Thermodynamic properties of ThxU1−xO2 (0 < x < 1) based on quantum-mechanical calculations and Monte-Carlo simulations

Th_xU_1−xO_2+y binary compositions occur in nature, uranothorianite, and as a mixed oxide nuclear fuel. As a nuclear fuel, important properties, such as the melting point, thermal conductivity, and the thermal expansion coefficient change as a function of composition. Additionally, for direct disposal of Th_xU_1−xO₂, the chemical durability changes as a function of composition, with the dissolution rate decreasing with increasing thoria content. UO₂ and ThO₂ have the same isometric structure, and the ionic radii of 8-fold coordinated U⁴⁺ and Th⁴⁺ are similar (1.14 nm and 1.19 nm, respectively). Thus, this binary is expected to form a complete solid solution. However, atomic-scale measurements or simulations of cation ordering and the associated thermodynamic properties of the Th_xU_1−xO₂ system have yet to be determined. A combination of density-functional theory, Monte-Carlo methods, and thermodynamic integration are used to calculate thermodynamic properties of the Th_xU_1−xO₂ binary (ΔH_mix, ΔG_mix, ΔS_mix, phase diagram). The Gibbs free energy of mixing (ΔG_mix) shows a miscibility gap at equilibration temperatures below 1000 K (e.g., E_exsoln = 0.13 kJ/(mol cations) at 750 K). Such a miscibility gap may indicate possible exsolution (i.e., phase separation upon cooling). A unique approach to evaluate the likelihood and kinetics of forming interfaces between U-rich and Th-rich has been chosen that compares the energy gain of forming separate phases with estimated energy losses of forming necessary interfaces. The result of such an approach is that the thermodynamic gain of phase separation does not overcome the increase in interface energy between exsolution lamellae for thin exsolution lamellae (10 Å). Lamella formation becomes energetically favorable with a reduction of the interface area and, thus, an increase in lamella thickness to >45 Å. However, this increase in lamellae thickness may be diffusion limited. Monte-Carlo simulations converge to an exsolved structure [lamellae || ] only for very low equilibration temperatures (below room temperature). In addition to the weak tendency to exsolve, there is an ordered arrangement of Th and U in the solid solution [alternating U and Th layers || {1 0 0}] that is energetically favored for the homogeneously mixed 50% Th configurations. Still, this tendency to order is so weak that ordering is seldom reached due to kinetic hindrances. The configurational entropy of mixing (ΔS_mix) is approximately equal to the point entropy at all temperatures, indicating that the system is not ordered.