Phase field simulation on the electromechanical response of poled barium titanate polycrystals with oxygen vacancies

This work investigates the electromechanical response of poled barium titanate (BaTiO₃) polycrystals with oxygen vacancies at room temperature. A phase field model is developed for ferroelectric polycrystals, coupled with the time-dependent Ginzburg-Landau theory and the oxygen vacancies diffusion, to demonstrate the interaction between oxygen vacancies and domain evolutions. To generate grain structures, the phase field model for grain growth is also employed. The hysteresis loop (polarization vs electric field curve) and butterfly loop (strain vs electric field curve) are computed, and the effects of grain size and oxygen vacancy density on the dielectric and piezoelectric properties of the BaTiO₃ polycrystals are discussed.