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Volume 29, Issue 3
Numerical Discretization of Variational Phase Field Model for Phase Transitions in Ferroelectric Thin Films

Ruotai Li, Qiang Du & Lei Zhang

DOI: 10.4208/cicp.OA-2020-0118

Commun. Comput. Phys., 29 (2021), pp. 729-746.

Published online: 2021-01

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  • Abstract

Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational forms of the electrostatic energy and the relaxation dynamics of the polarization vector. The spatial discretization combines the Fourier spectral method with the finite difference method to handle three-dimensional mixed boundary conditions. It allows for an efficient semi-implicit discretization for the time integration of the relaxation dynamics. This method avoids explicitly solving the electrostatic equilibrium equation (a Poisson equation) and eliminates the use of associated Lagrange multipliers. We present several numerical examples including phase transitions and polarization switching processes to demonstrate the effectiveness of the proposed method.

  • Keywords

Ferroelectric, phase field, phase transition, polarization switching, minimum energy path.

  • AMS Subject Headings

37N15, 49S05, 65K10, 65N22, 65Z05, 74N99, 78M30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-729, author = {Li , RuotaiDu , Qiang and Zhang , Lei}, title = {Numerical Discretization of Variational Phase Field Model for Phase Transitions in Ferroelectric Thin Films}, journal = {Communications in Computational Physics}, year = {2021}, volume = {29}, number = {3}, pages = {729--746}, abstract = {

Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational forms of the electrostatic energy and the relaxation dynamics of the polarization vector. The spatial discretization combines the Fourier spectral method with the finite difference method to handle three-dimensional mixed boundary conditions. It allows for an efficient semi-implicit discretization for the time integration of the relaxation dynamics. This method avoids explicitly solving the electrostatic equilibrium equation (a Poisson equation) and eliminates the use of associated Lagrange multipliers. We present several numerical examples including phase transitions and polarization switching processes to demonstrate the effectiveness of the proposed method.

}, issn = {1991-7120}, doi = {https://doi.org/ 10.4208/cicp.OA-2020-0118}, url = {http://global-sci.org/intro/article_detail/cicp/18564.html} }
TY - JOUR T1 - Numerical Discretization of Variational Phase Field Model for Phase Transitions in Ferroelectric Thin Films AU - Li , Ruotai AU - Du , Qiang AU - Zhang , Lei JO - Communications in Computational Physics VL - 3 SP - 729 EP - 746 PY - 2021 DA - 2021/01 SN - 29 DO - http://doi.org/ 10.4208/cicp.OA-2020-0118 UR - https://global-sci.org/intro/article_detail/cicp/18564.html KW - Ferroelectric, phase field, phase transition, polarization switching, minimum energy path. AB -

Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational forms of the electrostatic energy and the relaxation dynamics of the polarization vector. The spatial discretization combines the Fourier spectral method with the finite difference method to handle three-dimensional mixed boundary conditions. It allows for an efficient semi-implicit discretization for the time integration of the relaxation dynamics. This method avoids explicitly solving the electrostatic equilibrium equation (a Poisson equation) and eliminates the use of associated Lagrange multipliers. We present several numerical examples including phase transitions and polarization switching processes to demonstrate the effectiveness of the proposed method.

Li , RuotaiDu , Qiang and Zhang , Lei. (2021). Numerical Discretization of Variational Phase Field Model for Phase Transitions in Ferroelectric Thin Films. Communications in Computational Physics. 29 (3). 729-746. doi: 10.4208/cicp.OA-2020-0118
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