Crystal and quasicrystal structures in Al-Mn-Si alloys

Abstract

We show that the \ensuremath{\alpha}-(AlMnSi) crystal structure is closely (and systematically) related to that of the icosahedral Al-Mn-Si alloys. Using a modification of the ``projection'' method of generating icosahedral structures from six-dimensional lattices, we find a simple description of the \ensuremath{\alpha}-(AlMnSi) structure. This structure, and (we conjecture) the icosahedral one, can also be described as a packing of 54-atom icosahedral clusters.