The Hume-Rothery Rules for Structurally Complex Alloy Phases

Abstract

The underlying physics behind the Hume-Rothery rules, which have earned great reputations over the past century in the field of materials science in designing new alloys, is reviewed. The discussion is developed following several key themes: (a) what is the critical depth and width of the pseudo-gap to stabilize a complex metallic alloy?, (b) what does the Hume-Rothery stabilization mechanism mean?, (c) the existence of FsBz-induced and orbital hybridization-induced pseudo-gaps, (d) the need of distinguishing two different electron concentrations e/a and VEC, (e) are most quasicrystals really scaled in terms of e/a and stabilized via the FsBz-induced pseudo-gap mechanism? The answer is "no".

Hexagonal-Diamond-like Gold Lattices, Ba and (Au,T)3 Interstitials, and Delocalized Bonding in a Family of Intermetallic Phases Ba2Au6(Au,T)3 (T = Zn, Cd, Ga, In, or Sn)

“…Rather, such electron-poor polar intermetallics are more or less closer to the Hume−Rothery phases. The latter have been classically identified with α-, β-, γ-, and η-brass-type phases, which form at e/a ratios of ≈1.4, 3/2, 21/13, and 7/4, respectively, in noble metal alloys (e.g., Cu−Zn, Cu−Cd, Ag−Ga, Au−Ga, and Au− Sn), 4 regardless of the solute elements added to the noble metals. 3 Recently, some quasicrystals (QCs) and their corresponding approximants (ACs) with e/a values in the range of ca.…”

“…1.7−2.2 have also been identified as new types of Hume−Rothery phases. 4 All of these electron-poor but relatively orbitally rich systems characteristically feature high coordination numbers (12−18) for the metal atoms, as do the simple metals.…”

Comments Concerning Some Features of Phase Diagrams and Phase Transformations

“…27) Also at about the same time, Hume-Rothery in England similarly emphasized the stabilizing electron concentration role in alloy phases and the value for the -brasses to be e=a ¼ 21=13 ¼ 1:615, characteristic of the two typical stoichiometric formulas in copper based alloys, Cu 5 Zn 8 and Cu 9 Al 4 , which he considered as being compound-like (for a more detailed historical account of these developments please see Ref. 28)). …”

Quasicrystals: What do we know? What do we want to know? What can we know?

“…In the early days of quasicrystal research, many QCs were discovered based on the working hypothesis of electronic stabilization by the Hume-Rothery mechanism (for a review see Tsai, 2003). Indeed, in several cases a pseudogap has been identified at the Fermi energy, originating either from Fermi-surface/pseudoBrillouin zone nesting or from the hybridization between d and p states (see Lin & Corbett, 2007;Tamura et al, 2004;Suchodolskis et al, 2003;Mizutani, 2016 (Bak, 1982, and references therein). This can be interpreted in such a way that once the chemical composition approximates that needed for the formation of a pseudogap at E F , the close-tospherical pseudo-Brillouin zone of an IQC lowers the energy more than the less-symmetric cubic Brillouin zone of even a high-order AC.…”