INVESTIGATIONS IN THE AG-MG AND AG-AL-MG SYSTEMS .1. MODELS FOR CUBICAPPROXIMANTS OF ICOSAHEDRAL QUASI-CRYSTALS IN THE AG-AL-MG SYSTEM

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 I3-cluster concept sho wed 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 dodecah edron, the rhombic icosahedron, and the rhombic triacontahedron, are u sed to build periodic structures. Together with an atomic decoration o f the zonohedra the complete structures of a FK-type i/i-approximant, a MI-type I/i-approximant, a 2/1-approximant, and a 3/2-approximant ar e generated. The structures of the models are described. The FK-type i /i-approximant is isostructural to the Bergman phase Mg-32(Al,Zn)49. T he MI-type 1/1 approximant is an almost bcc packing of Mackay icosahed ra and therefore one variant of the cubic 1/1-approximants within the I3-family. The two higher approximants contain regions which are typic al 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 Angstrom and 2 828 atoms in the unit cell. But there are only six different coordinat ion polyhedra in it. Calculated single crystal precession photographs along the twofold, threefold, and fivefold directions as well as powde r diffraction patterns are shown and compared with experimental data o f other authors. (C) 1997 Elsevier Science S.A.