Eingefrorene Unordnung und Magnetismus in TiFe_1tn2-Laves-Phase-Dünnschichten

In der vorliegenden Arbeit wird die binäre intermetallische Verbindung TixFe1-x im C14 Laves-Phase Stabilitätsbereich anhand von dünnen Schichten untersucht. TiFe2 weist zwei energetisch nahezu entartete magnetische Grundzustände auf. Dies führt zu einer starken Korrelation von strukturellen und magnetischen Eigenschaften, die im Rahmen dieser Arbeit untersucht wurden. Es wurden daher epitaktische Schichten mit variabler Zusammensetzung im C14 Stabilitätsbereich auf Al2O3 (001)-orientierten Substraten mittels Molekularstrahlepitaxie präpariert und strukturell charakterisiert. Die temperatur- und magnetfeldabhängigen magnetischen Eigenschaften dieser Proben wurden mittels DC-SQUID Magnetisierungsmessungen bestimmt. Es zeigte sich eine magnetische Phasenseparation von Antiferromagnetismus und Ferromagnetismus in Abhängigkeit von der Zusammensetzung. Aus den charakteristischen Ordnungstemperaturen konnte ein magnetisches Phasendiagramm für dünne Schichten und niedrige Aligning-Felder erstellt werden. Ein Phasendiagramm für Volumenproben bei hohem Magnetfeld unterscheidet sich von diesem im Wesentlichen durch den Einfluß von Fe-Segregation in den Volumenproben, welche bei der epitaktischen Präparation nicht auftritt. Anhand von Monte-Carlo Verfahren, denen ein „quenched random disorder“ Modell zugrunde lag, wurde das Verhalten der Dünnschichtproben simuliert und daraus ein magnetisches Phasendiagramm abgeleitet. Das simulierte und experimentelle Phasendiagramm stimmt in den wesentlichen Punkten überein. Die Unterschiede sind durch die speziellen Wachstumseigenschaften von TiFe2 erklärbar. Als Ergebnis kann die magnetische Phasenseparation in diesem System als Auswirkung einer Symmetriebrechung durch Substitution in der Einheitszelle beschrieben werden.

Single polymers at surfaces: adsorption and detachment

This thesis is concerned with the adsorption and detachment of polymers at planar, rigid surfaces. We have carried out a systematic investigation of adsorption of polymers using analytical techniques as well as Monte Carlo simulations with a coarse grained off-lattice bead spring model. The investigation was carried out in three stages. In the first stage the adsorption of a single multiblock AB copolymer on a solid surface was investigated by means of simulations and scaling analysis. It was shown that the problem could be mapped onto an effective homopolymer problem. Our main result was the phase diagram of regular multiblock copolymers which shows an increase in the critical adsorption potential of the substrate with decreasing size of blocks. We also considered the adsorption of random copolymers which was found to be well described within the annealed disorder approximation. In the next phase, we studied the adsorption kinetics of a single polymer on a flat, structureless surface in the regime of strong physisorption. The idea of a ’stem-flower’ polymer conformation and the mechanism of ’zipping’ during the adsorption process were used to derive a Fokker-Planck equation with reflecting boundary conditions for the time dependent probability distribution function (PDF) of the number of adsorbed monomers. The numerical solution of the time-dependent PDF obtained from a discrete set of coupled differential equations were shown to be in perfect agreement with Monte Carlo simulation results. Finally we studied force induced desorption of a polymer chain adsorbed on an attractive surface. We approached the problem within the framework of two different statistical ensembles; (i) by keeping the pulling force fixed while measuring the position of the polymer chain end, and (ii) by measuring the force necessary to keep the chain end at fixed distance above the adsorbing plane. In the first case we treated the problem within the framework of the Grand Canonical Ensemble approach and derived analytic expressions for the various conformational building blocks, characterizing the structure of an adsorbed linear polymer chain, subject to pulling force of fixed strength. The main result was the phase diagram of a polymer chain under pulling. We demonstrated a novel first order phase transformation which is dichotomic i.e. phase coexistence is not possible. In the second case, we carried out our study in the “fixed height” statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain end is kept fixed at height h over the solid plane at different adsorption strength ε. The phase diagram in the h − ε plane was calculated both analytically and by Monte Carlo simulations. We demonstrated that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than the force, f, is used as an independent control parameter.

High precision swept volume approximation with conservative error bounds

In technical design processes in the automotive industry, digital prototypes rapidly gain importance, because they allow for a detection of design errors in early development stages. The technical design process includes the computation of swept volumes for maintainability analysis and clearance checks. The swept volume is very useful, for example, to identify problem areas where a safety distance might not be kept. With the explicit construction of the swept volume an engineer gets evidence on how the shape of components that come too close have to be modified.rnIn this thesis a concept for the approximation of the outer boundary of a swept volume is developed. For safety reasons, it is essential that the approximation is conservative, i.e., that the swept volume is completely enclosed by the approximation. On the other hand, one wishes to approximate the swept volume as precisely as possible. In this work, we will show, that the one-sided Hausdorff distance is the adequate measure for the error of the approximation, when the intended usage is clearance checks, continuous collision detection and maintainability analysis in CAD. We present two implementations that apply the concept and generate a manifold triangle mesh that approximates the outer boundary of a swept volume. Both algorithms are two-phased: a sweeping phase which generates a conservative voxelization of the swept volume, and the actual mesh generation which is based on restricted Delaunay refinement. This approach ensures a high precision of the approximation while respecting conservativeness.rnThe benchmarks for our test are amongst others real world scenarios that come from the automotive industry.rnFurther, we introduce a method to relate parts of an already computed swept volume boundary to those triangles of the generator, that come closest during the sweep. We use this to verify as well as to colorize meshes resulting from our implementations.

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.