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 UO 2 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 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 × 10 5 to 3.9 × 10 5 mol.m −3 (corresponding to helium-to-vacancy ratio of 0.3 to 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 UO 2 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 UO 2 . It corresponds to an atomic volume of 7.8 × 10 −30 m 3 , which is almost half of the value proposed with the original Brearley and MacInnes model (13 × 10 −30 m 3 ). 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 UO 2 . These critical pressures are in good agreement with those calculated with the Griffith criterion for brittle fracture.

Atomistic simulations of a helium bubble in silicon carbide

“…In this regime, the highest the temperature, the lowest the maximum density. Note that this behavior is not specific to silicon carbide, since previous computational investigations led to similar conclusions in iron [38] or uranium dioxide [19], for instance. Since almost all helium atoms remain in the bubble, these variations are evidently caused by the increase of the diameter with the He /V ratio, as seen in Fig.…”

“…Furthermore, our computed pressure values fall in between those two EOS. Note that recent investigations highlighted the influence on pressure of the interaction between matrix and helium atoms, stressing the need to redefine the EOS for helium in bubbles [19,[43][44][45][46]. However, this effect is especially important for small bubbles with diameters 1-2 nm, i.e.…”

“…Mechanisms leading to bubble formation have been extensively investigated, in particular for metals [13][14][15] and few other materials like silicon [16][17][18] or uranium dioxide [19]. However, most of available studies for silicon carbide concern the first stages of bubble formation, and in particular the stability and migration properties of a single embedded helium atom [20][21][22][23][24][25][26][27][28], as well as interactions between helium atoms or between helium and a vacancies cluster [7,[29][30][31][32].…”

The predicted shapes of voids and Xe bubbles in UO2

“…One essential difference between the previous MD work and the work presented here, other than the different species of gas atom, is that they started from a spherical configuration. The facet shape obtained previously [39,49] for smaller bubbles formed as a consequence of MD equilibration. It could be the case that as the bubble diameter increases the timescale necessary for the bubble to restructure to a faceted shape has become too long.…”

“…Other MD studies [39,49] have considered Xe and He faceted and spherical bubbles. One of the key findings in those studies was that spherical bubbles of Xe in UO 2 with a diameter between 1.2 nm and 1.5 nm are the most stable shape compared to different morphologies.…”