Computational studies of defects in graphene and carbon nanotubes

Carbon structures have a big role in nanoscience today because of their rich and promising electrical, mechanical and optical properties. However, advancing these properties requires understanding the underlying structure and its behavior. In addition to ideal systems, defects are frequently unavoidable in experiments; hence their e ects, along with their possibilities to enrich the functionalities of carbon nanostructures, should be investigated. This thesis concentrates on computational studies of various defects in graphene and carbon nanotubes. It combines investigations of changes in Raman-active modes of single-walled carbon nanotubes due to vacancies and bending, reconstructions for graphene edges, and adsorption and di usion mechanism of single gold atoms in graphene. Most of the results can be understood in terms of simple physical principles and relations to experiments are discussed in detail. E ects of carbon atom vacancies on Raman-active phonons are understood via their symmetry properties and structural weakening. However, the e ect of tube bending on Raman-active modes is complicated to understand. Bending proved to be computationally challenging, but our so-called wedge boundary conditions o ered a way to practical modeling. Wedge boundary conditions are free from constraints and nitesize e ects, and really make bending the only disturbance in the system. This kind of approach will be useful for other physical problems as well. In this thesis we found a new ground state for graphene edges a new edge beyond armchair and zigzag. We show that this speci c reconstruction of zigzag selfpassivates the edge against molecular hydrogen adsorption and increases the rigidity of the graphene edge. We discuss about the possibilities to identify the edge structure from scanning tunneling microscope (STM) images, Raman-active modes and vibrational properties relating the di erences to physical properties. This thesis also shows that gold atoms are thermally stable in-plane with graphene opening possibilities to tune the properties of carbon nanostructures. Our results con rm that, in addition to imaging, transmission electron microscope (TEM) has a great potential as a preparation tool for samples of carbon nanomaterials containing metals. Because contacts may dominate behaviour in nanosize systems, understanding the metal-carbon interface through defects like vacancies is important. With the help of TEM-beam there can be a way to selectively make direct contacts with metals and carbon nanostructures at any point of the lattice, not only at the edges