Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal

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

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.

Formation of an Intermediate Valence Icosahedral Quasicrystal in the Au-Sn-Yb System

We report on the formation of a new icosahedral quasicrystal (iQC) in the Au-Sn-Yb alloy system. This iQC has a primitive icosahedral lattice with a lattice constant a_ico of 0.5447(7) nm and a composition that was determined to be Au_60.0Sn_26.7Yb_13.3. X-ray absorption spectroscopy measurement of the near Yb L₃ edge demonstrates that the Yb valence in the iQC is an intermediate valence between divalent (4f¹⁴) and trivalent (4f¹³) at ambient pressure and was determined to be 2.18+. The results are compared to those for a corresponding 2/1 cubic approximant crystal. The formation of this new iQC is discussed in terms of the atomic size factor (δ) and the valence electron-to-atom ratio (e/a).

Ted Janssen and aperiodic crystals

Ted Janssen’s contributions to the field of aperiodic crystals are reviewed.

This article reviews some of Ted Janssen’s (1936–2017) major contributions to the field of aperiodic crystals. Aperiodic crystals are long-range ordered structures without 3D lattice translations and encompass incommensurately modulated phases, incommensurate composites and quasicrystals. Together with Pim de Wolff and Aloysio Janner, Ted Janssen invented the very elegant theory of superspace crystallography that, by adding a supplementary dimension to the usual 3D space, allows for a deeper understanding of the atomic structure of aperiodic crystals. He also made important contributions to the understanding of the stability and dynamics of aperiodic crystals, exploring their fascinating physical properties. He constantly interacted and collaborated with experimentalists, always ready to share and explain his detailed understanding of aperiodic crystals.

Developments in the structural science of materials

Recent developments in the structural science of materials and the growing power of computational methods in this field are discussed.

Mysteries of icosahedral quasicrystals: how are the atoms arranged?

Higher-dimensional structure analysis of quasicrystals is now possible. Yamada et al. [IUCrJ (2016), 3, 247-258] have solved the atomic structure of icosahedral ScZn7.33 including the characteristic imperfections.