Quasicrystals are solids that exhibit symmetries long thought forbidden in nature. Since their discovery in a rapidly solidified Al–Mn alloy in 1984, the central issue in the field has been to understand why they form. Are they energetically stable compounds or stabilized by entropy? In recent years, major strides have been made in determining atomic structure, largely by direct imaging using advanced electron microscopy. One system is now known to be energetically stabilized, and quasicrystals are therefore firmly established as a new physical state of matter. They represent a unique packing of atomic clusters some tens of atoms in size, with substantial localized fluctuations, referred to as phasons. Understanding phasons may in future allow their unique macroscopic properties to be tailored for useful materials applications.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 23 February 2018
Scientific Reports Open Access 29 September 2017
Scientific Reports Open Access 01 March 2016
Subscribe to Journal
Get full journal access for 1 year
only $9.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metalic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984).
Dubost, B., Lang, J.-M., Tanaka, M., Sainfort, P. & Audier, M. Large AlCuLi single quasicrystals with triacontahedral solidification morphology. Nature 324, 48–50 (1986).
Tsai, A. P., Inoue, A. & Masumoto, T. A stable quasicrystal in Al-Cu-Fe system. Jpn J. Appl. Phys. 26, L1505–L1507 (1987).
Ohashi, W. & Spaepen, F. Stable Ga-Mg-Zn quasi-periodic crystals with pentagonal dodecahedral solidification morphology. Nature 330, 555–556 (1987).
Tsai, A. P. in Physical Properties of Quasicrystals (ed. Stadnik, Z. M.) 5–50 (Springer, 1999).
Stephens, P. W. & Goldman, A. I. Sharp diffraction maxima from an icosahedral glass. Phys. Rev. Lett. 56, 1168–1171 (1986); ibid 57, 2331 (1986).
Pauling, L. Apparent icosahedral symmetry is due to directed multiple twinning of cubic crystals. Nature 317, 512–514 (1986); ibid So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal. Phys. Rev. Lett. 58, 365–368 (1987).
Levine, D. & Steinhardt, P. J. Quasicrystals: A new class of ordered structures. Phys. Rev. Lett. 53, 2477–2480 (1984).
Desiraju, G. R. In search of clarity. Nature 423, 485 (2003).
Bak, P. Icosahedral crystals: Where are the atoms? Phys. Rev. Lett. 56, 861–864 (1986).
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).
Elser, V. & Henley, C. L. Crystal and quasicrystal structures in Al-Mn-Si alloys. Phys. Rev. Lett. 55, 2883–2886 (1985).
Audier, M. et al. Structural relationships in intermetallic compounds of the Al-Li-(Cu, Mg, Zn) system. Phil. Mag. B 60, 437–466 (1989).
Hiraga, K., Sugiyama, K. & Ohsuna, T. Atomic cluster arrangements in cubic approximant phases of icosahedral quasicrystals. Phil. Mag. A 78, 1051–1064 (1998).
Janot, C. & de Boissieu, M. Quasicrystals as a hierarchy of clusters. Phys. Rev. Lett. 72, 1674–1677 (1994).
Ishihara, K. N. & Yamamoto, A. Penrose patterns and related structures. I. Superstructure and generalized Penrose patterns. Acta Crystallogr. A 44, 508–516 (1988).
Bendersky, L. Quasicrystal with one-dimensional translational symmetry and a tenfold rotation axis. Phys. Rev. Lett. 55, 1461–1463 (1985).
Hiraga, K. in Advances in Imaging and Electron Physics (ed. Hawks P. W.) 37–98 (Academic, London, 1998).
Abe, E., Takakura, H. & Tsai, A. P. Ho arrangement in the Zn6Mg3Ho icosahedral quasicrystal studied by atomic-resolution Z-contrast STEM. J. Electron Microsc. 50, 187–195 (2001).
Beeli, C. & Horiuchi, S. The structure and its reconstruction in the decagonal Al70Mn17Pd13 quasicrystal. Phil. Mag. B 70, 215–240 (1994).
Tsuda, K. et al. Structure of Al-Ni-Co decagonal quasicrystals. Phil. Mag. A 74, 697–708 (1996).
Penrose, R. The role of aesthetics in pure and applied mathematical reserach. Bull. Inst. Math. Applic. 10, 266–271 (1974).
Burkov, S. Structure model of the Al-Cu-Co decagonal quasicrystal. Phys. Rev. Lett. 67, 614–617 (1991); ibid Modeling decagonal quasicrystals: random assembly of interpenetrating decagonal clusters. J. Phys. 2, 695–706 (1992).
Henley, C. L. in Quasicrystals: The State of the Art (eds DiVincenzo, D. & Steinhardt, P. J.) 429–524 (World Scientific, Singapore, 1991).
Joseph, D., Ritsch, S. & Beeli, C. Distinguishing quasiperiodic from random order in high-resolution TEM images. Phys. Rev. B 55, 8175–8183 (1997).
Ritsch, S. et al. Highly perfect decagonal Al-Co-Ni quasicrystal. Phil. Mag. Lett. 74, 99–106 (1996).
Abe, H. et al. Atomic short-range order in an Al72Ni20Co8 decagonal quasicrystal by anomalous X-ray scattering. Jpn J. Appl. Phys. 39, L1111–L1114 (2000).
Pennycook, S. J. & Boatner, L. A. Chemically sensitive structure imaging with a scanning transmission electron microscope. Nature 336, 565–567 (1988).
Pennycook, S. J. & Jesson, D. E. High-resolution Z-contrast imaging of crystals. Ultramicroscopy 37, 14–38 (1991); ibid High-resolution incoherent imaging of crystals. Phys. Rev. Lett. 64, 938–941 (1990).
Saitoh, K. et al. Structural study of an Al72Ni20Co8 decagonal quasicrystal using the high-angle annular dark-field method. Jpn J. Appl. Phys. 36, L1400–1402 (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. Geometriae Dedicata 62, 1–17 (1996).
Steinhardt, P. J. & Jeong, H.-C. A simpler approach to Penrose tiling with implications for quasicrystal formation. Nature 382, 433–435 (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).
Mihalkovic, M. et al. Total-energy-based prediction of a quasicrystal structure. Phys. Rev. B 65, 104205 (2002).
Goedecke, T. et al. Isothermal sections of phase equilibria in the Al-AlCo-AlNi system. Z. Metallkd. 89, 687–698 (1998).
Hume-Rothery, W. Researches on the nature, properties, and conditions of formation of intermetallic compounds, with special reference to certain compounds of tin.-I.-V. J. Inst. Met. 36, 295–361 (1926).
Ritsch, S. et al. The existence regions of structural modifications in decagonal Al-Co-Ni. Phil. Mag. Lett. 78, 67–75 (1998).
Hiraga, K. et al. Structural characteristics of Al-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, 2354–2367 (2001).
Bak, P. Phenomenological theory of icosahedral incommensurate (“quasiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517–1519 (1985).
Levine, D. et al. Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Phys. Rev. Lett. 54, 1520–1523 (1985).
Socolar, T., Lubensky, T. & Steinhardt, P. J. Phonons, phasons and dislocations in quasicrystals. Phys. Rev. B 34, 3345–3360 (1986).
Urban, K. & Feuerbacher, M. Structurally complex alloy phases. J. Non-Cryst. Solids 334–335, 143–150 (2004).
Lubensky, T. C. et al. Distortion and peak broadening in quasicrystal diffraction patterns. Phys. Rev. Lett. 57, 1440–1443 (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).
de Boissieu, M. et al. Diffuse scattering and phason elasticity in the AlPdMn icosahedral phase. Phys. Rev. Lett. 75, 89–92 (1995).
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).
Francoual, S. et al. Dynamics of phason fluctuations in the i-AlPdMn quasicrystal. Phys. Rev. Lett. 91, 225501 (2003).
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).
Abe, E., Pennycook, S. J. & Tsai, A. P. Direct observation of a local thermal vibration anomaly in a quasicrystal. Nature 421, 347–350 (2003).
Takakura, H., Yamamoto, A. & Tsai, A. P. The structure of decagonal Al72Ni20Co8 quasicrystal. Acta Crystallogr. A 57, 576–585 (2001).
Abe, H. et al. Anomalous Debye-Waller factor associated with an order-disorder transformation in an Al72Ni20Co8 decagonal quasicrystal. J. Phys. Soc. Jpn 72, 1828–1831 (2003).
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).
Keppens, V. et al. Localized vibrational modes in metallic solids. Nature 395, 876–878 (1998).
Cohn, J. L. et al. Glasslike heat conduction in high-mobility crystalline semiconductors. Phys. Rev. Lett. 82, 779–782 (1999).
Mizutani, U., Takeuchi, T. & Sato, H. Atomic structure determination, electronic structure calculations and interpretation of electron transport properties of various 1/1–1/1–1/1 approximants. J. Phys. Condens. Matter 14, R767–R788 (2002).
Macia, E. May quasicrystals be good thermoelectric materials? Appl. Phys. Lett. 77, 3045–3047 (2000).
Gomez, C. P. & Lindin, S. Comparative structural study of the disordered MCd6 quasicrystal approximants. Phys. Rev. B 68, 024203 (2003).
Fisher, I. R. et al. Growth of large-grain R – Mg – Zn quasicrystals from the ternary melt (R = Y, Er, Ho, Dy and Tb). Phil. Mag. B 77, 1601–1615 (1998).
Tsai, A. P., Guo, J. Q., Abe, E., Takakura, H. & Sato, T. J. A stable binary quasicrystal. Nature 408, 537–538 (2000).
Weickenmeier, A. & Kohl, H. Computation of absorptive form factors for high-energy electron diffraction. Acta Crystallogr. A 47, 590–597 (1991).
We are grateful to A. P. Tsai, K. Saitoh, P. J. Steinhardt, H.-C. Jeong and H. Takakura for collaboration, on which the present article is based. We also thank T. J. Sato, M. Widom, C. L. Henley, M. Miharcovic, W. Steurer, M. de Boissieu, A. Yamamoto, N. Tanaka, K. Ishizuka and H. Inui for valuable comments and discussions. E.A. acknowledges support from the CREST-JST 'Fundamental properties of quasicrystals' project (1996-2001, Project leader: A. P. Tsai). Y.Y. and S.J.P. acknowledge support from the US department of Energy under contract numbers DE-AC36-99GO10337 and DE-AC05-00OR22725.
The authors declare no competing financial interests.
About this article
Cite this article
Abe, E., Yan, Y. & Pennycook, S. Quasicrystals as cluster aggregates. Nature Mater 3, 759–767 (2004). https://doi.org/10.1038/nmat1244
Morphologies of intermetallic compound phases in Sn-Cu and Sn-Co peritectic alloys during directional solidification
China Foundry (2022)
Structural Chemistry (2020)
Structural Chemistry (2019)
Nature Communications (2018)
Structural Chemistry (2018)