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

Abstract

We have carried out a comparative study of plausible non-180° domain configurations in the two- and three-phase states of lead-free ferroelectrics Ba(Ti_1−xZr_x)O₃ (0.02  ≤  x  ≤  0.08) and (Ba_0.85Ca_0.15)(Ti_0.90Zr_0.10)O₃, respectively, using the elastic matching approach. The phase contents and stress-relief conditions in Ba(Ti_0.93Zr_0.07)O₃ and (Ba_0.85Ca_0.15)(Ti_0.90Zr_0.10)O₃ strongly depend on domain types in the rhombohedral R3m phase, whereas domains of the orthorhombic Amm2 phase influence two-phase states in Ba(Ti_0.98Zr_0.02)O₃. Changes in unit-cell parameters of (Ba_0.85Ca_0.15)(Ti_0.90Zr_0.10)O₃ 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 (Ba_0.85Ca_0.15)(Ti_0.90Zr_0.10)O₃ 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 (Ba_0.85Ca_0.15)..(Ti_0.90Zr_0.10)O₃ can lead to an enhanced contribution from domain-wall displacements and therefore, to the large piezoelectric response in this important lead-free ferroelectric compound.