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

TL;DR

This study uses a phase-field model to analyze nanoscale ferroelectric domain patterns, revealing how external loads influence the stability of complex laminate structures at the nanoscale.

Contribution

It introduces a phase-field approach that incorporates gradient and strain energies to explore nanoscale ferroelectric domain pattern stability and external load effects.

Findings

Stripe patterns are lower energy than complex laminates without external load.

External electric fields and strains can stabilize complex laminate patterns.

Nanoscale domain patterns are sensitive to external boundary conditions.

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 multi-rank 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 behaviour 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 multi-rank 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, multi-rank 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 of nanoscale periodic patterns, and on the effect of external loads on these patterns.