Abstract
The traditional phase field method adopts periodic boundary conditions and thus can only be applied to a continuous medium. In this manuscript, an extended phase field model is developed to simulate the polarization switching in a finite ferroelectric body with free surfaces. The void region outside the ferroelectric body was modeled as an elastic body having the same elastic stiffness as the ferroelectrics as well as properly distributed eigenstrain which functions to satisfy the traction-free boundary condition. Based on this scheme, periodic boundary conditions can be applied to the discrete system including a finite ferroelectric body and the voids outside. The elastically inhomogeneous system can be solved easily. This model has high calculation efficiency and can be conveniently applied to finite ferroelectric bodies with arbitrary boundaries. Finally, the domain pattern formation in a ferroelectric nano-particle is simulated. The obtained polarization pattern and stress field are illustrated.
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References
Hu H.L., Chen L.Q.: Three-dimensional computer simulation of ferroelectric domain formation. J. Am. Ceram. Soc. 81, 492 (1998)
Wang J., Shi S.Q., Chen L.Q., Li Y.L., Zhang T.Y.: Phase field simulations of ferroelectric/ferroelastic polarization switching. Acta Mater. 52, 749 (2004)
Wang Y.U.: Field-induced inter-ferroelectric phase transformations and domain mechanisms in high-strain piezoelectric materials, insights from phase field modeling and simulation. J. Mater. Sci. 44, 5225 (2009)
Li Y.L., Hu S.Y., Chen L.Q.: Ferroelectric domain morphologies of (001) PbZr1−x Ti x O3 epitaxial thin film. J. Appl. Phys. 97, 034112 (2005)
Artemev A., Roytburd A.: Spinodal single-domain → polydomain transition and P–E hysteresisin thin ferroelectric films. Acta Mater. 58, 1004 (2010)
Wang J., Kamlah M., Zhang T.Y.: Phase field simulations of ferroelectric nanoparticles with different long-range-electrostatic and -elastic interactions. J. Appl. Phys. 105, 014104 (2009)
Su Y., Du J.N.: Existence conditions for single-vertex structure of polarization in ferroelectric nanoparticles. Appl. Phys. Lett. 95, 012903 (2009)
Hong L., Soh A.K., Liu S.Y., Lu L.: Vortex structure transformation of BaTiO3 nanoparticles through the gradient function. J. Appl. Phys. 106, 024111 (2009)
Hu S.Y., Chen L.Q.: A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater. 49, 1879 (2001)
Wang Y.U., Jin Y.M., Khachaturyan A.G.: Phase field microelasticity theory and simulation of multiple voids and cracks in single crystals and polycrystals under applied stress. J. Appl. Phys. 91, 6435 (2002)
Wang Y.U., Jin Y.M., Khachaturyan A.G.: Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films. Acta Mater. 51, 4209 (2003)
Khachaturyan A.G.: Theory of Structural Transformations in Solids. Wiley, New York (1983)
Hong L., Soh A.K., Song Y.C., Lim L.C.: Interface and surface effects on ferroelectric nano-thin films. Acta Mater. 56, 2966 (2008)
Hong L., Soh A.K., Liu S.Y., Lu L.: Vortex structure transformation of BaTiO3 nanoparticles through the gradient function. J. Appl. Phys. 106, 024111 (2009)
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Song, Y.C., Ni, Y. & Zhang, J.Q. Phase field model of polarization evolution in a finite ferroelectric body with free surfaces. Acta Mech 224, 1309–1313 (2013). https://doi.org/10.1007/s00707-013-0858-6
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DOI: https://doi.org/10.1007/s00707-013-0858-6