Evolution from successive phase transitions to "morphotropic phase boundary" in BaTiO₃-based ferroelectrics

Obtaining superior physical properties for ferroic materials by manipulating the phase transitions is a key concern in solid state physics. Here, we investigated the dielectric permittivity, piezoelectric coefficient d₃₃, storage modulus, and crystal symmetry of (1-x)Ba(Ti_0.8Zr_0.2)O₃-x(Ba_1-yCa_y)TiO₃ (BZT-xBC_yT) systems to demonstrate the gradual evolution process from successive phase transitions in BaTiO₃ to the morphotropic phase boundary (MPB) regime in BZT-xBC_0.3T. Furthermore, we analysed with a Landau-type theoretical model to show that the high field-sensitive response (dielectric permittivity) originates from a small polarization anisotropy and low energy barrier at the quadruple point. Together, the intermediate orthorhombic phase regime and the tetragonal-orthorhombic and orthorhombic-rhombohedral phase boundaries constitute the MPB. Our work not only reconciles the arguments regarding whether the structural state around the MPB corresponds to a single-phase regime or a multiple-phase-coexistence regime but also suggests an effective method to design high-performance functional ferroic materials by tailoring the successive phase transitions.