Rendiconti Lincei

, Volume 24, Supplement 1, pp 85–91 | Cite as

Quasicrystals: a brief history of the impossible

  • Paul J. Steinhardt


The 30-year history of quasicrystals is one in which, time after time, the conventional scientific view about what is possible has been proven wrong. First, quasicrystals were thought to be mathematically impossible; then, physically impossible; then, impossible unless synthesised in the laboratory under carefully controlled conditions. One by one, these strongly held views have been disproven, the last only recently as the result of the discovery of a natural quasicrystal found in a meteorite dating back to the formation of the solar system. This paper is a brief personal perspective on this history of misunderstanding and discovery.


Quasicrystals Icosahedral symmetry Diffraction Icosahedrite 



I wish to thank the Accademia dei Lincei and the organizers of the X-ray diffraction centenary for the invitation and generous hospitality. This paper describes research spanning more than 30 years that is too broad in scope to name all those to who deserve recognition. In addition to those named in the text, I would like to acknowledge the University of Pennsylvania, its material research laboratory, and particularly Tom Lubensky, Eli Burstein, Anthony Garito, Paul Heiney and Paul Chaikin for extraordinary support and encouragement during the very early days when the ideas seemed unreasonably risky. Praveen Chaudhari and the Thomas J. Watson IBM research laboratory also provided key support. There are many others who contributed in important ways to this field but who have not been included; I ask for their understanding given the limited length and selection of topics. Although the paper is intended to represent a personal perspective, only statements supported by documentation (available on request) plus living witnesses have been included to insure fidelity. This work is supported in part by the by the National Science Foundation Materials Research Science and Engineering Center program through New York University Grant DMR-0820341.


  1. Bancel PA (1991) In: Steinhardt PJ, DiVincenzo D (eds) Quasicrystals: the state of the art. World Scientific, Singapore, pp 17–56CrossRefGoogle Scholar
  2. Bancel PA, Heiney PA, Stephens PW, Goldman AI, Horn PM (1985) Structure of rapidly quenched Al–Mn. Phys Rev Lett 54:2422–2425CrossRefGoogle Scholar
  3. Bancel PA, Heiney PA, Horn PA, Steinhardt PJ (1989) Comment on a paper by Linus Pauling. Proc Nat Acad Sci USA 86:8600–8601CrossRefGoogle Scholar
  4. Bindi L, Steinhardt PJ, Yao N, Lu PJ (2009) Natural quasicrystals. Science 324:1306–1309CrossRefGoogle Scholar
  5. Bindi L, Steinhardt PJ, Yao N, Lu PJ (2011) Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal. Am Mineral 96:928–931CrossRefGoogle Scholar
  6. Bindi L, Eiler J, Guan Y, Hollister LS, MacPherson GJ, Steinhardt PJ, Yao N (2012) Evidence for the extra-terrestrial origin of a natural quasicrystal. Proc Nat Acad Sci USA 109:1396–1401CrossRefGoogle Scholar
  7. Duneau M, Katz A (1985) Quasiperiodic patterns. Phys Rev Lett 54:2688–2691CrossRefGoogle Scholar
  8. Elser V (1986) The diffraction pattern of projected structures. Acta Cryst. A42:36–43Google Scholar
  9. Florescu M, Torquato S, Steinhardt PJ (2009) Designer materials with large, complete photonic band gaps. Proc Nat Acad Sci USA 106:20658–20663CrossRefGoogle Scholar
  10. Henley C (1991) Random tiling models. In: DiVincenzo D, Steinhardt PJ (eds) Quasicrystals: the state of the art. World Scientific, Singapore, pp 429–524Google Scholar
  11. Kalugin PA, Kitaev AYu, Levitov LS (1985) 6-dimensional properties of Al(86)Mn(14) alloy. J Physique Lett 46:L601–L607CrossRefGoogle Scholar
  12. Kramer P, Neri R (1984) On periodic and non-periodic space fillings of Em obtained by projection. Acta Cryst A40:580–587Google Scholar
  13. Levine D, Steinhardt PJ (1983) Crystalloids. Patent disclosure UPENN-9-23–83Google Scholar
  14. Levine D, Steinhardt PJ (1984) Quasicrystals: a new class of ordered structures. Phys Rev Lett 53:2477–2480CrossRefGoogle Scholar
  15. Lu PJ, Steinhardt PJ (2007) Decagonal and nearly-perfect quasicrystalline penrose tilings in medieval islamic architecture. Science 315:609–613CrossRefGoogle Scholar
  16. Lu PJ, Deffeyes K, Steinhardt PJ, Yao N (2001) Identifying and indexing icosahedral quasicrystals from powder diffraction patterns. Phys Rev Lett 87:275507CrossRefGoogle Scholar
  17. Mackay A (1981) De Nive Quinquangula: on the pentagonal snowflakes. Sov Phys Crystallogr 26:517–522Google Scholar
  18. Mackay A (1982) Crystallography and the penrose pattern. Physica A 114:609–613CrossRefGoogle Scholar
  19. Man W, Florescu M, Matsuyama K. Yadak, P, Steinhardt, Torquato S, Chaikin P (2012) Experimental observation of photonic bandgaps in hyperuniform disordered material, submittedGoogle Scholar
  20. Nelson DR, Halperin BI (1979) Dislocation-mediated melting in two dimensions. Phys Rev B 19:2457–2484CrossRefGoogle Scholar
  21. Nelson DR, Toner J (1981) Bond orientational order, dislocation loops and melting of solids and smectic–A liquid crystals. Phys Rev B 24:363–387CrossRefGoogle Scholar
  22. Onoda GY, Steinhardt PJ, DiVincenzo DP, Socolar JES (1988) Growing perfect quasicrystals. Phys Rev Lett 60:2653–2656CrossRefGoogle Scholar
  23. Pauling L (1985) Apparent icosahedral symmetry is due to directed, multiple twinning of cubic crystals. Nature 317:512–514CrossRefGoogle Scholar
  24. Pauling L (1989) Icosahedral quasicrystals of intermetallic compounds are icosahedral twins of cubic crystals of three kinds, consisting of large (about 5000 atoms) icosahedral complexes in either a cubic body-centered or a cubic face-centered arrangement or smaller (about 1350 atoms) icosahedral complexes in the beta-tungsten arrangement. Proc Nat Acad Sci USA 86:8595–8599CrossRefGoogle Scholar
  25. Penrose R (1974) The role of aesthetics in pure and applied mathematical research. Bull Inst Math Appl 10:266–271Google Scholar
  26. Razin LV, Rudashevskij NS, Vyalsov LN (1985) New natural intermetallic compounds of aluminum, copper and zinc—khatyrkite CuAl2, cupalite CuAl and zinc aluminides from hypui erbasites of dunite-harzburgite formation. Zapiski Vses Mineralog Obshch 114:90–100Google Scholar
  27. Shechtman D, Blech I (1985) The microstructure of rapidly solidified Al6Mn. Metallurgical Trans A16:1005–1012CrossRefGoogle Scholar
  28. Shechtman D, Blech I, Gratias D, Cahn J (1984) Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett 53:1951–1954CrossRefGoogle Scholar
  29. Steinhardt PJ, Bindi L (2012) In search of natural quasicrystals. Rep Prog Phys (in press)Google Scholar
  30. Steinhardt PJ, Nelson DR, Ronchetti M (1981) Icosahedral bond orientational order in supercooled liquids. Phys Rev Lett 47:1297–1300CrossRefGoogle Scholar
  31. Stephens PW, Goldman AI (1986) Sharp diffraction from an icosahedral glass. Phys Rev B 33:655–658CrossRefGoogle Scholar
  32. Torquato S, Stillinger FH (2003) Local density fluctuations, hyperuniformity, and order metrics. Phys Rev E 68(041113):1–25Google Scholar
  33. Tsai AP, Inoue A, Masumoto T (1987) A stable quasicrystal in Al–Cu–Fe system. Jap J Appl Phys 26:L1505CrossRefGoogle Scholar

Copyright information

© Accademia Nazionale dei Lincei 2012

Authors and Affiliations

  1. 1.Department of Physics, Princeton Center for Theoretical SciencePrinceton UniversityPrincetonUSA

Personalised recommendations