Abstract Al-based stable quasicrystals exist only in ternary alloy systems. According to the cluster line rule, these quasicrystals require three constituent elements. For the objective of determining if there is any quaternary quasicrystal, in this paper we have used the electron concentration and atomic size constant criteria to analyze the alloy phase evolution in the Al-Cu-Ni-Fe quaternary system. We have found no evidence of any quaternary quasicrystal. This result confirms the conclusions out of the cluster line rule that only three elements are sufficient to form a stable Al-based quasicrystal.
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