### Acta Crystallographica Section A

# Foundations of Crystallography

### Volume 69, Part 3 (May 2013)

## research papers

*Acta Cryst.* (2013). A**69**, 322-340 [ doi:10.1107/S0108767313005035 ]

### Cluster-packing geometry for Al-based F-type icosahedral alloys

**Abstract:** This paper presents a new, highly stable, periodic approximant to the Al-based F-type icosahedral quasicrystals, i-Al-Pd-TM (TM = transition metals). The structure of this intermetallic Al-Pd-Cr-Fe compound is determined *ab initio* using single-crystal X-ray diffraction, where the space group is identified to be and the lattice constant 40.5 Å. The structure is well described as a dense packing of clusters of two kinds, which are called the pseudo-Mackay-type and the mini-Bergman-type clusters. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the clusters are centred at the vertices of a canonical cell tiling, which corresponds to a 2 × 2 × 2 superstructure of Henley's cubic 3/2 packing, and that the parity of each vertex determines the kind of associated cluster. The proper quasi-lattice constant for describing the cluster packing is 1/ ( = golden mean) times the conventional one used to describe Al-based P-type icosahedral alloys. The superstructure ordering of the present approximant turns out to be of a different kind from the P-type superstructure ordering previously reported in i-Al-Pd-Mn. The present results will greatly improve the understanding of atomic structures of F-type icosahedral quasicrystals and their approximants.

**Keywords: F-type icosahedral quasicrystals; approximants; clusters; canonical cell tilings.**

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