Quasicrystalline nanocrystal superlattice with partial matching rules.

Expanding the library of self-assembled superstructures provides insight into the behaviour of atomic crystals and supports the development of materials with mesoscale order. Here we build on recent findings of soft matter quasicrystals and report a quasicrystalline binary nanocrystal superlattice that exhibits correlations in the form of partial matching rules reducing tiling disorder. We determine a three-dimensional structure model through electron tomography and direct imaging of surface topography. The 12-fold rotational symmetry of the quasicrystal is broken in sublayers, forming a random tiling of rectangles, large triangles and small triangles with 6-fold symmetry. We analyse the geometry of the experimental tiling and discuss factors relevant for the stabilization of the quasicrystal. Our joint experimental-computational study demonstrates the power of nanocrystal superlattice engineering and further narrows the gap between the richness of crystal structures found with atoms and in soft matter assemblies.