Simulations of two-dimensional crystalline and amorphous oxides

Over the last 20 years the study of low-dimensional systems has been extremely prolific, giving rise to new technological applications and new developments for fundamental research. In this context, two-dimensional network-forming oxides represent an intriguing and understudied class of materials, characterized by low-density network structures formed by covalent bonds. So far, only a couple of these systems have been synthesized, such as silica bilayers and boron-oxygen compounds. The physics of their three-dimensional equivalents is extremely rich and still debated, with an intricate interplay between polymorphism, diverse superstructural units and medium-range order. There are inherent difficulties in measuring the structure of these three-dimensional networks and this has significantly hindered our understanding of them. The synthesis of two-dimensional allotropes thus offers a unique opportunity to use standard surface techniques to examine their structure and dynamics, making these materials ideal benchmarks for testing and developing theories on network-forming glasses. In this thesis, we use a combination of ab initio techniques, large-scale classical simulations and rigorous comparison with experiments to describe the structure of two-dimensional crystalline and amorphous oxides at different length scales. Using experimental data, we develop an effective classical potential for the silica bilayer, which is able to reproduce fine structural details of experimental samples. We use this potential to study the glassy behavior of the system at low temperatures and to assess the relationship between structure and dynamics. For a boria monolayer, we devise an algorithm to perform a systematic search for crystalline polymorphs, and we use it to predict from first principles the structure of a recently synthesized boron-oxygen crystal. Using ab initio techniques, we characterize the structure, electronic properties and substrate interactions of the synthesized system, achieving an excellent agreement with the experimental data. After characterizing the crystalline monolayer, we focus on the amorphous structure, developing an algorithm to recover the atomic positions from the experimental images. This allows us to provide a first characterization of this new glassy system. Our results highlight the connection between atomic local environment and network topology, and suggest a strong similarity between different two-dimensional network-forming oxides. We also identify peculiar behaviors in these two-dimensional systems, such as the presence of large transient crystalline domains in the thermodynamically stable low-temperature liquid, which may point to a profound difference between glassy structure in two- and three-dimensions.