Al₄Mn quasicrystal atomic structure, diffraction data and Penrose tiling

Abstract

Abstract The modelling of the Al4Mn quasicrystal, recently proposed by Guyot and Audier (1985) on the basis of icosahedral atomic units characteristic of the crystalline phase α(AlFeSi) or α(AlMnSi), is analysed more deeply. After building the quasicrystal by connecting the basic structural units-double Al and Mn icosahedra with vacant centresm‐according to the rules previously described, it is found that the Mn and Al atoms lie in planes whose spacings are in agreement with X-ray or electron diffraction data. In terms of the three-dimensional Penrose tiling, two types of pairs of rhombohedral tiles are found: the first, with an edge length of 4·85 Å, decorated by atoms, defines the primitive cells; the second, inflated by a ratio φ2 (φ is the golden number), is decorated by the basic icosahedral units, and their stacking into a rhombic triacontahedron may suggest the existence of icosahedral vacancy defects. A satisfying comparison with high-resolution transmission electron micrographs is also made.