A new equation of state for helium nanobubbles embedded in UO2 matrix calculated via molecular dynamics simulations

Abstract

Molecular dynamics simulations have been carried out to determine the equation of state of helium inside nanobubbles embedded into a UO2 matrix. The parameters of the equation of state are fitted with the Brearley and MacInnes hard-sphere model based on the formalism of Carnahan-Starling used in fuel performance codes. This new equation of state takes into account the interactions between the surrounding UO2 matrix and the helium atoms. Four nanobubble sizes (diameters: 1, 2, 5, and 10 nm) have been investigated over four temperatures (300, 500, 700, and 900 K) and for initial helium concentration inside the bubble ranging from 0.33×105 to 3.9×105 mol.m−3 (corresponding to helium-to-vacancy ratio of 0.3–3.3, respectively). We find that helium atoms are inhomogeneously distributed inside the bubble. A boundary layer of 1 nm thickness appears at the bubble surface in which helium atoms are more concentrated and diffuse into the UO2 matrix. We also find a saturation concentration of the helium atoms that can be incorporated into the bubble. This concentration limit is equal to 1.6 helium atom per vacancy in UO2. It corresponds to an atomic volume of 7.8×10−30 m3, which is almost half of the value proposed with the original Brearley and MacInnes model (13×10−30 m3). For this threshold concentration and for bubble of diameter higher than 5 nm, nano-cracks and dislocations appear at the bubble surface. However, experimental observation is needed to confirm this finding. We calculated the critical pressures inside the bubble which yields to this onset of crack in UO2. These critical pressures are in good agreement with those calculated with the Griffith criterion for brittle fracture.