The SrTiO₃ 5 [001] twist grain boundary (GB) is studied using first‐principles density functional theory calculations. Three types of GB structures, SrO/SrO (S/S), SrO/TiO₂ (S/T), and TiO₂/TiO₂ (T/T), are modeled and their relative thermodynamic stabilities are examined. Our calculations show that the S/S and S/T structures can be formed within appropriate synthesis conditions, with the S/S structure thermodynamically favored over the S/T structure within a wide range of chemical potentials, while the T/T structure is unlikely to form. The segregation behavior of oxygen vacancies is also investigated by calculating oxygen vacancy formation energies with respect to the distance from GB plane. In the S/S system, oxygen vacancies tend to segregate to the layer adjacent to the GB layer, while in the S/T system, oxygen vacancies tend to segregate to the GB layer itself. In both S/S and S/T systems, oxygen vacancy formation energy is lower than that in bulk SrTiO₃. To clearly show the experimental conditions necessary to promote oxygen vacancy formation in the 2 GB systems, we also generate grain boundary phase diagrams for oxygen vacancy with respect to synthesis temperature and oxygen partial pressure. Our calculations reveal different segregation behaviors and distributions of oxygen vacancies in the S/S and S/T systems, providing a possible avenue for GB engineering.

中文翻译：

---

第一性原理在SrTiO3Σ5[001]扭曲晶界中形成氧空位

使用第一性原理密度泛函理论计算研究了SrTiO ₃ 5 [001]扭曲晶粒边界（GB）。三种GB结构，SrO / SrO（S / S），SrO / TiO ₂（S / T）和TiO ₂ / TiO ₂（T / T），进行建模并检查其相对热力学稳定性。我们的计算表明，可以在适当的合成条件下形成S / S和S / T结构，在广泛的化学势范围内，S / S结构在热力学上优于S / T结构，而T / T结构是不太可能形成。还通过计算相对于GB平面的距离的氧空位形成能来研究氧空位的偏析行为。在S / S系统中，氧空位倾向于偏析到与GB层相邻的层，而在S / T系统中，氧空位倾向于偏析到GB层本身。在S / S和S / T系统中，氧空位形成能均低于本体SrTiO ₃。为了清楚地显示促进2 GB系统中氧空位形成所必需的实验条件，我们还生成了关于氧空位相对于合成温度和氧分压的晶界相图。我们的计算揭示了S / S和S / T系统中氧空位的不同偏析行为和分布，为GB工程提供了可能的途径。