In this study, the structural, electronic, and elastic properties of cubic zirconium dioxide (c-ZrO₂) were investigated using the Density Functional Theory (DFT) approach. Lattice parameter optimization revealed that the lattice constant is 5.107 Å, the Zr–O bond length is 2.21 Å, and the unit cell density is 6.075 g/cm³ for the B3LYP functional. The bandgap width was determined to be 5.1722 eV. The investigation of the elastic properties of the cubic ZrO₂ crystal determined the Young’s modulus, bulk modulus, Poisson’s ratio, and hardness, which were found to be 315.91 GPa, 241 GPa, 0.282, and 13 (Hv), respectively, under zero external pressure. These results confirm the mechanical stability of ZrO₂.

This work presents a theoretical investigation of ionic conductivity in cubic zirconia (c-ZrO₂) doped with magnesium, using density functional theory (DFT) with the hybrid B3LYP functional as implemented in the CRYSTAL23 software package. It was found that the spatial arrangement of magnesium atoms and oxygen vacancies significantly affects the energy barriers for oxygen ion migration. Configurations with magnesium located along and outside the migration path were analyzed. The results show that when Mg²⁺ is positioned along the migration trajectory and near an oxygen vacancy, stable defect complexes are formed with minimal migration barriers ranging from 0.96 to 1.32 eV. An increased number of Mg atoms can lead to a further reduction in the barrier, although in certain configurations the barriers increase up to 3.0–4.6 eV. When doping occurs outside the migration path, the energy profile remains symmetric and moderate (0.9–1.1 eV), indicating only a weak background influence. These findings highlight the critical role of coordinated distribution of Mg atoms and oxygen vacancies along the migration pathway in forming efficient ion-conducting channels. This insight offers potential for designing high-performance zirconia-based electrolytes for solid oxide fuel cells and sensor applications.