Single-crystal structure of rapidly cooled alloys with icosahedral symmetry. I. experimental analysis

Crystallographic analysis is applied to a set of electron diffraction patterns taken from a rapidly cooled Al-Mn alloy to construct reciprocal-lattice patterns in agreement with the observed icosahedral results. The analysis leads to a proposed atomic scale model which is derived from two sets of experimental modulations, each of which has six independent modulation vectors. The underlying structure has a lattice, the unit cell of which involves 32 atomic sites with the required symmetry properties. The appearance of the experimental electron diffraction patterns is explained either by the coherent arrangement of this lattice with an irrational sublattice or by an independent set of modulations. The relationship of this structure to three-dimensional nonperiodic Penrose tilings is explored.