Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Yu Su, Chad M. Landis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

267 Citations (Scopus)

Abstract

A continuum thermodynamics framework is devised to model the evolution of ferroelectric domain structures. The theory falls into the class of phase-field or diffuse-interface modeling approaches. Here a set of micro-forces and governing balance laws are postulated and applied within the second law of thermodynamics to identify the appropriate material constitutive relationships. The approach is shown to yield the commonly accepted Ginzburg-Landau equation for the evolution of the polarization order parameter. Within the theory a form for the free energy is postulated that can be applied to fit the general elastic, piezoelectric and dielectric properties of a ferroelectric material near its spontaneously polarized state. Thereafter, a principle of virtual work is specified for the theory and is implemented to devise a finite element formulation. The theory and numerical methods are used to investigate the fields near straight 180° and 90° domain walls and to determine the electromechanical pinning strength of an array of line charges on 180° and 90° domain walls.

Original languageEnglish
Pages (from-to)280-305
Number of pages26
JournalJournal of the Mechanics and Physics of Solids
Volume55
Issue number2
DOIs
Publication statusPublished - Feb 2007
Externally publishedYes

Keywords

  • Domain switching
  • Ferroelectrics
  • Finite element methods
  • Phase-field modeling
  • Piezoelectrics

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