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Metal crystals with tetrahedral packing are known as Frank–Kasper phases, with large unit cells with the number of atoms numbering from hundreds to thousands. The main factors of the formation and stability of these phases are the atomic size ratio and the number of valence electrons per atom. The significance of the electronic energy contribution is analyzed within the Fermi sphere–Brillouin zone interaction model for several typical examples: Cu4Cd3, Mg2Al3 with over a thousand atoms per cell, and for icosahedral quasicrystal approximants with 146–168 atoms per cell. Our analysis shows that to minimize the crystal energy, it is important that the Fermi sphere (FS) is in contact with the Brillouin zones that are related to the strong diffraction peaks: the zones either inscribe the FS or are circumscribed by the FS creating contact at edges or vertices

Structurally Complex Frank–Kasper Phases and Quasicrystal Approximants: Electronic Origin of Stability