Sinusoidal Displacement Describes Disorder in CsPbBr₃ Nanocrystal Superlattices

Disorder is an intrinsic feature of all solids, from crystals of atoms to superlattices of colloidal nanoparticles. Unlike atomic crystals, in nanocrystal superlattices, a single misplaced particle can affect the positions of neighbors over long distances, leading to cumulative disorder. This elusive form of collective particle displacement leaves clear signatures in diffraction, but little is known about how it accumulates and propagates throughout the superlattice. Here we rationalize the propagation and accumulation of disorder in a series of CsPbBr₃ nanocrystal superlattices by using synchrotron grazing incidence small- and wide-angle X-ray scattering. CsPbBr₃ nanocrystals of colloidal softness S in the range of 0.3-0.7 were obtained by preparing particles with different sizes and ligand mixtures consisting of oleic acid and primary amines of variable lengths. Most diffraction patterns showed clear signatures of anisotropic disorder, with multilayer diffraction characteristics of high structural coherence visible only for the {100} axial directions and lost in all other directions. As the softness decreased, the superlattices transitioned to a more ordered regime where small-angle diffraction peaks became resolution-limited, and superlattice multilayer diffraction appeared for the (110) diagonal reflections. To rationalize these anisotropies in structural coherence and their dependence on superlattice softness, we propose a sinusoidal displacement model where longitudinal and transverse displacements modulate nanocrystal positions. The model explains experimental observations and advances the understanding of disorder in mesocrystalline systems as they approach the limits of structural perfection.