The first-principles calculation based on density functional theory (DFT) was used to study the oxidation resistance of atomically flat and atomic-step edges of Cu(111), diffusion of Cu atoms in different surfaces of alumina and interface properties of alumina and Cu(111), and magnetic properties of Mn-substituted strontium hexaferrite. The dissociation of oxygen molecules is the primary reason for the corrosion of metals, which deteriorates their application. Cu(111) flat surface, mono-atomic, and multi-atomic step edges were used to study oxygen diffusion. Penetration of oxygen on a Cu(111) flat surface requires high energy, indicating oxidation resistance. Our DFT result of oxygen diffusion into a mono-atomic step edge is an endothermic reaction. But the penetration of the O atom at the multi-atomic step edge is an exothermic reaction. We find mono-atomic step is as imperious as the flat surface; on the other hand, multi-atomic step edges are vulnerable to oxidation. This finding is consistent with the experimental results. In the second project, we find Al-terminated surface of alumina is more stable than Oterminated. The result of the ideal work of adhesion shows that the O-terminated surface has a better interface with Cu(111). Single Cu and clusters of Cu atoms were diffused through the Al and O terminating surfaces. The energy barrier for the diffusion of Cu atoms on the O-terminated surface is much higher than on the Al-terminating surface. Furthermore, the activation energies for clusters of multiple atoms migration are higher than for a single Cu atom. The results validate experimentally observed growth modes in the early stage of thin film growth. Next, we perform a DFT calculation to investigate the site preference and magnetic properties of Mn-substituted strontium hexaferrite. The site occupancies of substituted atoms were estimated by calculating the substitution energy. The magnetic properties of substituted hexaferrite were calculated by using formation probabilities. A decrease in saturation magnetization was observed with increasing Mn concentration.