Octahedral tilt transitions in the relaxor ferroelectric Na_1/2Bi_1/2TiO₃

The kinetics of octahedral tilt transitions in the lead-free relaxor material sodium bismuth titanate Na_1/2Bi_1/2TiO₃ (NBT) is investigated by electronic structure calculations within density functional theory. Energy barriers for transitions between tetragonal, rhombohedral and orthorhombic tilts in cation configurations with [001]- and [111]-order on the A-sites are determined by nudged elastic band calculations. By tilting entire layers of octahedra simultaneously we find that the activation energy is lower for structures with 001-order compared to such with 111-order. The energetic coupling between differently tilted layers is, however, negligibly small. By introducing a single octahedral defect we create local tilt disorder and find that the deformation energy of the neighboring octahedra is less in a rhombohedral than in a tetragonal structure. By successively increasing the size of clusters of orthorhombic defects in a rhombohedral matrix with 001-order, we determine a critical cluster size of about 40 Å . Thus groups of about ten octahedra can be considered as nuclei for polar nanoregions, which are the cause of the experimentally observed relaxor behavior of NBT. - Graphical abstract: Nine orthorhombic oxygen octahedral tilt defects in a rhombohedral tilt configuration. - Highlights: • Chemical order influences energy barriers of octahedral tilt transitions. • The octahedral deformation energy is lower in rhombohedral phases. • Tilt defect clusters are more likely in rhombohedral structures. • Tilt defect clusters can act as nuclei for polar nanoregions