Abstract

The combination effect of substitutional impurities of group IVB–VIB transition metals on the oxygen vacancy formation energy in rutile titania was studied by the projector augmented wave method within density functional theory. The pair interaction energy of impurity atoms was estimated depending on the interatomic distance. It was shown that the interaction in the Zr + Zr, Hf + Hf and Nb + Ta pairs leads to the energy preference of their orientation along the <100> direction at a distance of the lattice parameter a. The Mo + Mo and Nb + Mo pairs prefer to orient along the [001] direction at a distance of the lattice parameter c. If the impurity atoms are farther than the third neighbors, then their interaction can be neglected. It was found that the change in the oxygen vacancy formation energy due to doping with several impurities can be estimated as the sum of the energy changes due to single impurity divided by a coefficient whose value depends on the mutual arrangement of the impurity atoms.

中文翻译：

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过渡金属杂质对 TiO2 中氧空位形成能量的组合影响

摘要

采用密度泛函理论中的投影增强波方法研究了IVB-VIB族过渡金属取代杂质对金红石二氧化钛氧空位形成能的综合影响。根据原子间距离估计杂质原子的相互作用能。结果表明，Zr + Zr、Hf + Hf 和 Nb + Ta 对中的相互作用导致它们在距晶格参数a的距离处沿 <100> 方向取向的能量偏好。 Mo + Mo 和 Nb + Mo 对优选沿 [001] 方向以晶格参数c的距离取向。如果杂质原子比第三个邻居更远，那么它们的相互作用可以忽略不计。发现由于掺杂多种杂质而导致的氧空位形成能的变化可以估计为由于单一杂质而导致的能量变化的总和除以系数，该系数的值取决于杂质原子的相互排列。