The Tin dioxide (SnO2) and Titanium dioxide (TiO2) are very promising materials in Material science. The SnO2 is commonly used as a gas sensor while the TiO2 is used as a catalyst in many reactions. Despite of the usefulness of these two substances, their surface structures lack detail investigations in the previous years. The Low Energy Electron Diffraction (LEED) technique is commonly used to characterize surfaces in the past 40 years, it is a mature system that many researches rely on its result. However, structural analysis in LEED requires comparison with computational results based on pre-defined structure models, which is a time-consuming method and the results are not guaranteed to be found. The direct determinations of structure by Patterson function inversion methods introduced by Huasheng Wu and S. Y. Tong could provide a different path to search for surface structure. In the Patterson function, each maximum in the function corresponds to a relative position vector of atomic pairs. Multiple-angle-incident LEED has to be performed to obtain an artifact-free Patterson function. Serveal SnO2 and TiO2 surfaces have been characterized by LEED and Patterson function inversion. SnO2 (110), (100), (101) , Rutile TiO2 (110), Anatase TiO2 (110) have been prepared by argon ion sputtering and annealing cycles and the cleanness has been checked by Auger Electron Spectroscopy and LEED. Reconstruction is observed based on the study of the LEED patterns. SnO2 (110) surface shows a 4 x 1 reconstruction in UHV environment while it gives 1 x 1 under annealing in oxygen and C(2 x 2) at higher annealing temperature afterward. SnO2 (100) , (101) and Rutile TiO2 (110) surfaces show 1 x 1 reconstruction in UHV environment and the reconstruction persists for further annealing. The Anatase TiO2 (110) surface shows a 3 x 4 reconstruction in UHV environment. The 3 x 4 reconstruction of Anatase TiO2 (110) surface would raise research interests as it is quite a special reconstruction. Multiple-angle-incident LEED has been performed on the SnO2 (100), (101) and Rutile TiO2 (110) surfaces. Patterson function inversion is performed on the surfaces SnO2 (100) and Rutile TiO2 (110) . Only LEED is performed on SnO2 (110) , (101) and Anatase TiO2 (110) surfaces. From Patterson functions analysis, the surface atoms positions are determined for the surface SnO2 (100) and Rutile TiO2 (110). The results show that their reconstructions are negligible, but they have obvious relaxations. / published_or_final_version / Physics / Master / Master of Philosophy