Skip to main content
Log in

Quasicrystals: a brief history of the impossible

  • SI: XR DIFFRACTION
  • Published:
Rendiconti Lincei Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bancel PA (1991) In: Steinhardt PJ, DiVincenzo D (eds) Quasicrystals: the state of the art. World Scientific, Singapore, pp 17–56

    Chapter  Google Scholar 

  • Bancel PA, Heiney PA, Stephens PW, Goldman AI, Horn PM (1985) Structure of rapidly quenched Al–Mn. Phys Rev Lett 54:2422–2425

    Article  CAS  Google Scholar 

  • Bancel PA, Heiney PA, Horn PA, Steinhardt PJ (1989) Comment on a paper by Linus Pauling. Proc Nat Acad Sci USA 86:8600–8601

    Article  CAS  Google Scholar 

  • Bindi L, Steinhardt PJ, Yao N, Lu PJ (2009) Natural quasicrystals. Science 324:1306–1309

    Article  CAS  Google Scholar 

  • Bindi L, Steinhardt PJ, Yao N, Lu PJ (2011) Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal. Am Mineral 96:928–931

    Article  CAS  Google Scholar 

  • 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 109:1396–1401

    Article  CAS  Google Scholar 

  • Duneau M, Katz A (1985) Quasiperiodic patterns. Phys Rev Lett 54:2688–2691

    Article  Google Scholar 

  • Elser V (1986) The diffraction pattern of projected structures. Acta Cryst. A42:36–43

    CAS  Google Scholar 

  • Florescu M, Torquato S, Steinhardt PJ (2009) Designer materials with large, complete photonic band gaps. Proc Nat Acad Sci USA 106:20658–20663

    Article  CAS  Google Scholar 

  • Henley C (1991) Random tiling models. In: DiVincenzo D, Steinhardt PJ (eds) Quasicrystals: the state of the art. World Scientific, Singapore, pp 429–524

  • Kalugin PA, Kitaev AYu, Levitov LS (1985) 6-dimensional properties of Al(86)Mn(14) alloy. J Physique Lett 46:L601–L607

    Article  Google Scholar 

  • Kramer P, Neri R (1984) On periodic and non-periodic space fillings of Em obtained by projection. Acta Cryst A40:580–587

    Google Scholar 

  • Levine D, Steinhardt PJ (1983) Crystalloids. Patent disclosure UPENN-9-23–83

  • Levine D, Steinhardt PJ (1984) Quasicrystals: a new class of ordered structures. Phys Rev Lett 53:2477–2480

    Article  CAS  Google Scholar 

  • Lu PJ, Steinhardt PJ (2007) Decagonal and nearly-perfect quasicrystalline penrose tilings in medieval islamic architecture. Science 315:609–613

    Article  Google Scholar 

  • Lu PJ, Deffeyes K, Steinhardt PJ, Yao N (2001) Identifying and indexing icosahedral quasicrystals from powder diffraction patterns. Phys Rev Lett 87:275507

    Article  CAS  Google Scholar 

  • Mackay A (1981) De Nive Quinquangula: on the pentagonal snowflakes. Sov Phys Crystallogr 26:517–522

    Google Scholar 

  • Mackay A (1982) Crystallography and the penrose pattern. Physica A 114:609–613

    Article  Google Scholar 

  • Man W, Florescu M, Matsuyama K. Yadak, P, Steinhardt, Torquato S, Chaikin P (2012) Experimental observation of photonic bandgaps in hyperuniform disordered material, submitted

  • Nelson DR, Halperin BI (1979) Dislocation-mediated melting in two dimensions. Phys Rev B 19:2457–2484

    Article  CAS  Google Scholar 

  • Nelson DR, Toner J (1981) Bond orientational order, dislocation loops and melting of solids and smectic–A liquid crystals. Phys Rev B 24:363–387

    Article  CAS  Google Scholar 

  • Onoda GY, Steinhardt PJ, DiVincenzo DP, Socolar JES (1988) Growing perfect quasicrystals. Phys Rev Lett 60:2653–2656

    Article  CAS  Google Scholar 

  • Pauling L (1985) Apparent icosahedral symmetry is due to directed, multiple twinning of cubic crystals. Nature 317:512–514

    Article  CAS  Google Scholar 

  • 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 86:8595–8599

    Article  CAS  Google Scholar 

  • Penrose R (1974) The role of aesthetics in pure and applied mathematical research. Bull Inst Math Appl 10:266–271

    Google Scholar 

  • 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 114:90–100

    CAS  Google Scholar 

  • Shechtman D, Blech I (1985) The microstructure of rapidly solidified Al6Mn. Metallurgical Trans A16:1005–1012

    Article  Google Scholar 

  • Shechtman D, Blech I, Gratias D, Cahn J (1984) Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett 53:1951–1954

    Article  CAS  Google Scholar 

  • Steinhardt PJ, Bindi L (2012) In search of natural quasicrystals. Rep Prog Phys (in press)

  • Steinhardt PJ, Nelson DR, Ronchetti M (1981) Icosahedral bond orientational order in supercooled liquids. Phys Rev Lett 47:1297–1300

    Article  CAS  Google Scholar 

  • Stephens PW, Goldman AI (1986) Sharp diffraction from an icosahedral glass. Phys Rev B 33:655–658

    Article  CAS  Google Scholar 

  • Torquato S, Stillinger FH (2003) Local density fluctuations, hyperuniformity, and order metrics. Phys Rev E 68(041113):1–25

    Google Scholar 

  • Tsai AP, Inoue A, Masumoto T (1987) A stable quasicrystal in Al–Cu–Fe system. Jap J Appl Phys 26:L1505

    Article  CAS  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paul J. Steinhardt.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Steinhardt, P.J. Quasicrystals: a brief history of the impossible. Rend. Fis. Acc. Lincei 24 (Suppl 1), 85–91 (2013). https://doi.org/10.1007/s12210-012-0203-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12210-012-0203-3

Keywords

Navigation