Electronic structure of complex spd Hume-Rothery phases in transition-metal aluminides

The discovery of quasicrystals phases and approximants in Al(rich)-Mn system has revived the interest for complex aluminides containing transition-metal atoms. On one hand, it is now accepted that the Hume-Rothery stabilization plays a crucial role. On the other hand, transition-metal atoms have also a very important effect on their stability and their physical properties. In this paper, we review studies that unifies the classical Hume-Rothery stabilization for sp electron phases with the virtual bound state model for transition-metal atoms embedded in the aluminum matrix. These studies lead to a new theory for \"spd electron phases\". It is applied successfully to Al(Si)--transition-metal alloys and it gives a coherent picture of their stability and physical properties. These works are based on first-principles calculations of the electronic structure and simplified models, compared to experimental results. A more detailed review article is published in Prog. Mater. Sci. 50 (2005) p. 679-788.