## Abstract

Spontaneous polarizations (P_{S}’s) of BaTiO_{3} and SrTiO_{3} 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 analytical formulas of P_{S} of SrTiO_{3}-BaTiO_{3} system expressed by ion positions; a single formula predicts both macroscopic and atomic-scale P_{S} of SrTiO_{3}, BaTiO_{3} and SrTiO_{3}-BaTiO alloys. The accuracy of the formula is demonstrated by the application to experiments, BaTiO_{3}-SrTiO_{3} (-CaTiO_{3}) alloys, Sr_{4}Ti_{4}O_{12} 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 SrTiO_{3} and BaTiO_{3} and indicate that BaTiO_{3} and SrTiO_{3} 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.

Original language | English |
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Pages (from-to) | 315-323 |

Number of pages | 9 |

Journal | Computational Materials Science |

Volume | 158 |

DOIs | |

Publication status | Published - Feb 15 2019 |

## All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Chemistry(all)
- Materials Science(all)
- Mechanics of Materials
- Physics and Astronomy(all)
- Computational Mathematics