Mechanical properties and electronic structure of Cu-doped tin: a first-principle study.

Metal doping is an effective method for improving the toughness of ceramic materials and reducing coating fractures. In this study, first-principle calculations based on density functional theory were performed to study the formation energy, elastic constant, and electronic structure of Cu-doped TiN. The results reveal that Cu tends to replace the Ti sites in TiN crystal cells; with an increase in Cu concentration, the formation energy of the Cu-doped TiN system decreases. This indicates that the structural stability of Cu-doped TiN decreases. From the calculated elastic constant and the Voigt-Reuss-Hill approximation, it is evident that the bulk modulus B and shear modulus G decrease as the Cu concentration increases. However, G decreases more rapidly, thus increasing the B/G ratio. According to Paugh's ratio, the increase in B/G indicates an increase in the ductility of TiN. The results of the band structure, density of states, charge density, and Mulliken bond population analysis reveal that Cu doping reduces the covalent bond strength of TiN, enhances metallicity, and reduces the structural stability of the system, enhancing the toughness of TiN. The results of this study will provide theoretical and experimental guidance for improving the toughness of TiN coatings.