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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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.
This file contains Supplementary Notes, and Supplementary Figures 1-9 with Legends.
About this article
Materials Chemistry Frontiers (2019)