Abstract
In this article, a set of equivalent variational formulations for computing the driving forces for domain switching in ferroelectric materials is presented. It is proven that these formulations allow the free adoption of any couple of mechanical and electric fields as independent variables while obtaining consistent results. In addition, explicit expressions are provided for each formulation which allows for the study of the phase transformation process under different constraints.
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References
Merz W.J.: Domain formation and domain wall motions in ferroelectric BaTiO 3 single crystals. Phys. Rev. 95, 690–698 (1954)
Eng L.M., Güntherodt H.-J., Schneider G.A., Köpke U., Saldana J.M.: Nanoscale reconstruction of surface crystallography from three-dimensional polarization distribution in ferroelectric barium-titanate ceramics. Appl. Phys. Lett. 74, 233–235 (1999)
Scott J.F.: Applications of Modern Ferroelectrics. Science. 315, 954–959 (2007)
Merz W.J.: Double hysteresis loop of BaTiO 3 at the Curie point. Phys. Rev. 91, 513–517 (1953)
Kinoshita K., Yamaji A.: Grain-size effects on dielectric properties in barium titanate ceramics. J. Appl. Phys. 47, 371–373 (1976)
Uchino K., Sadanaga E., Hirose T.: Dependence of the crystal structure on particle size in barium titanate. J. Am. Ceram. Soc. 72, 1555–1558 (1989)
Fong D.D., Stephenson G.B., Streiffer S.K., Eastman J.A., Auciello O., Fuoss P.H., Thompson C.: Ferroelectricity in ultrathin perovskite films. Science 304, 1650–1653 (2004)
Hwang S.C., Lynch C.S., McMeeking R.M.: Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall. Mater. 43, 2073–2084 (1995)
Burcsu E., Ravichandran G., Bhattacharya K.: Large electrostrictive actuation of barium titanate single crystals. J. Mech. Phys. Solid 52, 823–846 (2004)
Hamano T., Towner D.J., Wessels B.W.: Relative dielectric constant of epitaxial BaTiO 3 thin films in the GHz frequency range. Appl. Phys. Lett. 83, 5274–5276 (2003)
Yimnirun R., Ananta S., Meechoowas E., Wongsaenmai S.: Effects of uniaxial stress on dielectric properties lead magnesium niobatelead zirconate titanate ceramics. Phys. Status Solidi. B 36, 1615–1619 (2003)
Nambu S., Sagala D.: Domain formation and elastic long-range interaction in ferroelectric perovskites. Phys. Rev. B 50, 5838–5847 (1994)
Li Y.L., Hu S.Y., Liu Z.K., Chen L.Q.: Phase-field model of domain structures in ferroelectric thin film. Appl. Phys. Lett. 78, 3878–3880 (2001)
Zhang W., Bhattacharya K.: A computational model of ferroelectric domains. Part I: model formulation and domain switching. Acta Mater. 53, 185–198 (2005)
Chen L.Q.: Phase-field method of phase transitions/domain structures in ferroelectric thin films: review. J. Am. Ceram. Soc. 91, 1835–1844 (2008)
Aubry S., Fago M., Ortiz M.: A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials. Comp. Meth. Appl. Mech. Eng. 192, 2823–2843 (2003)
Kim S.-J., Jiang Q.: A finite element model for rate-dependent behavior of ferroelectric ceramics. Int. J. Solids Struct. 39, 1015–1030 (2002)
Kamlah M., Liskowsky A.C., McMeeking R.M., Balke H.: Finite element simulation of a polycrystalline ferroelectric based on a multidomain single crystal switching model. Int. J. Solids Struct. 42, 2949–2964 (2005)
Arockiarajan A., Sivakumar S.M., Sansour C.: A thermodynamically motivated model for ferroelectric ceramics with grain boundary effects. Smart Mater. Struct. 52, 440–445 (2010)
Jayabal K., Menzel A., Arockiarajan A., Srinivasan M.S.: Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: application of a polygonal finite element approach. Comput. Mech. 48, 421–435 (2011)
Li Q., Kuna M.: Inhomogeneity and material configurational forces in three dimensional ferroelectric polycrystals. Eur. J. Mech. A Solids 31, 77–89 (2012)
Huber J.E., Fleck N.A., Landis C.M., McMeeking R.M.: A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47, 1663–1697 (1999)
Li J., Weng G.J.: A theory of domain switch for the nonlinear behavior of ferroelectric. Proc. R. Soc. Lond. A 455, 3493–3511 (1999)
Li J., Weng G.J.: A micromechanics-based hysteresis model for ferroelectric ceramics. J. Intell. Mater. Syst. Struct. 12, 79–91 (2001)
Li W.F., Weng G.J.: Micromechanical simulation of spontaneous polarization in ferroelectric crystals. J. Appl. Phys. 90, 2484–2491 (2001)
Li W.F., Weng G.J.: A theory of ferroelectric hysteresis with a superimposed stress. J. Appl. Phys. 91, 3806–3815 (2002)
Li W.F., Weng G.J.: A micromechanics-based thermodynamic model for the domain switch in ferroelectric crystals. Acta Mater. 52, 2489–2496 (2004)
Su Y., Weng G.J.: The shift of Curie temperature and evolution of ferroelectric domain in ferroelectric crystals. J. Mech. Phys. Solids 53, 2071–2099 (2005)
Li J., Liu D.: On ferroelectric crystals with engineered domain configurations. J. Mech. Phys. Solids 52, 1719–1742 (2004)
Su Y., Weng G.J.: A self-consistent polycrystal model for the spontaneous polarization of ferroelectric ceramics. Proc. R. Soc. Lond. A 462, 1763–1789 (2006)
Yen J.H., Shu Y.C., Shieh J., Yeh J.H.: A study of electromechanical switching in ferroelectric single crystals. J. Mech. Phys. Solids 56, 2117–2135 (2008)
Weng G.J., Wong D.T.: Thermodynamic driving force in ferroelectric crystals with a rank-2 laminated domain pattern, and a study of enchanced electrostriction. J. Mech. Phys. Solids 57, 571–597 (2009)
Weng G.J.: A theory of triple hysteresis in ferroelectric crystals. J. Appl. Phys. 106, 074109 (2009)
Su Y., Landis C.M.: Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning. J. Mech. Phys. Solids 55, 280–305 (2007)
Su Y., Weng G.J.: Microstructural evolution and overall response of an initially isotropic ferroelectric polycrystal under an applied electric field. Mech. Mater. 41, 1179–1191 (2009)
Tang W., Fang D.N., Li J.Y.: Two-scale micromechanics-based probabilistic modeling of domain switching in ferroelectric ceramics. J. Mech. Phys. Solids 57, 1683–1701 (2009)
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Zheng, S.F., Tuncer, E.A. & Cuitiño, A.M. Variations in predicting domain switching of ferroelectric ceramics. Acta Mech 223, 2243–2256 (2012). https://doi.org/10.1007/s00707-012-0702-4
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DOI: https://doi.org/10.1007/s00707-012-0702-4