Local and average structures of ceramic ${\mathrm{Ba}}_{1-x}$Sr${}_x$${\text{TiO}}_3$ solid solutions have been reconciled using Reverse Monte Carlo (RMC) refinements of atomic positions that employ simultaneous fitting of neutron total scattering data, x-ray absorption fine structure, and patterns of diffuse scattering in electron diffraction. These refinements enable explicit reconstruction of three-dimensional atomic configurations without any effective parameters. The results reveal cube- and parallelepiped-shaped probability density distributions for Ti atoms in the cubic and tetragonal phases of BaTiO${}_3$, respectively. These distributions are consistent with the split Ti sites (eight for the cubic and four for the tetragonal polymorphs) separated by ≈0.2 Å. The characters of Ti distributions are retained in the solid solutions, but the magnitude of Ti off-centering decreases as $x$ increases. The Ti displacements remain correlated along the octahedral chains, at least up to $x$ = 0.5, as manifested in the sheets of diffuse scattering in electron diffraction patterns; the correlation parameters and lengths have been quantified using RMC analyses. The ion-size difference between Ba and Sr is accommodated through the approximately isotropic relaxation of the oxygen atoms, which shift toward Sr; a similar relaxation is observed for the Ti atoms. Local Ti off-centering diminishes as the number of Sr atoms in the coordination groups [TiO${}_x$Ba${}_{8-n}$Sr${}_n$] increases.

• Received 23 October 2013
• Revised 25 November 2013

DOI:https://doi.org/10.1103/PhysRevB.89.024106