Emergence of Long-Range Order in BaTiO3 from Local Symmetry-Breaking Distortions

By using a symmetry motivated basis to evaluate local distortions against pair distribution function data, we show without prior bias, that the off-center Ti displacements in the archetypal ferroelectric BaTiO3 are zone centered and rhombohedral-like across its known ferroelectric and paraelectric phases. We construct a simple Monte Carlo model that captures our main experimental findings and demonstrate how the rich crystallographic phase diagram of BaTiO3 emerges from correlations of local symmetry-breaking distortions alone. Our results strongly support the order-disorder picture for these phase transitions, but can also be reconciled with the soft-mode theory of BaTiO3 that is supported by some spectroscopic techniques.