Thermodynamics of doping and vacancy formation in BaZrO3 perovskite oxide from density functional calculations

Density functional calculations combined with thermodynamical modeling have been used to investigate defect formation in a perovskite-structured oxide in equilibrium with an oxygen containing atmosphere. We have calculated the electronic structure and formation energies for anion and cation vacancies and for Ga, Gd, In, Nd, Sc, and Y dopants incorporated on different lattice sites in BaZrO3. On energetic grounds, it is found that most of the investigated dopants (with the possible exception of Nd and Gd) preferably substitute for Zr atoms in the lattice. The interaction between dopants was found to be repulsive and correlated with the ionic radius of the dopant, while the dopant-oxygen vacancy interaction was found attractive. We also show that oxygen vacancies are not thermodynamically stable at low temperatures, but will form at the high temperatures and low oxygen partial pressures typically used during synthesis of the material.