Multilayer Diffraction Reveals That Colloidal Superlattices Approach the Structural Perfection of Single Crystals

Colloidal superlattices are fascinating materials made of ordered nanocrystals, yet they are rarely called "atomically precise". That is unsurprising, given how challenging it is to quantify the degree of structural order in these materials. However, once that order crosses a certain threshold, the constructive interference of X-rays diffracted by the nanocrystals dominates the diffraction pattern, offering a wealth of structural information. By treating nanocrystals as scattering sources forming a self-probing interferometer, we developed a multilayer diffraction method that enabled the accurate determination of the nanocrystal size, interparticle spacing, and their fluctuations for samples of self-assembled CsPbBr3 and PbS nanomaterials. The multilayer diffraction method requires only a laboratory-grade diffractometer and an open-source fitting algorithm for data analysis. The average nanocrystal displacement of 0.33 to 1.43 Å in the studied superlattices provides a figure of merit for their structural perfection and approaches the atomic displacement parameters found in traditional crystals.