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The presented study was motivated by the dynamic phenomena observed in basic catalytic surface reactions, especially by bi- and tristability, and the interactions between these stable states. In this regard, three reaction-diffusion models were developed and examined using bifurcation theory and numerical simulations.
A first model was designed to extend the bistable CO oxidation on Ir(111) to include hydrogen and its oxidation. The differential equation system was analyzed within the framework of bifurcation theory, revealing three branches of stable solutions.
One state is characterized by high formation rates (upper rate state, UR), while the other two branches display low formation rates (lower rate (LR) \& very low rate (VLR) states).
The overlapping branches form the shape of a `swallowtail', the curve of saddle-node bifurcations forming two cusps. Increasing the temperature leads to a subsequent unfolding and hence decreases the system complexity.
A series of numerical simulations representing possible experiments was conducted to illustrate the experimental accessibility (or the lack) of said states. Relaxation experiments show partially long decay times. Quasistatic scanning illustrates the existence of all three states within the tristable regime and their respective conversion once crossing a fold.
A first attempt regarding the state dominance in reaction-diffusion fronts was done. While UR seems to dominate in 1D, a 2D time-evolution shows that LR invades the interphase between UR and VLR.
Subsequently, a generic monospecies mock model was used for the comprehensive study of reaction-diffusion fronts. A quintic polynomial as reaction term was chosen, derived by the sixth-order potential associated with the `butterfly bifurcation'. This ensures up to three stable solutions($u_{0}$,$u_{1}$,$u_{2}$), depending on the four-dimensional parameter space.
The model was explored extensively, identifying regions with similar behaviors.
A term for the front velocity connecting two stable states was derived, depending only on the relative difference of the states' potential wells.
Equipotential curves were found, where the front velocity vanishes of a given front. Numerical simulations on a two-dimensional, finite disk using a triangulated mesh supported these findings.
Additionally, the front-splitting instability was observed for certain parameters. The front solution $u_{02}$ becomes unstable and divides into $u_{01}$ and $u_{12}$, exhibiting different front velocities. A good estimate for the limit of the front splitting region was given and tested using time evolutions.
Finally, the established mock model was modified from continuous to discrete space, utilizing a simple domain in 1D and three different lattices in 2D (square, hexagonal, triangular).
For low diffusivities or large distances between coupling nodes, fronts can become pinned, if the parameters are within range of the equipotential lines. This phenomenon is known as propagation failure and its extent in parameter space was explored in 1D. In 2D, an estimate was given for remarkable front orientations respective to the lattice using a pseudo-2D approximation. Near the pinning region, front velocities differ significantly from the continuous expectation as the shape of the curve potential becomes significant. Factors that decide the size and shape of the pinning regions are the coupling strength, the lattice, the front orientation relative to the lattice, and the front itself. The bifurcation diagram shows a snaking curve in the pinning region, each alternating branch representing a stable or unstable frozen front solution. Numerical simulations supported the observations concerning propagation failure and lattice dependence.
Furthermore, the influence of front orientation on the front velocity was explored in greater detail, showing that fronts with certain lattice-dependent orientations are more or less prone to propagation failure. This leads to the possibility of pattern formation, reflecting the lattice geometry. An attempt to quantify the front movement depending on angular front orientation has shown reasonable results and good agreement with the pseudo-2D approach.
To render the surface of a material capable of withstanding mechanical and electrochemical loads, and to perform well in service, the deposition of a thin film or coating is a solution. In this project, such a thin film deposition is carried out. The coating material chosen is titanium nitride (TiN) which is a ceramic material known to possess a high hardness (>10 GPa) as well as good corrosion resistance. The method of deposition selected is high power impulse magnetron sputtering (HiPIMS) that results in coatings with high quality and enhanced properties. Sputtering is a physical process that represents the removal or dislodgment of surface atoms by energetic particle bombardment. The term magnetron indicates that a magnetic field is utilized to increase the efficiency of the sputtering process. In HiPIMS, a high power is applied in pulses of low duty cycles to a cathode that is sputtered and that consists of the coating material. As result of the high power, the ionization of the sputtered material takes place giving the possibility to control these species with electric and magnetic field allowing thereby the improvement and tuning of coating properties. However, the drawback of HiPIMS is a low deposition rate.
In this project, it is demonstrated first that it is possible to deposit TiN coating using HiPIMS with an optimized deposition rate, by varying the magnetic field strength. It was found that low magnetic field strength (here 22mT) results in a deposition rate similar to that of conventional magnetron sputtering in which the average power is applied continuously, called also direct current magnetron sputtering (dcMS). The high deposition rate at low magnetic field strength was attributed to a reduction in the back attraction probability of the sputtered species. The magnetic field strength did not show noticeable influence on the mechanical properties. The proposed explanation was that the considered peak current density interval 1.22-1.72 A∙cm-2 does not exhibit dramatic changes in the plasma dynamics.
In a second part, using the optimized deposition rate, the optimized chemical composition of TiN was determined. It was shown that the chemical composition of TiN does not significantly influence the corrosion performance but impacts considerably the mechanical properties. It was also shown that the corrosion resistance of the coatings deposited using HiPIMS was higher than that of the coatings deposited using dcMS.
The third study was the effect of annealing post deposition on the properties of TiN coating deposited using HiPIMS. The hardness of the coatings showed a maximum at 400°C reaching 24.8 GPa. Above 400°C however, a lowering of the hardness was measured and was due to the oxidation of TiN which led to the formation of TiN-TiO2 composites with lower mechanical properties.
The coating microscopic properties such as crystal orientation, residual stresses, average grain size were determined from X-ray diffraction data and the roughness was measured using atomic force microscopy. These properties were found to vary with the magnetic field strength, the chemical composition as well as the annealing temperature.