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2014 | 126 | 2 | 531-534
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Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

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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|_{c}^2]^{3/2}, where |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 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 Al_6TM (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 MX_1 (M = Li and Na, X_1 = 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.
  • Nagoya Industrial Science Research Institute, 1-13 Yotsuya-dori, Chikusa-ku, Nagoya, 464-0819, Japan
  • Aichi University of Education, Kariya-shi, Aichi, 448-8542, Japan
  • Nagoya Institute of Technology, Department of Frontier Materials, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
  • Theoretical Physics, University of Kassel, 34132 Kassel, Germany
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