Quadratic effects in multiphonon transition rates in solids

In this paper we explore the contribution of quadratic impurity—phonon coupling terms on nonradiative multiphonon transition rates in solids. It is demonstrated that the quadratic terms may increase substantially the transition rate and may modify quantitatively the energy gap law. Such effects will be exhibited even when the quadratic coupling is too weak to be observable in the optical spectra.     

Die Analyse hochfluorierter Kohlenwasserstoffe, demonstriert am Beispiel fluorierter n-Hexane

Zusammenfassung Gemische von Perfluor-n-hexan und Monohydrogen-perfluor-n-hexanen sind gaschromatographisch analysiert worden. Während bei der gaschromatographischen Trennung perfluorierter Kohlenwasserstoffe Fluor-Kohlenstoff- und Fluor-Chlor-Kohlenstoffverbindungen als besonders geeignete stationäre, flüssige Phasen gelten, hat sich im vorliegenden Falle Di-n-butylmaleat gut bewährt.Es werden die Infrarotspektren von 1 H-Perfluor-n-hexan, 2 H-Perfluor-n-hexan und 3 H-Perfluor-n-hexan vorgelegt und die Massenspektren dieser Verbindungen verglichen.

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Summary Mixtures of perfluoro-n-hexane and monohydrogen-perfluoro-n-hexanes were analysed by gaschromatography.While fluorocarbons and chlorofluorocarbons are known to be especially suitable media for the separation of flourocarbons by gaschromatography, in the case considered di-n-butyl maleate as a stationary liquid phase has proved to be useful.The infrared spectra of 1 H-perfluoro-n-hexane, 2 H-perfluoro-n-hexane, and 3 H-perfluoro-n-hexane are given and the mass spectra of these compounds are compared.

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Vortragender: Dr. K. Abraham.

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Das für die Untersuchung erforderlich, gewesene Kobalttrifluorid ist uns in dankenswerter Weise von den Farbwerken Hoechst, Frankfurt/M.-Höchst, zur Verfügung gestellt worden. Herrn Dr. W. Meise, Farbenfabriken Bayer, Leverkusen, danken wir auch an dieser Stelle herzlich für die exakten IR-Messungen an unseren Präparaten.     

Subject Index to Volume 31

Subject Index

Subject Index to Volume 31     

Layer-by-layer assembly of ordinary and composite coordination multilayers

Coordination self-assembly of bishydroxamate-based metal-organic multilayers on gold employing a layer-by-layer (LbL) approach was investigated. It is shown that the solution chemistry of the participating metal ion has a marked influence on the composition and properties of the multilayers. Use of Ce4+ and particularly zirconium(IV) acetylacetonate (Zr(acac)4) solutions in the ion-binding step of multilayer construction leads to multilayers with a near-stoichiometric metal ion-to-ligand ratio, suggesting a structure close to that predicted by a simple coordination self-assembly scheme. On the other hand use of a ZrCl4 solution as the source of metal ions in the multilayer construction leads to a multilayer with greater thickness and a large excess of Zr(IV), evenly distributed between the organic layers. In the latter case, a ratio of ca. 1:2 between the excess Zr and oxygen, as well as long-term Zr4+ binding experiments showing deposition of ZrO2, suggest the formation of a zirconia-type nanophase between the bishydroxamate organic repeat units during multilayer self-assembly. Hence, while the multilayer prepared using Zr(acac)4 solution appears to represent a "true" coordination-based structure, the one prepared using ZrCl4 is best described as a composite organic-ceramic multilayer. Composite multilayers prepared in this way display different properties from those of the stoichiometric ones, such as improved dielectric behavior and higher stiffness. Even greater mechanical stability is obtained with multilayers constructed using alternate binding of ZrCl4 and Ce4+. The concept of LbL formation of coordination-based composite organic-ceramic structures may be useful in obtaining nanometer-scale structures with tunable properties.     

Sharp ULP rounding error bound for the hypotenuse function

The hypotenuse function, , is sometimes included in math library packages. Assuming that it is being computed by a straightforward algorithm, in a binary floating point environment, with round to nearest rounding mode, a sharp roundoff error bound is derived, for arbitrary precision. For IEEE single precision, or higher, the bound implies that and . Numerical experiments indicate that this bound is sharp and cannot be improved.