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An electron concentration parameter, expressed as the number of itinerant electrons per number of atoms N in a structural unit cell of an alloy, e/uc, is a useful parameter that can be used in interpreting the origin of a band structure pseudogap often evident at the Fermi level for structurally complex metallic alloy phases. It can be expressed in terms of the interference condition e/uc = pi/3[broken vertical bar G broken vertical bar(2)(c)](3/2), where vertical bar G(c)(2) is the square of the critical reciprocal lattice vector associated with the specific set of lattice planes interfering with electrons at the Fermi level. This parameter is similar to the well-known Hume-Rothery electron concentration parameter ela, which represents the number of electrons per atom and is linked with e/uc through the relation e/uc = N(e/a). We have demonstrated that certain complex metallic alloy structures appear to be stable at or near certain values of ela. We show that the e/a = 1.60 rule holds for the sub-group of gamma-brasses with space group 1 (4) over bar 3m and Pearson symbol cI52, the e/a = 4.34 rule for skutterudite compounds with Im (3) over bar and cI32, the e/a = 2.74 rule for Al6TM (TM = Mn, Tc, Re, Fe, and Ru) compounds with Cmcm and oC28, the e/a = 1.62 rule for the sub-group of the Heusler compounds with Fm3m and cF16, and the e/a = 2.09 rule for the sub-group of Zintl compounds MX1 (M = Li and Na, X-1 = Al, Ga, In, and TI) with Fd (3) over barm and cF32. The ela rule holds in sub-groups of isostructural compounds, regardless of the degree of orbital hybridizations and the polarity involved.

Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys