Thermodynamische Untersuchungen im System Gold—Cadmium

Zusammenfassung Flüssige und feste Legierungen im System Au–Cd wurden von 60 bis 90 At% Cd zwischen 653° und 873°K mit derEMK-Methode untersucht und thermodynamische Eigenschaften berechnet. Die Aktivitäten von Cd zeigen stark negative Abweichungen vom idealen Verhalten. Die partiellen molaren Enthalpien sind negativ und verschieben sich mit zunehmender Temperatur zu weniger negativen Werten, die partiellen molaren Entropien sind positiv und nehmen mit zunehmender Temperatur zu. Aus eigenen Werten und Literaturdaten wurden integrale thermodynamische Größen für die Schmelzen im gesamten System Au–Cd bei 1000°K berechnet. Für einige feste Cd-reiche Phasen wurden ebenfalls Aktivitäten erhalten und aus den Knickpunkten derEMK-Temperatur-Kurve Temperaturen von Phasenübergängen bestimmt.

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Thermodynamic investigations in theAu–Cd-system

Liquid and solid alloys in the Au–Cd system were investigated between 60 and 90 at % Cd and 653°–873°K by theemf method, and thermodynamic properties were calculated. The activities of Cd exhibit strong negative deviations from ideal behavior. Partial molar enthalpies are negative and become less so with increasing temperature; partial molar entropies are positive and increase with increasing temperature. A consistent set of integral thermodynamic data for liquid solutions of the entire Au–Cd system at 1000°K were calculated using values taken from the literature. Activities for some solid Cd-rich phases were also obtained. From discontinuities in theemf vs. temperature curve temperatures of phase transitions were determined.

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Mit 5 Abbildungen

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Herrn Prof. Dr.H. Nowotny gewidmet.     

The probabilistic solution of the dirichlet problem for\tfrac{1}{2}\Delta + \left\langle {a,\nabla } \right\rangle + b with singular coefficients

We investigate weak solutions ofLu=?p, whereL= \(\tfrac{1}{2}\Delta + \left\langle {a,\nabla } \right\rangle + b\) and |a|²,b andp belong to the Kato classK ^d (d≥3). We shall characterize the weak solutions by a probabilistic mean value property. This characterization includes a continuity principle. Our second regularity result states that for a weak solutionu, |?u|² belongs locally to K^d. Regarding the inhomogeneous Dirichlet problem forL, we shall prove the corresponding gauge theorem and an existence and uniqueness result.     

Efficient kinetic resolution of a racemic 7-membered biaryl lactone: enantioselective synthesis of 2,2′-dihydroxymethyl-1,1′-binaphthyl

A novel pathway to enantiomerically pure 2,2′-dihydroxymethyl-1,1′-binaphthyl is described, through kinetic resolution of its racemic 7-membered biaryl lactone precursor. Oxazaborolidine-assisted borane reduction of this lactone proceeds with very high enantioselectivity (k_rel=50). For optimum results on a preparative scale, a ‘three fractions strategy’ is suggested, which combines kinetic resolution and fractional crystallization and leads to both atropisomers in high enantiomeric excess.     

Electrophoretic clean-up of organic acids from coffee for the GC/MS analysis

The clean-up presented here includes a free flow field step electrophoresis followed by ultrafiltration. Thus, organic acids can be separated from non-acidic and high-molecular compounds in roasted and instant coffee. The acids are identified by gas chromatography/mass spectrometry after freeze-drying and trimethylsilylation. With the method presented, 31 acids could be identified in commercial roasted coffee blends and in instant coffee, among them for the first time in coffee: 3-hydroxypropionic, 2-oxobutyric, glyceric, 2,4-dihydroxybutyric, 5-hydroxymethylfuran-2-carboxylic and 2-hydroxyglutaric acid.     

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

Switchable magnetic bottles and field gradients for particle traps

Versatile methods for the manipulation of individual quantum systems, such as confined particles, have become central elements in current developments in precision spectroscopy, frequency standards, quantum information processing, quantum simulation, and alike. For atomic and some subatomic particles, both neutral and charged, a precise control of magnetic fields is essential. In this paper, we discuss possibilities for the creation of specific magnetic field configurations which find application in these areas. In particular, we pursue the idea of a magnetic bottle which can be switched on and off by transition between the normal and the superconducting phase of a suitable material in cryogenic environments, for example, in trap experiments in moderate magnetic fields. Methods for a fine-tuning of the magnetic field and its linear and quadratic components in a trap are presented together with possible applications.     

Theoretical study of new acceptor and donor molecules based on polycyclic aromatic hydrocarbons

Functionalized polycyclic aromatic hydrocarbons (PAHs) are an interesting class of molecules in which the electronic state of the graphene-like hydrocarbon part is tuned by the functional group. Searching for new types of donor and acceptor molecules, a set of new PAHs has recently been investigated experimentally using ultraviolet photoelectron spectroscopy (UPS). In this work, the electronic structure of the PAHs is studied theoretically with the help of B3LYP hybrid density functionals. Using the ΔSCF method, electron binding energies have been determined which affirm, specify and complement the UPS data. Symmetry properties of molecular orbitals are analyzed for a categorization and an estimate of the related signal strength. While σ-like orbitals are difficult to detect in UPS spectra of condensed film, calculation provides a detailed insight into the hidden parts of the electronic structure of donor and acceptor molecules. In addition, a diffuse basis set (6-311++G**) was used to calculate electron affinity and LUMO eigenvalues. The calculated electron affinity (EA) provides a classification of the donor/acceptor properties of the studied molecules. Coronene-hexaone shows a high EA, comparable to TCNQ, which is a well-known classical acceptor. Calculated HOMO-LUMO gaps using the related eigenvalues have a good agreement with the experimental lowest excitation energies. TD-DFT also accurately predicts the measured optical gap.