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Direct Atomic-Scale Observation of a Local Thermal Vibration Anomaly in a Quasicrystalline Al72Ni20Co8 Compound

E. Abe1, A. P. Tsai2, and S. J. Pennycook3

Nature 421, 347 (2003)

Full Article (PDF 384 KB)

Direct, real-space imaging of a local thermal vibration anomaly in a solid has been demonstrated for the first time, through atomic-resolution ADF-STEM observations of an Al72Ni20Co8 quasicrystal. Significant changes of ADF contrast were seen at specific Al sites depending on the observation temperature as well as the angular range of the detector, as seen in the Figure. The origin of this anomalous contrast is well-explained by changes in Debye-Waller factor. This implies a change in the mean-square thermal vibration amplitude of the atoms at these specific sites, a local thermal vibration anomaly. The long-range distribution of these specific Al sites is quasiperiodically correlated on a length-scale of 2nm, which can be interpreted in terms of quasiperiodically-equivalent atomic sites defined within the framework of hyperspace crystallography.

These observations are directly relevant to a key issue concerning lattice dynamics in a quasicrystalline solid: the nature of the phason – the phason is an extra elastic degree of freedom specific to the quasicrystals (in addition to the usual phonons in crystals) and has been theoretically predicted to cause localized fluctuations.This work demonstrates an additional advantages of ADF-STEM. By performing angle-resolved and/or in-situ heating/cooling experiments, ADF-STEM now can determine not only the atomic structure but also the local thermal vibration amplitudes in a solid that crucially affect the physical properties of materials.


Direct Imaging of a Thermal Vibration Anomaly


Debye-Waller factor contrast

High-angle Range
Low-angle Range

High-angle range
(inner-angle ~50 mrad)

Low-angle range
(inner-angle ~35mrad)

Fig. 1. Determination of the nucleation pathway for single wall carbon nanotubes during laser ablation growth. First-principles calculations show the excess energy per carbon atom relative to a graphite for various clusters on a Ni surface. Structures containing hexagons are shown as solid points, structures containing pentagons as squares. Points are labeled according to the number of (pentagons, hexagons) in each structure. It is clear that pentagons are incorporated at the earliest stages in order to facilitate curvature, and reduce the energy associated with dangling bonds at the perimeter.
  1. Guest scientist on leave from National Institute for Materials Science, Japan, email
  2. National Institute for Materials Science, Japan
  3. Condensed Matter Sciences Division, ORNL

 Oak Ridge National Laboratory