Icosahedral symmetry described by an incommensurately modulated crystal structure model

A crystal structure model of an incommensurately modulated structure is presented. Although six different reciprocal vectors are used to describe the model, all calculations are done in three dimensions making calculation of the real-space structure trivial. Using this model, it is shown that both the positions of the bragg reflections and information about the relative intensities of these reflections are in full accordance with the diffraction patterns reported for microcrystals of the rapidly quenched Al86Mn14 alloy. It is also shown that at least the local structure possesses full icosahedral symmetry with distances which are in agreement with the nearest-neighbor distances between Al-Mn and Al-Al atoms in the crystalline compound Al6Mn.