Electrostatic potential analysis of ferroelectrics using convergent-beam electron diffraction and electron holography

Kenji Tsuda1, Falk Röder2, Axel Lubk2, Daniel Wolf2, Dorin Geiger2 and Hannes Lichte2

1Institute 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 V0 because CBED patterns are insensitive to the change of V0. 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 LiNbO3 and KNbO3. 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 LiNbO3 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

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AMTC Letters Vol. 2 (2010)

© 2010 Japan Fine Ceramics Center

boundaries in KNbO3 for detecting a small potential jump due to the rotation of polarization at the boundaries. New reconstruction techniques were used for reducing noises in the obtained phase images. References 1. K. Tsuda, M. Tanaka, Acta Cryst. A55, 939-954 (1999). 2. K. Tsuda, K. Takagi, Y. Ogata, T. Hashimoto, M. Tanaka, Acta Cryst. A58, 514-525 (2002).

3. Y. Ogata, K. Tsuda, Y. Akishige, M. Tanaka, Acta Cryst. A60, 525-531 (2004). 4. Y. Ogata, K. Tsuda, M. Tanaka, Acta Cryst. A64, 587-597 (2008). 5. H. Lichte and M. Lehmann, Rep. Prog. Phys. 71, 016102 (2008). 6. K. Momma, F. Izumi, J. Appl. Cryst. 41, 653–658 (2008).

FIG. 1. CBED patterns of LiNbO3 taken with (a) the [210] and (b) [110] incidences at an accelerating voltage of 100kV.

FIG. 2. Schematic diagram of the crystal structure of LiNbO3

refined using CBED, drawn with a software VESTA [6].

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AMTC Letters Vol. 2 (2010)

© 2010 Japan Fine Ceramics Center