Quasicrystalline order in self-assembled binary nanoparticle superlattices


The discovery of quasicrystals in 1984 changed our view of ordered solids as periodic structures1,2 and introduced new long-range-ordered phases lacking any translational symmetry3,4,5. Quasicrystals permit symmetry operations forbidden in classical crystallography, for example five-, eight-, ten- and 12-fold rotations, yet have sharp diffraction peaks. Intermetallic compounds have been observed to form both metastable and energetically stabilized quasicrystals1,3,5; quasicrystalline order has also been reported for the tantalum telluride phase with an approximate Ta1.6Te composition6. Later, quasicrystals were discovered in soft matter, namely supramolecular structures of organic dendrimers7 and tri-block copolymers8, and micrometre-sized colloidal spheres have been arranged into quasicrystalline arrays by using intense laser beams that create quasi-periodic optical standing-wave patterns9. Here we show that colloidal inorganic nanoparticles can self-assemble into binary aperiodic superlattices. We observe formation of assemblies with dodecagonal quasicrystalline order in different binary nanoparticle systems: 13.4-nm Fe2O3 and 5-nm Au nanocrystals, 12.6-nm Fe3O4 and 4.7-nm Au nanocrystals, and 9-nm PbS and 3-nm Pd nanocrystals. Such compositional flexibility indicates that the formation of quasicrystalline nanoparticle assemblies does not require a unique combination of interparticle interactions, but is a general sphere-packing phenomenon governed by the entropy and simple interparticle potentials. We also find that dodecagonal quasicrystalline superlattices can form low-defect interfaces with ordinary crystalline binary superlattices, using fragments of (33.42) Archimedean tiling as the ‘wetting layer’ between the periodic and aperiodic phases.

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Figure 1: Periodic binary superlattices self-assembled from 13.4-nm Fe 2 O 3 and 5-nm Au nanocrystals.
Figure 2: Dodecagonal quasicrystals self-assembled from spherical nanoparticles.
Figure 3: Structure of the interface between quasicrystalline and crystalline phases.


  1. 1

    Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)

    ADS  CAS  Article  Google Scholar 

  2. 2

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

    ADS  CAS  Article  Google Scholar 

  3. 3

    DiVincenzo, D. P. & Steinhardt, P. J. (eds). Quasicrystals: The State of the Art 2nd edn (World Scientific, 1999)

  4. 4

    Keys, A. S. & Glotzer, S. C. How do quasicrystals grow? Phys. Rev. Lett. 99, 235503 (2007)

    ADS  Article  Google Scholar 

  5. 5

    Abe, E., Yan, Y. & Pennycook, S. J. Quasicrystals as cluster aggregates. Nature Mater. 3, 759–767 (2004)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Conrad, M., Krumeich, F. & Harbrecht, B. A dodecagonal quasicrystalline chalcogenide. Angew. Chem. Int. Ed. 37, 1383–1386 (1998)

    Article  Google Scholar 

  7. 7

    Zeng, X. et al. Supramolecular dendritic liquid quasicrystals. Nature 428, 157–160 (2004)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Hayashida, K., Dotera, T., Takano, A. & Matsushita, Y. Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers. Phys. Rev. Lett. 98, 195502 (2007)

    ADS  Article  Google Scholar 

  9. 9

    Mikhael, J., Roth, J., Helden, L. & Bechinger, C. Archimedean-like tiling on decagonal quasicrystalline surfaces. Nature 454, 501–504 (2008)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Murray, C. B., Kagan, C. R. & Bawendi, M. G. Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies. Annu. Rev. Mater. Sci. 30, 545–610 (2000)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Shevchenko, E. V., Talapin, D. V., Kotov, N. A., O’Brien, S. & Murray, C. B. Structural diversity in binary nanoparticle superlattices. Nature 439, 55–59 (2006)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Eldridge, M. D., Madden, P. A. & Frenkel, D. Entropy-driven formation of a superlattice in a hard-sphere binary mixture. Nature 365, 35–37 (1993)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Shevchenko, E. V., Talapin, D. V., Murray, C. B. & O’Brien, S. Structural characterization of self-assembled multifunctional binary nanoparticle superlattices. J. Am. Chem. Soc. 128, 3620–3637 (2006)

    CAS  Article  Google Scholar 

  14. 14

    Leunissen, M. E. et al. Ionic colloidal crystals of oppositely charged particles. Nature 437, 235–240 (2005)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Kalsin, A. M. et al. Electrostatic self-assembly of binary nanoparticle crystals with a diamond-like lattice. Science 312, 420–424 (2006)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Grünbaum, B. & Shephard, G. C. Tilings and Patterns (Freeman, 1986)

    Google Scholar 

  17. 17

    Ueda, K., Dotera, T. & Gemma, T. Photonic band structure calculations of two-dimensional Archimedean tiling patterns. Phys. Rev. B 75, 195122 (2007)

    ADS  Article  Google Scholar 

  18. 18

    Frank, F. C. & Kasper, J. S. Complex alloy structures regarded as sphere packing. II. Analysis and classification of representative structures. Acta Crystallogr. 12, 483–499 (1959)

    CAS  Article  Google Scholar 

  19. 19

    Sopousek, J. & Kruml, K. Sigma-phase equilibrium and nucleation in Fe–Cr–Ni alloys at high temperature. Scripta Mater. 35, 689–693 (1996)

    CAS  Article  Google Scholar 

  20. 20

    Widom, M. Bethe ansatz solution of the square-triangle random tiling model. Phys. Rev. Lett. 70, 2094–2097 (1993)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Oxborrow, M. & Henley, C. L. Random square-triangle tilings: a model for twelve fold-symmetric quasicrystals. Phys. Rev. B 48, 6966–6998 (1993)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Leung, P. W., Henley, C. L. & Chester, G. V. Dodecagonal order in a two-dimensional Lennard-Jones system. Phys. Rev. B 39, 446–458 (1989)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  23. 23

    Ishimasa, T., Nissen, H.-U. & Fukano, Y. New ordered state between crystalline and amorphous in Ni-Cr particles. Phys. Rev. Lett. 55, 511–513 (1985)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Glotzer, S. C. & Keys, A. S. A tale of two tilings. Nature 454, 420–421 (2008)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Chen, Z. & O’Brien, S. Structure direction of II-VI semiconductor quantum dot binary nanoparticle superlattices by tuning radius ratio. ACS Nano 2, 1219–1229 (2008)

    CAS  Article  Google Scholar 

  26. 26

    Joseph, D. & Elser, V. A model of quasicrystal growth. Phys. Rev. Lett. 79, 1066–1069 (1997)

    ADS  CAS  Article  Google Scholar 

  27. 27

    Zoorob, M. E., Charlton, M. D. B., Parker, G. J., Baumberg, J. J. & Netti, M. C. Complete photonic bandgaps in 12-fold symmetric quasicrystals. Nature 404, 740–743 (2000)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Hyeon, T., Lee, S. S., Park, J., Chung, Y. & Na, H. B. Synthesis of highly crystalline and monodisperse maghemite nanocrystallites without a size-selection process. J. Am. Chem. Soc. 123, 12798–12801 (2001)

    CAS  Article  Google Scholar 

  29. 29

    Hines, M. A. & Scholes, G. D. Colloidal PbS nanocrystals with size-tunable near-infrared emission: observation of post-synthesis self-narrowing of the particle size distribution. Adv. Mater. 15, 1844–1849 (2003)

    CAS  Article  Google Scholar 

  30. 30

    Park, J. et al. Ultra-large-scale syntheses of monodisperse nanocrystals. Nature Mater. 3, 891–895 (2004)

    ADS  CAS  Article  Google Scholar 

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We thank S. O’Brien, W. Heiss, A. P. Alivisatos, T. Witten, W. Green and J. Urban for discussions and V. Altoe for help with analytical TEM studies. D.V.T. acknowledges support from the US National Science Foundation (NSF) CAREER Program under award number DMR-0847535 and the NSF MRSEC Program under award number DMR-0213745. M.I.B. acknowledges financial support from the Austrian Nanoinitiative. The work at the Center for Nanoscale Materials, Argonne National Laboratory, was supported by the US Department of Energy under contract number DE-AC02-06CH11357.

Author Contributions E.V.S. carried out experimental studies of the Fe2O3–Au nanoparticle system, M.I.B. studied the PbS–Pd system and X.Y. and J.C. studied the Fe3O4–Au system. D.V.T. analysed the experimental data. D.V.T. and C.B.M initiated and supervised the work. D.V.T and E.V.S. wrote the paper. All authors discussed the results and commented on the manuscript.

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Correspondence to Dmitri V. Talapin or Elena V. Shevchenko.

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Talapin, D., Shevchenko, E., Bodnarchuk, M. et al. Quasicrystalline order in self-assembled binary nanoparticle superlattices. Nature 461, 964–967 (2009). https://doi.org/10.1038/nature08439

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