Plausible domain configurations and phase contents in two- and three-phase BaTiO3-based lead-free ferroelectrics

We have carried out a comparative study of plausible non-180 degrees domain configurations in the two-and three-phase states of lead-free ferroelectrics Ba(Ti1-xZrx)O-3 (0.02 <= x <= 0.08) and (Ba0.85Ca0.15)(Ti0.90Zr0.10)O-3, respectively, using the elastic matching approach. The phase contents and stress-relief conditions in Ba(Ti0.93Zr0.07)O-3 and (Ba0.85Ca0.15)(Ti0.90Zr0.10)O-3 strongly depend on domain types in the rhombohedral R3m phase, whereas domains of the orthorhombic Amm2 phase influence two-phase states in Ba(Ti0.98Zr0.02)O-3. Changes in unit-cell parameters of (Ba0.85Ca0.15)(Ti0.90Zr0.10)O-3 at poling lead to the complete stress relief in three-phase (P4mm + Amm2 + R3m) structures by increasing the volume fraction of the R3m phase. A link between the heterophase/domain structures and high piezoelectric activity in (Ba0.85Ca0.15)(Ti0.90Zr0.10)O-3 is discussed. Based on our results, we state that equal or almost equal volume fractions of the domain types at the three-phase coexistence in (Ba0.85Ca0.15)(Ti0.90Zr0.10)O-3 can lead to an enhanced contribution from domain-wall displacements and therefore, to the large piezoelectric response in this important lead-free ferroelectric compound