Institute of Multidisciplinary Research for Advanced Materials, Tohoku University
○Kenji Tsuda Michiyoshi Tanaka

We have been developing a method to refine crystal structural parameters using convergent-beam electron diffraction (CBED) (Tsuda and Tanaka, Acta Cryst. A55, (1999) 939; Tsuda et al., Acta Cryst. A58, (2002) 514; Ogata et al., Acta Cryst. A60, (2004) 525). The method is based on the non-linear least-squares fitting between full dynamical calculations and experimental intensities of two-dimensional CBED patterns. The CBED method provides the following advantages for the analysis of ferroelectric materials: (1) The CBED technique allows us to obtain diffraction intensity data from a single domain even though the specimen has a complex ferroelectric domain structure. (2) The direction of ferroelectric polarization can be readily identified from a CBED pattern. (3) CBED directly measures electrostatic potential.

We have applied the present method to the electrostatic potential analysis of the ferroelectric phase of perovskite BaTiO₃. BaTiO₃ has been extensively studied due to its fundamental and technological importance. Zero-loss filtered CBED patterns were obtained from the ferroelectric phase at room temperature using an energy-filtering transmission electron microscope JEM-2010FEF. The atom positions, anisotropic Debye-Waller factors and Fourier coefficients of the electrostatic potential for low-order reflections were refined using the CBED patterns. The electrostatic potential was obtained by Fourier synthesis.

In the obtained electrostatic potential, the lowest potential valley was found at the position between the nearest-neighbor Ti and O atoms, which is attributed to the covalent bonding electrons between the Ti and O atoms. It is interesting to note that the absorption potential showed a characteristic anomaly in the vicinity of the Ti site.