Evidence for subsurface ordering of oxygen vacancies on the reduced CeO2(111) surface using density-functional and statistical calculations.

Oxygen vacancies on ceria (CeO(2)) surfaces play a crucial role in catalytic applications, yet whether vacancies are at surface or subsurface sites on reduced CeO(2)(111), and whether vacancies agglomerate or repel each other, is still under discussion, with few and inconsistent experimental results. By combining density-functional theory (DFT) in the DFT+U (U is an effective onsite Coulomb interaction parameter) approach and statistical thermodynamics, we show that the energetically most stable near-surface oxygen vacancy structures for a broad range of vacancy concentrations, Θ (1/16 ≤ Θ ≤ 1 monolayer) have all vacancies at subsurface oxygen sites and predict that the thermodynamically stable phase for a wide range of reducing conditions is a (2 × 2) ordered subsurface vacancy structure (Θ = 1/4). Vacancy-induced lattice relaxations effects are crucial for the interpretation of the repulsive interactions, which are at the basis of the vacancy spacing in the (2 × 2) structure. The findings provide theoretical data to support the interpretation of the most recent experiments, bringing us closer to solving the debate.