High-quality single-crystal X-ray diffraction data are used to determine the crystal structures of two types of 3/2 periodic approximants (PAs) to face-centred icosahedral quasicrystals, which were previously reported to form in the quaternary Al-Pd-W-Fe system. Both structures are composed of two types of atomic clusters, referred to as mini-Bergman clusters and pseudo-Mackay clusters, which are densely packed without incorporating glue atoms. A reliable structural refinement has been succeeded for one of the structures, demonstrating that its cluster-packing geometry can be described using the canonical-cell tiling model. This structure is identified as the cubic 23 · 3/2 PA, closely resembling those previously reported in the Al-Pd-TM-Fe (TM = Cr, Mo) and Al-Pd-Ru systems. Furthermore, the correlation between the local geometry of each atomic site and the atomic species occupying it is found to be comparable to that observed in the corresponding Al-Pd-Cr-Fe compound. The second type of 3/2 PA, which the data suggest to be a twinned trigonal crystal, has so far only allowed for preliminary structural refinement. The results indicate a distinct cluster arrangement from the cubic 23 · 3/2 PA, characterized by the inclusion of a significantly shorter inter-cluster linkage of 4.3 Å. This observation implies that an extension of the conventional canonical-cell tiling model is necessary to fully describe the structure of the trigonal 3/2 PA.
Aoyama et al. (Fri,) studied this question.