The atomic structure of the Bergman-type icosahedral quasicrystal based on the Ammann–Kramer–Neri tiling

Abstract

In this study, the atomic structure of the ternary icosahedral ZnMgTm quasicrystal (QC) is investigated by means of single‐crystal X‐ray diffraction. The structure is found to be a member of the Bergman QC family, frequently found in Zn–Mg–rare‐earth systems. The ab initio structure solution was obtained by the use of the Superflip software. The infinite structure model was founded on the atomic decoration of two golden rhombohedra, with an edge length of 21.7 Å, constituting the Ammann–Kramer–Neri tiling. The refined structure converged well with the experimental diffraction diagram, with the crystallographic R factor equal to 9.8%. The Bergman clusters were found to be bonded by four possible linkages. Only two linkages, b and c, are detected in approximant crystals and are employed to model the icosahedral QCs in the cluster approach known for the CdYb Tsai‐type QC. Additional short b and a linkages are found in this study. Short interatomic distances are not generated by those linkages due to the systematic absence of atoms and the formation of split atomic positions. The presence of four linkages allows the structure to be pictured as a complete covering by rhombic triacontahedral clusters and consequently there is no need to define the interstitial part of the structure (i.e. that outside the cluster). The 6D embedding of the solved structure is discussed for the final verification of the model.

The physical space model of the Tsai-type quasicrystal

“…The same atomic decoration was assumed for all orientations of each type of rhombohedron. It is a typical application of the tiling-and-decoration routine (Elser & Henley, 1985), previously applied to both decagonal (Kuczera et al, 2011(Kuczera et al, , 2012Buganski et al, 2019) and icosahedral QCs (Buganski et al, 2020a). Atomic decoration was applied to 3 inflated rhombohedra with an edge length of 24.1 A ˚.…”

“…The starting model was obtained based on the procedure described by Buganski et al (2020a). The main idea was to find the maxima of electron density calculated within randomly selected rhombohedra of the AKNt.…”

“…Initially, the intention was to test whether it was possible to construct a real-space model of a Tsai QC with rhombohedral units. The atomic structure of i-ZnMgTm has already been solved using rhombohedral units of the Ammann-Kramer-Neri tiling (AKNt) (Buganski et al, 2020a;Kramer & Neri, 1984), by exploiting a 3 inflation rule for primitive icosahedral QCs (Ogawa, 1985;Guyot & Audier, 2014). As a natural progression, in our first objective we aimed to explore whether the same methodology can be applied to QCs with different cluster shell structures.…”

Insight into the structure of decagonite – the extraterrestrial decagonal quasicrystal

“…For the purpose of this research, the physical space structure refinement was exploited. This approach was utilized recently for several DQCs and also IQCs, resulting in the first detailed model of the Bergman-type IQC (Buganski et al, 2020b). Even so, the approach is questioned as to why the local ordering of atoms is prioritized more than long-range order, the presumption is further confirmed by the highresolution electron microscopy at least for DQCs (Li et al, 2016;Hiraga, 2002).…”

Dualized Ammann-Kramer-Neri tiling

“…The Ammann-Kramer-Neri (AKN) tiling [1,2] is a prototypal tiling with icosahedral symmetry, often used to model the underlying global geometry of icosahedral quasicrystals [3,4,5,6]. The prototiles of the AKN tiling are two kinds of rhombohedra called acute and obtuse rhombohedra (Fig.…”