Atomic Structure of Quasicrystals. I. Structure Factor of Icosahedral Clusters

Abstract

Structure factors of 9 icosahedral clusters were calculated. Icosahedral clusters discussed are 12 atoms at five-fold symmetry sites C₅ (icosahedron), 20 atoms at C₃ sites (dodecahedron), 30 atoms at C₂ sites, 60 atoms at mirror sites, 12 and 20 atoms at C₅ and C₃ sites (triacontahedron), 12 and 30 atoms at C₅ and C₂ sites, 30 and 20 atoms at C₂ and C₃ sites, 12, 30 and 20 atoms at C₅, C₂ and C₃ sites (star-shaped polyhedron), and 12, 30Al and 12Mn atoms at C₅, C₂ and C₅ sites (Mackay 54). Furthermore, the structure factors of quasicrystal obtained by the projection from the 6-dimensional cubic lattice are calculated. A comparison of the calculated electron-diffraction-intensity with the experimental one gives the unit length τ times the Al–Al bond length (τ=(\sqrt5+1)⁄2: the golden ratio).