Mackay clusters and beyond in icosahedral quasicrystals seen from 6D space

Abstract

It is a great pleasure and honour for us to participate to the celebration of the 90th birthday of Alan Mackay, one of the most inspired crystallographers of our time who has been the authentic predecessor of the quasicrystal discovery. We discuss here several ways to construct Mackay-type atomic clusters and others for describing quasicrystalline structures from the standard 6D framework. We show that they are several simple solutions for both the 6D natural cluster and the original Mackay derivation that are consistent with special points of the basic icosahedral 6D lattice and the actually determined clusters in usual cubic 1/1 approximants of the icosahedral phases. This technique works as well for describing the two first shells of the so-called Bergman clusters but the situation is far more complicated for the so-called Tsai cluster that cannot be directly obtained from the icosahedral cut and projection of the simple 6D lattice special points without significantly large differences in the radii of the various orbits with respect to their actual positions in the YbCd icosahedral-type alloys. This shows that the 6D approach using special points as locations of the mean atomic surfaces—although very efficient for constructing initial simple models of the icosahedral phases—requires subsequent refinement techniques, especially in the actual locations and sizes of the various atomic orbits of the implied clusters, for leading to final acceptable structural models.