Designing high piezoelectric properties at the BaTiO₃-PbZrO₃-PbTiO₃ phase boundary by Landau-Devonshire theory

Ferroelectric materials possessing exceptional piezoelectric attributes have garnered widespread utilization in various applications. Solid solution systems improve piezoelectric properties through multiphase mixing, but the methodologies for effective design remain wanting. Based on the Landau-Devonshire theory, we propose a theoretical design method. Binary materials with morphotropic phase boundary (MPB) compositions are added with new elements to increase the free energy of the original stabilized phase and lower the energy barrier (EB). Flatter EBsand higher piezoelectric coefficients are found at the phase boundaries of the ternary system. By calculating the phase diagram, piezoelectric coefficient, dielectric constant, polarization, and EBs, we reveal the origin of the highest piezoelectric coefficient at the phase boundaries. This study underscores the importance of the EBs for polarization rotation in characterizing piezoelectric properties and proposes a theoretical design method for exploring materials with high piezoelectric coefficients.