ABSTRACT
As discussed in Chapter 3, the pioneering theory put forward by Mott and Jones in 1936 [1] certainly served as a milestone in establishing a basic idea for interpreting the Hume-Rothery electron concentration rule, which relates phase stability to the Fermi surface. However, since the discovery of the neck in the Fermi surface contours of pure Cu by Pippard in 1957, one could not help but recognize that the free-electron model Mott and Jones relied on is far from being satisfactory. Needless to say, the presence of the neck in pure Cu cannot be reproduced from the free-electron model.* Moreover, recent research after the 1990s on the stability of quasicrystals and their approximants, discovered by using the Hume-Rothery electron concentration rule as a guide, has gradually built up a general consensus such that the stability of such structurally complex metallic alloys (CMAs) is also most likely a consequence of lowering the electronic energy brought
about by the development of a deep pseudogap at the Fermi level. Since a pseudogap cannot be generated from the free-electron model, first-principles band calculations must be employed as a key tool to evaluate quantitatively the valence band structure and to show why a pseudogap is formed near the Fermi level in CMAs.
