Systematik der Seltenerdmetall-Blei-Legierungen

Zusammenfassung Das systematische Verhalten (sowie dessen Fehlen) der Seltenerdmetall-Blei-Legierungen wird untersucht. Es wurden 12 verschiedene Verbindungsstöchiometrien beobachtet. Fast alle dreiwertigen Lanthanidenelemente bilden die PhasenR ₅Pb₃,R ₅Pb₄ undRPb₃. Von den anderen möglichen Stöchiometrien kommen, mit Ausnahme vonRPb₂, nur von einigen Lanthaniden Verbindungen vor. Die bekannten kristallographischen Daten werden durchbesprochen und die Existenz und Nichtexistenz einiger Phasen auf Grund kristallchemischer Theorien diskutiert. Das Schmelzverhalten derR-reichen Eutektika und der PhasenR ₅Pb₃,RPb₂ undRPb₃ wird dargestellt. Die bekannten Informationen über diese Legierungen werden auf der Basis der relativen Volumskontraktionen und des 4f-Beitrags zur Bindung überprüft und die Ergebnisse zu Voraussagen über die relativen Stabilitäten der VerbindungenR ₅Pb₃,RPb₂ undRPb₃ verwertet.

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Systematics of the rare earth-lead alloys

The systematic behavior (and also the lack of it) in the rare earth-lead alloys is examined. Twelve different compound stoichiometries have been observed. Nearly all of the trivalent lanthanide elements form theR ₅Pb₃,R ₅Pb₄, andRPb₃ phases. For the other stoichiometries, except for possiblyRPb₂, compounds exist for only a limited number of the lanthanide elements. The known crystallographic data are reviewed, and the existence and nonexistence of some of the phases are discussed on the basis of crystal chemistry theories. The melting behaviors of theR-rich eutectic and theR ₅Pb₃,RPb₂ andRPb₃ phases are presented. The known information on these alloys is examined on the basis of the relative volume contractions and the 4f contribution to the bonding, and the results are used to predict the relative stabilities of theR ₅Pb₃,RPb₂, andRPb₃ compounds.

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Mit 8 Abbildungen

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Herrn Prof. Dr.H. Nowotny gewidmet.

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Die Arbeiten wurden im Ames-Laboratorium der US-Atomenergie-kommission durchgeführt (Beitrag Nr. 2972).     

Absolutberechnung der Normalfrequenzen des Hydrogendifluoridions

Zusammenfassung Mit Hilfe eines einfachen quantenmechanischen Näherungsansatzes wird versucht, Bindungsabstände und Normalfrequenzen des Hydrogendifluoridions sowie des entsprechenden deuterierten Ions zu berechnen. Hierbei wird die Elektronenwechselwirkung der beiden Fluoridionen untereinander durch einen der Statistik entlehnten Ausdruck berücksichtigt. Die Methode liefert für die Abstände gute, für die Normalfrequenzen durchaus befriedigende Ergebnisse.

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On the basis of a quantum mechanical treatment the bond distances and the normal frequences of the hydrogen difluoride ion and its deuterated analogue are calculated. The electronic interaction of the two fluoride ions is approximated by a statistical calculation. The results are in fairly good agreement with the experimental values.

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Résumé Sur la base d'un traitement quantique simple, le calcul des distances de liaison et des fréquences normales est tenté pour l'ion de bifluorure d'hydrogène et son analogue deutéré. L'intéraction électronique des deux ions fluorures est approximée au moyen d'un calcul statistique. Les résultats sont en très bon accord avec les valeurs expérimentales.

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Der Deutschen Forschungsgemeinschaft danken wir für die Gewährung eines Stipendiums an Karl Hensen.     

Alkyl- and aryl-substituted corroles. 4. Solvent effects on the electrochemical and spectral properties of cobalt corroles

Solvent effects on the electrochemistry and spectroscopic properties of alkyl- and aryl-substituted corroles in nonaqueous media are reported. The oxidation and reduction of six compounds containing zero to seven phenyl or substituted phenyl groups on the macrocycle were studied in four different nonaqueous solvents (CH(2)Cl(2), PhCN, THF, and pyridine) containing 0.1 M tetra-n-butylammonium perchlorate. Dimers were formed upon oxidation of all corroles in CH(2)Cl(2), but this was not the case in the other three solvents, where either monomers or dimers were formed upon oxidation depending upon the solvent Gutmann donor number and the number or location of aryl substituents on the macrocycle. The half-wave potentials were analyzed as a function of the number of aryl substituents on the macrocycle as well as the concentration of added pyridine to PhCN solutions of the compound, and these data were combined with data from the spectroelectrochemistry experiments to determine the stoichiometry of the species actually in solution after the first oxidation or first reduction of each compound. The results of these experiments indicate that reduction of the bispyridine adduct (Cor)Co(III)(py)(2) proceeds via the monopyridine complex (Cor)Co(III)(py) to give in each case the unligated cobalt(II) corrole [(Cor)Co(II)](-). In contrast, pyridine remains coordinated after electrooxidation, and the final product was characterized as [(Cor)Co(III)(py)(2)](+).     

New minimal geodesics in the group of symplectic diffeomorphisms

We compute the Hofer distance for a certain class of compactly supported symplectic diffeomorphisms of ²ⁿ. They are mainly characterized by the condition that they can be generated by a Hamiltonian flow _H ^t which possesses only constantT-periodic solutions for 0 <T 1. In addition, we show that on this class Hofer's and Viterbo's distances coincide.     

Pattern-specific neural network design

We present evidence that the performance of the traditional fully connected Hopfield model can be dramatically improved by carefully selecting an information-specific connectivity structure, while the synaptic weights of the selected connections are the same as in the Hopfield model. Starting from a completely disconnected network we let genuine Hebbian synaptic connections grow, one by one, until a desired degree of stability is achieved. Neural pathways are thus fixed notbefore, butduring the learning phase.     

Some analytical semigroups occurring in probability theory

One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.