$\alpha \text{−}\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ is widely used for high-temperature structural materials in the form of polycrystals, and the physical and chemical properties are significantly influenced by the impurity types and their concentrations. Although the concentrations of some impurities in $\alpha \text{−}\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ have been experimentally investigated, there are no detailed reports on the point-defect structures and their charge states. In this study, we systematically investigate the point-defect structures of native defects, group IIA (Be, Mg, Ca, Sr, and Ba) and group IV (C, Si, Ge, Sn, and Pb) impurities by using Heyd-Scuseria-Ernzerhof hybrid functional combined with a finite-size supercell correction. We found that although the favorable defect types in the group IIA impurities are independent of the atmosphere (or oxygen partial pressure), the impurity defects in group IV show a strong dependence on the atmosphere and the impurity types. On the basis of the defect energetics, we calculate the impurity concentrations as a function of temperature for the respective extreme conditions. This could be useful for controlling the properties of $\alpha \text{−}\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$, especially sintering behaviors.

中文翻译：

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α-Al2O3中IIA和IV组杂质的第一性原理计算

$\alpha \text{-}\mathrm{一种}{\mathrm{升}}_2{\mathrm{Ø}}_3$以多晶形式广泛用于高温结构材料，其物理和化学性质受杂质类型及其浓度的显着影响。虽然一些杂质的浓度在$\alpha \text{-}\mathrm{一种}{\mathrm{升}}_2{\mathrm{Ø}}_3$经过实验研究，没有关于点缺陷结构及其电荷状态的详细报道。在这项研究中，我们使用Heyd-系统地研究了天然缺陷，IIA组（Be，Mg，Ca，Sr和Ba）和IV组（C，Si，Ge，Sn和Pb）杂质的点缺陷结构。 Scuseria-Ernzerhof混合功能结合有限大小的超级单元校正。我们发现，尽管IIA组杂质中的有利缺陷类型与大气（或氧分压）无关，但IV组中的杂质缺陷显示出对大气和杂质类型的强烈依赖性。根据缺陷能量学，我们计算了相应极端条件下杂质浓度与温度的关系。这对于控制...的属性可能很有用$\alpha \text{-}\mathrm{一种}{\mathrm{升}}_2{\mathrm{Ø}}_3$，尤其是烧结行为。