Investigations in the AgMg and AgAlMg systems I. Models for cubic approximants of icosahedral quasicrystals in the AgAlMg system

Abstract

In this paper models of cubic approximants in the AgAlMg system are developed and their structure chemistry is described. The analysis of two complex binary AgMg phases by means of the 13-cluster concept showed that a third component is necessary to construct quasicrystals or large approximants. The four unit cells of the quasiperiodic tiling by Levine, Steinhardt and Socolar, the rhombohedron, the rhombic dodecahedron, the rhombic icosahedron, and the rhombic triacontahedron, are used to build periodic structures. Together with an atomic decoration of the zonohedra the complete structures of a FK-type 1 1 -approximant, a MI-type 1 1 -approximant, a 2 1 -approximant, and a 3 2 -approximant are generated. The structures of the models are described. The FK-type 1 1 -approximant is isostructural to the Bergman phase Mg 32(Al,Zn) 49. The MI-type 1 1 -approximant is an almost bcc packing of Mackay icosahedra and therefore one variant of the cubic 1 1 -approximants within the I3-family. The two higher approximants contain regions which are typical of I3-phases and regions of Frank-Kasper type. The 3 2 -approximant has a large unit cell with a lattice parameter of 37.96 Å and 2828 atoms in the unit cell. But there are only six different coordination polyhedra in it. Calculated single crystal precession photographs along the twofold, threefold, and fivefold directions as well as powder diffraction patterns are shown and compared with experimental data of other authors.