Phase-field modeling of ferroelectric to paraelectric phase boundary structures in single-crystal barium titanate

Ferroelectric perovskite materials have been shown to exhibit a large electrocaloric effect near phase transitions. We develop a computational model based on a phase-field approach to characterize the structure of ferroelectric to paraelectric phase boundaries for planar configurations under generalized plane strain with temperatures near the Curie temperature. A nonlinear finite element method is used to solve for the phase boundary structure of a representative unit cell with a 180 degrees ferroelectric laminate for a range of domain widths. The temperature at which the phase boundary can be found increases with domain width, approaching the Curie temperature asymptotically. The excess free energy density per unit area of the boundary increases with domain width. As expected, closure domains form between the ferroelectric and paraelectric phase, and the shape of the closure domains evolves from triangular to needle-shaped as the domain width increases. The entropy jump across the phase boundary is quantified and is shown to increase with domain width as well. A planar configuration with a 90 degrees ferroelectric laminate is investigated, but shown to be physically unlikely due to the high stress levels required to achieve strain compatibility between the phases. Possible three-dimensional structures of the ferroelectric-paraelectric phase boundary are also discussed.