Local structure of Ba(Ti,Zr)O₃ perovskite-like solid solutions and its relation to the band-gap behavior

Local structures in BaTi_1-xZr_xO₃ solid solutions were analyzed using x-ray absorption fine structure (XAFS) measurements and density-functional theory (DFT) calculations. We demonstrate that for low concentrations of Ti, isolated Ti atoms in the relatively large octahedral sites of the BaZrO₃ lattice acquire centrosymmetric coordination with average Ti-O distances shorter than those in BaTiO ₃. In contrast for higher concentrations of Ti, Ti atoms having one or more Ti as their B-site nearest neighbors undergo polar off-center displacements. Our DFT calculations confirm both effects. These results combined with the previously published data suggest that isolated polarizable ions on the B sites of a relatively expanded host perovskite lattice remain nonpolar by symmetric relaxation of the nearest-neighbor oxygen atoms to yield nearly ideal bond lengths around the dopant species. For neighboring Ti atoms, such symmetric relaxation is impossible, and these atoms are displaced off center. Our XAFS measurements did not detect any significant deviations from a random distribution of Ti and Zr in the present samples except for compositions close to BaTiO₃. The DFT calculations suggest that the dominant effect of the local displacements on band-gap values for this system is determined by the shortest Ti-O bonds due to strong Ti 3d-O 2p hybridization; however, local displacements have only a secondary effect on the band-gap behavior.