The atomic structures of three cubic approximants (cAPs), Y_12.7Cd_61.8Mg_25.5 [2/1 cAP with space group Pa3, a = 25.0654 (1) Å] and Er_12.5Cd_72.0Mg_15.5 [2/1 cAP with Pa3, a = 24.9658 (1) Å], and Y_14.5Cd_66.1Mg_19.4 [1/1 cAP with Im3, a = 15.4577 (1) Å], were investigated using X-ray structure analysis. The two 2/1 cAPs were found to be isostructural to the binary 2/1 cAP, YbCd_5.8, which is composed of two building units, namely Tsai-type rhombic triacontahedron (RTH) cluster and double-Friauf polyhedron (DFP). The 1/1 cAP, in contrast, was found to be isostructural to the binary 1/1 cAP, YbCd₆, which is composed solely of the RTH cluster. The refined structure models of the three cAPs exhibit substitutional disorders due to the Mg content that enters into Cd sites of the parent binary cAPs. In addition, in the 2/1 cAPs, the Y3(Er3) site on the third icosahedron shell of the RTH cluster and two positions inside DFP, Y5(Er5) sites, are partially mixed with Mg. Moreover, characteristic positional disorders owing to orientational disorder in the first shell of the RTH cluster is observed in all the three cAPs. A close relationship between the occupational disorder of the Y3(Er3) and Y5(Er5) sites in 2/1 cAPs and the elemental distribution in their first coordination shells is revealed.

中文翻译：

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三元 R-Cd-Mg (R = Y, Er) 系统中的 2/1 和 1/1 立方近似值

三个立方近似物 (cAPs)、Y _12.7 Cd _61.8 Mg _25.5 [2/1 cAP 与空间群Pa 3 , a = 25.0654 (1) Å] 和 Er _12.5 Cd _72.0 Mg _15.5 [2/1 cAP 与Pa 的原子结构在图 3 中， 使用 X 射线结构分析研究了 a = 24.9658 (1) Å] 和 Y _14.5 Cd _66.1 Mg _19.4 [1/1 cAP 与Im 3，a = 15.4577 (1) Å]。发现两个 2/1 cAP 与二元 2/1 cAP、YbCd _5.8具有同构，它由两个构建单元组成，即蔡型菱形三角三面体（RTH）簇和双Friauf多面体（DFP）。相比之下，发现 1/1 cAP 与二元 1/1 cAP、YbCd ₆同构，它仅由 RTH 集群组成。由于进入母体二元 cAP 的 Cd 位点的 Mg 含量，三个 cAP 的精细结构模型表现出置换紊乱。此外，在 2/1 cAP 中，RTH 簇的第三个二十面体壳上的 Y3(Er3) 位点和 DFP 内的两个位置 Y5(Er5) 位点与 Mg 部分混合。此外，在所有三个 cAP 中都观察到由于 RTH 簇的第一壳中的定向障碍引起的特征性位置障碍。揭示了 2/1 cAP 中 Y3(Er3) 和 Y5(Er5) 位点的职业障碍与其第一配位壳中的元素分布之间的密切关系。