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

TL;DR

This paper models Yb-based valence-fluctuating crystals as approximants to a hypothetical dodecagonal quasicrystal, providing a structural framework that links known crystal types and their heavy fermion properties.

Contribution

It constructs a 5D quasicrystal model based on Pd-Sn-Yb systems, unifying the understanding of related Yb-based crystal structures and their properties.

Findings

Proposes a 5D quasicrystal model with specific crystallographic sites.

Shows the quasicrystal comprises columns projecting to known crystal fragments.

Suggests the model as a platform for understanding heavy fermion behavior.

Abstract

The hexagonal ZrNiAl-type (space group: P-62m) and the tetragonal Mo2FeB2-type (space group: P4/mbm) structures, which are frequently 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 5-dimensional crystal (space group: P12/mmm, aDD=5.66 {\AA} and c=3.72 {\AA}) consists of four types of acceptance regions located at the following crystallographic sites; Yb [00000], 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 3-dimensional space, the quasicrystal is composed of three types of columns, of which c-projections correspond to a square, an equilateral triangle and a 3-fold hexagon. They are fragments of two known crystals, the hexagonal {\alpha}-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.