Formation of the cerium orthovanadateCeVO4:DFT+Ustudy

We report density functional theory calculations of the structural, electronic, and thermodynamic properties of cerium orthovanadate ($\mathrm{Ce}\mathrm{V}{\mathrm{O}}_{4}$) employing the local density approximation (LDA), generalized gradient approximation (GGA-PBE), $\mathrm{LDA}+U$, and $\mathrm{GGA}\text{\ensuremath{-}}\mathrm{PBE}+U$ functionals. The $\mathrm{LDA}+U$, $\mathrm{GGA}\text{\ensuremath{-}}\mathrm{PBE}+U$, LDA, and GGA-PBE equilibrium volumes deviate by $\ensuremath{-}2.4%$, $+3.6%$, $\ensuremath{-}7.4%$, and $\ensuremath{-}0.8%$, respectively, from experimental results. $\mathrm{DFT}+U$ (DFT) predicts an antiferromagnetic (ferromagnetic) insulating (metallic) ground state, which is in agreement with experimental observations. $\mathrm{DFT}+U$ yields Ce and V ions in the $III+$ and $V+$ oxidation state, respectively. $\mathrm{Ce}\mathrm{V}{\mathrm{O}}_{4}$ can be obtained by the reaction between ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ and ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ [$\frac{1}{2}{\mathrm{Ce}}_{2}{\mathrm{O}}_{3}(\mathrm{s})+\frac{1}{2}{\mathrm{V}}_{2}{\mathrm{O}}_{5}(\mathrm{s})\ensuremath{\rightarrow}\mathrm{Ce}\mathrm{V}{\mathrm{O}}_{4}(\mathrm{s})$] under an inert atmosphere, which is described as exoenergetic $(\ensuremath{\mid}\ensuremath{\Delta}{H}_{0}\ensuremath{\mid}=1.6\ensuremath{-}1.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ by all functionals. The reaction $\frac{1}{2}{\mathrm{Ce}}_{2}{\mathrm{O}}_{3}(\mathrm{s})+\frac{1}{2}{\mathrm{V}}_{2}{\mathrm{O}}_{5}(\mathrm{s})\ensuremath{\rightarrow}\mathrm{Ce}{\mathrm{O}}_{2}(\mathrm{s})+\mathrm{V}{\mathrm{O}}_{2}(\mathrm{s})$ is exoenergetic with $\ensuremath{\mid}\ensuremath{\Delta}{H}_{0}\ensuremath{\mid}=0.75$, 0.25, 1.70, and $1.24\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for $\mathrm{LDA}+U$, $\mathrm{GGA}\text{\ensuremath{-}}\mathrm{PBE}+U$, LDA, and GGA-PBE, respectively. Hence, ${\mathrm{V}}^{V+}$ is more easily reduced to ${\mathrm{V}}^{IV+}$ than ${\mathrm{Ce}}^{IV+}$ to ${\mathrm{Ce}}^{III+}$, but the difference is small as obtained with $\mathrm{DFT}+U$, $\mathrm{PBE}+U$, in particular. The variation of this reaction energy is due to the different performance of the various approaches for the description of the change in oxidation state of cerium, $IV+$ to $III+$ [J. L. F. Da Silva et al., Phys. Rev. B 75, 045121 (2007)]. The small difference between the ${\mathrm{V}}^{V}$ and ${\mathrm{Ce}}^{IV}$ reducibilities may have consequences for the use of $\mathrm{Ce}{\mathrm{O}}_{2}$ as support of ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ catalysts in selective oxidation.