Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys
U. Mizutania, H. Satob, M. Inukaic and E.S. Zijlstrad
aNagoya Industrial Science Research Institute, 1-13 Yotsuya-dori, Chikusa-ku, Nagoya, 464-0819, Japan
bAichi University of Education, Kariya-shi, Aichi, 448-8542, Japan
cNagoya Institute of Technology, Department of Frontier Materials, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
dTheoretical Physics, University of Kassel, 34132 Kassel, Germany
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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 = π/3[|G|c2]3/2, where |G|c2 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 e/a, 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 e/a. We show that the e/a = 1.60 rule holds for the sub-group of gamma-brasses with space group I4̅3m and Pearson symbol cI52, the e/a = 4.34 rule for skutterudite compounds with Im3̅ 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 Fm3̅m and cF16, and the e/a = 2.09 rule for the sub-group of Zintl compounds MX1 (M = Li and Na, X1 = Al, Ga, In, and Tl) with Fd3̅m and cF32. The e/a rule holds in sub-groups of isostructural compounds, regardless of the degree of orbital hybridizations and the polarity involved.

DOI: 10.12693/APhysPolA.126.531
PACS numbers: 71.20.Be, 71.20.Lp, 71.15.Mb