bpy)_(3~(2 ))could be enhanced in the presence of rutin in basic solution on platinum electrode. At pH 9.9, light emission intensity was found to be linear with rutin in the range of 1-50 mmol/L.     

Zweikernige silylenverbrückte Cyclopentadienylrhodiumbis(ethen)-Komplexe,photochemische Reaktion mit Benzolderivaten und selektiver Einschluß von Methylcyclopentan in das Kristallgitter von [Me2Si{3-But-C5H3Rh(C2H4)2}2]

Dinuclear Silylene Bridged Cyclopentadienylrhodiumbis(ethene) Complexes, Photochemical Reaction with Benzene Derivatives, and Selective Inclusion of Methylcyclopentane into the Crystal Lattice of [Me₂Si{3-Bu^t-C₅H₃Rh(C₂H₄)₂}₂] By reaction of [{(C₂H₄)₂RhCl}₂] with Na₂[Me₂Si(C₅H₄)₂] or with Li₂[Me₂Si(3-Bu^t-C₅H₃)₂] in THF the dinuclear silylene bridged complexes [Me₂Si{C₅H₄Rh(C₂H₄)₂}₂] 1 and [Me₂Si{3-Bu^t-C₅H₃Rh(C₂H₄)₂}₂] 2 , respectively, were synthesized. Due to the asymmetric substitution of the five-membered rings and their hindered rotation around the Si? C axes, 2 is formed as three isomers. The X-ray structure analysis of 2 obtained from hexane reveals the selective inclusion of methylcyclopentane, the content of which in the solvent is about 17%, into the crystal lattice. UV irradiation of 1 in hexane in the presence of benzene causes elimination of the ethene ligands yielding the μ-η³:η³ benzene complex [Me₂Si(C₅H₄Rh₂)₂C₆H₆] which cannot be separated from unreacted 1 . However, separation is possible in case of the hexamethylbenzene compound 4 analogous with 3 .     

Ein verschärfter und verallgemeinerter Satz von Alexandrov

In this paper we prove the following theorem: Suppose that n≥3 and 1≤jn $$(\forall a,b) d(a,b) : = \sum\limits_{\nu = 1}^j { (a_\nu - b_\nu )^2 - \sum\limits_{\nu = j + 1}^n { (a_\nu - b_\nu )^2 .} }$$ If a function f:?ⁿ→?ⁿ satisfies the condition: (*) $$(\forall x,y \in \mathbb{R}^n ) d(f(x),f(y)) = 0 \Leftrightarrow d(x,y) = 0,$$ then f is affine. Moreover, f preserves distances up to a constant factor C≠0, i.e. d(f(x),f(y))=C·d(x,y) for every x,y. In contrast to Alexandrov's result [1] we do not assume that f is bijective, and we also do not assume that j=n?1. A very important part of our proof will be the discussion of a functional equation.