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

TL;DR

This paper develops accurate analytical formulas for spontaneous polarization in SrTiO3-BaTiO3 systems based on ab initio calculations, enabling precise predictions across various compositions and conditions.

Contribution

It introduces a universal analytical formula for spontaneous polarization derived from ion positions, validated against experimental data and applicable to multiple related materials.

Findings

A single formula predicts PS of SrTiO3, BaTiO3, and alloys.

The formula accurately matches experimental polarization measurements.

Oxygen displacement is identified as the primary origin of PS.

Abstract

Spontaneous polarizations (PSs) of BaTiO3 and SrTiO3 under various conditions are calculated ab initio using different exchange-correlation functionals. The extensive theoretical sets of PS vs. ion positions are found to lie on a single curve, despite the chemical differences and the wide variations of PS and lattice parameters. This uncovers accurate simple analytical formulas of PS of SrTiO3-BaTiO3 system expressed by ion positions; a single formula predicts both macroscopic and atomic-scale PS of SrTiO3, BaTiO3 and SrTiO3-BaTiO alloys. The accuracy of the formula is demonstrated by the application to experiments, BaTiO3-SrTiO3 (-CaTiO3) alloys, Sr4Ti4O12 with PS // 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 PS of SrTiO3 and BaTiO3 and indicate that BaTiO3 and SrTiO3 may transforms into new state by an extremely large strain, e.g., -3%. Furthermore, the earlier prediction of headon domain without aid of defects was confirmed. The present procedures for finding formulas can be applied to other materials.