A refined analysis of oxygen potential of M_yU_1-yO_2+x (M = M³⁺and M2+) by lattice statistics based on the grand partition function and the Flory methods

Partial molar thermodynamic quantities (ΔG_O2, ΔS_O2and ΔH_O2) of solid solutions M_yU_1-yO_2+x (M = M³⁺and M²⁺, x{greater-than above equal above less-than}0) were calculated using a cation-cation complex model in combination with the lattice statistics based on the grand partition function method or the Flory method. With these refined methods, configurational entropies were obtained without any discrepancies between the numbers of lattice sites and the sum of ions and complexes. The cation-cation complex model assumes the formation of (M³⁺U⁵⁺) complex for M_y³U_1-yO_2+x while two kinds of complexes, i.e. (M²⁺U⁵⁺) and M²⁺2U⁵⁺ for M_y²⁺U_1-yO_2+x. The experimental results that the steepest change of ΔG_O2 arises at x < 0 for M_y²⁺U_1-yO_2+x were well explained by the relation of this model, i.e. x = -(1 - α/2)y with 1 < α < 2. The calculated ΔG_O2 values were in good agreement with the experimental results for lanthanum, magnesium and europium solid solutions.