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.

1. Sciences et Ingénierie des Matériaux et Procédés, INPGrenoble CNRS UJF, BP 75 38402 St Martin d'Hères Cedex, France
2. Institut Laue Langevin, BP 156, 38042 Grenoble, Cedex 9, France
3. Institute of Physics, Slovak Academy of Sciences, 84228 Bratislava, Slovakia
4. J-PARC Center, Japan Atomic Energy Agency, 2-4, Shirakatashirane, Tokai, Naka, Ibaraki 319-1195, Japan
5. RIKEN/SPring-8, 1-1-1 Kouto, Sayo, Hyogo 679-5143, Japan
6. JASRI/SPring-8, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan
7. Laboratoire Léon Brillouin, CEA Saclay, 91191 Gif sur Yvette Cedex, France
8. Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
9. Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
10. CEA-Grenoble, DRFMC-SPSMS-MDN, 38054 Grenoble Cedex 9, France
11. Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
12. Laboratoire de Spectrometrie Physique, Universite Joseph Fourier, BP 87, 38402 St Martin d'Hères Cedex, France
13. Neutron Science Laboratory, Institute for Solid State Physics, University of Tokyo, 106-1 Shirakata, Tokai, Ibaraki 319-1106, Japan
14. Institute of Multidisciplinary Research for Adavanced Materials, Tohoku University, Sendai 980-8577, Japan
15. National Institute for Material Science, Tsukuba 305-0044, Japan
16. 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

Correspondence to: Marc de Boissieu¹ e-mail: Marc.de-boissieu@ltpcm.inpg.fr

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