The effects of Ti and Zr doping concentrations on the mechanical properties and electronic structure of the reduced Ce1−xMxO1.785 were studied. The calculated results show that elastic moduli of Ce1−xTixO1.875 decreased, while those of Ce1−xZrxO1.875 increased. Ce0.625Ti0.375O1.875 that undergoes structural transformation at 37.5 at.% Ti. Ce1−xMxO1.875 is ductile material. The degree of anisotropy of Ce1−xTixO1.875 decreased sharply at 25 at.% Ti, while that of Ce1−xZrxO1.875 almost unchanged with the increase of Zr concentration. Ti and Zr doping has little effect on the electronic structure of the unreduced Ce1−xMxO₂. Ti and Zr doping reduced the formation energy of O vacancy, and Ti doping was more conducive to the formation of O vacancy. The density of states of the reduced Ce1−xMxO1.875 exhibited spin splitting and was magnetic. Zr atom transferred 0.24–0.27 e more than Ti atom to the nearest O atoms, and Zr–O bond has stronger covalency and higher bond energy.

中文翻译：

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掺杂浓度对还原的 Ce1−xMx O1.785 (M = Ti, Zr) 弹性性能和电子结构的影响来自第一原理

Ti和Zr掺杂浓度对还原Ce的力学性能和电子结构的影响1-X米X○1.785进行了研究。计算结果表明，Ce的弹性模量1-X钛X○1.875减少，而 Ce1-X锆X○1.875增加。铈0.625钛0.375○1.875在 37.5 at.% Ti 下发生结构转变。铈1-X米X○1.875是韧性材料。Ce的各向异性程度1-X钛X○1.875在 25 at.% Ti 时急剧下降，而 Ce1-X锆X○1.875随着 Zr 浓度的增加几乎没有变化。Ti和Zr掺杂对未还原Ce的电子结构影响不大1-X米X氧₂。Ti和Zr掺杂降低了O空位的形成能，Ti掺杂更有利于O空位的形成。还原的 Ce 的态密度1-X米X○1.875表现出自旋分裂并具有磁性。Zr原子比Ti原子多向最近的O原子转移0.24~0.27 e，Zr-O键具有更强的共价键和更高的键能。