On the remarkable thermal stability of nanocrystalline cobalt via alloying

Nanostructured Co materials are produced by severe plastic deformation via alloying with small amounts of C and larger amounts of Cu. The thermal stability of the different nanostructured Co materials is studied through isothermal annealing at different temperatures for various times and compared to the stability of severe plastically deformed high-purity nanocrystalline Co. The microstructural changes taking place during annealing are evaluated by scanning electron microscopy, transmission electron microscopy and microhardness measurements. In the present work it is shown that the least stable nanostructured material is the single-phase high purity Co. Alloying with C improves the thermal stability to a certain extent. A remarkable thermal stability is achieved by alloying Co with Cu resulting in stabilized nanostructures even after annealing for long times at high temperatures. The essential reason for the enhanced thermal stability is to be found in the immiscibility of both components of the alloy

Kreisplanarität von Level-Graphen

In this dissertation we generalise the notion of level planar graphs in two directions: track planarity and radial planarity. Our main results are linear time algorithms both for the planarity test and for the computation of an embedding, and thus a drawing. Our algorithms use and generalise PQ-trees, which are a data structure for efficient planarity tests.In dieser Arbeit wird der Begriff Level-Planarität von Graphen auf zwei Arten erweitert: Spur-Planarität und radiale Level-Planarität. Die Hauptergebnisse sind Linearzeitalgorithmen zum Testen dieser Arten von Planarität und zur Erstellung einer entsprechenden Einbettung und somit einer Zeichnung. Die Algorithmen verwenden und generalisieren PQ-Bäume, eine bei effizienten Planaritätstests verwendete Datenstruktur

Phase decomposition and nano structure evolution of metastable nanocrystalline Cu-Co solid solutions during thermal treatment

Nanocrystalline and ultrafine-grained Cu100-xCox (x = 26 and 76) solid solutions have been prepared by severe plastic deformation (SPD) of elemental powder mixtures. For both concentrations a supersaturated solid solution fcc phase was identified after the deformation process with grain sizes of less than 50 nm for Co rich solutions and around 100 nm for Cu rich solutions. Additionally, synthesis of nanocrystalline materials in the Cu-Co alloy system by electrodeposition has been conducted. Microstructural characterization by scanning and transmission electron microscopy, differential scanning calorimetry, and microhardness measurements are used to investigate the structural evolution, the thermal stability and mechanical properties of the different nanocrystalline Cu-Co alloy materials during isothermal and non-isothermal annealing. In this study it is shown that the phase decomposition of the metastable Cu-Co solid solutions has a significant influence on their thermal stability, which can be linked to the underlying microstructure that forms during annealing

Separation of noncommutative differential calculus on quantum Minkowski space

Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is shown that this problem can be overcome by a separation of variables. We study the action of the universal L-matrix, appearing in the coproduct of partial derivatives, on generators. Powers of he resulting quantum Minkowski algebra valued matrices are calculated. This leads to a nonlinear coordinate transformation which essentially separates the calculus. A compact formula for general derivatives is obtained in form of a chain rule with partial Jackson derivatives. It is applied to the massive quantum Klein-Gordon equation by reducing it to an ordinary q-difference equation. The rest state solution can be expressed in terms of a product of q-exponential functions in the separated variables.Comment: 33 page

On the process of co-deformation and phase dissolution in a hard-soft immiscible CuCo alloy system during high-pressure torsion deformation

In this study, dual phase Cusingle bondCo composites with a total immiscibility in the solid state and a very different initial phase strength are deformed by severe plastic deformation. Nanocrystalline supersaturated solid solutions are reached in all Cusingle bondCo composites independent of the initial composition. The deformation and mechanical mixing process is studied thoroughly by combining scanning electron microscopy, transmission electron microscopy, three-dimensional atom probe tomography and nanoindentation. The indentation hardness of the Cu and Co phase and its evolution as a function of the applied strain is linked to deformation and mechanical mixing process to gain a better understanding how the phase strength mismatch of the Cu and Co phase effects the amount of co-deformation and deformation-induced mixing. Our results show that co-deformation is not a necessary requirement to achieve mechanical mixing