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Electronic properties of the two rutiles TiO<sub>2</sub> and VF<sub>2</sub>: A comparative study

AbstractResults of first‐principles, density‐functional LMTO‐ASA calculations on the two title compounds and of unrestricted Hartree‐Fock (UHF) calculations on VF2 are reported. The calculations on the crystalline materials were performed with special emphasis on optimising all (three) structural parameters, on the valence density of states and the valence electron density, and on the possible existence of spin polarisation. In addition, full‐potential LMTO calculations on isolated monomers were carried through in order to examine the nearest‐neighbour (TiO and VF) chemical bonds in detail and to understand the consequences of various approximations in describing the potential for the crystal. The LMTO‐ASA calculations reproduce the correct lattice constants with, however, some overestimate for VF2. Also the nearest‐neighbour TiO and VF bond lengths are reproduced correctly by the LMTO calculations, whereas the c/a ratios are significantly overestimated. By analysing the charge densities of the isolated monomers we conclude that the overestimates in the c/a ratios are due to the ASA (Atomic‐Sphere Approximation), which does not describe the quadrupole‐quadrupole interactions of the compounds sufficiently accurately. The Hartree‐Fock calculations yield lattice constants for VF2 very close to experiment. Also in agreement with experiment, TiO2 is found to be non‐magnetic and insulating/semiconducting. In contrast, VF2 is found to be metallic within the LMTO‐ASA method, although the density‐functional calculations indicate that magnetic effects will change the compound into an insulator as it is according to experiment. On the other hand, in agreement with experimental evidence, UHF yields a non‐metallic structure. It further shows the stability of a number of patterns of magnetic ordering.

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Viscous fingering at the liquid/liquid interface between two coexisting phases of mixtures with a miscibility gap

AbstractThe influence of the viscosity contrast factor A [( = η“‐η′)/(η“+η), η, shear viscosity: (′)(”), indices of the coexisting phases; η“&gt;η′]on the formation of viscous fingers at a mechanically unstable liquid/liquid interface of mixtures with a miscibility gap in a narrow rectangular glass cell (closed Hele‐Shaw cell) is studied. The systems used for the experiments are: (a) 2‐butoxyethanol (C4E1)/water mixtures of critical composition. They are studied in the vicinity of the lower critical point at temperatures above the critical temperature [1.05 &lt; (η”η') &lt; 2.0, corresponding to 0.05&lt;A&lt;0.4]. A is varied by changing the temperature of the mixture; (b) poly(ethylene glycol) (PEG)/dextran (D)/water mixtures at different compositions in the vicinity of the plait point at constant temperature [10&lt;(η“/η')&lt;40, corresponding to 0.762&lt;A&lt;0.950]. The liquid/liquid interfacial tension of both systems is small (σ&lt;0.1 mN m−1). The experimental results are analysed in terms of theoretical work of Tryggvason and Aref (J. Fluid. Mech. 177, 207 (1985)). The viscous fingering process is treated as a two‐dimensional viscous flow. For small values of A (&lt;0.12; system (C4El1/water) the growth rates of the viscous fingers in the upward and downward direction have about the same value and the fingers have a similar shape. At larger values of A (&gt;0.3) the fingers formed by the phase with the higher viscosity advance faster into the phase with the lower viscosity than the fingers advancing in the opposite direction. This effect is pronounced in the system PEG/D/water for which A has large values (A&gt;0.75). In this system the viscous fingers formed by the phase with the higher viscosity are long and narrow whereas that formed by the low viscosity phase are short and broad. The temperature dependence of the mean distance &lt;l&gt; between viscous fingers of the system C4E1/water advancing in opposite directions approaches the theoretically expected dependence at temperature differences (Tp‐Tc)&gt;l K corresponding to a ratio (λmax/b) &gt; 3 (λmax, wave length of fasted growing interfacial instability; b, width of the glass cell). The experiments show that the preferential wetting of the glass walls of the Hele‐Shaw cell by one of the coexisting liquid phases leads to a three‐dimensional shape of the viscous fingers.

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Kinetics of the Birch reduction

AbstractBecause of contradictions in the literature, we reinvestigated the kinetics of the Birch reduction, i.e. the hydrogenation of benzene and its derivatives in metal ammonia solutions (MAS: containing solvated electrons e− and metal cations M+) with alcohols to yield the corresponding cyclohexa‐1,4‐dien compounds (e.g. 2 Li+2CH3OH+C6H6⟹2CH3OLi+C6H8). The kinetics of this reaction are obscured since the hydrogen reaction proceeds parallel to it (2Li+2CH3OH⟹2CH3OLi+H2). The two reactions differ in their activation energies (6.5 and 22.5 kJ/Mol resp.); and in the series of the alkali metals Li, Na and K the rate of the Birch reduction decreases, whereas that of the hydrogen reaction increases. However, in the metal concentration range around 0.01 M. both reactions have within the experimental error the same reaction order with respect to the metal (≈︁0.8). Both are accelerated by addition of alkali cations common to the dissolved alkali metal, and both are decelerated by addition of alkali cation complexing cryptands. Thus we conclude that the cations are involved in the kinetics of both reactions, probably by forming intermediate ion pairs or shifting pre‐equilibria in which solvated electrons are involved. The experimental data of both reactions can be described very well with the rate laws v(B) = kBf2[e−][Li+)[CH3OH][C6H6]and v(H)=kHf2[e−][Li+](CH3OH]resp. (f activity coefficients after Debye‐Hückel) inserting the concentrations of e− and Li+ as calculated from the known thermodynamics of LiAS. The experimental rate constants kB and kH are the products of the rate constants of the rate determining steps and the equilibrium constants of the pre‐equilibria.

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