A modified Vegard's law for multisite occupancy of Ca in BaTi O₃ -CaTi O₃ solid solutions

The site occupancy of Ca in the CaTi O3 -BaTi O3 solid solution has been investigated through an analysis of the lattice parameters and ferroelectric phase transition temperature variation. The lattice volume was found to vary in a nonlinear manner with different amounts of Ca2+ ions occupying the Ba and Ti sites near the pure BaTi O3 end member. To model the lattice volume trends in this complex case, we modify the classical Vegard's law and incorporate a lattice volume correction to account for the ionic compensation of the acceptor charge CaTi″, with oxygen vacancies V O . The paraelectric-ferroelectric phase transition temperature shows further evidence of a non-linear variation with composition. This is also consistent with site occupancy changes. From lattice volume and phase transition temperature variations on the Ba-site occupancy compositions, the maximum concentration of Ti-site occupancy (y) was determined and found to be approximately 0.007±0.002 and then found to remain constant for higher concentrations of Ca, specifically (0.03<x+y<0.1, Ba1-x Cax+y Ti1-y O3-y).