### 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 |
---|---|

Pages (from-to) | 315-323 |

Number of pages | 9 |

Journal | Computational Materials Science |

Volume | 158 |

DOIs | |

Publication status | Published - Feb 15 2019 |

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### All Science Journal Classification (ASJC) codes

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