Abstract
The atomic structure of quasicrystals1 — solids with long-range order, but non-periodic atomic lattice structure — is often described as the three-dimensional generalization of the planar two-tile Penrose pattern2. Recently, an alternative model has been proposed3,4,5 that describes such structures in terms of a single repeating unit3,4,5 — the three-dimensional generalization of a pattern composed of identical decagons. This model is similar in concept to the unit-cell description of periodic crystals, with the decagon playing the role of a ‘quasi-unit cell’. But, unlike the unit cells in periodic crystals, these quasi-unit cells overlap their neighbours, in the sense that they share atoms. Nevertheless, the basic concept of unit cells in both periodic crystals and quasicrystals is essentially the same: solving the entire atomic structure of the solid reduces to determining the distribution of atoms in the unit cell. Here we report experimental evidence for the quasi-unit-cell model by solving the structure of the decagonal quasicrystal Al72Ni20Co8. The resulting structure is consistent with images obtained by electron and X-ray diffraction, and agrees with the measured stoichiometry, density and symmetry of the compound. The quasi-unit-cell model provides a significantly better fit to these results than all previous alternative models, including Penrose tiling.
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Acknowledgements
We thank R. Kilaas of Total Resolution, Inc. for lending us the MacTempas software package for this project. This work was partially supported by the US Department of Energy at Princeton, and by CREST (Core Research for Evolutional Science and Technology) of Japan Science and Technology Corporation (JST).
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Steinhardt, P., Jeong, HC., Saitoh, K. et al. Experimental verification of the quasi-unit-cell model of quasicrystal structure. Nature 396, 55–57 (1998). https://doi.org/10.1038/23902
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DOI: https://doi.org/10.1038/23902
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