Cerium oxide has become an outstanding material in catalytic applications over the last decades. In this thesis, the morphology and atomic structure of thick cerium oxide films and ceria single crystals is investigated by non-contact atomic force microscopy (NC-AFM) and Kelvin probe force microscopy (KPFM). The ceria films are prepared by annealing cycles from room temperature up to 1100K in ultra high vacuum (UHV) and in an oxygen atmosphere. The films exhibit large smooth terraces separated predominantly by O-Ce-O triple layer height step edges but in contrast to the ceria single crystals some inhomogeneities are observed on the terraces. By annealing the film at 1020K to 1070K in UHV several intermediate phases can be stabilized ranging from the fully oxidized phase CeO2 to the fully reduced phase Ce2O3. These phases have a unique stoichiometry with regular arranged vacancies in the surface and subsurface as revealed by density functional theory (DFT) calculations. The film can be reoxidized by annealing in an oxygen atmosphere as shown by X-ray spectroscopy (XPS). The annealing in oxygen atmosphere also results in a surface with less inhomogeneities. This makes the ceria films an excellent model system for catalytic applications. Further in this thesis a measurement series exhibiting absorbed water on the film surface is presented and discussed. Also line defects observed on the film and on the single crystal are analyzed.

Computational approaches play an important role in today's materials science owing to the remarkable advances in modern supercomputing architecture and algorithms. Ab initio simulations solely based on a quantum description of matter are now very able to tackle materials problems in which the system contains up to a few thousands atoms. This dissertation aims to address the modern electronic structure calculation methods applied to a range of various materials such as liquid and amorphous phase materials, nanostructures, and small organic molecules. Our simulations were performed within the density functional theory framework, emphasizing the use of real-space ab initio pseudopotentials. On the first part of our study, we performed liquid and amorphous phase simulations by employing a molecular dynamics technique accelerated by a Chebyshev-subspace filtering algorithm. We applied this technique to find l- and a- SiO₂ structural properties that were in a good agreement with experiments. On the second part, we studied nanostructured semiconducting oxide materials, i.e., SnO₂ and TiO₂, focusing on the electronic structures and optical properties. Lastly, we developed an efficient simulation method for non-contact atomic force microscopy. This fast and simple method was found to be a very powerful tool for predicting AFM images for many surface and molecular systems. / text

Different methods for the determination of cantilever properties in non-contact atomic force microscopy (NC-AFM) are under investigation. A key aspect is the determination of the cantilever stiffness being essential for a quantitative NC-AFM data analysis including the extraction of the tip-surface interaction force and potential. Furthermore, a systematic analysis of the displacement noise in the cantilever oscillation detection is performed with a special focus on the thermally excited cantilever oscillation. The propagation from displacement noise to frequency shift noise is studied under consideration of the frequency response of the PLL demodulator. The effective Q-factor of cantilevers depends on the internal damping of the cantilever as well as external influences like the ambient pressure and the quality of the cantilever fixation. While the Q-factor has a strong dependence on the ambient pressure between vacuum and ambient pressure yielding a decrease by several orders of magnitude, the pressure dependence of the resonance frequency is smaller than 1% for the same pressure range. On the other hand, the resonance frequency highly depends on the mass of the tip at the end of the cantilever making its reliable prediction from known cantilever dimensions difficult. The cantilever stiffness is determined with a high-precision static measurement method and compared to dimensional and dynamic methods. Dimensional methods suffer from the uncertainty of the measured cantilever dimensions and require a precise knowledge its material properties. A dynamic method utilising the measurement of the thermally excited cantilever displacement noise to obtain cantilever properties allows to characterise unknown cantilevers but requires an elaborative measurement equipment for spectral displacement noise analysis. Having the noise propagation in the NC-AFM system fully characterised, a proposed method allows for spring constant determination from the frequency shift noise at the output of the PLL demodulator with equipment already being available in most NC-AFM setups.