A systematic first-principle study is conducted to calculate bulk modulus, elastic constants, phonon-dispersion curves, and electronic structures of ${\text{CeO}}_2$, ${\text{ThO}}_2$, and their ordered binary alloys ${\text{Ce}}_x{\text{Th}}_{8-x}{\text{O}}_{16}$ with $x=1$, 2, 4, 6, and 7 using local-density approximation (LDA), generalized gradient approximation (GGA), $\text{LDA}+U$, and $\text{GGA}+U$ approaches. In order to get accurate results for these type of systems including $f$ electrons [$\text{Ce}\left(4f\right)$ and $\text{Th}\left(5f\right)$] we optimized the $U$ parameter for use in $\text{LDA}+U$ and $\text{GGA}+U$ approaches. The computed structural, mechanical, and electronic properties of ${\text{CeO}}_2$ and ${\text{ThO}}_2$ are observed to display strong correlation with experimental data. In particular, the best agreement with experiment is obtained within the $\text{LDA}+U$ in which on-site Coulomb interaction parameter $\left(U_{eff}\right)$ for Ce and Th are taken as 6.0 and 5.0 eV. To check the stability of alloy forms, phonon-dispersion curves of ${\text{Ce}}_x{\text{Th}}_{8-x}{\text{O}}_{16}$ with $x=2$, 4, and 6 are computed. In all concentrations, mechanical stability conditions are satisfied for alloys. Furthermore, we observed no negative phonon branches in the phonon spectrum of alloys. Our calculations indicated a strong effect of concentration, $x$, on the electronic structure of ${\text{Ce}}_x{\text{Th}}_{8-x}{\text{O}}_{16}$.

• Received 30 April 2009

DOI:https://doi.org/10.1103/PhysRevB.80.014108