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Computer simulation of domain evolution and twin microstructure formation in single crystals under external electric field (with field directions highlighted in top row) applied along nonpolar axes during ferroelectric phase transition. (a) Tetragonal ferroelectric phase under electric field applied along nonpolar  direction. [(b) and (c)] Rhombohedral ferroelectric phase under electric field applied along nonpolar  and  directions, respectively. Bottom row shows fully developed engineered domain configurations consisting of structural twins (twin boundaries in tetragonal phase are highlighted by dashed black lines for clarity) with head-to-tail polarization patterns (with polarization directions highlighted in individual domains).
(a) Simulated herringbone microstructure under  electric field. (b) Simulation of correlated ferroelectric nucleation. Note that polarization length in (b) is less than 0.1% of equilibrium value in (a).
Computer simulation of dependence of domain wall density in engineered domain configuration on nonpolar electric field magnitude. Open symbols represent individual simulation results. Filled symbols represent average results. Symbols ▽ and △ correspond to quenching to and , respectively.
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