Abstract
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.
Highlights
Common metallic structures are based on high-symmetry atomic cells, such as face-centered cubic, close-packed hexagonal, and body-centered cubic, that have a coordination number of either 12 or 8+6
In the present paper the model of the Fermi-sphere–Brillouin zone (FS–BZ) interaction is applied to complex structures, considering the Fermi sphere (FS) inscribed into the BZ, as well as the FS enveloped inner zones contacting the edges or vertices
Structurally-complex alloy phases with tetrahedrally-packed polyhedra of Frank-Kasper type are discussed with reference to the free-electron model of Brillouin zone-Fermi sphere interactions
Summary
Common metallic structures are based on high-symmetry atomic cells, such as face-centered cubic (fcc), close-packed hexagonal (hcp), and body-centered cubic (bcc), that have a coordination number of either 12 or 8+6 These structures are found in elements in their metallic phases; they are formed in binary alloys and compounds if constituent elements have small differences in atomic size and electronegativity. Similar atomic packings exist in icosahedral quasicrystals, known as Mackay-type, Bergman-type, and Tsai-type These clusters build the structures of quasicrystal approximants with the periodic arrangements in the bcc cell (1/1 type) or more complex periodic structures. In the present paper the model of the Fermi-sphere–Brillouin zone (FS–BZ) interaction is applied to complex structures, considering the FS inscribed into the BZ, as well as the FS enveloped inner zones contacting the edges or vertices Both cases of FS–BZ configuration should affect the band-structure energy and decrease the crystal energy
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