Theoretical study of mixing energetics in homovalent fluorite-structured oxide solid solutions

Abstract Mixing energies (Δ H mix ) for fluorite-structured (Zr 1− x Ce x )O 2 and (Th 1− x Ce x )O 2 solid solutions are computed from density functional theory (DFT), employing cluster-expansion (CE), special-quasirandom-structure (SQS), and continuum-elasticity approaches. These systems are of interest as models for actinide-dioxide mixtures, due to the availability of calorimetric data which allows a direct assessment of the accuracy of the different computational methods for calculating Δ H mix in such fluorite-structured solid solutions. The DFT-based SQS and CE results for solid solutions with random configurational disorder are in very good agreement, and are used along with the calorimetry data to test the accuracy of a linear-elasticity model which allows predictions of the Δ H mix under the assumption that the dominant contribution in these homovalent solid solutions arises from elastic strain energy. The linear-elasticity models describe the mixing energies to within an accuracy of approximately 2 and 0.1 kJ/mol for the Zr and Th based systems, respectively. The excellent accuracy for the ThO 2 -based system is interpreted to result from the smaller size mismatch, and corresponding high accuracy of the linear elasticity approximation. We thus apply elasticity theory to estimate the magnitudes of Δ H mix for (Th 1− x M x )O 2 and (U 1− x M x )O 2 actinide-dioxide solid solutions, with M = U, Th, Ce, Np, Pu and Am, for which the degree of size mismatch is comparable to that in (Th 1− x Ce x )O 2 ; the results yield elastic contributions to Δ H mix with a maximum magnitude of 3 kJ/mol.