The formalism of electronic density-functional theory (DFT), with Hubbard-U corrections ($\text{DFT}+U$), is employed in a computational study of the energetics of fluorite-structured U${}_{1-x}$Ce${}_x$O${}_2$ mixtures. The computational approach makes use of a procedure which facilitates convergence of the calculations to multiple self-consistent $\text{DFT}+U$ solutions for a given cation arrangement, corresponding to different charge states for the U and Ce ions in several prototypical cation arrangements. Results indicate a significant dependence of the structural and energetic properties on the nature of both charge and cation ordering. With the effective Hubbard-U parameters that reproduce well the measured oxidation-reduction energies for urania and ceria, we find that charge transfer between U${}^{4+}$ and Ce${}^{4+}$ ions, leading to the formation of U${}^{5+}$ and Ce${}^{3+}$, gives rise to an increase in the mixing energy in the range of 4–14 kJ/mol of the formula unit, depending on the nature of the cation ordering. The results suggest that although charge transfer between uranium and cerium ions is disfavored energetically, it is likely to be entropically stabilized at the high temperatures relevant to the processing and service of urania-based solid solutions.

• Received 7 December 2010

DOI:https://doi.org/10.1103/PhysRevB.84.085131