Theoretical study ofCeO2doped with tetravalent ions

We have used density functional theory calculations within the $\mathrm{LDA}+U$ formulation to investigate how small amounts of dissolved $\mathrm{Si}{\mathrm{O}}_{2}$, $\mathrm{Ge}{\mathrm{O}}_{2}$, $\mathrm{Sn}{\mathrm{O}}_{2}$, or $\mathrm{Pb}{\mathrm{O}}_{2}$ affect the redox thermodynamics of ceria $(\mathrm{Ce}{\mathrm{O}}_{2})$. Compared to pure ceria, reduction is facilitated and the reducibility increases in the sequence of $\mathrm{Ce}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{Sn}{\mathrm{O}}_{2}$, $\mathrm{Ce}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{Ge}{\mathrm{O}}_{2}$, and $\mathrm{Ce}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{Si}{\mathrm{O}}_{2}$, which correlates with the decrease of the ionic radii of the solutes. For low solute concentrations, there is an inverse relation between high reducibility and the solution energy of tetravalent solutes. $\mathrm{Ce}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{O}}_{2}$ is unique in the sense that the initial reduction occurs by $\mathrm{Pb}(IV)\ensuremath{\Rightarrow}\mathrm{Pb}(II)$ instead of the usual $\mathrm{Ce}(IV)\ensuremath{\Rightarrow}\mathrm{Ce}(III)$ reaction. Among the investigated ceria compounds, $\mathrm{Ce}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{O}}_{2}$ has the lowest reduction energy and rather low solution energy. We have studied how the solution and reduction energies depend on the concentration of Si, Ge, Sn, Pb, Ti, Zr, Hf, and Th solute ions. While the solution energy increases monotonously with concentration, the reduction energy first decreases, as compared to pure ceria (except for Th, which exhibits a small increase), and with further increase of solute concentration, it either remains almost constant (Zr, Hf, and Th) or slightly increases (Ti, Si, Ge, and Sn).