Importance of the Spin–Orbit Interaction for a Consistent Theoretical Description of Small Polarons in Pr-Doped CeO2,The Journal of Physical Chemistry C

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Importance of the Spin–Orbit Interaction for a Consistent Theoretical Description of Small Polarons in Pr-Doped CeO2
The Journal of Physical Chemistry C ( IF 3.3 ) Pub Date : 2020-06-24 , DOI: 10.1021/acs.jpcc.0c05352
Kathrin Michel _{1,

2} , Tor S. Bjørheim ₃ , Truls Norby ₃ , Jürgen Janek _{1,

2} , Matthias T. Elm _{1,

2,

4}

Affiliation

Ce_1–xPr_xO_2−δ (CPO) is a prominent mixed ionic and electronic conductor known for its unique oxygen storage capacity due to two redox-active cations. The oxygen storage properties depend on both the redox behavior and mobility of ions and electrons. The electronic properties of CPO are defined by the f-states of the two lanthanides and described within the model of small polarons. The theoretical treatment of small polarons is already challenging; additionally, the description of heavier elements, such as the lower transition metals and lanthanides, typically involves relativistic effects, such as spin–orbit coupling (SOC). These affect the electronic properties of materials and, therefore, also the thermodynamic parameters, such as phase stability and redox potential. Up to now, the f-electrons of Pr-ions and the corresponding redox chemistry have not been treated computationally, and their contribution to the mixed conduction and oxygen storage capacity in CPO has been neglected. Here, we investigate both the stoichiometric and defective CPO with respect to the localized electrons in the Pr(4f)-states. Density functional theory plus Hubbard U calculations were performed with and without the implementation of SOC. Only when accounting for relativistic interactions in the calculations, CPO shows semiconducting behavior with polaronic intragap states, in agreement with experimental findings, while otherwise, a metal-like behavior with degenerated f-states right at the Fermi level is found. Our results distinctly reveal the importance of spin–orbit interactions for a correct theoretical description of polarons in f-states. The electronic structure of CPO is revised, that is, the energetic and geometric overlap of states and, therefore, the bonding interactions within the crystal.

中文翻译：

自旋-轨道相互作用对于Pr掺杂CeO ₂中小极化子的一致理论描述的重要性

Ce _{1– x} Pr _x O _2−δ（CPO）是一种杰出的离子和电子混合导体，由于具有两个氧化还原活性阳离子而具有独特的储氧能力。储氧性能取决于氧化还原行为以及离子和电子的迁移率。CPO的电子性质由两个镧系元素的f态定义，并在小极化子模型中描述。小极化子的理论处理已经具有挑战性。另外，较重元素的描述，例如较低的过渡金属和镧系元素，通常涉及相对论效应，例如自旋-轨道耦合（SOC）。这些影响材料的电子特性，因此也影响热力学参数，例如相稳定性和氧化还原电势。到现在，Pr离子的f电子和相应的氧化还原化学尚未经过计算处理，而它们对CPO中混合导电性和储氧能力的贡献已被忽略。在这里，我们调查的化学计量和有缺陷的CPO相对于Pr（4f）状态中的本地电子。密度泛函理论加Hubbard在有或没有实施SOC的情况下都执行了U计算。仅在计算中考虑相对论相互作用时，CPO才会显示具有极化子能隙状态的半导体行为，与实验结果相符，否则，会发现在费米能级上具有简并f态的类金属行为。我们的结果清楚地揭示了自旋-轨道相互作用对于在f态中极化子的正确理论描述的重要性。修改了CPO的电子结构，即状态的高能和几何重叠，以及晶体内的键相互作用。

更新日期：2020-07-23

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