Accurate semiempirical analytical formulas for spontaneous polarization by crystallographic parameters of SrTiO₃-BaTiO₃ system

Spontaneous polarizations (P_S’s) of BaTiO₃ (BTO) and SrTiO₃ (STO) under various conditions are calculated ab initio using different exchange-correlation functionals. The extensive theoretical sets of P_S vs. ion positions are found to lie on a single curve, despite the chemical differences and the wide variations of P_S and lattice parameters.
This uncovers accurate simple easy-to-use analytical formulas of P_S of STO-BTO system; The formulas express STO, BTO, and both ordered and disordered STO-BTO alloys much better than conventional Born effective charge approaches. The accuracy of the formulas is demonstrated by the application to experiments, STO-BTO (-CaTiO₃) alloys, Sr₄Ti₄O₁₂ with P_S // a-axis, a parallel domain, and a headon domain.
In addition, the present results verify empirically that oxygen displacement is the primary identifier and the origin of P_S of STO and BTO and indicate that BTO and STO may transforms into new state by an extremely large strain, e.g., −3%.The present procedures for finding formulas can be applied also to other materials.
Y. Watanabe, Comput. Mater. Sci. 158, 315 (2019).