Showing papers by "Technical University of Dortmund published in 1973"

On the theory of vortex motion in an inhomogeneous superconducting film

Abstract: A phenomenological theory is presented giving an account of the pinning effect which occurs when vortex motion in a superconducting film is hindered by inhomogeneities of the material. In particular, the theory incorporates the interaction (pinning) potential between a vortex and the material defects, as well as long wavelength distortion of the vortex lattice. A recent observation of quantum interference effects of a moving vortex lattice can be explained successfully. It is shown how the pinning potential and the elastic constants can be obtained from experiment.

Electron-phonon interaction in an impure metal

Abstract: On the basis of the existing theory of ultrasonic attenuation, a model Hamiltonian is derived which has to replace the Frohlich Hamiltonian, at least in an impure metal. Whilst the imaginary part of the phonon self-energy is easily connected with the ultrasonic attenuation constant, the same quantity of the electrons allows no conclusion on inelastic collisions in this case. Therefore, from the linear response function, a kinetic equation for the electrons is derived. It is found that the time between inelastic collisions with phonons increases if impurities are added to the metal.

Guiding concepts relating to trace analysis

Abstract: ‘Trace’ is a term much used in colloquial language; it has many connotations and should not be ‘appropriated’ to denote ‘scales of working’ in chemistry. The concept “scope of analysis” is proposed instead. The quantities “amount of substance”, “mass” and “concentration” are critically considered and it is proposed that more use of a logarithmic presentation of concentration values should be made. The role of the “blank portion” of measured quantities with respect to trace determinations is pointed out; “analytical signal” and “analytical noise” are discussed. Linearization of the “calibration function” and elimination of the blank measures are required for extrapolation of calibration functions to low concentrations. The different calibration methods (σ, α, δ, ω) are presented; the importance of “rating” analysis and “gradual” analyses with coarsened scales is pointed out. The ‘type’ of information, the “informing power” provided by a procedure and the “information required” by the analytical problem are discussed. The “topological structure” of a procedure is shown to be decisive for its applicability to trace determinations. “Selectivity” and “sensitivity” are defined as metric quantities to be calculated from the “calibration matrix” of the procedure. High values of these two quantities are required for ‘trace work’. “Specificity” is mentioned only. Finally some remarks about the “limit of detection” and the “limit of guarantee of purity” are made to clear up common mistakes, made when applying these useful concepts.

Polariton Fusion in CuCl

Abstract: Selection rules and frequency dependence for fusion of two polaritons to a longitudinal exciton or a transverse polariton are discussed for crystals of point symmetry Td. Within certain approximations, the transition probability depends only on the polarization of the two polariton beams and on the K-vector of the final state. The theoretical predictions are found to be in good agreement with two-photon absorption measurements for the first exciton in CuCl. Es werden Auswahlregeln und Frequenzabhangigkeit der Fusion von zwei Polaritonen zu einem longitudinalen Exziton oder einem transversalen Polariton fur Kristalle mit Td-Punktsymmetrie diskutiert. Innerhalb gewisser Naherungen hangt die Ubergangswahrscheinlichkeit nur von der Polarisation der beiden Polaritonenbandel und von dem K-Vektor des Endzustandes ab. Die theoretischen Ergebnisse stimmen gut mit Messungen der Zweiphotonenabsorption am ersten Exziton von CuCl uberein.

Electronic Spectra of Trigonal and Disordered Phases of Tellurium and Selenium. I. Theory

Abstract: The electronic density of states of trigonal and amorphous tellurium and selenium are calculated in the energy region of the two-highest-valence-band triplets and the two-lowest-conduction-band triplets. The calculations are performed using the pseudopotential scheme. The structural model for the amorphous phases is based on the assumption that the average short-range order is the same as in the trigonal crystals. The main results are that (i) the density of states of the amorphous phases of both materials is essentially structureless in the energy region of the second-conduction-band triplet; (ii) some fine structure is maintained in the two valence bands and the first conduction band. These can be associated with parts of the density of states contributed from a region of the Brillouin zone along the ${k}_{z}$ axis. The results are compared to those obtained by using a tight-binding approximation. The comparison with experimental data will be performed in an accompanying paper.

Note on a paper of B. Grünbaum on acyclic colorings

Abstract: The aim of this short note is to improve some recent results of B. Grunbaum by some remarks. We use Grunbaum's notations.

Basisches Verhalten von Epoxiden in Gegenwart von Halogenid-Ionen, I. Dehydrohalogenierung von Halogenalkanen mit Epoxiden in Gegenwart von Halogenid-Ionen

Abstract: Epoxide uberfuhren in Gegenwart von Halogenid-Ionen Halogenalkane in Alkene. IR- und NMR-spektroskopische Geschwindigkeitsmessungen legen nahe, das das substituierte 2-Halogenathylat-Ion (z. B. 3) als Base fungiert. Basic Behavior of Epoxides in the Presence of Halide Ions, I. Dehydrohalogenation of Haloalkanes with Epoxides in the Presence of Halide Ions Epoxides convert haloalkanes into alkenes in the presence of halide ions. Kinetic studies with the aid of i.r. and n.m.r. spectroscopy Indicate that 2-haloethoxide ions (e. g. 3) act as proton acceptors.

Chemische Anwendungen der Raman-Spektroskopie

Abstract: Die Raman-Spektroskopie ist – wie auch die IR-Spektroskopie – eine Methode zur Untersuchung des Schwingungsspektrums von Molekulen und Kristallen. Beide Methoden sind komplementar: Andert sich bei einer Schwingung die Polarisierbarkeit des Molekuls, so erscheint sie als Raman-Bande, andert sich das Dipolmoment, so ist sie als IR-Bande zu beobachten. Schwingungen unpolarer Bausteine und totalsymmetrische Schwingungen von Molekulen zeigen sich oft nur im Raman-Spektrum. Beide Spektren, gemeinsam ausgewertet, geben Aufschlus uber die Symmetrien und Strukturen von Molekulen und Kristallen, uber Eigenschaften der chemischen Bindungen und zwischenmolekulare Wechselwirkungen. Bis vor etwa zehn Jahren konnte man Raman-Spektren praktisch nur von mehreren Gramm farbloser flussiger Stoffe erhalten. Die Laser-Lichtquellen anderten die Situation vollig. Die erforderlichen Probemengen liegen jetzt im Milli-und Mikrogrammbereich. Gase, Flussigkeiten und feste Stoffe, insbesondere luftempfindliche und aggressive Proben, Einkristalle, Kristallnadeln und Fasern sowie wasrige Losungen lassen sich untersuchen. Identifizierungen und Strukturaufklarungen von Molekulen, biochemische Analysen und Analysen im Umweltschutz sind wichtige Anwendungen der Raman-Spektroskopie. Sie ist jetzt ein leistungsfahiger Partner der ubrigen Methoden der instrumentellen Analyse.

Electronic Spectra of Trigonal and Disordered Phases of Tellurium and Selenium. II. Experiment

Abstract: The electronic structures of trigonal tellurium and trigonal selenium have been investigated by photoemission, using conventional energy-distribution curves (EDC's) and their second derivatives which reveal significant fine structure, embedded, but hardly observable, in EDC's. The two $p$ valence bands (${p}_{1} \mathrm{and} {p}_{2}$) and the second conduction band (SCB) are explored for both materials except for ${p}_{1}$ in the case of Se. In particular, the bottom of the SCB is positioned 4.6 and 6.1 eV above the upper edge of ${p}_{2}$ in Te and Se, respectively. The spectral structure is interpreted in terms of partial contributions to the total density of states (DOS) of restricted regions of the Brillouin zone, namely, about the $\ensuremath{\Delta}$ axis and point $H$, as obtained theoretically in Paper I of this work. A similar study is carried out on disordered films of Te and Se, deposited in ultrahigh vacuum onto a flame-polished silica substrate. A comparison between the photoemission spectra obtained from these films and those obtained from trigonal Te and Se reveal a sharp attenuation of the conduction-band-DOS structure in agreement with the theoretical results, Paper I. The valence-band total DOS in these films exhibit more subtle disorder effects, characterized by (i) the loss of the contribution of point $H$ and (ii) the preservation of the $\ensuremath{\Delta}$ contribution. In addition, it is shown that, depending on the thermal treatment of the films, two sets of disordered configurations may be obtained in Te: one [$a\ensuremath{-}\mathrm{Te}(1)$] which can effectively be approximated by disordering the trigonal Te lattice, and the other [$a\ensuremath{-}\mathrm{Te}(2)$] which represents a further departure from this lattice and could, therefore, be approached via deformation of a different (possibly simple cubic) lattice. Because of the relatively good fit achieved in the experimental electronic structure of the disordered Se films using the trigonal approach, these films do not seem to contain a majority of ${\mathrm{Se}}_{8}$ rings but might rather consist of a mixture of small weekly distorted Se chains, possibly amalgamated with a small proportion of rings.

Abfangreaktionen kurzlebiger Radikale, XI. Über die radikalische Substitution am Stickstoff: Der induzierte Zerfall von 2‐Tetrazenen

Abstract: Der radikalische Zerfall von Tetraphenyl-2-tetrazen (1a) und 1,4-Dicyclohexyl-1,4-diphenyl-2-tetrazen (1b) wird durch Trialkylzinnhydrid beschleunigt. Beim Angriff von Stannyl-Radikalen an N-1 oder N-4 entstehen in einer SH2α-Reaktion N2, Stannylamin und ein Radikal ·N(R)R′, das durch R3SnH zum Amin abgefangen wird oder mit einem Stannyl-Radikal bei niedriger Hydrid-Konzentration rekombiniert. Auch Dicarbazolyldiazen 1c reagiert analog, nicht jedoch Dipiperidinodiazen (1d). Einflusse der Stabilisierung von Grund- und Ubergangszustand auf den Spontan- wie den induzierten Zerfall werden diskutiert, Werte fur t1/2, k, ΔH* und ΔS* angegeben. Auch Tetraphenylhydrazin wird durch Stannyl-Radikale beschleunigt gespalten. Reactions of Short-Life Radicals, XI. Free Radical Substitution at the Nitrogen Atom: The Induced Degradation of 2-Tetrazenes The radical degradation of tetraphenyl-2-tetrazene (1a) and 1,4-dicyclohexyl-1,4-diphenyl-2-tetrazene (1b) is found to be accelerated by trialkyltin hydride. Stannyl radicals attack at N-1 or N-4. In a SH2α reaction, N2, the corresponding stannylamine and a radical ·N(R)R′ are formed. The latter is scavenged by R3SnH giving the amine; or it recombines with a stannyl radical at low hydride concentrations. Dicarbizolyldiazene 1c reacts by the same way, but not so the dipiperidinodiazene (1d). Importance of stabilization of ground and transition states on the spontaneous and the induced degradation are discussed. Values of t1/2, k, ΔH±, and ΔS± are given. Stannyl radicals also accelerate the splitting of tetraphenylhydrazine.