Interpretation of some Yb-based valence-fluctuating crystals as approximants to a dodecagonal quasicrystal.

The hexagonal ZrNiAl-type (space group: P <inline-graphic></inline-graphic> 2m) and the tetragonal Mo2FeB2-type (space group: P4/mbm) structures, which are formed in the same Yb-based alloys and exhibit physical properties related to valence-fluctuation, can be regarded as approximants of a hypothetical dodecagonal quasicrystal. Using Pd-Sn-Yb system as an example, a model of quasicrystal structure has been constructed, of which five-dimensional crystal (space group: P12/mmm, a DD = 5.66 Å and c = 3.72 Å) consists of four types of acceptance regions located at the following crystallographic sites; Yb [0 0 0 0 0], Pd[1/3 0 1/3 0 1/2], Pd[1/3 1/3 1/3 1/3 0] and Sn[1/2 00 1/2 1/2]. In the three-dimensional space, the quasicrystal is composed of three types of columns, of which c-projections correspond to a square, an equilateral triangle and a three-fold hexagon. They are fragments of two known crystals, the hexagonal α-YbPdSn and the tetragonal Yb2Pd2Sn structures. The model of the hypothetical quasicrystal may be applicable as a platform to treat in a unified manner the heavy fermion properties in the two types of Yb-based crystals. [ABSTRACT FROM AUTHOR]