Pair distribution function in icosahedral AlMnSi alloy

Abstract

A model for the structure of an icosahedral AlMn alloy was made by projection from the six-dimensional space. The Mackay icosahedra are located on the twelvefold vertices of the three-dimensional Penrose tiling made by the projection, and manganese atoms are distributed on the rest of the vertices. Additional aluminium atoms are arranged on the diagonal lines on the rhombic surfaces of the unit rhombohedra. The X-ray structure factor and the pair distribution function were calculated for the model and they were compared with those obtained from the Mo Kα X-ray diffraction profile of the icosahedral Al₇₇Mn₂₀Si₃. The agreement between them is very good except for the pair distribution function in the region with r less than 0.6 nm, indicating that the present model reflects quite well the essential part of the structure of the icosahedral phase.