Low energy periodic microstructure in ferroelectric single crystals

Nien-Ti Tsou, Ingo Münch, John E. Huber*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

Two distinct modelling approaches are used to find minimum energy (equilibrium) microstructural states in tetragonal ferroelectric single crystals. The first approach treats domain walls as sharp interfaces and uses analytical solutions of the compatibility conditions at domain walls to identify multi-rank laminate microstructures that are free of residual stress and electric field. The second method treats domain walls as diffuse interfaces, using a phase-field model in 3-dimensions. This is computationally intensive, but takes the full field equations into account and allows a more general class of periodic microstructure to be explored. By searching for minimum energy configurations of a cube of tetragonal material, candidate unit cells of a periodic microstructure are identified. Adding periodic boundary conditions allows the assembly of the unit cells into a macro-structure of low energy. A noteworthy structure identified in this way is a "hexadomain" vortex consisting of six tetragonal domains meeting along the major diagonal of a cube. Several of the structures identified by the phase-field model are found to be special cases of multirank laminate structure. Thus the analytical approach offers a fast method for finding equilibrium microstructures, while the phase-field model provides a validation of these solutions.

Original languageEnglish
Title of host publicationIUTAM Symp on Multiscale Modell of Fatigue, Damage and Fract in Smart Mater
Subtitle of host publicationProc of the IUTAM Symp on Multiscale Modell of Fatigue, Damage and Fract in Smart Mater held in Freiberg DEU, Sep.1-4, 2009
PublisherSpringer Verlag
Pages287-296
Number of pages10
ISBN (Print)9789048198863
DOIs
StatePublished - 1 Jan 2011

Publication series

NameIUTAM Bookseries
Volume24
ISSN (Print)1875-3507

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    Tsou, N-T., Münch, I., & Huber, J. E. (2011). Low energy periodic microstructure in ferroelectric single crystals. In IUTAM Symp on Multiscale Modell of Fatigue, Damage and Fract in Smart Mater: Proc of the IUTAM Symp on Multiscale Modell of Fatigue, Damage and Fract in Smart Mater held in Freiberg DEU, Sep.1-4, 2009 (pp. 287-296). (IUTAM Bookseries; Vol. 24). Springer Verlag. https://doi.org/10.1007/978-90-481-9887-0-27