Showing papers by "University of Stuttgart published in 1977"

Bounds for effective elastic moduli of disordered materials

Abstract: Recently P.H. Dederichs and R. Zeller (1973) have developed a formal theory of the bounds of odd order n for the effective elastic moduli of linearly elastic, disordered materials. The bounds are established by use of statistical information given in terms of correlation functions up to order n (= 1, 3, 5,…). This theory is extended to include the bounds of even order n. It is indicated how these bounds can be made optimum under the given statistical information. The results for bounds of even and odd order are obtained in forms which resemble Neumann series, containing multiple integrals up to order (n−1). These integrals can be calculated for certain materials which are classified in terms of a gradual statistical homogeneity, isotropy and disorder. Materials which possess these properties up to the correlation functions of nth order are called overall grade n materials. The optimum bounds for overall grade 2 and grade 3 materials are given explicitly. Optimum bounds for materials which are of grade ∞ in homogeneity and isotropy (i.e. (statistically) perfectly homogeneous and isotropic) and, at the same time, disordered of grade 2 or 3 are also derived. Those for grade 2 in disorder are the Z. Hashin and S. Shtrikman's (1963) bounds. Those for grade 3 are the narrowest, explicit bounds so far derived for random elastic materials. They contain within themselves the so-called self-consistent elastic moduli.

Viscous Dissipation in Shear Flows of Molten Polymers

Abstract: Publisher Summary Heat transfer in flowing molten polymers is largely influenced by rheology–– the rheological properties of the polymer and by the flow geometry. The rheology of steady shear flow can treat most of the heat transfer problems completely. This chapter discusses the heat transfer problem, and classifies the heat transfer and viscous dissipation in molten polymers. The heat transfer in shear flow is analyzed and a large emphasis is laid on replacing the commonly used idealized boundary conditions–– constant wall temperature or constant wall heat flux by more general conditions. The heat transfer at the wall is described by an outer temperature difference and the Biot number that is used successfully for describing the boundary conditions for temperature calculations in solids. The Biot number is appropriate for describing the boundary conditions between isothermal and adiabatical, as they occur in real processes. A unifying concept is developed that makes it possible to comprise the most important shear flow cases into a single one that can be solved with one numerical program. The nonviscometric flow in channels and flow with free boundaries is also discussed. An example of heat transfer in unsteady unidirectional shear flow is also provided.

Auger lifetimes for excitons bound to neutral donors and acceptors in Si

Abstract: The lifetimes of excitons bound to the neutral donors Li, P, and As and neutral acceptors B, Al, Ga, and In in silicon are determined by time-resolved photoluminescence measurements at 4.2 K and a strong dependence on the binding energy of the donor or acceptor is found. This dependence can be understood assuming a localized phononless Auger-process to be the main recombination mechanism. A theoretical calculation using approximate wavefunctions is presented and leads to a very good agreement with the experimental results. Die Lebensdauern gebundener Exzitonen an den neutralen Donatoren Li, P und As sowie den Akzeptoren B, Al, Ga und In in Silizium werden bei 4,2 K mit zeitaufgeloster Photolumineszenzspektroskopie gemessen. Es ergibt sich eine starke Abhangigkeit von der Bindungsenergie der entsprechenden Storstelle. Man kann diese Abhangigkeit verstehen, wenn man einen lokalisierten, phononenfreien Auger-Prozes als wesentlichen Rekombinationsmechanismus annimmt. Eine theoretische Berechnung der Lebensdauer unter Verwendung angenaherter Wellenfunktionen ergibt eine sehr gute Ubereinstimmung mit den experimentellen Ergebnissen.

Auger recombination in GaAs and GaSb

Abstract: In highly excited GaAs and GaSb luminescence bands above the band gap at $h\ensuremath{ u}={E}_{g}+{\ensuremath{\Delta}}_{0}$ are observed, which are explained by radiative recombination of Auger-excited holes in the split-off valence band with free or shallow bound conduction-band electrons. An extremely weak luminescence continuum in both materials between $h\ensuremath{ u}={E}_{g}$ and $h\ensuremath{ u}=2{E}_{g}$, which shows no distinct structure within the experimental resolution, is ascribed to the radiative recombination of relaxing Auger electrons in the conduction band. The role of the split-off valence band for hole-hole-electron (hhe) Auger recombination is explained. From spectroscopic data the hhe Auger coefficients ${C}_{p}$ for GaAs [${C}_{p}{(\mathrm{GaAs})}_{77 \mathrm{K}}\ensuremath{\approx}{10}^{\ensuremath{-}(31\ifmmode\pm\else\textpm\fi{}1)}$ ${\mathrm{cm}}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$] and for GaSb [${C}_{p}{(\mathrm{GaSb})}_{77 \mathrm{K}}\ensuremath{\approx}{10}^{\ensuremath{-}(25\ifmmode\pm\else\textpm\fi{}1)}$ ${\mathrm{cm}}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$] are estimated, in rough agreement with theoretically predicted values. The dependence of the luminescence intensities of the investigated emission bands in GaSb at ${E}_{g}$ and at ${E}_{g}+{\ensuremath{\Delta}}_{0}$ on the exciting light density and on the doping concentration leads to the conclusion that in $p$-type GaSb band-to-band Auger recombination occurs. The surprisingly high intensity of the emission, which is connected with a hhe Auger process, in $n$-type GaSb(Te) and its strange dependence on the excitation power is explained by a band-to-acceptor Auger process. It is believed that this acceptor is the doubly ionizable native defect in GaSb, which is always present.

Prediction of primary normal stress difference from shear viscosity data using a single integral constitutive equation

Abstract: Based on a single integral constitutive equation with a strain-dependent memory function, a relation between the primary normal stress functionθ and the shear viscosity functionη is proposed. According to this theory, the primary normal stress functionθ can be obtained from viscosity data by simple differentiation of the viscosity functionη with respect to the shear rate $$\dot \gamma$$ , and multiplication by a factor (−1/n). The material parametern is thereby associated with the strain dependence of the memory function. This relation was compared with the viscosity and primary normal stress data of six polymer melts, three polymer solutions, and an aluminium-soap solution, which were measured by several research groups and are available in the literature. In spite of the vast differences in physical constitution and chemical structure of the melts and solutions considered, agreement between predicted and measured values was encouraging.

Self-diffusion in copper at “low” temperatures

Abstract: A low-energy argon ion-beam sputtering system was developed and applied to serial sectioning in a radiotracer study of “low”-temperature self-diffusion of copper. Very thin uniform sections with thicknesses between several nm and a few hundred nm were removed from copper single crystals of extremely low dislocation density. Gaussian penetration curves are observed. The self-diffusion coefficient was measured over the temperature range 574 to 905 K and varies between about 3 × 10−19 and 6 × 10−13 cm2 s−1. In conjunction with the high-temperature data of Rothman and Peterson the present data are analysed in terms of mono- and divacancy contributions to the total diffusivity. In the temperature range of the present study the divacancy contribution is almost completely negligible. For the sum of formation and migration enthalpy of a mono-vacancy a best value of 2.04 eV is obtained.

On the direct calculation of localized HF orbitals in molecule clusters, layers and solids

Abstract: It is shown that the computational effort involved in HF calculations can be considerably reduced by applying the following concepts: 1) the use of a localization operator for the direct determination of localized non-orthogonal HF orbitals, 2) the approximation of the interaction potential between different localization centres by a Hartree-like ansatz, 3) the successive calculation of many-body corrections to molecular properties such as the total energy. A numerical application to LiH layers and solid LiH is described.

Wavelength dependence of gain saturation in GaAs lasers

Abstract: The amplification of light in GaAs lasers is calculated self-consistently. It is shown that the wavelength dependence of the gain saturation is caused by the change of the chemical potential within the excited region due to the coupling of the carrier density with the photon density via the stimulated emission process. The effect of the wavelength dependent gain saturation on the stimulated emission spectra is calculated and compared with experimental results. Comparison of different recombination models indicates that a band-to-band transition without k -selection rules including tail states is the most appropriate description of the experimental data even for pure material.

Positron lifetimes and annihilation lineshape in Cd and au from 4.2 K to the melting points

Abstract: By means of an integrated source-specimen technique the temperature dependence of positron lifetimes and annihilation lineshapes has been measured, on the same specimens of gold and cadmium from 4.2K to the melting points, and also in electronirradiated and quenched gold. The anomalous temperature dependence of positron annihilation at intermediate temperatures (200 to 350 K in Cd, 270 to 750 K in Au) discovered by Lichtenberger, Schulte, and MacKenzie is confirmed. The data are incompatible with the idea that the intermediate temperature dependence is due to thermal expansion. They are well explained by an extension of the trapping model which includes the formation of metastable self-trapped positrons. From lineshape measurements after electron irradiation at 180 K and after quenching it is deduced that the trapping rate of positrons at vacancy-type defects in Au is temperature independent below room temperature.

Microdynamics and time-evolution of macroscopic non-Markovian systems

Abstract: The time evolution of the single event probability of macroscopic variables is studied from a microscopic point of view. The explicit consideration of the preparation of the initial microdistribution leads to a unique decomposition of the macrodynamics into two parts, a local and instantaneous one and a nonlocal and retarded one. In this retarded, i.e., non-Markovian master equation no inhomogeneity occurs in contrast to previous approaches. It is shown that the retarded master equation can exactly be transformed into a time-convolutionless and homogeneous form\(\dot p(t) = \Gamma (t)p(t)\), which generates a substitutive Markov process with the same single event behaviour as the process in question.

Notizen: Ray Path and Reflection Mechanisms in Crayfish Eyes

Abstract: In crayfish eyes image formation not due to refraction but to total internal and multilayer reflection in an orthogonal mirror system is described. Relevant optical parameters (geometry and refractive indices) in this eye are determined.

Enzyme activities in the serum of rainbow trout, Salmo gairdneri Richardson; the effects of water temperature*

Abstract: Activities of lactate dehydrogenase, hydroxy butyric dehydrogenase, glutamic oxalacetic transaminase, glutamic pyruvic transaminase, glutamate dehydrogenase, creatinine kinase, alkaline phosphatase, and leucine amino peptidase were determined in the sera of rainbow trout. The animals had previously been adapted to temperatures of 3.5, 6, 8, 10, 12.5, 15, 17, 19, 21.5 and 23° C. Most of the enzyme activity increased with the rise in temperature. The activity of alkaline phosphatase decreased in the range 6–19° C, while the changes in the glutamate dehydrogenase activity took a complex course. The results are compared with the findings of other authors.

Energy gap reduction in superconducting tin films by quasiparticle injection

Abstract: In Sn-I-Sn-I-Pb tunneling structures the energy gap ~Sn of Sn is reduced by quasiparti­ cle injection via single-particle tunneling between the Sn films. ~Sn as function of the quasiparticle density is probed by the Pb contact and found in agreement with the theory of OWen and Scalapino. An instability of the energy gap of Sn is observed at the critical gap reduction ratio predicted by this theory for a first-ortler phase transition. Nonequilibrium quasiparticle distributions in superconductors can be produced by photonl - 3 and phonon4 irradiation or by quasiparticle 5 injection via tunneling. Under constant injection conditions the stationary quasiparticle energy distribution is determined by the energy distribution of the primary quasiparticle injection or excitation rates, by the energy dependence of relaxation and recombination probabilities, and by secon­ dary quasiparticle excitation and pair-breaking rates via phonon absorption. Since phonons are emitted in quasiparticle decay, the phonon escape probability from the superconducting film into the substrate and the intrinsic phonon decay also have a strong influence on the stationary quasi­ particle energy distribution. Whereas the gener­ al problem of the quasiparticle distribution can be solved numerically,6 two important simple models have been discussed in the past: For the limit of recombination lifetimes long compared to relaxation times, Owen and Scalapino7 pro­ posed a nonequilibrium quasiparticle distribution in which the excess number of quasiparticles is characterized by a chemical potential p* > 0 and their energy distribution by the unperturbed lat­ tice temperature T. Since most superconducting films show high phonon trappingS by pairbreaking, Parker9 proposed a model in which an elevated temperature T* > T describes the number of quasi­ particles and their energy distribution. A signifi­ cant difference between the two models is that the "/1* model" predicts a first-order phase transi­ tion as the number of excess quasiparticles is in­ creased, whereas the "T* model" does not. Dif­ ferent experiments with optical excitation of qua­ siparticles 2,3.1o did not give clear evidence in fa­ vor of one of the two models. In this communication we report on experiments with quasiparticle injection via tunneling between two Sn films and probing the energy gap and the quasiparticle population with a Pb contact. In ac­ cord with the 11-* model we find that the gap reduction as function of the quasiparticle density is stronger than in the thermal case and we observe an instability of the energy gap at the predicted critical gap reduction. The sample consists of two overlapping Sn films and one Pb film, width and thickness of each film being 1.4 mm and 1000 A, respectively (Fig. 1). Silicon single crystals are used as substrates which are cooled by direct contact to the liquid­ He bath on the backside. The front surface with the Sn-J-Sn-J-Pb structure can be kept under vac­ uum or also exposed to liquid He. By 15-min glow-discharge oxidation in O2 at 100 mTorr the tunneling resistance in the Sn-J-Sn junctions re­ sulted with the higher voltage asymptotic value of R",,?25 mn. For the Sn-J-Pb junctions typical values are Roo'" 1 mn. The increased tunneling resistance in the Sn-J-Sn contact was necessary for obtaining a high stationary quasiparticle popu­ lation at injection currents below the critical cur­ rents of the film structure. This allows high bat­ tery voltages and primary quasiparticle injection energies at multiples of the energy gap with suc­ cessive relaxation-phonon emission and reabsorp­ tion by pairbreaking increaSing the effective rate of quasiparticle excitations. Using conventional electronic measuring tech

The superposition image in the eye ofEphestia kühniella

Abstract: Superposition images according to Exner (1891) are observed behind fresh eye-cups ofEphestia which were mounted with gelatine on a cover-glass and kept in a moist chamber. Their position was determined as 125±15 μm proximal to the crystalline cone tip having made allowance for the passage of light through media of different refractive indices. This distance places the image in the rhabdom layer as determined by histology. The same holds for the superposition image constructed from calculated ray paths in the dioptric system ofEphestia. The computer aided calculation was based on refractive index measurements in cornea and cone. It was carried out by applying Snell's law for infinitesimally thin sections. The dioptric system shows properties analogous to a Kepler telescope adjusted for infinity. Parallel incoming light with an angle of up to 22° to the axis is focused in a plane about half way down the cone and leaves the cone again in direction of the rhabdom layer almost parallel. The angular magnification of the system is 1.32.

Stratified two‐phase flog of molten polymers in circular dies

Abstract: A theoretical study has been carried out on the steady, axisymmetric two-phase flow of molten polymers in circular dies. For both fluids, the shear rate dependence of the viscosity is described by a power law and the temperature dependence by an exponential function. Taking into account viscous dissipation, a numerical program has been developed to predict the radial position of the interface between the two fluids, the developing temperature and velocity fields, the shear rates, the shear stresses, the pressure drop as well as the field of shear deformation and the residence time distribution for different thermal boundary conditions. The numerical program is applied to the flow of a high-viscous polymer melt, (high density polyethylene), surrounded by a small annulus of less viscous polymer ni lt, (low density polyethylene). Computed results are shown graphically.