Unsupervised Learning and Fourier Analysis Methods for Crystal Orientation Mapping of Electron Microscopy Data

The study and development of groundbreaking materials have been, in part, developed through their own crystalline nature, opening a vast field focused on the comprehension of how and why crystalline structures appear to be self-assembled. Among these structures, crystalline artifacts are ubiquitous in materials despite the production method. The key here would be the density of crystal defects distributed along the material, and of course, their order and dimensionality. The span of certain types of defects can provoke desired properties within the material, which will allow it to go further into the manufacturing of a device. For this reason, is of vital importance to use characterization techniques to inquire about this. For this reason, techniques based on electron microscopy has been employed to classify materials and their properties. In general, transmission electron microscopy have been exploited for several decades as an analytical technique for structural studies of materials. Nowadays, this technique has achieved atomic resolution using aberration correctors, making it perfect to study all kinds of nanostructures and their properties due to the quantum confinement effects. Pristine high resolution TEM images have information encoded that can be of great help when certain physical attributes are contained, in general, Fourier transform methods can be employed to retrieve information lost in the image collection by retrieving information from the phase. During the first part of this PhD project, the collection of imaging and diffraction data in TEM for diverse samples was obtained and studied with classical TEM imaging processing tools parallel to other advanced algorithms for phase retrieval (geometric phase analysis), to study. Also, techniques such as the weak beam condition were employed to produce a contrast difference among structural defects. GaN/Si and SrTiO$3$ samples were grown and studied by crystallographic means, being crucial the understanding of crystal growth of interfaces of these heterojunctions, as they determine the propagation of the number of defects in a device or can present other physical properties such as strong spin-orbit interaction as a consequence of the strain caused by the crystal growth. The design and deployment of a computational algorithm involving Gabor filters was proposed to study geometrical metallic nanoparticles at atomic level, this was then extrapolated to the generation of an algorithm capable of localizing particles and generating crystal orientation mappings at atomic level using unsupervised learning methods of all kinds of crystalline samples, this pipeline have the potential to be used in artificial intelligence algorithms for dynamic evolution of systems in TEM. The last part of the research then was focused on the measurement of relative orientations of graphene bilayers. We have proposed that certain orientations are prone to be preferred during the deposition process spontaneously due special interfaces generated, these will have simpler displacement fields that contain interfacial dislocations with fewer Burgers vectors to choose from. These pseudo-stable conformations will reorient themselves spontaneously as they simplify their strain fields.