Fission gas in thoria

The fission gases Xe and Kr, formed during normal reactor operation, are known to degrade fuel performance, particularly at high burn-up. Using first-principles density functional theory together with a dispersion correction (DFT + D), in ThO₂ we calculate the energetics of neutral and charged point defects, the di-vacancy (DV), different neutral tri-vacancies (NTV), the charged tetravacancy (CTV) defect cluster geometries and their interaction with Xe and Kr. The most favourable incorporation point defect site for Xe or Kr in defective ThO₂ is the fully charged thorium vacancy. The lowest energy NTV in larger supercells of ThO₂ is NTV3, however, a single Xe atom is most stable when accommodated within a NTV1. The di-vacancy (DV) is a significantly less favoured incorporation site than the NTV1 but the CTV offers about the same incorporation energy. Incorporation of a second gas atom in a NTV is a high energy process and more unfavourable than accommodation within an existing Th vacancy. The bi-NTV (BNTV) cluster geometry studied will accommodate one or two gas atoms with low incorporation energies but the addition of a third gas atom incurs a high energy penalty. The tri-NTV cluster (TNTV) forms a larger space which accommodates three gas atoms but again there is a penalty to accommodate a fourth gas atom. By considering the energy to form the defect sites, solution energies were generated showing that in ThO₂−x the most favourable solution equilibrium site is the NTV1 while in ThO₂ it is the DV