Energetics of mixing in ThO₂-CeO₂ fluorite solid solutions

Mixing enthalpies (ΔH_mix) of ThO₂-CeO ₂ solid solutions with respect to cubic fluorite ThO₂ and CeO₂ have been measured by high temperature oxide melt solution calorimetry. The system shows a slightly positive mixing enthalpy, with a maximum value of ΔH_mix = 3.7 ± 2.5 kJ/mol at 50% Ce/(Ce + Th). Based on the regular-solution model, with an interaction parameter of 15.1 ± 2.2 kJ/mol fit to the measured data, the phase diagram is predicted to feature a miscibility gap with a calculated critical temperature of 908 ± 132 K. The results are complemented by density-functional-theory and Monte-Carlo calculations, which provide positive mixing enthalpies and a miscibility-gap phase diagram, in qualitative agreement with calorimetric results. The calculations suggest small effects of short-range order (clustering) on the mixing enthalpy above the miscibility gap. The calculated values of ΔH_mix are within the error bars of the measured values, but consistently smaller in magnitude. An analysis of the calculated results indicates that the dominant contribution to the mixing enthalpy arises from the elastic energy associated with cation size mismatch, allowing predictions of the behavior in ThO₂-UO₂ and ThO ₂-PuO₂ systems. The analysis also suggests that the slightly smaller values of the computed ΔH_mix relative to experiment can be attributed to an underestimation of the magnitude of the elastic moduli in the calculations.