The Hume-Rothery rules have been successfully used for the design of new alloys, including solid solutions, intermetallics, and a few commonly known icosahedral quasicrystals. Yet when the alloys become more chemically complex and consist of more than four principal elements, it remains an open question whether the Hume-Rothery rules are still valid for designing chemically complex icosahedral quasicrystals, or high-entropy icosahedral quasicrystals. In this work, quaternary and quinary alloys were systematically designed to possess electron per atom (e/a) ratios and average atomic radii $\left(R_a\right)$ comparable to those of the stable Al-Cu-Fe icosahedral quasicrystal, by alloying with Co and Ni. Icosahedral quasicrystals were identified in the quaternary alloys Al-Cu-Fe-Co and Al-Cu-Fe-Ni but with significantly reduced volume fractions compared to Al-Cu-Fe. Notably, the icosahedral quasicrystal was absent in the quinary alloy Al-Cu-Fe-Co-Ni. The 6D quasilattice constant (${\mathrm{a}}_{6\mathrm{D}}$) of the icosahedral quasicrystal decreased upon alloying, with Co inducing a larger reduction than Ni. Compositional analyses revealed Al-O, Fe-Co, Cu-Ni, and Fe-Ni substitutions within the icosahedral quasicrystal, with Ni partitioning approximately equally between Cu and Fe. Our findings show the limitations of applying the Hume-Rothery rules as a predictive guideline for icosahedral quasicrystals Al-Cu-Fe containing Co or Ni. Furthermore, the simulated electronic structure of the 3/2 icosahedral approximant demonstrated the formation of a pseudogap, clarified the mechanism of Fe-Co substitution, and reinforced the importance of the critical e/a ratio. Crystal Orbital Hamilton Population (COHP) analysis revealed that Al acted as the primary stabilizer of the icosahedral structure, whereas Cu could be replaced for enhanced phase stability.

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• Quasicrystals
• Transition metal alloys
• Scanning electron microscopy
• X-ray diffraction