Electron density contour maps via Rietveld-MEM analysis using HR-XRD for the polycrystalline ferroelectric BCZT


  • Guillermo Herrera-Perez CIMAV
  • J. Plaisier Elettra-Sincrotrone Triestre S. C. p. A.
  • A. Reyes-Rojas Centro de Investigacion en Materiales Avanzados S. C.
  • L. Fuentes-Cobas Centro de Investigacion en Materiales Avanzados S. C.




XRD, ceramics, BCZT, electron density


The maximum entropy method in combination with the Rietveld refinement method applied to the analysis (Rietveld-MEM analysis) of high-resolution x-ray diffraction (HR-XRD) is an important tool to elucidate the electron density distribution and chemical bonding nature of materials. In this work, we present the comparison of electron density distribution obtained from the Rietveld-MEM analysis for polycrystalline perovskite BaTiO3 (reference sample) and Ba0.9Ca0.2Ti0.9Zr0.1O3 (BCZT). To perform this task, HR-XRD patterns using synchrotron radiation were acquired. Tetragonal phase with P4mm (No.99) space group and pseudo-Voigt function were considered to model the HR-XRD peaks by the Rietveld method using the profile fitting Fullprof suite program. VESTA software was used to visualize 3D, 2D electron density distribution maps and line profiled to monitor the chemical bonding nature between Ba-O and Ti-O interactions and to visualize the off-center displacement of Ti cations by the incorporation of Zr and Ca cations. The interaction between Ti contours with O contours in the electron density distribution and the minimum electron density values revealed the enhancement of covalent nature and predominant ionic nature between barium and oxygen ions in the BCZT. To monitor the ferroelectric hysteresis behavior, polarization versus electric field curves complement the characterization of these samples.



H.M. Rietveld, A profile refinement method for nuclear and magnetic structures, J. Appl. Crystallogr. 2(2), (1969) 65-71, https://doi.org/10.1107/S0021889869006558

J. Rodriguez-Carbajal, Recent advances in magnetic structure determination by neutron powder diffraction, Physica B: Condensed Matter. 192, (1993) 55-69, https://doi.org/10.1016/0921-4526(93)90108-1

D.M. Collins, Electron density images from imperfect data by iterative entropy maximization, Nature 298, (1982) 49-51, https://doi.org/10.1038/298049a0

M. Sakata, M. Sato, Accurate structure analysis by the maximum-entropy method, Acta Cryst. A46, (1990) 263-270, https://doi.org/10.1107/S0108767389012377

K. Momma, F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, (2011) 1271-1276, https://doi.org/10.1107/S0021889811038970

A. Rother, M. Reibold, H. Lichte, T. Leisegang, P. Levin Paufler D.C. Meyer, S. Gemming, I. Chaplygin, G. Seifert, A. Ormeci, H. Rosner, X-ray investigation, high-resolution electron holography, and density functional calculations of single-crystalline BaTiO3, Phys. Rev. B. 74, (2006) 134116, https://doi.org/10.1103/PhysRevB.74.134116

S. Sasikumar, T.K. Thirumalaisamy, S. Saravanakumar, S. Asath-Bahadur, D. Sivaganesh, I.B. Shameem Banu, Effect of neodymium doping in BaTiO3 ceramics on structural and ferroelectric properties, J. Mater. Sci: Mater. Electron. 31, (2020) 1535-1546, https://doi.org/10.1007/s10854-019-02670-6

I. B. Catellani, G.M. Santos, J.C. Pastoril, I.A. Santos, L.F. Cótica, R. Guo, A.S. Bhalla, Study of the BaTiO3 electronic structure using the maximum entropy method and density functional theory calculations, Integrated Ferroelectrics 174(1), (2016) 104-110, https://doi.org/10.1080/10584587.2016.1192926

B. Garbarz-Glos, K. Bormanis D. Sitko, Effect of Zr4+ Doping on the Electrical Properties of BaTiO3 Ceramics, Ferroelectrics 417(1), (2011) 118-123, https://doi.org/10.1080/00150193.2011.578508

W. Liu, X. Ren, Large Piezoelectric Effect in Pb-Free Ceramics, Phys. Rev. Lett. 103(25), (2009) 257602, https://doi.org/10.1103/PhysRevLett.103.257602

G.H. Kwei, A.C. Lawson, S.J.L. Billinge, S.W. Cheong, Structures of the ferroelectric phases of barium titanate, J. Phys. Chem. 97(10), (1993) 2368-2377, https://doi.org/10.1021/j100112a043

K. Jiménez, G. Herrera, Lead-free piezoelectric ceramics as candidates on the development of morphing winglets in aircrafts, J. Mater. Sci. Eng. A 8(1-2), (2018) 32-42, https://doi.org/10.17265/2161-6213/2018.1-2.005

J. Mangaiyararasi, R. Saravanan M.M. Ismail, Chemical bonding and charge density distribution analysis of undoped and lanthanum doped barium titanate ceramics. J. Chem. Sci. 128(12), (2016) 1913-1921, https://doi.org/10.1007/s12039-016-1190-1

S. Urek, M. Drofenik, D. Makovec, Sintering and properties of highly donor-doped barium titanate ceramics, J. Mater.Sci. 35, (2000) 895-901, https://doi.org/10.1023/A:1004794223988

M.H. Lin, H.-Y. Lu, Densification retardation in the sintering of La2O3-doped barium titanate ceramic, Mater.Sci. Eng. A. 323, (2002) 167-176, https://doi.org/10.1016/S0921-5093(01)01356-9

Q.-J. Liu, N.-C. Zhang, F.-S. Liu, H.-Y. Wang, Z.-T. Liu, BaTiO3: Energy, geometrical and electronic structure, relationship between optical constant and density from first-principle calculations, Optical Mater. 35, (2013) 2629-2637, https://doi.org/10.1016/j.optmat.2013.07.034

E. Orhan, J.A. Varela, A. Zenatti, M.F.C. Gurgel, F.M. Pontes, E.R. Leite, E. Longo, P.S. Pizani, A.. Beltràn, J. Andrès, Room-temperature photoluminescence of BaTiO3: Joint experimental and theoretical study, Phys. Rev. B 71, (2005) 085113, https://doi.org/10.1103/PhysRevB.71.085113

B. Luo, X. Wang, E. Tian, G. Li, L. Li L, Electronic structure, optical and dielectric properties of BaTiO3/CaTiO3/SrTiO3 ferroelectric superlattices from first-principles calculations, J. Mater. Chem. C. 3, (2015) 8625, https://doi.org/10.1039/C5TC01622C

J. Mangaiyarkkarasi, S. Sasikumar, O.V. Saravanan, R. Saravanan, Electronic structure and bonding interaction in Ba1-xSrxZr0.1T0.9O3 ceramics, Front. Mater. Sci. 11(2), (2017) 182-189, https://doi.org/10.1007/s11706-017-0376-x

R.E. Cohen, H. Krakauer, Electronic structure studies of differences in ferroelectric behaviour of BaTiO3 and PbTiO3, Ferroelectrics 136, (1992) 65-83, https://doi.org/10.1080/00150199208016067

K. Fujii, H. Kato, K. Omoto M. Yashima J. Chen, X. Xing, Experimental visualization of the Bi-O covalency in ferroelectric bismuth ferrite (BiFeO3) by synchrotron X-ray powder diffraction analysis, Phys. Chem. Chem. Phys. 15, (2013) 6779, https://doi.org/10.1039/C3CP50236H

S. Sasikumar, S. Saravanakumar, S.A. Bahadur, D. Sivaganesh, Electronic structure, optical and chemical bonding properties of strontium doped Barium Titanate, Optik 206, (2020) 163752, https://doi.org/10.1016/j.ijleo.2019.163752

G. Herrera-Pérez, O. Solis-Canto G. Silva-Vidaurri, S. Pérez-García R. Borja-Urby, F. Paraguay-Delgado, G. Rojas-George, A. Reyes-Rojas, L. Fuentes-Cobas, Multiplet structure for perovskite-type Ba0.9Ca0.1Ti0.9Zr0.1O3 by core-hole spectroscopies, J. Appl. Phys. 128, (2020) 064106, https://doi.org/10.1063/5.0014496

H. Beltrán, B. Gómez, N. Masó E. Cordoncillo, P. Escribano, A.R. West, Electrical properties of ferroelectric BaTi2O5 and dielectric Ba6Ti17O40 ceramics, J. Appl. Phys. 128, (2005) 064106, https://doi.org/10.1063/1.1862766




How to Cite

Herrera-Perez G, Plaisier J, Reyes-Rojas A, Fuentes-Cobas L. Electron density contour maps via Rietveld-MEM analysis using HR-XRD for the polycrystalline ferroelectric BCZT. Supl. Rev. Mex. Fis. [Internet]. 2022 Feb. 18 [cited 2022 Jul. 2];3(1):010601 1-. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/5998



06 I National Congress of the Mexican Society of Synchrotron Light