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Nuclear and charge density distributions in ferroelectric PbTiO3: maximum entropy method analysis of neutron and X-ray diffraction data

  • Jinlong Zhu (a1) (a2), Wei Han (a2), Jianzhong Zhang (a1), Hongwu Xu (a1), Sven C. Vogel (a1), Changqing Jin (a2), Fujio Izumi (a3), Koichi Momma (a3), Yukihiko Kawamura (a3) and Yusheng Zhao (a1) (a2) (a4)...


We conducted in-situ high-temperature neutron and X-ray diffraction studies on tetragonal PbTiO3. Using a combination of Rietveld analysis and Maximum Entropy Method, the nuclear and charge density distributions were determined as a function of temperature up to 460 °C. The ionic states obtained from charge density distributions reveal that the covalency of Pb–O2 bonds gradually weakens with increasing temperature. The spontaneous polarizations calculated from the contributions of ionic state, ionic displacement, and nuclear polarization, are in good agreement with the experimental measurements. This method provides an effective approach to determine spontaneous polarizations in multiferroics with high-current leakage and low resistance.


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Aoyagi, S., Kuroiwa, Y., Sawada, A., Tanaka, H., Harada, J., Nishibori, E., Takata, M., and Sakata, M. (2002). “Direct observation of covalency between O and disordered Pb in Cubic PbZrO3 ,” J. Phys. Soc. Jpn. 71, 23532356.
Cohen, R. E. (1992). “Origin of ferroelectricity in perovskite oxides,” Nature (London) 358, 136138.
Fontana, M. D., Idrissi, H., and Wojcik, K. (1990). “Displacive to order-disorder crossover in the Cubic-Tetragonal phase transition of PbTiO3 ,” Europhys. Lett. 11, 419424.
Gavrilyachenko, V. G., Spinko, R. I., Martynenko, M. A., and Fesenko, E. G. (1970). “Spontaneous polarization and coercive field of lead titanate,” Sov. Phys. Solid State 12, 1203.
Glazer, A. M. and Mabud, S. A. (1978). “Powder profile refinement of lead zirconate titanate at several temperatures. II. Pure PbTiO3 ,” Acta Crystallogr. B 34, 10651070.
Hoshikawa, A., Igawa, N., Yamauchi, H., and Ishii, Y. (2005). “Neutron powder diffraction study of methane deuterohydrate by the maximum entropy method,” J. Phys. Chem. Sol. 66, 18101814.
Igawa, N., Taguchi, T., Hoshikawa, A., Fukazawa, H., Yamauchi, H., Utsumi, W., and Ishii, Y. (2010). “CO2 motion in carbon dioxide deuterohydrate determined by applying maximum entropy method to neutron powder diffraction data,” J. Phys. Chem. Sol. 71, 899905.
Izumi, F. (2004). “Beyond the ability of Rietveld analysis: MEM-based pattern fitting,” Solid State Ionics 172, 16.
Izumi, F. and Kawamura, Y. (2006). “Three-dimensional visualization of nuclear densities by MEM analysis from time-of-flight neutron powder diffraction data,” Bunseki Kagaku 55, 391395.
Izumi, F. and Momma, K. (2011). “Three-dimensional visualization of electron- and nuclear-density distributions in inorganic materials by MEM-based technology,” IOP Conf. Ser.: Mater. Sci. Eng. 18, 022001.
Kuroiwa, Y., Aoyagi, S., Sawada, A., Harada, J., Nishibori, E., Takata, M., and Sakata, M. (2001). “Evidence for Pb-O covalency in tetragonal PbTiO3 ,” Phys. Rev. Lett. 87, 217601.
Larson, A. C. and Von Dreele, R. B. (2004). General Structure Analysis System (GSAS) (Report LAUR 86-748). Los Alamos, New Mexico: Los Alamos National Laboratory.
Momma, K. and Izumi, F. (2011). “VESTA 3 for three-dimensional visualization of crystal volumetric and morphology data,” J. Appl. Crystallogr. 44, 12721276.
Nelmes, R. J. and Kuhs, W. F. (1985). “The crystal structure of tetragonal PbTiO3 at room temperature and at 700 K,” Sol. Stat. Commun. 54, 721723.
Nishimura, S., Kobayashi, G., Ohoyama, K., Kanno, R., Yashima, M., and Yamada, A. (2008). “Experimental visualization of lithium diffusion in LixFePO4 ,” Nat. Mater. 7, 707711.
Remeika, J. P. and Glass, A. M. (1970). “The growth and ferroelectric properties of high resistivity single crystals of lead titanate,” Mater. Res. Bull. 5, 3745.
Rietveld, H. M. (1969). “A profile refinement method for nuclear and magnetic structures,” J. Appl. Crystallogr. 2, 6571.
Sakata, M. and Sato, M. (1990). “Accurate structure analysis by the maximum-entropy method,” Acta Crystallogr. Sect. A 46, 263270.
Shirane, G. and Hoshino, S. (1951). “On the phase transition in lead titanate,” J. Phys. Soc. Jpn. 6, 265270.
Takata, M., Nishibori, E., Kato, K., Sakata, M., and Moritomo, Y. (1999). “Direct observation of orbital order in manganites by MEM charge-density study,” J. Phys. Soc. Jpn. 68, 21902193.
Vogel, S. C., Hartig, C., Lutterotti, L., Von Dreele, R. B., Wenk, H. R., and Williams, D. J. (2004). “Texture measurements using the new neutron diffractometer HIPPO and their analysis using the Rietveld method,” Powder Diffr. 19, 6568.
Wenk, H.-R., Lutterotti, L., and Vogel, S. (2003). “Texture analysis with the new HIPPO TOF diffractometer,” Nucl. Instrum. Methods Phys. Res., Sect. A 515, 575588.
Yashima, M. (2009). “Diffusion pathway of mobile ions and crystal structure of ionic and mixed conductors – A brief review,” J. Ceram. Soc. Jpn. 117, 10551059.



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