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Lattice dynamics of the Zn–Mg–Sc icosahedral quasicrystal and its Zn–Sc periodic 1/1 approximant

Nature Materials volume 6, pages 977–984 (2007)Cite this article

Abstract

Quasicrystals are long-range-ordered materials that lack translational invariance, so the study of their physical properties remains a challenging problem. Here, we have carried out inelastic-X-ray- and neutron-scattering experiments on single-grain samples of the Zn–Mg–Sc icosahedral quasicrystal and of the Zn–Sc periodic cubic 1/1 approximant, with the aim of studying the respective influence of the local order and of the long-range order (periodic or quasiperiodic) on lattice dynamics. Besides the overall similarities and the existence of a pseudo-gap in the transverse dispersion relation, marked differences are observed, the pseudo-gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of a pseudo-Brillouin-zone in the quasicrystal. These results are compared with simulations on atomic models and using oscillating pair potentials, and the simulations reproduce in detail the experimental results. This paves the way for a detailed understanding of the physics of quasicrystals.

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Figure 1: Cluster structure and diffraction pattern of the i-ZnMgSc QC and its 1/1 Zn–Sc approximant.
Figure 2: Response function measured in transverse geometry by inelastic neutron scattering for the ZnSc 1/1 approximant and the ZnMgSc QC.
Figure 3: Longitudinal excitations: comparison between the measured dispersion relation and the simulated response function S(Q,E).
Figure 4: Transverse excitations: comparison between the measured dispersion relation and the simulated response function S(Q,E).
Figure 5: Comparison between the experiment and the simulation for a few representative constant-Q energy scans.
Figure 6: Fitted pair potential used in the simulation.

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Acknowledgements

We acknowledge the LLB, the ILL and the Spring-8 facilities for the allocation of beam time. We thank Y. Kaneko for his help in sample preparation. Part of the work has been initiated within the European Complex Metallic Alloy Network of Excellence. M.M. has been supported by a CNRS grant during his stay at the SIMAP, and by the Slovak grant agency APVV-0413-06. M.d.B. acknowledges the financial support of the Tohoku University during his stay at the IMRAM.

Author information

Author notes

  1. Sonia Francoual

    Present address: Present address: National High Magnetic Field Laboratory, Los Alamos National Laboratory, MPA-NHMFL, TA-35, Bldg. 0127, MS E536, Los Alamos, New Mexico 87545, USA,

Authors and Affiliations

  1. Sciences et Ingénierie des Matériaux et Procédés, INPGrenoble CNRS UJF, BP 75 38402 St Martin d’Hères Cedex, France

    Marc de Boissieu, Sonia Francoual & Marek Mihalkovič

  2. Institut Laue Langevin, BP 156, 38042 Grenoble, Cedex 9, France

    Sonia Francoual, Pierre Bastie & Roland Currat

  3. Institute of Physics, Slovak Academy of Sciences, 84228 Bratislava, Slovakia

    Marek Mihalkovič

  4. J-PARC Center, Japan Atomic Energy Agency, 2-4, Shirakatashirane, Tokai, Naka, Ibaraki 319-1195, Japan

    Kaoru Shibata

  5. RIKEN/SPring-8, 1-1-1 Kouto, Sayo, Hyogo 679-5143, Japan

    Alfred Q. R. Baron

  6. JASRI/SPring-8, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan

    Alfred Q. R. Baron & Satoshi Tsutsui

  7. Laboratoire Léon Brillouin, CEA Saclay, 91191 Gif sur Yvette Cedex, France

    Yvan Sidis & Bernard Hennion

  8. Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan

    Tsutomu Ishimasa & Hiroyuki Takakura

  9. Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA

    Dongmei Wu & Thomas Lograsso

  10. CEA-Grenoble, DRFMC-SPSMS-MDN, 38054 Grenoble Cedex 9, France

    Louis-Pierre Regnault

  11. Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

    Franz Gähler

  12. Laboratoire de Spectrometrie Physique, Universite Joseph Fourier, BP 87, 38402 St Martin d’Hères Cedex, France

    Pierre Bastie

  13. Neutron Science Laboratory, Institute for Solid State Physics, University of Tokyo, 106-1 Shirakata, Tokai, Ibaraki 319-1106, Japan

    Taku J. Sato

  14. Institute of Multidisciplinary Research for Adavanced Materials, Tohoku University, Sendai 980-8577, Japan

    An-Pang Tsai

  15. National Institute for Material Science, Tsukuba 305-0044, Japan

    An-Pang Tsai

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  1. Marc de Boissieu
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Correspondence to Marc de Boissieu.

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de Boissieu, M., Francoual, S., Mihalkovič, M. et al. Lattice dynamics of the Zn–Mg–Sc icosahedral quasicrystal and its Zn–Sc periodic 1/1 approximant. Nature Mater 6, 977–984 (2007). https://doi.org/10.1038/nmat2044

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