Abstract
The atomic structures of three cubic approximants (cAPs), Y(12.7)Cd(61.8)Mg(25.5) [2/1 cAP with space group Pa 3, a = 25.0654 (1) Å] and Er(12.5)Cd(72.0)Mg(15.5) [2/1 cAP with Pa 3, a = 24.9658 (1) Å], and Y(14.5)Cd(66.1)Mg(19.4) [1/1 cAP with Im 3, 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, YbCd(6), 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.