Experimental approach to the determination of mechanism and kinetics of heterogeneous solid state reactionsA S →B S +C G

Structural and morphological investigations of the solid state decomposition process of Ni(SCN)₂(C₅H₅N)₄ single crystals to microcrystalline Ni(SCN)₂(C₅H₅N)₂ reveal a contracting sphere reaction mechanism. Reconsidering possible artefacts registered by quantitative thermoanalytical measurements a pathway for the determination of specific and reproducible kinetic parameters for the rate-limiting step is described.

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Zusammenfassung Strukturelle und morphologische Untersuchungen der Zersetzung von Ni(SCN)₂(C₅H₅N)₄-Einkristallen zu polykristallinem Ni(SCN)₂(C₅H₅N)₂ haben gezeigt, da\ diese Festkörperreaktion nach einem Kugelkontraktions-Reaktionsmechanismus verlÄuft. Unter Berücksichtigung der bei quantitativen thermoanalytischen Messungen möglicherweise auftretenden Artetakte wurde ein Weg zur Bestimmung der spezifischen und reproduzierbaren kinetischen Parameter für den geschwindigkeitsbestimmenden Schritt aufgezeigt.

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Ni(SCN)₂(C₅H₅N)₄ Ni(SCN)₂(C₅H₅N)₂ . , , , .

     

Structure and dynamics of dinuclear zirconium(IV) complexes

We have determined by X-ray crystallography the structures of three dinuclear zirconium(IV) complexes containing the heptadentate ligand dhpta (where H(5)dhpta = 1,3-diamino-2-propanol-N,N,N',N'-tetraacetic acid, 1) and different countercations: K(2)[Zr(2)(dhpta)(2)].5H(2)O (2.5H(2)O), Na(2)[Zr(2)(dhpta)(2)].7H(2)O.C(2)H(5)OH (3.7H(2)O.C(2)H(5)OH), and Cs(2)[Zr(2)(dhpta)(2)].H(5)O(2).Cl.4H(2)O (4.H(5)O(2).Cl.4H(2)O). In the K(I) complex 2, crystallized from water, the two Zr(IV) ions are 3.5973(4) A apart and bridged via two alkoxo groups (average Zr-O 2.165 A). Each Zr(IV) is eight-coordinate and also bound to two N atoms (average Zr-N 2.448 A), and four carboxylate O atoms (average Zr-O 2.148 A). The two dhpta ligands in the dinuclear unit have different conformations. One face of the complex contains an array of 14 oxygen atoms and interacts strongly with the two K(I) ions, one of which is 6-coordinate, the other 8-coordinate, which are 3.922(4) A apart and bridged by a carboxylate O and by two water molecules. The structures of the dinuclear anion [Zr(2)(dhpta)(2)](2-) in the Na(I) complex 3 and in the Cs(I) complex 4 are essentially identical to that found in complex 2, although the alkali metal ions coordinate differently to the oxygen-rich face. All Zr(IV) ions have a distorted triangulated dodecahedral geometry. Although the crystal structure of complex 2 does not indicate the presence of acidic protons, in 4 an [H(5)O(2)](+) unit is strongly H-bonded to an oxygen atom of a coordinated carboxylate group. 1D and 2D (1)H and (13)C NMR spectroscopic and potentiometric studies reveal two deprotonations with pK(a) values of 9.0 and 10.0. At low pH, two carboxylate groups appear to undergo protonation accompanied by chelate ring-opening, and the complex exhibits dynamic fluxional behavior in which the two magnetically nonequivalent dhpta ligands exchange at a rate of 11 s(-1) at pH 3.30, 298 K, as determined from 2D EXSY NMR studies. Ligand interchange is not observed at high pH (>11). The same crystals of complex 2 were obtained from solutions at pH 3 or 12. The dynamic configurational change is therefore mediated by the aqueous solvent.     

Optical properties of frustrated cholesteric liquid crystals

In a previous article, we proposed a model to explain the unwinding transition in an electric field of a frustrated cholesteric liquid crystal sandwiched between two glass plates imposing a homeotropic anchoring. We found that three distinct solutions exist in materials of negative dielectric anisotropy: first, the homeotropic nematic at small thickness and small voltage, second, a translationally invariant configuration (TIC) at large voltage and, third, the cholesteric fingers. In this article, we study some optical properties of these solutions. We show first that the TIC rotates the polarization of light. Its 'apparent' rotatory power is calculated exactly and is compared with the experimental data when the TIC-nematic phase transition is second order. The agreement between theory and experiment is excellent. We show in particular that there exist discrete values of the voltage for which the TIC has a pure rotatory power. We then calculated the optical contrast of the fingers when they are observed between crossed polarizers. The agreement with experiment is still satisfactory, in spite of the approximate form of the director field chosen to describe the topology of the finger.     

Polarographische Bestimmung von Molybd?n neben anderen Metallen

Zusammenfassung Es wird eine polarographische Bestimmungsmethode für Molybdän in Gegenwart anderer Metalle beschrieben. Molybdän(VI) gibt in Anwesenheit einer 0,25 M Ammoniumtartratlösung eine gut reproduzierbare Reduktionsstufe bei E _1/2= – 1,27 V (GKE). Die Methode wurde mit guten Ergebnissen bei der Molybdänbestimmung in Legierungen (Fehler ±1%) und mineralischem Gestein (Fehler –2%) angewandt. Der störende Einfluß von größeren Mengen Chrom(VI) wird durch ein beschriebenes säulen-chromatographisches Trennverfahren mit Hilfe des Anionenaustauschers Wofatit SBW beseitigt. Ein zehnfacher Überschuß an W(VI), Mn(II), Ni(II), Cu(II) und Tl(I) sowie gleiche Mengen an Fe(II), Fe(III), Cd(II), Co(II), V(V) und Bi(III) stören nicht.

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Summary A polarographic method for the determination of molybdenum in presence of other metals is described. Molybdenum (VI) yields a well-defined cathodic wave in ammonium tartrate medium (0.25 M) at E _1/2= –1.27 V vs. S.C.E. The results obtained have been applied to the determination of molybdenum in ores (error ±1%) and alloys (error –2%). The interfering influence of greater amounts of chromium(VI) is eliminated by ion-exchange with the strongly basic anion-exchanger Wofatit SBW. A ten-fold excess of W(VI), Mn(II), Ni(II), Cu(II) and Tl(I) as well as equal amounts of Fe(II), Fe(III), Cd(II), Co(II), V(V) and Bi(III) do not interfere.

     

Solution-Structure and Aggregation Behavior of Two Dilithiostyrene Derivatives

The solution structure and the aggregation behavior of (E)-2-lithio-1-(2-lithiophenyl)-1-phenylpent-1-ene ( 1 ) and (Z)-2-lithio-1-(2-lithiophenyl)ethene ( 2 ) were investigated by one- and two-dimensional ¹H-, ¹³C-, and ⁶Li-NMR spectroscopy. In Et₂O, both systems form dimers which show homonuclear scalar ⁶Li,⁶Li spin-spin coupling. In the case of 2 , extensive ⁶Li,¹H coupling is observed. In tetrahdrofuran and in the presence of 2 mol of N,N,N′,N′-tetramethylethylylenediamine (tmeda), the dimeric structure of 1 coexists with a monomer. The activation parameters for intra-aggregate exchange in the dimers of 1 and 2 ( 1 (Et₂O): ΔH≠ = 62.6 ± 13.9 kJ/mol, ΔS≠ = 5.8 ± 14.0 J/mol K, ΔG≠(263) = 61.1 kJ/mol; 2 (dimethoxyethane): ΔH≠ = 36.9 ± 6.5 kJ/mol, ΔS≠ = ?61 ± 25 J/mol K, ΔG≠(263) = 54.0 kJ/mol) and the thermodynamic parameters for the dimer-monomer equilibrium for 1 (ΔH°; = 26.7 ± 5.5 kJ/mol, ΔS° = 63 ± 27 J/mol K), where the monomer is favored at low temperature, were determined by dynamic NMR studies.     

Evolution of the delta13C signature related to total carbon contents and carbon decomposition rate constants in a soil profile under grassland

Evolution of the total carbon (C) content and the (13)C enrichment (delta(13)C signature) of soil organic matter (SOM) with increasing depth in a soil profile under permanent grassland (C(3) vegetation) were investigated. The relationship between the total C content and the delta(13)C signature at different depths in the upper 30 cm of the soil profile could be well fitted by the Rayleigh equation (y = -29.8 - 2.3x, R(2) = 0.95, p < 0.001), describing the enrichment in (13)C as resulting from isotopic fractionation associated with C mineralization (isotope enrichment factor epsilon = -2.3 per thousand). Potential C dynamics of SOM in four depth intervals of the profile (0-10, 10-20, 20-30 and 30-40 cm depth) were investigated through an incubation study. The C decomposition rate constants decreased with increasing sampling depth from 0.0479 yr(-1) (0-10 cm sampling depth) to 0.0256 yr(-1) (30-40 cm sampling depth) and were highly correlated (y = 0.02 + 0.13x, R(2) = 0.93, p < 0.05) with the corresponding deltadelta(13)C values (average change of the delta(13)C signature per depth increment). These results suggest that changes of the delta(13)C signature of SOM in undisturbed soil profiles under continuous C(3) vegetation may serve as an indicator of the variation of SOM quality with increasing depth.     

Operators of fibered groups

Let (G, ) denote a finite groupG with fibration . The group Aut (G, ) of operators of (G, ) is closely related to the group of collineations of (G, ). In this paper we investigate the geometric properties imposed on (G, ) by requiring that Aut (G, )=AutG. We find that in many instances this algebraic property restricts the geometry to a very special form.Dedicated to Professor Helmut Karzel on the occasion of his 60th birthday.     

Heavy doping with Sn of GaAs layers grown by molecular beam epitaxy for non-alloyed ohmic contacts

High Sn-doping of molecular beam epitaxy (MBE) grown GaAs layers for non-alloyed ohmic contacts is presented. The highly doped layers were studied by van der Pauw-Hall measurements, Raman spectroscopy, low-temperature photoluminescence and scanning electron microscope. The highest free electron concentration of 8×10¹⁸ cm^–3 and the lowest resistivity of 8× ×10^–4 cm were achieved. Doping limit of Sn in GaAs is discussed. Using the heavily Sn-doped GaAs layers and the in situ Sn deposition the non-alloyed ohmic contacts with specific contact resistance of 8×10^–5 cm² and highly linearI–V characteristics were obtained.This results were presented at the symposium Molecular Beam Epitaxy, Frankfurt/Oder, GDR, March 23–27, 1987.     

Schwarz Iterative Methods: Infinite Space Splittings

We prove the convergence of greedy and randomized versions of Schwarz iterative methods for solving linear elliptic variational problems based on infinite space splittings of a Hilbert space. For the greedy case, we show a squared error decay rate of \(O((m+1)^{-1})\) for elements of an approximation space \(\mathscr {A}_1\) related to the underlying splitting. For the randomized case, we show an expected squared error decay rate of \(O((m+1)^{-1})\) on a class \(\mathscr {A}_{\infty }^{\pi }\subset \mathscr {A}_1\) depending on the probability distribution.