Showing papers by "University of Stuttgart published in 1972"

The coupled coherent and incoherent motion of excitons and its influence on the line shape of optical absorption

Abstract: We treat the coupled coherent and incoherent motion of Frenkel excitons by a model calculation. The model contains the four parametersa (distance of neighbouring atoms),J (exchange interaction integral), γo (describing the strength of the local energy fluctuations) and γ1 (a measure of the fluctuations of the exchange interaction integral, i.e. nonlocal fluctuations). Calculation of the optical absorption of systems with two differently oriented molecules/unit cells results in the Davydov-splitting given by Δ=8J and the linewidth given by Γ=γo+γ1. From the equation of motion of the density matrix we derive a diffusion equation. The diffusion constant is given by $$D = \frac{{a^2 }}{\hbar }\left( {2\gamma _1 + \frac{{J^2 }}{{\gamma _1 + \Gamma }}} \right)$$ . Comparison with experiment yields γo=70cm−1, γ1=0.1 cm−1 at room temperature and Γ<1 cm−1 at 4.2 °K. Using these numerical values and the criterium of Haken and Strobl we derive that at room temperature the exciton motion is incoherent and may be described by a hopping process whereas at low temperature it is coherent.

Fluorescence in neodymium ultraphosphate

Abstract: The properties of the Nd-ultraphosphate NdP 5 O 14 (NdUP), a crystalline material that appears to be a promising candidate for an efficient Nd laser, are described. The Nd concentration of 4.1021/cm3is ∼60 times higher than the upper limit useful for doped laser crystals ( \simI percent) like Nd:YAG. Despite the much higher Nd concentration the linewidths and cross sections of the major transitions are shown to be very similar to those of Nd:YAG. Therefore, it is expected that the gain per unit length in NdUP is also ∼60 times higher than in Nd:YAG. The crystal structure, the absorption and fluorescence spectra, level assignments, and various other features of NdUP are reported. Other rare earths form similar insoluble stable compounds. Most of them are transparent from the UV to the near IR except for the absorption bands of the metal ions.

Fluctuation-dissipation theorems for systems in non-thermal equilibrium and applications

Abstract: The linear response theory of systems obeying Fokker-Planck equations is discussed under the assumption that the principle of detailed balance is satisfied. This theory is used to obtain fluctuation-dissipation theorems for systems in a non-thermal equilibrium state corresponding to the steady state solution of the Fokker-Planck equation. Some of the aspects of the threshold region of a single mode laser (without detuning) are discussed. In particular it is shown that, contrary to the results established recently by others, the “linear susceptibility” χ(Ω) is acontinuous function of the pump parameterp. The results are then specialized to Gaussian Markov process in which case an alternate form of the fluctuation-dissipation theorems is also given. Finally few other generalizations of the fluctuation-dissipation theorems are also briefly discussed.

Luminescence and photoconductivity of undoped p-GaSb

Abstract: A doubly ionizable acceptor (binding energies of EA = 34.5 meV, EC = 102 meV), which is responsible for the hole concentration in undoped GaSb, is identified by photoluminescence experiments at 2 K. Growth experiments, using nonstoichiometric melts, show that this acceptor is connected with a lack of antimony in the crystals. Experimental photoluminescence data, concerning the free exciton recombination at 810 meV and an emission line at 795.5 meV (possibly a bound exciton) as well as new phonon satellites, are presented. Finally, photoconductance measurements at the same samples give further information about excitons in GaSb. Der doppelt ionisierbare Akzeptor (Bindungsenergien EA = 34,5 meV und EC = 102 meV), der die hohe Locherkonzentration in undotiertem GaSb verursacht, wird durch Photolumineszenzexperimente bei 2 K identifiziert. Untersuchungen an Kristallen, die aus Schmelzen mit unterschiedlichem Antimongehalt gezogen wurden, zeigen, das dieser Akzeptor auf einem Mangel an Antimon im Kristall beruht. Weiterhin wird uber experimentelle Photolumineszenzdaten berichtet, die sowohl die Rekombination des freien Exzitons bei 810 meV und eine Emissionslinie bei 795,5 meV (wahrscheinlich ein gebundenes Exziton) als auch neue Phononensatelliten betreffen. Schlieslich geben Photoleitfahigkeitsmessungen an den gleichen Proben weitere Information uber Exzitonen in GaSb.

Large Deflection Analysis of Prestressed Networks

Abstract: A finite element computer procedure is developed, based on the matrix displacement method, for the analysis of large prestressed networks. The mathematical theory including the effect of the nonlinear contribution of the so-called geometrical stiffness are first reviewed on a novel basis. The iterative attainment of the equilibrium is considered in detail, both as far as theory and practice are concerned. The important question of the determination of an initial trial geometry of the network surface in which the equilibrium is only satisfied approximately is considered next. Attention is also paid to the layout of the initial net on the mathematical surface. The last main section reviews the practical organization of a network analysis in a computer. Following the assembly of the initial data, the measures are enumerated which are necessary for ensuring a given prestress condition. Finally practical steps for accelerating convergence and the selection of a simplified net are presented.

Laser emission from an organic molecular crystal

Abstract: A tunable organic crystal laser is described. Cleaved platelets of fluorene containing 2 × 10−3 anthracene emitted polarized light pulses at λ = 408 nm, with a pulse amplitude of 10 W and a pulse duration of ≦ 3 ns, when pumped by a 1 kW nitrogen laser. Ein durchstimmbarer organischer Kristall-Laser wird beschrieben. Gespaltene Fluoren-Plattchen, die 2 × 10−3 Anthrazen enthielten, emittierten polarisierte Lichtimpulse bei λ = 408 nm mit einer Pulsamplitude von 10 W und einer Pulsdauer von ≦ 3 ns, nach-dem sie mit einem 1 kW Stickstoff-Laser gepumpt worden waren.

The influence of point-defect clusters on fatigue hardening of copper single crystals

Abstract: In order to investigate quantitatively the influence of point-defect clusters on the saturation stress in metal fatigue, the yield stress for uni-directional deformation was measured as a function of temperature between 78 and 300 °K on copper single crystals which had been fatigue-hardened into saturation at room temperature. Weak beam transmission electron micrographs of these specimens revealed a cell-like dislocation array with a low point-defect cluster density in the dislocation-poor interior and a high cluster density in the dislocation-rich walls of the cells. The size distribution of the defect clusters was found to be exponential for both the cell interior and the cell walls. A quantitative analysis of the yield stress measurements together with the electron-microscopical data showed that the saturation stress of fatigued copper single crystals is controlled by internal stresses and defect clusters within the interior of the cells which impede the dislocation motion through these regions. Zur quantitativen Untersuchung des Einflusses von Punktfehlstellen-Agglomeraten auf die Sattigungsspannung bei der Ermudung von Metallen wurde die kritische Schubspannung fur einachsige Verformung von Kupfer-Einkristallen in Abhangigkeit von der Verformungstemperatur zwischen 78 und 300 °K gemessen, nachdem diese bei Raumtemperatur bis in die Sattigung ermudet worden waren. Elektronenmikroskopische „weak-beam„-Aufnahmen dieser Proben zeigten eine zellartige Versetzungsanordnung mit hohen Dichten an Punktfehler-Agglomeraten in den versetzungsreichen Zellwanden und niedrigen Agglomerat-Dichten im versetzungsarmen Zellinnern. Die Grosenverteilung der Agglomerate ist sowohl im Innern als auch in den Wanden der Zellen exponentiell. Eine quantitative Auswertung der Fliesspannungsmessungen unter Einbeziehung der elektronenmikroskopischen Daten zeigte, das die Sattigungsspannung ermudeter Kupfer-Einkristalle durch die Behinderung der Versetzungsbewegung durch innere Spannungen und Punktfehlstellen-Agglomerate im Zellinnern bestimmt wird.

Solutions of the fokker--planck equation in detailed balance.

Abstract: The solutions of the Fokker-Planck equation in detailed balance are investigated. Firstly the necessary and sufficient conditions obtained by Graham and Haken are derived by an alternative method. An equivalent form of these conditions in terms of an operator equation for the Fokker-Planck Liouville operator is given. Next, the transition probability is expanded in terms of an biorthogonal set of eigenfunctions of a certain operatorL. The necessary and sufficient conditions for detailed balance leads to a simple operator equation forL. This operator equation guarantees that on!y half of the biorthogonal set needs to be calculated. Finally the dependence of the eigenvalues on the reversible and irreversible drift coefficient is discussed.

Methods of elastoplastic analysis

Abstract: The paper presents a number of alternative procedures for the solution of elasto-plastic problems by the matrix displacement or finite element method. In particular, the iterative initial strain and stress approaches are fully developed. Attention is also focused on the tangent stiffness method in association with an efficient modification technique. Convergence criteria are set up for the initial strain and stress methods. It is proved that the latter will only diverge, if an actual break-down of the structure occurs. In order to speed up the eventually slow convergence of the initial stress method a procedure is suggested which has proved very useful in conjunction with the initial strain approach. The theoretically deduced convergence properties of the iterative methods are verified by the numerical results obtained for some illustrative elasto-plastic problems.

Seismotektonische Traverse von der Nordsee bis zum Apennin

Abstract: Die auf ihre Erdbebentatigkeit hin untersuchte Traverse ist 1300 km lang und erstreckt sich von der Doggerbank (54° N) bis zum nordlichen Apennin (44° N). In einem Tiefenschnitt entlang der Traverse wird die raumliche Verteilung der Erdbebenherde betrachtet. In der Zahl der Herde und ihrer Anordnung zeigen sich Unterschiede zwischen den verschiedenen Teilgebieten der Traverse (Niederrheinische Bucht, Oberrhein-Graben, Schwabische Alb, Alpen, Apennin). Bezuglich der Herdtiefe ist ein gemeinsames Merkmal fast aller Gebiete, das sich die Erdbebenherde auf die oberen 20–25 km der Erdkruste beschranken. Die starkste seismische Aktivitat ist im Tiefenbereich von 2–12 km festzustellen. Dieses Ergebnis ist fur das Verhalten der einzelnen Krustenabschnitte bei rezenter Bruchtektonik von Bedeutung. Lediglich im Bereich der Doggerbank scheinen die Herde an der Basis der Erdkruste oder im obersten Erdmantel zu liegen, was auf besondere seismotektonische Verhaltnisse in diesem Gebiet hindeutet. Demgegenuber zeigt die Herdtiefenverteilung im Alpengebiet trotz abweichender Krustenstruktur keine Besonderheiten gegenuber dem nordlichen und sudlichen Vorland. Vergleicht man den aus seismographischen Messungen abgeleiteten rezenten Spannungszustand von Erdbebengebiet zu Erdbebengebiet, so ergibt sich fur die Alpen und das nordlich anschliesende Gebiet bis zur Nordsee ein sehr einheitliches Bild fur die Orientierung der horizontalen Hauptspannungen (groste Hauptspannung NW-SE, kleinste Hauptspannung SW-NE). Im Apennin ist die Spannungsverteilung gerade umgekehrt.

The influence of exciton motion on spin-resonance absorption

Abstract: We use a stochastic model for the exciton motion which comprises both the coherent and the incoherent motion. The incoherent part is taken care of by a stochastic process which allows the local excitation energy and the transition matrix element to fluctuate by means of a Markovian process. The interaction between the spins and their surroundings is described by the usual spin-Hamiltonian which is, however, simplified to a spin 1/2 particle (instead of the triplet state). In the present paper we solve exactly the two limiting cases of completely coherent and incoherent motion (for two molecules). In the incoherent case the influence of the exchange interaction integral is taken into account by perturbation theory. We find expressions which are immediately comparable with ESR-experimental data. This comparison and additional information derived from optical absorption measurements allow us to determine all free parameters of our model uniquely. In particular, the fluctuations of the exchange interaction integral (with strength γ1) play an important role. From these parameters we may furthermore calculate the correlation time of the proton spin resonance in agreement with experimental data. The results show clearly that at room temperature in anthracene crystals the exciton undergoes a hopping process.

Sensitized photooxygenation according to type i mechanism (radical mechanism) ‐ part i. flash photolysis experiments

Abstract: — The photooxygenation of allylthiourea (ATU) sensitized by thionine does not occur according to the singlet oxygen mechanism but rather proceeds via the formation of radicals. In oxygen-free solution the primary process is a redox reaction between the thionine triplet and ATU where a semithionine- and an ATU-radical are formed. In further reaction steps the leuco form of the dye is finally produced (reductive photobleaching; D R mechanism after Koizumi). The primary process in an oxygen-containing aqueous solution is the same, since at high concentrations of ATU (0·2M) the amount of semithionine formed by a photolytic flash, as well as the time course of disappearance of semithionine, does not depend on the oxygen content of the solution. The reformation of thionine following flash photolysis has been investigated with regard to oxygen concentration and pH dependence. Two different excitation intensities were used. A quadratic dependence of thionine reformation on excitation intensity at high oxygen concentration was observed, indicating a reaction between two photoproducts. The dependence of the reaction rate of semithionine on the ionic strength has been investigated. These experiments show that the reaction partner of semithionine carries a charge of + 1 in oxygen-free as well as in oxygen-saturated solution.

General Treatment of Structural Modifications

Abstract: In order to perform modifications of structures analyzed by the Matrix Displacement Method, a direct computer-oriented approach is presented enabling the treatment of coupled combinations of three possible types of modifications, namely, removal of freedoms, addition of freedoms, and modification of elements. The formulation is extended to cover modifications of elements in substructures together with the corresponding modification to the main structure. The method is derived from the laws of partitioned matrices and Boolean transformation of freedoms within the structural stiffness matrix, and fully exploits symmetry and positive-definiteness. The presented form of the modification equations allows the use of an alternative existing approach of updating the triangularized factor of the structural stiffness matrix due to the modification of elements. The method is extended to provide a recursive hypermatrix Cholesky algorithm. All formulations are accompanied by operation counts to enable rapid determination of break-even points for reanalysis or possible iterative solutions.

Nonlinear canonical transformations in the coupling between degenerate high and low energy excitations

Abstract: In microscopic many-body physics the coupling between the motion of fast particles (electrons) and slow particles (nuclei) is universal. The standard Born-Oppenheimer decoupling procedure breaks down, if the energy separation in the “fast” system is of the same order as the elementary excitation in the “slow” system. In this case “dynamical resonance” effects are to be expected. In the present investigation a model system of a coupling between a doubly degenerate high energy excitation and doubly degenerate low energy oscillator is handled by a non-linear canonical transformation which is shown to be quasi-exact in the sense that it diagonalizes the Hamiltonian in both extremal coupling cases. The transformation has some flexibility, so that the diagonalization regions can be enlarged. It is employed to calculate the “zero-phonon” optical response, which indeed displays aresonance effect. Likewise, another nonlinear transformation is devised, which only in the strong coupling limit yields diagonalization. This latter transformation in a natural way leads to the conventional semi-classical approaches to the dynamical Jahn-Teller problem. The results gotten with it are identical with those from our transformation in the strong coupling limit. On the basis of our results some remarks are made concerning the possible impact of the breakdown of the adiabatic approximation in other regions.

On the long-range order in superconducting intercalated layer compounds

Abstract: The correlation of the order parameter is studied in layer compounds in which adjacent metallic layers are coupled by Josephson coupling. It is shown that the long-range order is established over the whole system due solely to this coupling, even if very weak. The correlation length is anisotropic. The anisotropy ratios are related to the coupling strength.

Symmetrische verallgemeinerte Wannierfunktione. I. Definition und Grundlagen

Abstract: Einer beliebigen abgeschlossenen Bandgruppe, die aus v miteinander entarteten Bandern bestehe, werden v verallgemeinerte Wannierfunktionen zugeordnet, die nach einer Darstellung der Punktgruppe des Kristalls transformiert werden und optimal lokalisiert sind. Es wird untersucht, wie weit die Struktur der verallgemeinerten Wannierfunktionen durch die Symmetrie des Kristalls und das Symmetrieverhalten der Blochfuktionen, die zu der betrachteten Bandgruppe gehoren, bestimmt wird. Insbesondere wird gezeigt, das durch den Symmetrietyp der Bandgruppe das Symmetrieverhalten der verallgemeinerten Wannierfunktionen und ihr Symmetriemittelpunkt festgelegt wird. To a complete group of v degenerate bands, v generalized Wannier functions are assigned which transform according to a representation of the point group of the crystal and are best localized. The question is investigated to what extent the structure of the generalized wannier functions is determined by the symmetry of the crsytal and teh symmetry behaviour of the Bloch functions is belonging to the considerd band group. In particular it is shown that the symmetry type of the band group determines the symmetry behaviour of the generalized Wannier functions and their symmetry centre.

Der einfluss des basisbahnwiderstandes und der ladungsträgermultiplikation auf das ausgangskennlinienfeld von planartransistoren

Abstract: Zusammenfassung Mit Hilfe eines verteilten Transistormodells wird der Einflus des Basisbahnwiderstandes und der Ladungstragermultiplikation in der Kollektorsperrschicht auf das Ausgangskennlinienfeld von Planartransistoren berechnet. Dabei beschrankt sich die Arbeit auf den Kennlinienbereich, bei dem das Produkt aus Multiplikationsfactor und Stromverstarkung (in Basisschaltung) groser als eins ist. Bei konstanter Basis-Emitter-Spannung treten bei einem bestimmten Basisstrom rucklaufige Kennlinien auf. Dieser Strom ist nur vom Schichtwiderstand der Basis unter dem Emitter und der Emitterstruktur abhangig. Bei konstantem Emitterstrom schnurt sich die injizierende Emitterflache bei einem endlichen Basisstrom nicht nur bei Zylinder sondern auch bei Streifengeometrie punktformig ein, so das die Raumladung in der Kollektorfeldzone durch bewegliche Ladungstrager modifiziert wird. Je nach Beschaffenheit der Epitaxschicht wird hierdurch der Kennlinienverlauf verschiedenartig beeinflust. Experimentelle Ergebnisse zeigen eine zufriedenstellende Ubereinstimmung mit der Theorie.