Nanoscale periodic domain patterns in tetragonal ferroelectrics: A phase-field study

A. Renuka Balakrishna, J. E. Huber, and I. Münch
Phys. Rev. B 93, 174120 – Published 31 May 2016

Abstract

Ferroelectrics form domain patterns that minimize their energy subject to imposed boundary conditions. In a linear, constrained theory, that neglects domain-wall energy, periodic domain patterns in the form of multirank laminates can be identified as minimum-energy states. However, when these laminates (formed in a macroscopic crystal) comprise domains that are a few nanometers in size, the domain-wall energy becomes significant, and the behavior of laminate patterns at this scale is not known. Here, a phase-field model, which accounts for gradient energy and strain energy contributions, is employed to explore the stability and evolution of the nanoscale multirank laminates. The stress, electric field, and domain-wall energies in the laminates are computed. The effect of scaling is also discussed. In the absence of external loading, stripe domain patterns are found to be lower-energy states than the more complex, multirank laminates, which mostly collapse into simpler patterns. However, complex laminates can be stabilized by imposing external loads such as electric field, average strain, and polarization. The study provides insight into the domain patterns that may form on a macroscopic single crystal but comprising nanoscale periodic patterns, and on the effect of external loads on these patterns.

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  • Received 5 November 2015
  • Revised 18 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.174120

©2016 American Physical Society

Authors & Affiliations

A. Renuka Balakrishna1,*, J. E. Huber1, and I. Münch2

  • 1Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, England, United Kingdom
  • 2Institute for Structural Analysis, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany

  • *Corresponding author: ananya.renukabalakrishna@eng.ox.ac.uk.

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Vol. 93, Iss. 17 — 1 May 2016

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