Study of charged defects for substitutionally doped chromium in hexagonal barium titanate from first-principles theory

We have studied the defect properties of substitutionally doped chromium in hexagonal barium titanate using the density functional theory together with the generalized gradient approximation restricted to exclusively electronic compensation of the charged defect. The supercell used in our studies is large enough to mimic a chromium concentration of about 2 mol%, which corresponds to an amount typically applied in experiments. Chromium is found to prefer the Ti sites inside the face-sharing oxygen octahedra compared with the other non-equivalent Ti sites within the exclusively corner-sharing octahedra of the hexagonal host lattice. Analysis of formation energy, derived from the total energies of defective supercells in various charge states and systematic post-processing, shows that the charge state of -1 is stable for wide range of Fermi energy within the band gap. The charge state of 0 is only stable for a very low electron concentration, i.e. for highly oxidizing conditions. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim