Prediction of the limits of isomorphous substitutions of strontium or barium by sodium and actinides for their immobilization in molybdates M1– <i>x</i> (Na0.5An0.5) <i>x</i> MoO4 (M = Sr or Ba) with a scheelite-type structure

Within the crystal energy theory of isomorphous substitutions, mixing energies (interaction parameters), critical decomposition temperatures (stability), limits of isomorphous substitutions, and capacities of isomorphous matrices concerning actinides were calculated. The thermodynamic stability regions of solid solutions in the Sr1–x(Na0.5An0.5)xMoO4 and Ba1–x(Na0.5An0.5)xMoO4 (where An denotes actinides) systems were evaluated. It has been shown that the magnitudes of the total mixing energy and critical decomposition temperatures are determined primarily by differences in the sizes of the substituting structural units and increase with the atomic number of the actinide. Decomposition domes of the solid solutions over the concentration range from x = 0 to 1.0 in increments of x = 0.05 are presented, allowing the determination of the decomposition temperature for a given composition, the equilibrium substitution limit at a given temperature, and the regions of thermodynamic stability. Under the temperature conditions recommended by the IAEA for radioactive waste disposal (below 373 K), continuous series of solid solutions Sr1–x(Na0.5An0.5)xMoO4 are thermodynamically stable in the case of actinides from Ac to Pu series, and are metastable or decompose for heavier actinides or in the case of solid solutions in the Ba1–x(Na0.5An0.5)xMoO4 systems. At 373 K, the isomorphous capacities (substitution limits) of SrMoO4 matrices concerning actinides were determined. The asymmetric solid solutions of the Ba1–x(Na0.5An0.5)xMoO4 systems follow not only the well-known Goldschmidt polarity (directionality) rule but also the second polarity (decomposition) rule of solid solutions previously proposed by us: “The decomposition temperature of an asymmetric regular solid solution at equal solute content is higher when based on the component with a smaller substituting structural unit size and lower when based on the component with a larger one.”