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Aperiodic Crystals pp 101–107Cite as

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

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Abstract

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.

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References

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Acknowledgements

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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Authors and Affiliations

  1. Nagoya Industrial Science Research Institute, 1-13 Yotsuya-dori, Chikusa-ku, Nagoya, 464-0819, Japan

    U. Mizutani

  2. Toyota Technological Institute, Hisakata, Tempaku-ku, Nagoya, 468-8511, Japan

    M. Inukai

  3. Aichi University of Education, Kariya-shi, Aichi, 448-8542, Japan

    H. Sato

  4. Department of Physics, Chuo University, 1-13-27 Kasuga, Tokyo, 112-8551, Japan

    K. Nozawa

  5. Theoretical Physics, University of Kassel, 34132, Kassel, Germany

    E. S. Zijlstra

Authors
  1. U. Mizutani
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  2. M. Inukai
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  3. H. Sato
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  4. K. Nozawa
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  5. E. S. Zijlstra
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Corresponding author

Correspondence to U. Mizutani .

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Editors and Affiliations

  1. School of Chemistry, The University of Sydney, Sydney, 2006, New South Wales, Australia

    Siegbert Schmid

  2. Research School of Chemistry, The Australian National University, Building 35, Canberra, 0200, Australia

    Ray L. Withers

  3. School of Physics & Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel

    Ron Lifshitz

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Mizutani, U., Inukai, M., Sato, H., Nozawa, K., Zijlstra, E.S. (2013). Hume–Rothery Stabilization Mechanism in Tsai-Type Cd6Ca Approximant and e/a Determination of Ca and Cd Elements in the Periodic Table. In: Schmid, S., Withers, R., Lifshitz, R. (eds) Aperiodic Crystals. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6431-6_14

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