When nanoparticles (NPs) are assembled from solution, a common assembly method of choice is either solution destabilization or solvent evaporation technique. The destabilization of the NP solution by non-solvents results in the formation of faceted supercrystals (SCs) while periodic film-like assemblies are typically formed by solvent evaporation. Here, we reveal the effect of non-solvents in washing, dispersing, and crystallizing NPs. Small angle neutron scattering (SANS) is employed for monitoring the ligand shell of NPs in solutions upon introduction of various non-solvents. The SC crystallization process is traced in situ with small-angle X-ray scattering (SAXS), and the structures of the resulting single-crystalline SCs are examined in detail by mapping the reciprocal space using SAXS and wide-angle X-ray scattering. Our study suggests that the relative miscibility of the non-solvent with solvents and ligands 4111 determines the solvation and thickness of the ligand shell and thereby the resulting structure of SCs. In the early stage of crystallization, truncated octahedral PbS NPs form SCs with face-centered cubic (fcc) symmetry. In the later stage, the fcc symmetry is preserved in the SC formed by larger (5.60 nm) NPs, but the SC assembled from smaller (4.14 nm) NPs undergoes a phase transition into body-centered cubic (bcc) lattice via Bain transformation, becoming a polycrystalline SC containing three structurally correlated bcc domains and one untransformed fcc domain. Our study provides the detailed understanding of the non-solvent effect that impacts beyond the formation of SCs, enabling the judicious selection of solvent/non-solvent mixtures for NP purification.