Site Occupancy of Rare-Earth Cations in BaTiO₃

A systematic study on the site occupancy of rare-earth cations in Ba-rich and Ti-rich BaTiO 3 fired in reducing atmosphere is performed. The corresponding lattice relaxation is used as an indicator of site occupancy and, to a lesser extent, defect structures. Accurate lattice parameters are obtained from X-ray diffraction data that is analyzed with the maximum likelihood method to account for correlated errors in the c and a lattice parameters. Comparisons of lattice volume as a function of ionic radius of the dopant reveals three regimes, with the intermediate sized cations (0.087 nm \leqslant r \leqslant0.094 nm where r is the ionic radius in six-fold coordination) demonstrating amphoteric behavior (occupying A- or B-sites). Defect chemistry analysis of site occupancy links the importance of metal vacancy ratios and oxygen vacancy concentrations with site occupancy. The trends predicted from the defect chemistry analysis are consistent with the observed lattice relaxations.