• periodic lattices;
  • nanomaterials;
  • self-assembly;
  • small-angle scattering

A formalism is described which enables the simulation or fitting of small-angle scattering data (X-ray or neutron) for periodic heterogeneous lattices of arbitrary nano-objects. Generality is maximized by allowing for particle mixtures, anisotropic nano-objects and definable orientations of nano-objects within the unit cell. The model is elaborated by including a variety of kinds of disorder relevant to self-assembling systems: finite grain size, polydispersity in particle properties, positional and orientation disorder of particles, and substitutional or vacancy defects within the lattice. The applicability of the approach is demonstrated by fitting experimental X-ray scattering data. In particular, the article provides examples of superlattices self-assembled from isotropic and anisotropic nanoparticles which interact through complementary DNA coronas.