In this article we present a method based on ab initio calculations to predict compositions at morphotropic phase boundaries in lead-free perovskite solid solutions. This method utilizes the concept of flat free energy surfaces and involves the monitoring of pressure-induced phase transitions as a function of composition. As model systems, solid solutions of ${\text{Na}}_{1/2}$${\text{Bi}}_{1/2}$${\text{TiO}}_3$ with the alkali substituted ${\text{Li}}_{1/2}$${\text{Bi}}_{1/2}$${\text{TiO}}_3$ and ${\text{K}}_{1/2}$${\text{Bi}}_{1/2}$${\text{TiO}}_3$ and the alkaline earth substituted ${\text{CaTiO}}_3$ and ${\text{BaTiO}}_3$ are chosen. The morphotropic compositions are identified by determining the composition at which the phase transition pressure equals zero. In addition, we discuss the different effects of hydrostatic pressure (compression and tension) and chemical substitution on the antiphase tilts about the [111] axis ($a^{-}{a}^{-}{a}^{-}$) present in pure ${\text{Na}}_{1/2}$${\text{Bi}}_{1/2}$${\text{TiO}}_3$ and how they develop in the two solid solutions ${\text{Na}}_{1/2}$${\text{Bi}}_{1/2}$${\text{TiO}}_3$–${\text{CaTiO}}_3$ and ${\text{Na}}_{1/2}$${\text{Bi}}_{1/2}$${\text{TiO}}_3$–${\text{BaTiO}}_3$. Finally, we discuss the advantages and shortcomings of this simple computational approach.

• Received 29 November 2013
• Revised 24 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.054105