Phase stability, electronic structures and elastic properties of (U,Np)O₂ and (Th,Np)O₂ mixed oxides

Mixing enthalpies (ΔHmix) of U1-xNpxO2 and Th1-xNpxO2 solid solutions are derived from atomic scale simulations based on density functional theory (DFT) employing the generalised gradient approximation corrected with an effective Hubbard parameter (Ueff). The variation of structural and electronic properties of UO2 and NpO2 with collinear ferromagnetic (FM), collinear anti-ferromagnetic (AFM) and non-collinear anti-ferromagnetic arrangements of the uranium and neptunium magnetic moments are investigated while ramping up Ueff from 0 eV to 4 eV (the Ueff-ramping method). A combination of the Ueff-ramping method to treat the presence of metastable magnetic states and special-quasirandom structures (SQS) for the random distribution of Np atoms in UO2 and ThO2 is employed to calculate ΔHmix of U1-xNpxO2 and Th1-xNpxO2 mixed oxides (MOX). The effect of collinear FM and AFM ordering is also considered in determining the ΔHmix. The calculated ΔHmix of Th1-xNpxO2 MOX were positive compared to the end members and nearly symmetric around x = 0.5 and ΔHmix of the AFM configuration were higher compared to the FM configuration maximum by 0.19 kJ mol-1. The ΔHmix of U1-xNpxO2 MOX were negative up to U0.50Np0.50O2 with a maximum value of -1.21 kJ mol-1 for U0.4375Np0.5625O2 whereas Np-rich (U,Np)O2 MOX compositions exhibited ΔHmix close to zero. Values of ΔHmix for (Th,Np)O2 are consistent with a simple miscibility-gap phase diagram while those for (U,Np)O2 suggest more complex behaviour. Nevertheless, lattice parameter variation with composition still follows a Vegard's law relationship. Finally, single crystal elastic constants of pure oxides and MOX are reported. The linear-elasticity models describe the mixing energies to within an accuracy of approximately 1 kJ mol-1 for the U1-xNpxO2 and Th1-xNpxO2 MOX systems.