Evaluation of Potential Function of Core-Shell Model for PbTiO3 Ferroelectric Material and Its Application for Polarization Calculation
Main Article Content
Abstract
In this study, the core-shell model is used to calculate the electric polarization for PbTiO3 ferroelectric material, in which, the interaction potential functions among atoms are determined by the fitting method based on the results from the first principle calculation. The investigations obtained show that the remnant polarization increases under tension and decreases under compression. The remnant polarization decreases with increasing the temperature. The phase transition from the ferroelectric phase to the paraelectric phase is determined at 605K and can occur at lower temperatures of 0K, 300K, 400K, 500K if the compression strain are 8%, 6%, 5%, 2%, corresponding. The hysteresis loop shrinks as the temperature increases and degrades into a curve at the temperature of 605K.
Keywords
PbTiO3, Core-shell model, Ferroelectric polarization, Effect of temperature, Effect of mechanical strain
Article Details
References
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nanowires from atomistic simulations, Sci. Rep 5
(2015) 1-6,
http://doi.org/10.1038/srep17294.
memories, Science 246(4936) (1989) 1400-1405,
http://doi.org/10.1126/science.246.4936.1400.
[2] L.E. Cross, Ferroelectric Materials for
Electromechanical Transducer Applications. Jpn. J.
Appl. Phys, 34 (Part 1, No. 5B) (1995) 2525–2532,
http://doi.org/10.1143/JJAP.34.2525.
[3] S. Zhang, F. Li, X. Jiang, J. Kim, J. Luo & X. Geng,
Advantages and challenges of relaxor-PbTiO3
ferroelectric crystals for electroacoustic transducers–
A review, Prog. Mater. Sci. 68 (2015) 1–66,
http://doi/org/10.1016/j.pmatsci.2014.10.002.
[4] P.P. Khirade, S.D. Birajdar, A.V. Raut & K.M.
Jadhav, Multiferroic iron doped BaTiO3
nanoceramics synthesized by sol-gel auto
combustion: Influence of iron on physical properties,
Ceram. Int. (2016) 1-11,
http://doi.org/10.1016/j.ceramint.2016.05.021.
[5] M.A. Morales, R. Clay, C. Pierleoni, D.M. Ceperley,
First-principle methods: A perspective from quantum
Monte Carlo, Entropy. 16(1) (2013) 287–321,
http://doi.org/10.3390/e16010287.
[6] S. Tinte et al, Atomistic modelling of BaTiO3 based
on first-principles calculations, J.Phys. Condens.
Matter. 11 (1999) 9679-9690,
http://doi.org/10.1088/0953-8984/11/48/325.
[7] R.E. Cohen, Origin of ferroelectricity in perovskite
oxides, Nature 358(6382) (1992) 136–138,
http://doi: 10.1038/358136a0.
[8] B. Meyer, J. Padilla, & D. Vanderbilt, Theory of
PbTiO3, BaTiO3, and SrTiO3 surfaces, Faraday
Discussions 114 (1999) 395–405,
https://doi.org/10.1039/A903029H.
[9] C. Bungaro & K.M. Rabe, Coexistence of
antiferrodistortive and ferroelectric distortions at the
PbTiO3 (001) surface, Phys. Rev. B 71(3) (2005)
035420(9),
http://doi.org/10.1103/PhysRevB.71.035420.
[10] H.J. Mang & H.A. Weidenmuller, Shell-Model
theory of the Nucleus, Annu. Rev. Nucl. Sci.18(1)
(1968) 1–26,
http://doi.org/10.1146/annurev.ns.18.120168.000245.
[11] B.G. Dick & A.W. Overhauser, Theory of the
Dielectric Constants of Alkali Halide Crystals, Phys.
Rev. 112(1) (1958) 90–103,
http://doi/org/ 10.1103/PhysRev.112.90.
[12] P. Giannozzi et al, Quantum espresso: a modular and
open-source software project for quantum
simulations of materials, J.Phys. Condens. Matter
21(9) (2009) 395502,
http://doi.org/10.1088/0953-8984/21/39/395502.
[13] D. M. Ceperley and B. J. Alder, Ground State of the
Electron Gas by a Stochastic Method, Phys. Rev.
Lett. 45(7) (1980) 566–569,
http://doi.org// 10.1103/PhysRevLett.45.566.
[14] J.P. Perdew & A. Zunger, Self-interaction correction
to density-functional approximations for manyelectron systems, Phys. Rev. B 23(10) (1981) 5048–
5079,
http://doi.org/10.1103/PhysRevB.23.5048.
[15] D. Vanderbilt, Soft self-consistent pseudopotentials
in a generalized eigenvalue formalism, Phys. Rev. B
41 (1990) 7892-7895,
http://doi.org/10.1103/PhysRevB.41.7892.
[16] H.J. Monkhorst and J.D. Pack, Special points for
Brillouin-zone integrations, Phys. Rev. B 13 (1976)
5188-5192,
http://doi.org/10.1103/PhysRevB.13.5188.
[17] T. Kitamura, Y. Umeno, F. Shang, T. Shimada, and
K. Wakahara, “Development of Interatomic Potential
for Pb(Zr,Ti)O3 Based on Shell model,” J. Solid
Mech. Mater. Eng., vol. 1, no. 12 (2007) 1423–1431,
http://doi.org/10.1299/jmmp.1.1423.
[18] J.D. Gale, A.L. Rohl, The General Utility Lattice
Program (GULP), Mol. Simul, Vol. 29, No. 5 (2003)
291-341,
http://doi.org/10.1080/0892702031000104887.
[19] M. Sepliarsky and R.E. Cohen, First-principles based
atomistic modeling of phase stability in PMN–xPT, J.
Phys. Condens. Matter. 23(43) (2011) 435902,
http://doi.org/10.1088/0953-8984/23/43/435902.
[20] T. Kitamura, Y. Umeno, F. Shang, T. Shimada, and
K. Wakahara, Development of Interatomic Potential
for Pb(Zr,Ti)O3 Based on Shell model, J. Solid Mech.
Mater. Eng., vol. 1, no. 12 (2007) 1423–1431,
http://doi.org/10.1299/jmmp.1.1423.
[21] H.N. Lee, S.M. Nakhmanson, M.F. Chisholm, H.M.
Christen, K.M. Rabe & D. Vanderbilt, Suppressed
Dependence of Polarization on Epitaxial Strain in
Highly Polar Ferroelectrics, Phys. Rev. Lett. 98
(2007) 217602,
http://doi.org/10.1103/PhysRevLett.98.217602.
[22] M. Sepliarsky and R.E. Cohen, Development of a
Shell Model Potential for Molecular Dynamics for
PbTiO3 by Fitting First Principles Results, Am. Inst.
Phvsics, Vol. 36 (2002) 36-44,
http://doi.org/10.1063/1.1499550.
[23] R.K. Behera, Effect of surfaces, domain walls and
grain boundaries on ferroelectricity in lead titanate
using atomic scale simulations, University of florida,
2009,
[24] O. Gindele, A. Kimmel, M.G. Cain & D. Duffy,
Shell Model force field for Lead Zirconate Titanate
Pb(Zr1–xTix)O3, J. Phys. Chem. C 119(31) (2015)
17784–17789,
http://doi.org/10.1021/acs.jpcc.5b03207.
[25] V.G. Bhide, K.G. Deshmukh & M.S. Hegde,
Ferroelectric properties of PbTiO3, Physica 28(9)
(1962) 871–876,
http://doi/org/10.1016/0031-8914(62)90075-7.
[26] R. Herchig, C.-M. Chang, B. K. Mani & I.
Ponomareva, Electrocaloric effect in ferroelectric
nanowires from atomistic simulations, Sci. Rep 5
(2015) 1-6,
http://doi.org/10.1038/srep17294.