MODEL QUASI-LATTICE FOR AL-MN DECAGONAL QUASI-CRYSTAL

A model quasilattice for the Al-Mn decagonal quasicrystal is proposed. It is a periodic stacking of two-dimensional pentagonal quasilattices with the period c= 1.24 nm. The space group is P10(5)/mmc and the one period is written as CCBAR where C is a composite layer with the point group D5h and CBAR is related to C by the screw axis 10(5). The composite layer C is composed of five layers as B2B1AB1B2 and the central layer A is on the mirror plane. The layers B1 and B2 form the puckered layer B=B1B2 and C is written as B*AB with B*(=B2B1) being the mirror image of B. The layer A is obtained by decorating a pentagonal variation of the Penrose tiling with pentagons, stars, boats and thin rhombi and the remaining two layers, B1 and B2, are two-dimensional quasilattices decorating the pentagonal Penrose tiling.