We report a first-principles investigation of the energetics and structure properties of $\mathrm{Ce}{\mathrm{O}}_{1.50}$ in the hexagonal $\left({\mathrm{La}}_2{\mathrm{O}}_3\right)$, cubic (bixbyite), and monoclinic structures. Our calculations are based on density functional theory within the local density approximation (LDA), generalized gradient approximation (GGA), $\mathrm{LDA}+U$, and $\mathrm{GGA}+U$ functionals. The hexagonal (cubic) structure is $53\mathrm{meV}∕\mathrm{Ce}{\mathrm{O}}_{1.50}$ $(57\mathrm{meV}∕\mathrm{Ce}{\mathrm{O}}_{1.50})$ lower in energy than the cubic (hexagonal) structure using $\mathrm{LDA}+U$ $(\mathrm{GGA}+U)$, which is consistent (in disagreement) with experimental observations. Thus, these results might indicate a superior description of cerium oxides by the $\mathrm{LDA}+U$ functional. We found that $V_0^{\mathrm{Ce}{\mathrm{O}}_{1.50},\text{hexagonal}}\approx V_0^{\mathrm{Ce}{\mathrm{O}}_2,\text{fluorite}}$, while $V_0^{\mathrm{Ce}{\mathrm{O}}_{1.50},\text{cubic}}$ is 4%–9% larger than $V_0^{\mathrm{Ce}{\mathrm{O}}_2,\text{fluorite}}$, where $V_0$ is the equilibrium volume per f.u. Therefore, only the results for $\mathrm{Ce}{\mathrm{O}}_{1.50}$ in the cubic structure can explain the volume expansion of $\mathrm{Ce}{\mathrm{O}}_2$ upon reduction conditions, which supports experimental observations of a cubiclike structure for partially reduced $\mathrm{Ce}{\mathrm{O}}_2$. The volume expansion is due to the change in the oxidation state of the Ce atoms from ${\mathrm{Ce}}^{\mathrm{IV}+}$ in $\mathrm{Ce}{\mathrm{O}}_2$ to ${\mathrm{Ce}}^{\mathrm{III}+}$ in $\mathrm{Ce}{\mathrm{O}}_{1.50}$ without changes in the lattice structure.

• Received 26 July 2007

DOI:https://doi.org/10.1103/PhysRevB.76.193108