Electronic Structure of Transition Atoms in Quasi-Crystals and Hume-Rothery Alloys

A model describing the electronic structure of transition metal atoms in Hume-Rothery alloys and quasi-crystals is constructed by adding to the classical Anderson Hamiltonian a potential V B ( K ) that describes the diffraction of conduction electrons by Bragg planes near the Fermi surface. Strong deviation from the virtual bound state is observed for realistic parameters. Furthermore, the scattering of the conduction states by the d -orbitals changes the partial density of conduction states. This results in a contribution to the apparent negative valency of transition elements in Hume-Rothery alloys. The results are systematically compared with ab initio calculations for a series of Hume-Rothery alloys and are in good agreement.