08 Fakultät Mathematik und Physik
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Item Open Access Microscopic calculation of line tensions(2008) Merath, Rolf-Jürgen Christian; Dietrich, Siegfried (Prof. Dr.)In this work the line tension has been determinded with molecular resolution, which in this context marks the forefront of research. A semi-microscopic line tension theory based on the sharp-kink approximation has been further developed. The sharp-kink results concerning wetting and line tension behavior deviate considerably from the fully microscopic results. A hybrid line tension theory has been introduced, which employs an improved effective interface potential for the SK line tension calculation. For most of the studied cases the results from this hybrid method describe the fully microscopic line tension values semi-quantitatively. However, for a tailored system with relatively strong spatial variations of the substrate potential and of the solid-liquid interfacial density the hybrid method fails and does not predict the correct order of magnitude of the line tension values. Hence in general the fully microscopic approach is required, if one is interested in quantitatively reliable line tension values or/and if the validity of the hybrid method for the considered system has not been checked. The calculation of the line tension of a liquid wedge is an important contribution for understanding the shape of very small droplets (below the micrometer range). Furthermore a proposal is given, how axisymmetric sessile droplets can be addressed efficiently within DFT.Item Open Access Ambient pressure oxidation of Ag(111) surfaces : an in-situ X-ray study(2008) Reicho, Alexander; Dosch, Helmut (Prof. Dr.)The oxidation of metals plays an outstanding role in everyday life. Typical phenomena are the formation of rust on steel or oxide scales on copper, showing up as a green patina. The formation of metal oxides is not always an unwanted process. The functionality of many materials is directly related to their controlled oxidation. The most prominent examples are passivating oxide layers on stainless steel. Relevant for this thesis are industrially applied heterogeneous catalytic reactions for the synthesis of many chemical products, where gaseous reactants are in contact with the solid surface of the catalyst. Oxidation reactions are very important in this context, leading to a big need of understanding of these processes in research and development. Thereby, the active oxygen species on the surface and selectivity and poisoning of the catalyst have to be studied on an atomic scale. The high temperature and high pressure oxidation of the 4d transition metals Ru, Rh, Pd and Ag is a matter of particular interest, because these metals are widely used as oxidation catalysts. On Ruthenium one observes the formation of RuO2(110) bulk oxide islands at elevated temperatures and oxygen pressure. In the case of the Pd(100) and Rh(111) surface oxidation can lead to the formation of so-called surface oxides. These oxides are structurally related to the bulk oxide of the respective element. Furthermore, surface oxides are ultra thin oxides containing one metallic layer surrounded by two oxygen layers, giving rise to an oxygen-metal-oxygen sequence perpendicular to the surface plane. A future vision is to get a direct microscopic control of the emerging surface structures and ultimately of the real-time oxidation/reduction dynamics allowing one to tailor such catalytic reactions to better performance. A necessary prerequisite to the microscopic control is the full atomistic understanding of the surface structures which form at high temperature and at high oxygen pressures. Silver plays a unique role in heterogeneous catalysis. Supported Ag catalysts are used for the selective oxidation ('epoxidation') of ethylene and for the partial oxidation of methanol to formaldehyde. Ethylene oxide and its derivates are basic chemicals for industry, used in a many technologies with a world-wide production of more than 10 million tons as in medicine for disinfection, sterilization, or fumigation, or in transport and energy technologies for engine antifreeze and heat transfer. Because of its ability to kill most bacteria, formaldehyde is extensively used as disinfectant and as preservative in vaccinations. Therefore, the optimisation of these two Ag-supported catalytic reactions is of paramount importance. Current strategies employed in the industrial process to enhance selectivity include the empirical use of inhibitors (Cl) and promoters (Cs), however, on the way to a knowledge-based control of these reactions one has first to understand the surface structure of oxidized silver under relevant conditions in full detail. The formation of extended Ag(111) facets is observed on polycrystalline silver during the above industrial catalytic oxidation reactions, in turn fundamental research (experiment and theory) has been devoted to the detailed understanding of oxidation of this surface. The formation of an oxygen induced p(4x4) reconstruction on the Ag(111) surface is known since the early 70s. A surface oxide trilayer model, based on a three-layer slab of Ag2O(111), was proposed. Accordingly, the Ag(111) surface seemed to show a similar behaviour like Pd and Rh, being neighbours in the periodic table. Further theoretical calculations predicted the stability of this reconstruction under industrially relevant conditions. Nevertheless, several questions remained unsolved: the stability of the p(4x4) reconstruction under industrially relevant conditions was not checked experimentally, the structural model of the p(4x4) structure was not proven by a crystallographic method and previously unknown structures might play an important role for the catalytic activity of Ag(111) facets. Our experimental approach is based on the nowadays routinely available highly brilliant x-ray radiation produced by third generation synchrotron light sources. This radiation is used by us in three surface sensitive x-ray techniques. In-situ surface x-ray diffraction (SXRD) allows the identification and determination of structural models of surface reconstructions under industrially relevant conditions. This technique is combined with high resolution core level spectroscopy (HRCLS) and normal incidence x-ray standing wave absorption (NIXSW), giving insight into the local binding geometry of the oxygen and silver atoms.Item Open Access TRSS: a new version of program TRS for a different geometry(1992) Schmitz, Joachim; Trebin, Hans-Rainer; Rössler, UlrichQuantum resonances in the bands of semiconductors under uniaxial stress provide very detailed information on the band parameters. However, the analysis of experimental data is difficult. Computer programs based on an adequate theoretical model make this task easier. Program TRSS calculates energy eigenvalues, wave functions and oscillator strengths for direct inter- and intraband dipole transitions. The magnetic field is applied parallel to the [001] crystal axis while the uniaxial stress is directed perpendicular [100] to it.Item Open Access Liquid-crystalline blue phase III and structures of broken icosahedral symmetry(1993) Longa, Lech; Fink, Werner; Trebin, Hans-RainerThe structure of the liquid-crystalline blue phase III (BPIII) is still unknown and remains one of the mysteries of liquid-crystal physics. We take all icosahedral space-group symmetries of the reciprocal space for BPIII and study their thermodynamic stability within the frame of an extended de Gennes–Ginzburg–Landau free-energy expansion. The stability of the icosahedral structures is compared with that of the cholesteric phase and of the cubic blue phases. Strikingly, even though the extended model contains three extra parameters, we could not detect a region of parameter space where icosahedral structures are absolutely stable just below the isotropic phase.Item Open Access Makroskopische Quasikristalle(1990) Kramer, Peter; Trebin, Hans-RainerFünf Jahre ist es her, daß Dan Shechtman (Technion, Haifa) an der Metallegierung Al86Mn14 ein scharfes Elektronenbeugungsmuster mit Ikosaedersymmetrie fand. Weitreichende Ordnung, dokumentiert durch Bragg-Reflexe, und nicht-kristallographische Ikosaedersymmetrie mit fünfzähligen Achsen haben die Strukturphysiker in den Jahren seither veranlaßt, eine Fülle von Modellen für atomare Anordnungen zu entwickeln, die zwischen den periodischen klassischen Kristallen mit Fernordnung und den nur nahgeordneten amorphen Strukturen liegen. Erste Modellvorstellungen von Quasikristallen entnahm man den Penrose-Mustern. Sie bilden in zwei Raumdimensionen eine lückenlose Überdeckung der Ebene mit zwei Arten von Zellen in der Form einer spitzen und einer stumpfen Raute.Item Open Access Theory of liquid crystalline phases in biaxial systems(1992) Longa, Lech; Trebin, Hans-RainerGeneral properties of SO(3) - symmetric free- energy expansion for biaxial systems are studied. In particular, all invariants in powers of a traceless and symmetric quadrupole tensor order parameter and a vector order parameter are identified and their relation to possible local structures are found. A new class of polar, chiral biaxial phases are predicted.Item Open Access Spontaneous polarization in chiral biaxial liquid crystals(1990) Longa, Lech; Trebin, Hans-RainerA phenomenological theory of polar structures in chiral biaxial liquid crystals is constructed exploiting the properties of a symmetric and traceless tensor order parameter field Q αβ(r) and of a polar field Pα(r). Full advantage is taken of the symmetry of the order parameters by systematic use of the method of integrity bases, which allows us to establish an expansion of the most general SO(3)-invariant free-energy density to arbitrary powers in the components Qαβ and Pα. A coordinate-independent parametrization of the invariants is introduced that yields a classification of local polar structures and some predictions about possible topologies of phase diagrams without the necessity of performing numerical calculations. As one prominent result, the theory predicts a polar, chiral biaxial state that exists due to a piezoelectric coupling of a chiral biaxial tensor field and the polarization field and which disappears if tensor is uniaxial. We then provide a general theory of flexopolarization in biaxial systems. A general biaxial system is described by 12 fundamental flexopolarization modes. Special cases, obtained by imposing symmetry restrictions to the tensor field Q, reduce the number of modes. Finally, the theory is applied to chiral phases. Simple polar chiral structures including cholesteric and smectic-C* liquid crystals are analyzed. In particular, it is shown that if the smectic-C* phase is stabilized due to the piezoelectric coupling between Q, P, and a density wave, then it must be described as a biaxial uniform spiral with at least two nonvanishing commensurate harmonics. The minimization of the quadratic part of the Landau–de Gennes energy supplemented by (flexo)polarization terms may give rise to incommensurate two- or three-dimensional polar structures that can be stabilized by cubic terms.Item Open Access Aktivierungsvolumen und chemische Umgebung von thermischen Leerstellen in intermetallischen Verbindungen(2000) Müller, Markus A.; Schaefer, Hans-Eckhardt (Prof.Dr.)Im Rahmen dieser Arbeit wurde mit Methoden der nuklearen Festkörperphysik, nämlich der Positronenzerstrahlung, der Positronenlebensdauerspektroskopie und der Dopplerverbreiterung der Elektron-Positron-Zerstrahlungsphotonen, Leerstellen in intermetallischen Verbindungen untersucht. Dabei konnten erstmals spezifisch die Aktivierungsvolumen für die Bildung und Wanderung thermischer Leerstellen und die chemische Umgebung, d.h. das Untergitter dieser Leerstellen bestimmt werden. Für Fe61Al39 wurde im Temperaturbereich von Ta = 681 K bis 610 K die Gleichgewichtseinstellung der Leerstellenkonzentration beobachtet. Dabei wurden zwei Einstellprozesse beobachtet. Für das Leerstellenbildungsvolumen erhält man 1,5 Atomvolumen, während für den hauptsächlichen Einstellprozess ein relativ hohes Leerstellenwanderungsvolumen von 4,6 Atomvolumen gefunden wird. Die koinzidente Dopplerspektroskopie wurde als weitere Messmethode zur spezifischen Untersuchung der chemischen Umgebung von Leerstellen in Festkörpern eingeführt. Es wurde damit möglich, unterschiedliche chemische Umgebungen des in einer Leerstelle zerstrahlenden Positrons aus der elementspezifischen Impulsverteilung der Positronenzerstrahlung mit Rumpfelektronen zu identifizieren. Danach besteht die Umgebung der Leerstelle in Fe61Al39 im thermischen Gleichgewicht bei 770 K vorwiegend aus Aluminiumatomen. Damit ist erstmals der direkte experimentelle Nachweis dafür erbracht, dass die thermische Leerstelle in Fe61Al39 auf dem Eisenuntergitter gebildet wird. Dies stimmt mit theoretischen Untersuchungen überein, wonach die Bildung von Al-Leerstellen energetisch ungünstiger ist. Bei weiteren binären und ternären Legierungen konnte die koinzidente Dopplerspektroskopie ebenfalls erfolgreich zur Defektcharakterisierung eingesetzt werden.Item Open Access Disclinations in quasicrystals [Erratum](1987) Bohsung, Jörg; Trebin, Hans-RainerThe most significant feature in the transition from the quasicrystalline to the amorphous state is the loss of long-range bond-orientational order. Disclinations are candidates for elementary excitations which destroy angular correlations. Generalizing the topological defect classification, we investigate point singularities in two-dimensional pentagonal quasicrystals and construct disclinations, dislocations, and disclination dipoles.Item Open Access Die atomare Dynamik dekagonaler Quasikristalle(1999) Bunz, DietmarDie Struktur von Quasikristallen erlaubt phasonische Flips, das heißt Atome können auf alternative Positionen springen, ohne daß die Gesamtstruktur verändert wird. Schwerpunkt der Arbeit ist das Auffinden dieser phasonischen Flips in AlCuCo mit Hilfe molekulardynamischer Simulationen. Zum Aufspüren dieser Flips wurde in ein vorhandenes Molekulardynamikprogramm ein Flip-Detektor implementiert. Zur genaueren Untersuchung der gesamten Atombewegungen wurde eine Methode zur interaktiven Darstellung des gesamten zeitlichen Verlaufs einer Simulation entwickelt. Neben den erwarteten korrelierten Sprüngen in den dekagonalen Schichten sind weitere korrelierte Bewegungen im Quasikristall sichtbar.