Understanding Fe₃O₄ Nanocube Assembly with Reconstruction of a Consistent Superlattice Phase Diagram

Nanocube (NC) assemblies display complex superlattice behaviors, which require a systematic understanding of their nucleation and growth as well transformation toward construction of a consistent superlattice phase diagram. This work made use of Fe₃O₄ NCs with controlled environments, and assembled NCs into three-dimensional (3D) superlattices of simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc), acute and obtuse rhombohedral (rh) polymorphs, and 2D superlattices of square and hexagon. Controlled experiments and computations of in situ and static small-angle X-ray scattering (SAXS) as well as electron microscopic imaging revealed that the fcc and bcc polymorphs preferred a primary nucleation at the early stage of NC assembly, which started from the high packing planes of fcc(111) and bcc(110), respectively, in both 3D and 2D cases. Upon continuous growth of superlattice grain (or domain), a confinement stress appeared and distorted fcc and bcc into acute and obtuse rh polymorphs, respectively. The variable magnitudes of competitive interactions between configurational and directional entropy determine the primary superlattice polymorph of either fcc or bcc, while emergent enhancement of confinement effect on enlarged grains attributes to late developed superlattice transformations. Differently, the formation of a sc polymorph requires a strong driving force that either emerges simultaneously or is applied externally so that one easy case of the sc formation can be achieved in 2D thin films. Unlike the traditional Bath deformation pathway that involves an intermediate body-centered tetragonal lattice, the observed superlattice transformations in NC assembly underwent a simple rhombohedral distortion, which was driven by a growth-induced in-plane compressive stress. Establishment of a consistent phase diagram of NC-based superlattices and reconstruction of their assembly pathways provide critical insight and a solid base for controlled design and scalable fabrication of nanocube-based functional materials with desired superlattices and collective properties for real-world applications.