Polycrystalline (ceramic) ferroelectrics have properties that depend on grain size and texture. Most models for grain boundaries in ferroelectrics treat them as sharp interfaces and neglect the structural degrees of freedom at the interface; whereas, grain boundary models for non-polar materials routinely account for this structural effect.
Here, variational methods have been employed to predict equilibrium and metastable grain boundary configurations in polar materials containing point defects. Grain boundary energetics are derived in a self-consistent framework for ferroelectric bi-crystals and ceramics.
There are two kinds of grain boundary: one with a paraelectric core and the other with a finite polarisation at the grain boundary core. We determine the energetics and conditions for transitions in grain boundary state for ferroelectric bi-crystals without point defects. Further, we predict interface states for tilt grain boundaries in barium titanate with point defects.