Abstract
The atomic structures of three cubic approximants (cAPs), Y12.7Cd61.8Mg25.5 [2/1 cAP with space group Pa 3, a = 25.0654 (1) Å] and Er12.5Cd72.0Mg15.5 [2/1 cAP with Pa 3, a = 24.9658 (1) Å], and Y14.5Cd66.1Mg19.4 [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, YbCd5.8, 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.
Highlights
Icosahedral quasicrystals possess long-range order which generates sharp peaks in the diffraction diagram along with a rotational symmetry incompatible with translational symmetry (Shechtman et al, 1984; Levine & Steinhardt, 1984)
The atomic structure of the two 2/1 cubic approximants (cAPs) in the ternary Y-CdMg and Er-Cd-Mg systems, and the 1/1 cAP in the Y-Cd-Mg system was investigated by X-ray single-crystal analysis
The atomic structure of the Y-Cd-Mg 1/1 cAP was found to be isostructural to the parent binary YCd6 1/1 cAP which consists of the rhombic triacontahedron (RTH) unit
Summary
Icosahedral quasicrystals (iQCs) possess long-range order which generates sharp peaks in the diffraction diagram along with a rotational symmetry incompatible with translational symmetry (Shechtman et al, 1984; Levine & Steinhardt, 1984). 2/1 cAPs are often highlighted as the simplest cAPs that involve both the RTH and DFP units This implies that a suitable 2/1 cAP could provide insight into the occupational disorder that persists in the binary iQCs, i-R-Cd (with R 61⁄4 Yb) and i-Sc-Zn. To date, the only reported 2/1 cAPs in binary alloy systems, YbCd5.8 and Ca13Cd76, are free from chemical disorder, in that the icosahedron shell and diagonal positions of DFP are purely occupied by Yb and Ca, respectively (Pay Gomez & Lidin, 2001). Our refined structure models show that the Cd sites of the parent binary Yb-Cd cAPs are partially substituted with Mg. In addition, we find that in both the 2/1 cAPs, Mg partially substitutes some R sites which belong to a unique crystallographic position in the third icosahedron shell of the RTH unit and to the diagonal positions of the DFP unit. We summarized the important characteristics of the atomic structures
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