Quasicrystalline order in self-assembled binary nanoparticle superlattices

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(3-5). Quasi-crystals 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 Ta1.6Te composition(6). Later, quasicrystals were discovered in soft matter, namely supramolecular structures of organic dendrimers(7) and tri-block copolymers(8), and micrometre-sized colloidal spheres have been arranged into quasicrystalline arrays by using intense laser beams that create quasi-periodic optical standing-wave patterns(9). 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 (3(3).4(2)) Archimedean tiling as the 'wetting layer' between the periodic and aperiodic phases.