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

Mixing energies (ΔH_mix) for fluorite-structured (Zr _1-xCe_x)O₂ and (Th_1-xCe _x)O₂ 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 ΔH_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 ΔH_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 ThO₂-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 ΔH_mix for (Th_1-xM_x)O₂ and (U_1-xM_x)O₂ 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-xCe_x)O₂; the results yield elastic contributions to ΔH_mix with a maximum magnitude of 3 kJ/mol.