A method to calculate equilibrium concentrations of gas and defects in the vicinity of an over-pressured bubble in UO2

Abstract

We present a method devised to calculate the equilibrium concentration of point defects and gas atoms in the vicinity of a bubble in UO2. First, we neglect the mechanical energy stored in the solid around an over-pressured bubble and then we explain how to take it into account. We apply the method to helium in interstitial positions in UO2, and compare our theoretical value of Henry’s constant with experiments and a molecular dynamics computation. Then, we apply the method to xenon in a Schottky defect and use it to assess the realism of two scenarios elaborated to explain the “paradox of annealing experiments”, i.e. “why a large proportion of gas is released from grains in annealing experiments on irradiated fuel, even though there are thousands of intragranular bubbles to trap the gas?” These two scenarios (thermal resolution or blockage of trapping due to the stress field around the bubbles) were both found to be unrealistic, at least with the formation energies available from ab initio calculations, and with the assumption made to calculate the Z3 term of the partition function. This term is related to the vibration frequencies of xenon atoms in Schottky defects and lattice atoms close to defects.