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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Bak, P. Phenomenological theory of icosahedral incommensurate (“quasiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517–1519 (1985)
Janssen, T. Crystallography of quasi-crystals. Acta Crystallogr. A 42, 261–271 (1986)
Yamamoto, A. Crystallography of quasiperiodic crystals. Acta Crystallogr. A 52, 509–560 (1996)
Socolar, T., Lubensky, T. & Steinhardt, P. J. Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34, 3345–3360 (1986)
Jaric, M. V. & Nelson, D. R. Diffuse scattering from quasicrystals. Phys. Rev. B 37, 4458–4472 (1988)
Ishii, Y. Phason softening and structural transitions in icosahedral quasicrystals. Phys. Rev. B 45, 5228–5239 (1992)
Henley, C. L. in Quasicrystals: The State of the Art (eds DiVincenzo, D. & Steinhardt, P. J.) 429–524 (World Scientific, Singapore, 1991)
Jeong, H. C. & Steinhardt, P. J. Finite-temperature elasticity phase transition in decagonal quasicrystals. Phys. Rev. B 48, 9394–9403 (1993)
Bancel, P. A. in Quasicrystals: The State of the Art (eds DiVincenzo, D. & Steinhardt, P. J.) 17–55 (World Scientific, Singapore, 1991)
Colella, R., Zhang, Y., Sutter, J. P., Ehrlich, S. N. & Kycia, S. W. Debye-Waller factors in a quasicrystal. Phys. Rev. B 63, 014202 (2000)
Dolinsek, J., Apih, T., Simsic, M. & Dubois, J. M. Self-diffusion in icosahedral Al72.4Pd20.5Mn7.1 and phason percolation at low temperatures studied by 27Al NMR. Phys. Rev. Lett. 82, 572–575 (1999)
Coddens, G. & Steurer, W. Time-of–flight neutron-scattering study of phason hopping in decagonal Al-Co-Ni quasicrystals. Phys. Rev. B 60, 270–276 (1999)
Edagawa, K., Suzuki, K. & Takeuchi, S. High resolution transmission electron microscopy observation of thermally fluctuating phasons in decagonal Al-Cu-Co. Phys. Rev. Lett. 85, 1674–1677 (2000)
de Boissieu, M. et al. Diffuse scattering and phason elasticity in the AlPdMn icosahedral phase. Phys. Rev. Lett. 75, 89–92 (1995)
Zeger, G., Plachke, D., Carstanjen, H. D. & Trebin, H.-R. Quasicrystalline d-AlCuCo identified as random tiling by ion channeling combined with particle-induced X-ray emission. Phys. Rev. Lett. 82, 5273–5276 (1999)
Pennycook, S. J. & Jesson, D. E. High-resolution Z-contrast imaging of crystals. Ultramicroscopy 37, 14–38 (1991); Atomic-resolution Z-contrast imaging of interfaces. Acta Metall. Mater. 40, S149–S159 (1992)
Muller, D. A., Edward, B., Kirkland, E. J. & Silcox, J. Simulation of thermal diffuse scattering including a detailed phonon dispersion curve. Ultramicroscopy 86, 371–380 (2001)
Ritsch, S. et al. Highly perfect decagonal Al-Co-Ni quasicrystal. Phil. Mag. Lett. 74, 99–106 (1996)
Saitoh, K. et al. Structural study of an Al72Ni20Co8 decagonal quasicrystal using the high-angle annular dark-field method. Jpn. J. Appl. Phys. 36, L1400–L1402 (1997)
Yan, Y., Pennycook, S. J. & Tsai, A. P. Direct imaging of local chemical disorder and columnar vacancies in ideal decagonal Al-Ni-Co quasicrystals. Phys. Rev. Lett. 81, 5145–5148 (1998)
Steinhardt, P. J. et al. Experimental verification of the quasi-unit-cell model of quasicrystal structure. Nature 396, 55–57 (1998); correction Nature (399), 84 (1999)
Gummelt, P. Construction of Penrose tilings by a single aperiodic protoset. Geom. Dedicata 62, 1–17 (1996)
Abe, E. et al. Quasi-unit cell model for an Al-Ni-Co ideal quasicrystal based on clusters with broken tenfold symmetry. Phys. Rev. Lett. 84, 4609–4612 (2000)
Yan, Y. & Pennycook, S. J. Chemical ordering in Al72Ni20Co8 decagonal quasicrystals. Phys. Rev. Lett. 86, 1542–1545 (2001)
Abe, H. et al. Anomalous Debye-Waller factor associated with an order-disorder transformation in an Al72Ni20Co8 decagonal quasicrystal. J. Phys. (submitted)
Henley, C. L., Mihalkovic, M. & Widom, M. Total-energy-based prediction for d(AlNiCo). J. Alloys Comp. 342, 221–227 (2002)
Takakura, H., Yamamoto, A. & Tsai, A. P. The structure of decagonal Al72Ni20Co8 quasicrystal. Acta Crystallogr. A 57, 576–585 (2001)
Cervellino, A., Haibach, T. & Steurer, W. Structure solution of the basic decagonal Al-Co-Ni phase by the atomic surfaces modeling method. Acta Crystallogr. B 58, 8–33 (2002)
Hiraga, K., Ohsuna, T. & Nishimura, S. An ordered arrangement of atom columnar clusters in a pentagonal quasiperiodic lattice of an Al-Ni-Co decagonal quasicrystal. Phil. Mag. Lett. 80, 653–659 (2000)
Weickenmeier, A. & Kohl, H. Computation of absorptive form factors for high-energy electron diffraction. Acta Crystallogr. A 47, 590–597 (1991)
We thank H. Takakura, T. J. Sato, N. Tanaka, K. Ishizuka, M. Widom and C. L. Henley for discussions.
The authors declare that they have no competing financial interests.
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