Electrostatic potential analysis of ferroelectrics using convergent-beam electron diffraction and electron holography Kenji Tsuda 1 , Falk Röder 2 , Axel Lubk 2 , Daniel Wolf 2 , Dorin Geiger 2 and Hannes Lichte 2 1 Institute for Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan 2 Triebenberg Laboratory, Institute of Structure Physics, Technical University of Dresden, D-01062 Dresden, Germany A local crystal structure analysis method using convergent-beam electron diffraction (CBED) has been developed by Tsuda et al. [1-4]. The method is based on the fitting between theoretical calculations and experimental intensities of energy-filtered two dimensional CBED patterns containing both of zeroth-order Laue zone (ZOLZ) and higher-order Laue zone (HOLZ) reflections. Crystal structural parameters such as atom positions, atomic displacement parameters and low-order structure factors can be quantitatively refined in the fitting. The CBED structure analysis method has the following advantages: (1) Nanometer-size crystal structure analysis: CBED has a nanometer-scale spatial resolution. (2) Dynamical diffraction effect: CBED intensities contain phase information of crystal structure factors through the strong dynamical effect. (3) Electrostatic potential analysis: Fourier coefficients of electrostatic potential are directly determined by CBED. Recently, the three-dimensional electrostatic potential and electron distributions of silicon in the unit cell was successfully visualized using CBED data alone [4]. The CBED method is, however, not applicable to the measurement of mean inner electrostatic potential V 0 because CBED patterns are insensitive to the change of V 0 . This can be resolved by electron holography, which has been established as a powerful method to measure electrostatic potential distributions through the phase changes of object transmitting electron wave [5]. Thus, the combined use of the CBED and electron holography enables us to determine electrostatic potential distributions from atomic to mesoscopic scales. The CBED and off-axis electron holography techniques were applied to the ferroelectric phases of LiNbO 3 and KNbO 3 . The CBED and electron holography experiments were respectively performed using a JEM-2010FEF energy-filter transmission electron microscope at IMRAM, Tohoku university, and a Philips CM200FEG ST/Lorentz transmission electron microscopy at Triebenberg Lab., Technical University of Dresden. Figures 1 show CBED patterns of LiNbO 3 taken with (a) the [210] and (b) [110] incidences. The direction of the electric polarization can be identified from their pattern symmetries. The atom positions, atomic displacement parameters and low-order structure factors were refined from the fitting between the intensities of the CBED disks and those calculated with the dynamical diffraction theory. Figure 2 shows the schematic diagram of the refined crystal structure. The Nb atoms in the oxygen tetrahedral are found to be shifted by about 0.25Å in the c-direction, which directly accounts for the ferroelectric polarization in the c-direction. The electrostatic potential in the unit cell was reconstructed from the refined parameters. Electron holograms were obtained from specimen areas with 90° domain 96 AMTC Letters Vol. 2 (2010) © 2010 Japan Fine Ceramics Center