Abstract
It is shown that the approximant monoclinic crystal Al 13Fe 4, known as a (C 5) decagonal-approximant crystal for d-AlFe, is also a valuable approximant for the icosahedral quasicrystalline phase i-AlFeCu. The icosahedral local order, in a half-plane around Fe(5) sites, is similar, up to the sixth neighbor, to the one around the origin or around the body center site (empty sites) in the cubic (Pm 3 ) α-AlMnSi phase, with a greater chemical disorder and a stronger tendency to geometric frustration as indicated by more empty sites in the icosahedral shells. This similarity gives some information about possible icosahedral local order in the quasicrystalline phase i-AlFeCu, and the possible atomic surfaces in a 6D Euclidean hyperspace approach.
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