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 lattice. 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 phasons. 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 A1 atoms that sit at the phasonrelated 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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