Electronic origin of the orthorhombic Cmca structure in compressed elements and binary alloys

Formation of the complex structure with 16 atoms in the orthorhombic cell, space group Cmca (Pearson symbol oC16) was experimentally found under high pressure in the alkali elements (K, Rb, Cs) and polyvalent elements of groups IV (Si, Ge) and V (Bi). Intermetallic phases with this structure form under pressure in binary Bi-based alloys (Bi-Sn, Bi-In, Bi-Pb). Stability of the Cmca - oC16 structure is analyzed within the nearly free-electron model in the frame of Fermi sphere - Brillouin zone interaction. A Brillouin-Jones zone formed by a group of strong diffraction reflections close to the Fermi sphere is the reason for reduction of crystal energy and stabilization of the structure. This zone corresponds well to the 4 valence electrons in Si and Ge and leads to assume a spd-hybridization for Bi. To explain the stabilization of this structure within the same model in alkali metals, that are monovalent at ambient conditions, a possibility of an overlap of the core and valence band electrons at strong compression is considered. The assumption of the increase in the number of valence electrons helps to understand sequences of complex structures in compressed alkali elements and unusual changes in their physical properties such as electrical resistance and superconductivity

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

Metal crystals with tetrahedral packing are known as Frank-Kasper phases with large unit cells with the number of atoms 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 interactions model for several typical examples: Cu4Cd3, Mg2Al3 with over thousand atoms per cell, and for icosahedral quasicrystal approximants with 146 to 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.Comment: 10 pages, 3 figures, 1 tabl