Phase field modeling for domain characterization of ferroelectric materials

In this study we adopted a recently developed continuum mechanics-based non-equilibrium thermodynamics framework to investigate domain wall evolutions and interactions within ferroelectric materials. Furthermore, based on such framework, a finite element computing program is implemented to investigate the domain patterns of polarization within low dimensional ferroelectric nanostructures. It is observed from the computational results that the distribution of polarization in low-dimensional ferroelectric nanostructures appears to form vortex structures under open-circuit boundary conditions. The domain characterizations and the minimum geometric limits for existence of such single-vortex structure in ferroelectric nanodots and nanodisks have been numerically evaluated. The effect of intrinsic surface stress has been considered during the analysis.