Local distortion and octahedral tilting in BaCe_xTi_1−xO₃ perovskite

Ceramics with perovskite structure and composition BaCe_xTi_1−xO₃ (x = 0.02–0.30) show a progressive evolution with increasing x, from the long-range polar order of ferroelectric BaTiO₃ to the short-range polar order typical of relaxors. The ionic size mismatch between Ti⁴⁺ and Ce⁴⁺ determines strong local strains which have a significant impact on dielectric properties and phase transitions. The pair distribution function, coupled with transmission electron microscopy analysis, was applied to study the local structure. Because of the inner B-cation sizes, the superposition of rigid B—O octahedra with different volumes is not compatible with the construction of an ideal perovskite structure. In this light, local structure can be described by an original model which allows (i) different Ti—O and Ce—O distances and (ii) the typical distortions of the two end members: off-center displacement of Ti occurring in BaTiO₃ and octahedral tilt in BaCeO₃. The results show a clear difference, in terms of volumes, between oxygen octahedra with titanium and those related to cerium. In addition, the inclusion of cerium causes a tilt of its oxygen cage, as occurs in pure BaCeO₃, creating contra-rotations and distortions of the octahedra containing titanium. This complex arrangement entails a substantial distortion, increasing as a function of cerium amount, which strongly influences the directions of titanium displacements, their local correlation and consequently their long-range cooperative effects.