Superstructure formation in a ternary Yb-Cd-Mg 1/1 quasicrystal approximant

ABSTRACT

The superstructure and basic structure of ternary Yb-Cd-Mg 1/1 quasicrystal approximants with the compositions Yb${}_{12.9}$Cd${}_{78.4}$Mg${}_{8.8}$ and Yb${}_{13.3}$Cd${}_{64.2}$Mg${}_{22.5}$ were investigated using X-ray structural analysis. The former was determined to have a face-centred packing structure comprising two distinguishable Tsai-type rhombic triacontahedron clusters (space group $Fd\overline{3}$, $a=31.377(1)$ Å), while the latter was found to have a body-centred packing structure made of identical Tsai-type rhombic triacontahedron clusters (space group $Im\overline{3}$, $a=15.7596(4)$ Å). The distinction between the two types of clusters in the superstructure is based on the positional disorder of the first tetrahedron shell and the relative Cd/Mg occupancy at M5 sites in the fourth icosidodecahedron shell. In both the superstructure and basic structure, sites preferentially occupied by Mg typically have two Yb atoms among the atoms to which they are coordinated. Finally, a six-dimensional structural model of the primitive Tsai-type icosahedral quasicrystals was modified so as to incorporate the selective Cd/Mg occupation found in the 1/1 approximants.

KEYWORDS:

• Quasicrystals
• approximants
• structure analysis

Acknowledgments

The author would like to thank Y. Matsushita and A. Sato for technical assistance with the single-crystal XRD experiments at NIMS. I are also grateful to A. Yamamoto for reading this manuscript and useful comments. Finally, I thank A. P. Tsai for supporting during this work.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by Japan Society for the Promotion of Science JSPS KAKENHI grants (numbers JP18K13987 and JP19H05818).