document: Following fission, noble gas atoms will be distributed in the fuel matrix initially accommodated at point defects trap sites, generally thought to be Schottky trivacancy defects [4,5,31]. Diffusion to either bubbles or grain boundaries is then facilitated by associating a further uranium vacancy defect for the gas atom to ‘hop’ into, with the original vacancy then able to loop around to ensure continued diffusion. The rate determining step in the process is not the migration of the Xe itself but rather the rearrangement of the VU defect to facilitate net Xe diffusion [6–8]. Activation energies for the overall process depend on the availability of the defect trap sites, which in turn depends on the crystal stoichiometry. For Xe diffusion in UO2−x, UO2 and UO2+x the activation energies calculated using DFT are 7.04–12.92 eV, 4.15–7.88 eV and 1.38–4.07 eV with the ranges reflecting the way the calculations were performed depending on the charge states of the defects involved and the presence of a Jahn–Teller distortion [7]. Activation energies calculated using empirical pair potentials can vary strongly depending on the choice of potential. Govers et al. examined three different potentials for UO2 (those of Basak [9], Jackson [10] and Morelon [11]) coupled with different parameterisations for the U–Xe and O–Xe interactions from Geng [12] and Nicoll [13] and recommend values of 6.5 eV, 4.5 eV and 2.4 eV [6] for the different stoichiometric regimes in very good agreement with the experimental values of 6.0 eV, 3.9 eV and 1.7 eV respectively [14].
extractive_keyphrases: activation bubbles charge crystal defect trap sites dft diffusion empirical pair potentials fission fuel matrix gas atom grain boundaries ‘hop’ into jahn–teller distortion loop around migration noble gas atoms o–xe point defects trap sites potential potentials rearrangement schottky trivacancy defects uo2 uo2−x uranium u–xe vu xe
abstractive_keyphrases: crystal stoichiometry uo2+x vu defect xe diffusion