Correlations between tetragonality, polarization, and ionic displacement in PbTiO₃-derived ferroelectric perovskite solid solutions

We use first-principles density-functional theory calculations to investigate the dependence of tetragonality on local structure in a variety of ferroelectric solid solutions. We demonstrate that tetragonality is strongly coupled to the B -cation displacement and weakly coupled to the A -cation displacement. Examination of various Bi M3⁺ O3 additives to PbTiO₃ for different M3⁺ ionic sizes reveals that substitution of either small B cations or low doping of large B cations gives rise to large spontaneous polarization and tetragonality. Understanding how the phase transition temperature (Tc) and tetragonality are affected by Pb- and Bi-based perovskite additives provides a rational path for designing new high-temperature piezoelectric materials.