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Metal crystals with tetrahedral packing are known as Frank-Kasper phases withlarge unit cells with the number of atoms from hundreds to thousands. The mainfactors of the formation and stability of these phases are the atomic sizeratio and the number of valence electrons per atom. The significance of theelectronic energy contribution is analyzed within the Fermi sphere - Brillouinzone interactions model for several typical examples: Cu4Cd3, Mg2Al3 with overthousand atoms per cell, and for icosahedral quasicrystal approximants with 146to 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 Brillouinzones that are related to the strong diffraction peaks: the zones eitherinscribe the FS or are circumscribed by the FS creating contact at edges orvertices.

Structurally complex Frank-Kasper phases and quasicrystal approximants: electronic origin of stability