Atomic-Scale Valence State Distribution inside Ultrafine CeO₂ Nanocubes and Its Size Dependence

Atomic-scale analysis of the cation valence state distribution will help to understand intrinsic features of oxygen vacancies (V_O) inside metal oxide nanocrystals, which, however, remains a great challenge. In this work, the distribution of cerium valence states across the ultrafine CeO₂ nanocubes (NCs) perpendicular to the {100} exposed facet is investigated layer-by-layer using state-of-the-art scanning transmission electron microscopy-electron energy loss spectroscopy. The effect of size on the distribution of Ce valence states inside CeO₂ NCs is demonstrated as the size changed from 11.8 to 5.4 nm, showing that a large number of Ce³⁺ cations exist not only in the surface layers, but also in the center layers of smaller CeO₂ NCs, which is in contrast to those in larger NCs. Combining with the atomic-scale analysis of the local structure inside the CeO₂ NCs and theoretical calculation on the V_O forming energy, the mechanism of size effect on the Ce valence states distribution and lattice expansion are elaborated: nano-size effect induces the overall lattice expansion as the size decreased to ≈5 nm; the expanded lattice facilitates the formation of V_O due to the lower formation energy required for the smaller size, which, in principle, provides a fundamental understanding of the formation and distribution of Ce³⁺ inside ultrafine CeO₂ NCs.