Meso-crystallographic study of a three-dimensional self-assembled bimodal nanocrystal superlattice

Nanocrystal superlattices are attracting significant interest due to novel and peculiar collective properties arising from the interactions of the nanocrystals forming the superlattice. A large variety of superlattice structures can be obtained, involving one or more types of nanocrystals, with different sizes and concentrations. Engineering of the superlattice properties relies on accurate structural and morphological characterization, able to provide not only a fundamental feedback for synthesis procedures, but also relevant insight into their structural properties for possible applications. Electron microscopy and X-ray based techniques are complementary approaches for nanoscale structural imaging, which however become challenging in the presence of building blocks only a few nanometers in size. Here, a structure solution for a three-dimensional (3D) self-assembly of PbS nanocrystals with bimodal size distribution is obtained, by exploiting small-angle X-ray diffraction, transmission electron microscopy, crystallographic procedures, and geometric constraints. In particular, analysis of small-angle X-ray diffraction data, based on the Patterson function and on the single crystal model, is shown to provide relevant information on the 3D superlattice structure as well as on particle size, the scattering signal being sensitive to particles as small as 1.5 nm. The combined approach here proposed is thus demonstrated to effectively overcome important resolution limitations in the imaging of superlattices including small nanocrystals.