Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material
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419_2018_Article_1411.pdf
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2.44 MB
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Author(s)
Muench, I.
Huber, J. E.
Renuka Balakrishna, Ananya
Date Issued
June 2018
Journal
Archive of Applied Mechanics
Publisher
Springer-Verlag
Citation
Muench, I. et al. “Periodic Boundary Conditions for the Simulation of 3D Domain Patterns in Tetragonal Ferroelectric Material.” Archive of Applied Mechanics (June 2018): 1-18 © 2018 The Author(s)
Version
Final published version
Abstract
Periodic domain patterns in tetragonal ferroelectrics are explored using a phase field model calibrated for barium titanate. In this context, we discuss the standard periodic boundary condition and introduce the concept of reverse periodic boundary conditions. Both concepts allow the assembly of cubic cells in accordance with mechanical and electrical conditions. However, application of the reverse periodic boundary condition is due to an increased size of the RVE and enforces more complex structures compared to the standard condition. This may be of particular interest for other multiphysics simulations. Additionally, we formulate mechanical side conditions with minimal spherical (hydrostatic) stress, or conditions with controlled average strain. It is found that in sufficiently small periodic cells, only a uniform single domain, or the simplest stripe domains constitute equilibrium states. However, once the periodic cells are of order 20 domain wall widths in size, more complex, 3-dimensional patterns emerge. Some of these patterns are known from prior studies, but we also identify other domain patterns with long, ribbon-like domains threaded through them and some vortex-like structures. Keywords: Periodic boundary conditions; RVE simulation; Tetragonal ferroelectrics; Polarization patterns; Polarization vortex; Multiphysics simulations
MIT Department
Massachusetts Institute of Technology. Department of Materials Science and Engineering
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DOI of Published Version
https://doi.org/10.1007/s00419-018-1411-9
