1. Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
2. Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
3. Department of Chemistry,
4. Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
5. These authors contributed equally to this work.

Correspondence to: Dmitri V. Talapin^1,2,5Elena V. Shevchenko^2,5 Correspondence and requests for materials should be addressed to D.V.T. (Email: dvtalapin@uchicago.edu) or E.V.S. (Email: eshevchenko@anl.gov).

Abstract

The discovery of quasicrystals in 1984 changed our view of ordered solids as periodic structures^{1, 2} and introduced new long-range-ordered phases lacking any translational symmetry^{3, 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 quasicrystals^{1, 3, 5}; quasicrystalline order has also been reported for the tantalum telluride phase with an approximate Ta_1.6Te 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.

1. Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
2. Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
3. Department of Chemistry,
4. Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
5. These authors contributed equally to this work.

Correspondence to: Dmitri V. Talapin^1,2,5Elena V. Shevchenko^2,5 Correspondence and requests for materials should be addressed to D.V.T. (Email: dvtalapin@uchicago.edu) or E.V.S. (Email: eshevchenko@anl.gov).

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