On the nature of differences in the Ni charge states in barium and strontium titanates

XAFS studies of nickel-doped solid solution Ba_1–xSr_xTiO₃ show that the Ni charge state changes from 4 in SrTiO₃ to ~2.5 in BaTiO₃ as x is varied. First-principles electronic structure calculations show that nickel creates an impurity band in the forbidden gap of BaTiO₃ and SrTiO₃. Calculations of the formation energy of the oxygen vacancies explain the difference between the Ni charge states in these compounds by the different formation energies of these vacancies.