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

Abstract

The hexagonal ZrNiAl-type (space group: P 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.

Keywords:

• Approximant
• quasicrystal
• dodecagonal
• valence-fluctuation
• Yb-based

Acknowledgements

The authors thank Kotoba Toyonaga and Yuuki Hirashima for their contributions to this research project. This work was supported by JSPS KAKENHI grant number 17K05524. MM acknowledges support from VEGA 2/0082/17.