Surface structure and morphology of M[CoM′]O4M[CoM′]O_{4} (M = Mg, Zn, Fe, Co and M′ = Ni, Al, Mn, Co) spinel nanocrystals––DFT+U and TEM screening investigations

Plane wave periodic GGA-PBE+U density functional theory calculations were used to study the structure, surface energy, and equilibrium shape of faceted nanocrystals for a series of cubic (Fd3m) 2–3 AB2O4 spinels with the following formula: Co[Co2]O4, Mg[Co2]O4, Zn[Co2]O4, Co[NiCo]O4, Co[MnCo]O4, Fe[FeCo]O4, and Co[Al2]O4. Their bulk geometries (lattice constants and oxygen u parameters) as well as electronic and magnetic properties were computed and compared with experimental data. All planes, (100), (110), and (111), exposed by the spinel nanocrystallites of equilibrium morphology were taken into account, and their atomic structure, reconstruction, and stabilization were elucidated and systematized in terms of the structural oxygen u parameter. The strongest relaxation of the A cations was observed for the (100) plane, whereas that for the B cations was on the (111) plane. By using the calculated surface energy values, the shapes of the spinel nanocrystallites were predicted by means of the Wulff construction and classified according to their shapes into singly and doubly truncated hexahedra (rhombicuboctahedra) and truncated octahedra. The results were compared with experimental TEM and STEM pictures, corroborated by image simulation