Fig. 4.

First-principles calculations performed on stoichiometric CeO₂ and non-stoichiometric CeO_1.5. a Structural projections along the [100] and [110] directions for stoichiometric CeO₂. b Structural projections along the [100] and [110] directions for non-stoichiometric CeO_1.5, where the $V_O^{\bullet \bullet }$ are self-organised into clustered one-dimensional tunnels oriented in the [001] direction. c Effect of $\left[V_O^{\bullet \bullet }\right]$ on calculated spin-polarised total density of electronic states, showing spin-up (positive) and spin-down (negative) regions (Fermi energy levels shifted to zero). d Structural projections along the [100] direction for stoichiometric CeO₂ and non-stoichiometric CeO_1.5; surfaces of identical electronic charge are highlighted with blue colour; the electronic density increases around the Ce ions, which are located near the oxygen vacancies, compared to the stoichiometric system. Large yellow and small red spheres represent Ce and O ions, respectively