Nanoscale local structures of rhombohedral symmetry in the orthorhombic and tetragonal phases of BaTiO3studied by convergent-beam electron diffraction

The symmetries of the rhombohedral, orthorhombic, and tetragonal phases of barium titanate (BaTiO${}_{3}$) are investigated using convergent-beam electron diffraction. Nanometer-sized local structures with rhombohedral symmetry are observed in both the orthorhombic and tetragonal phases. This indicates that an order-disorder character exists in phase transformations of BaTiO${}_{3}$. The nanostructures in these phases are discussed in terms of an order-disorder model with off-centered Ti in the $\ensuremath{\langle}111\ensuremath{\rangle}$ directions.