Convergent-beam electron-diffraction-pattern symmetry of nanodomains in complex lead-based perovskite crystals

Convergent-beam electron diffraction (CBED) recorded using nanometre-sized probes, in principle, can detect the highest symmetry in a crystal. However, symmetry reduction may occur by overlapping crystal domains along the beam direction. Thus, delineating the relationship between the recorded and the crystal symmetry is important for studying crystals with complex nanodomains. This paper reports a study of the averaged local symmetry of 71°/109° rhombohedral (R), 90° tetragonal (T) and 180° monoclinic (M) nanodomain structures. The averaged symmetry of nanodomain structures is investigated by CBED simulations using the multislice method. The simulation results show that the 71°-R, 109°-R and 90°-T nanodomain structures partially mimic the monoclinic symmetries of Cm and Pm that have been proposed by the adaptive phase model. This study is also compared to the reported experimental CBED patterns recorded from PMN-31%PT.