A new equation of state for helium nanobubbles embedded in UO$_2$ matrix calculated via molecular dynamics simulations

Laurent van Brutzel (1, 2) , Alain Chartier (1, 2)

1 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
2 SCCME - Service de la Corrosion et du Comportement des Matériaux dans leur Environnement

Molecular dynamics simulations have been carried out to determine the equation of state of helium inside nanobubbles embedded into UO$_2$ matrix.The parameters of this 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 UO$_2$ 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 x 10$^5$ to 3.9 x 10$^5$ mol.m$^{-3}$ (corresponding to helium-to-vacancy ratio of 0.3-3.3, respectively). We observe 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 UO$_2$ matrix. We also observe a saturation of the helium atoms that can be incorporated into the bubble.This concentration limit is equal to 1.6 helium atom per vacancy in UO$_2$. It corresponds to an atomic volume of 7.8 x 10$^{-30}$ m$_3$, which is almost half of the value proposed with the original Brearley and MacInnes model (13 x 10$^{-30}$ m$_3$). For this threshold concentration and for bubble of diameter higher than 5nm, micro-cracks and dislocations appear at the bubble surface.We calculated the critical pressures inside the bubble that yields to this onset of crack in UO$_2$. These critical pressures are in good agreement with those calculated with the Griffith criterion for brittle fracture.

Keywords: Molecular dynamics; helium bubble; mechanical properties; equation of state

Domains: Nuclear Experiment [nucl-ex]; Nuclear Theory [nucl-th]

Laurent van Brutzel, Alain Chartier. A new equation of state for helium nanobubbles embedded in UO$_2$ matrix calculated via molecular dynamics simulations. Journal of Nuclear Materials, 2019, 518, pp.431-439. ⟨10.1016/j.jnucmat.2019.02.015⟩. ⟨cea-02339951⟩