The local environment of Bi and Ti atoms in the lead-free relaxor ferroelectric solid-solution ${\left({\mathrm{K}}_x{\mathrm{Na}}_{1-x}\right)}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ has been studied as a function of K concentration and as a function of temperature for the $x=0$ end member by x-ray absorption fine structure (XAFS). It is found that the local environment of Bi is much more distorted than that determined from conventional diffraction experiments. The shortest $\mathrm{Bi}-\mathrm{O}$ distances are determined to be $2.22\mathrm{\AA }$, and are $0.3\mathrm{\AA }$ shorter than those calculated from the crystallographic data. Several possible models of the Bi coordination environment, which are consistent with the XAFS data and provide bond-valence sums for Bi that are closer to the theoretical values, are proposed. The Ti displacement from the center of the oxygen octahedron increases with K concentration while the shortest $\mathrm{Bi}-\mathrm{O}$ distance shows no compositional dependence. In ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ the value of the Ti displacement is determined to be $0.18\mathrm{\AA }$. The changes of the macroscopic symmetry at the phase transition points in ${\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ do not lead to changes of the radial atomic distribution around Ti, which is well off-center over the whole temperature range up to and including the paraelectric cubic phase. The results can be explained by assuming the presence of structural disorder.

• Received 28 April 2004

DOI:https://doi.org/10.1103/PhysRevB.71.174114