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

The superstructure and basic structure of ternary Yb-Cd-Mg 1/1 quasicrystal approximants with the compositions Yb12.9Cd78.4Mg8.8 and Yb13.3Cd64.2Mg22.5 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 Fd3¯, 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 Im3¯, 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.