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Direct observation of a local thermal vibration anomaly in a quasicrystal

Abstract

Quasicrystals have long-range order with symmetries that are incompatible with periodicity, and are often described with reference to a higher-dimensional analogue of a periodic lattice1,2,3. Within the context of this ‘hyperspace’ crystallography, lattice dynamics of quasicrystals can be described by a combination of lattice vibrations and atomic fluctuations—phonons and phasons1,4. However, it is difficult to see localized fluctuations in a real-space quasicrystal structure, and so the nature of phason-related fluctuations and their contribution to thermodynamic stability are still not fully understood. Here we use atomic-resolution annular dark-field scanning transmission electron microscopy to map directly the change in thermal diffuse scattering intensity distribution in the quasicrystal, through in situ high-temperature observation of decagonal Al72Ni20Co8. We find that, at 1,100 K, a local anomaly of atomic vibrations becomes significant at specific atomic sites in the structure. The distribution of these localized vibrations is not random but well-correlated, with a quasiperiodic length scale of 2 nm. We are able to explain this feature by an anomalous temperature (Debye–Waller) factor for the Al atoms that sit at the phason-related sites defined within the framework of hyperspace crystallography. The present results therefore provide a direct observation of local thermal vibration anomalies in a solid.

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Figure 1: Atomic-resolution annular dark-field scanning transmission electron microscope (ADF-STEM) images of decagonal Al72Ni20Co8.
Figure 2: A decagonal cluster with a diameter of about 2 nm, a structural unit of Al72Ni20Co8.
Figure 3: Estimates of the thermal diffuse scattering cross-section of Al (σTDSAl; equation (2)) as a function of mean-square thermal vibration amplitude (〈u2〉).
Figure 4: ‘Phason’-related atomic sites in the Al72Ni20Co8 quasicrystal.

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Acknowledgements

We thank H. Takakura, T. J. Sato, N. Tanaka, K. Ishizuka, M. Widom and C. L. Henley for discussions.

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Correspondence to Eiji Abe.

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Abe, E., Pennycook, S. & Tsai, A. Direct observation of a local thermal vibration anomaly in a quasicrystal. Nature 421, 347–350 (2003). https://doi.org/10.1038/nature01337

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