Hume–Rothery Stabilization Mechanism in Tsai-Type Cd6Ca Approximant and e/a Determination of Ca and Cd Elements in the Periodic Table

  • U. MizutaniEmail author
  • M. Inukai
  • H. Sato
  • K. Nozawa
  • E. S. Zijlstra
Conference paper


We performed FLAPW electronic structure calculations with subsequent FLAPW-Fourier analysis for Tsai-type Cd6Ca containing 168 atoms per unit cell with space group \(Pm\bar{3}\). The square of the Fermi diameter (2k F )2, e/a and critical reciprocal lattice vector |G|2s were determined. The origin of the pseudogap across the Fermi level was interpreted in terms of the Hume–Rothery stabilization mechanism based on Fermi surface–Brillouin zone interactions (Fs–Bz) involved. The intuitively expected value of e/a=2.0 was confirmed. By extending our work to intermetallic compounds existing in the Cd–Ca binary alloy system, we determined the e/a values for Ca embedded in the polyvalent matrix Cd. The effective e/a for Ca was deduced to be two.


Hume–Rothery stabilization mechanism FLAPW-Fourier analysis Fs–Bz interactions Tsai-type approximant Valence of Ca 



One of the authors (UM) is grateful for the financial support of the Grant-in-Aid for Scientific Research (Contract No. 23560793) from the Japan Society for the Promotion of Science.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • U. Mizutani
    • 1
    Email author
  • M. Inukai
    • 2
  • H. Sato
    • 3
  • K. Nozawa
    • 4
  • E. S. Zijlstra
    • 5
  1. 1.Nagoya Industrial Science Research InstituteNagoyaJapan
  2. 2.Toyota Technological InstituteHisakataNagoyaJapan
  3. 3.Aichi University of EducationAichiJapan
  4. 4.Department of PhysicsChuo UniversityTokyoJapan
  5. 5.Theoretical PhysicsUniversity of KasselKasselGermany

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