Monoclinic distortion, polarization rotation and piezoelectricity in the ferroelectric Na_0.5 Bi_0.5 TiO ₃

The relationship between crystal structure and physical properties in the ferroelectric Na_0.5 Bi_0.5 TiO₃ (NBT) has been of interest for the last two decades. Originally, the average structure was held to be of rhombohedral (R3c) symmetry with a fixed polarization direction. This has undergone a series of revisions, however, based on high-resolution X-ray diffraction, total neutron scattering, and optical and electron microscopy. The recent experimental findings suggest that the true average symmetry is monoclinic (space group Cc), which allows for a rotatable spontaneous polarization. Neither polarization rotation nor its potentially important real role in enhanced piezoelectricity is well understood. The present work describes an in situ investigation of the average monoclinic distortion in NBT by time-resolved single-crystal X-ray diffraction under external electric fields. The study presents a high-resolution inspection of the characteristic diffraction features of the monoclinic distortion-splitting of specific Bragg reflections-and their changes under a cyclic electric field. The results favour a model in which there is direct coupling between the shear monoclinic strain and the polarization rotation. This suggests that the angle of polarization rotation under a sub-coercive electric field could be 30°or more.