Nanoscale order parameter and symmetry fluctuations in ferroelectric BaTiO₃ single crystal

Ferroelectric single crystals are widely applied for medical imaging, actuation, and sensor technologies due to their piezoelectric effect. However, the microscopic origin of ferroelectric phase transitions is still debated, despite many past efforts. Here, we report on a study of local crystal symmetry inside the ferroelectric domains of BaTiO₃ using convergent beam electron diffraction (SCBED) and nanometer-sized electron probes. The results demonstrate that the crystal symmetry is not homogeneous; regions of few tens nm retaining almost perfect symmetry are interspersed in regions of lower symmetry. The highly symmetric regions have the acentric tetragonal, orthorhombic, and rhombohedral symmetry for the ferroelectric phases of BaTiO₃ at different temperatures, which suggest the displacive model of ferroelectric phase transitions in BaTiO₃. However, the lowering of symmetry in some regions is consistent with the predictions of order-disorder phase transition mechanism. For future work, the SCBED technique will be further developed for simultaneous identification of polarization domains, determination of the local crystal symmetry, and identification of polarization, structural distortions and chemical bonding.