Combination Effect of Transition Metal Impurities on Oxygen Vacancy Formation Energetics in TiO₂

Abstract— The combination effect of substitutional impurities of group IVB–VIB transition metals on the oxygen vacancy formation energy in rutile titania was studied by the projector augmented wave method within density functional theory. The pair interaction energy of impurity atoms was estimated depending on the interatomic distance. It was shown that the interaction in the Zr + Zr, Hf + Hf and Nb + Ta pairs leads to the energy preference of their orientation along the <100> direction at a distance of the lattice parameter a. The Mo + Mo and Nb + Mo pairs prefer to orient along the [001] direction at a distance of the lattice parameter c. If the impurity atoms are farther than the third neighbors, then their interaction can be neglected. It was found that the change in the oxygen vacancy formation energy due to doping with several impurities can be estimated as the sum of the energy changes due to single impurity divided by a coefficient whose value depends on the mutual arrangement of the impurity atoms.