2 - Electron Theory of Complex Metallic Alloys

Abstract

Attempts to understand the stabilization mechanism of structurally complex metallic alloy (CMA) phases dates back to 1936 when Mott and Jones interpreted the stabilization of Cu5Zn8 and Al4Cu9 gamma-brasses containing 52 atoms per unit cell at particular electrons per atom ratio e/a in terms of the contact of the free electron sphere with the Brillouin zone. The Mott and Jones theory has been thought to serve as a milestone in establishing the Hume-Rothery electron concentration rule empirically established in the late 1920s. However, we have soon realized that it can be hardly applied when alloys contain transition metal (TM) elements as major constituent elements. The exploration of the phase stabilization mechanism for TM-bearing alloys has remained unsettled in physical metallurgy. In particular, the discovery of the Al-Mn quasicrystal by Shechtman et al. in 1984 and that of thermodynamically stable quasicrystals by Tsai et al. at more or less constant e/a values have intensified the interest in the Hume-Rothery electron concentration rule for TM-bearing compounds. Among numerous topics in the field of the electron theory of metals, the present authors focused on the e/a-dependent phase stabilization mechanism of CMAs, in particular, those containing a large amount of TM elements by making full use of the FLAPW formalism, in which wave functions outside the muffin-tin (MT) spheres are expanded into plane waves over allowed reciprocal lattice vectors. They have established the new Hume-Rothery electron concentration rule for CMAs in possession of a pseudogap at the Fermi level, regardless of whether TM elements are involved or not. The method to determine reliably the e/a value for TM elements has been also proposed. The relevant data for 3d-, 4d- and 5d-TM elements are presented.