Material descriptors for morphotropic phase boundary curvature in lead-free piezoelectrics

An important aspect of searching for alternatives to the current piezoelectric workhorse PZT (PbZr_xTi_1-xO₃) is to establish a vertical morphotropic phase boundary (MPB) in the composition-temperature phase diagram. However, the MPBs in most lead-free piezoelectrics, especially the BaTiO₃-based piezoelectrics, are not as vertical as that of PZT, resulting in serious temperature dependence of piezoelectric and dielectric properties. We investigate the dependence of the verticality of the MPB on polarization and strain related design descriptors in BaTiO₃-based and Pb-based systems. We find that the slope of the MPB decreases monotonically with the unit cell volume ratio of the tetragonal (T) and rhombohedral (R) ends; however, it increases with the ionic displacement ratio of the two ends. As the above two descriptors are not straight forward to access as a priori information, two parameters that relate to the atomic size and effective nuclear charge are introduced to enable an effective search for a desired MPB slope. Our study thus provides potential selection rules for developing Pb-free piezoelectrics with high temperature reliability.