Influence of temperature, initial grain-boundary bubble density and grain structure on fission gas behaviour in UO$_2$: a 3D hybrid multiscale study

TL;DR

This work addresses fission gas release and swelling in irradiated $UO_2$ by developing a hybrid multiscale framework that couples Xe cluster dynamics with a phase-field description of grain boundaries and intergranular bubbles in large 3D polycrystals. The approach resolves both intragranular gas trapping and intergranular bubble evolution, including GB migration and TJ networks, under two temperatures and with/without a free surface, using a weak Xolotl-MARMOT coupling in the MOOSE environment. Key findings show negligible evolution at 1200 K, rapid lenticular bubble growth and network formation with GB migration at 1600 K, and FS-driven denuded zones that suppress network connectivity and accelerate early FGR, with GB coverage reaching up to, but not exceeding, ~50%. These large-scale simulations provide mechanistic insight and quantitative metrics (GB/TJ coverages, gas arrival rates, FGR) to inform engineering-scale models and highlight the roles of temperature, initial bubble density, and FS conditions in fission gas behavior in $UO_2$.

Abstract

Fission gas swelling and release in UO$_2$ are governed by the coupled evolution of intragranular clusters and bubbles, migrating grain boundaries (GBs), triple junctions (TJs), and their eventual connection to a free surface (FS). We extend a hybrid multiscale framework that couples cluster dynamics (Xolotl) with a phase-field model (MARMOT) to large 3D polycrystals with heterogeneous GB and surface diffusion and evolving GB networks. We simulate 10- and 100-grain UO$_2$ microstructures at 1200 and 1600 K, with and without a FS, to interrogate bubble growth, coalescence, GB/TJ coverage, gas arrival at interfaces, and fission gas release (FGR). At 1200 K, both GB mobility and gas transport are low, yielding negligible bubble and GB evolution. At 1600 K, intergranular bubbles rapidly become lenticular and coalesce into networks while unpinned GBs migrate; fewer initial bubbles reduce coalescence but enhance GB migration due to less pinning and produce spikes in interfacial gas arrival rate due to GB sweeping. Bubble density versus mean projected area agrees with White's (2004) coalescence trend and remains on the left side of the analytical curve, in contrast to several prior simulations, likely due to the inclusion of GB migration. In domains with a FS, early release is rapid and bubbles near the FS collapse to form a denuded zone, suppressing local network connectivity; GB coverage rises and approaches but does not exceed 50%. TJ coverage remains low without preferential nucleation at TJs. To our knowledge, these are the first large-scale 3D mesoscale simulations of intergranular fission gas behavior that provide mechanistic insight and quantitative metrics to inform engineering-scale FGR models.

Figures (10)

• Figure 1: The initial microstructures with periodic boundary conditions, where (a) and (b) show the 10-grain polycrystals with 320 and 160 intergranular bubbles, respectively, and (c) shows the $100$-grain polycrystal with 600 bubbles. (d)--(f) show 2D slices of the 3D microstructures, indicated by the white dotted lines in (a)--(c). The images are shaded by the function $\Psi=\sum_{i=1}^{N}\eta_{ui}^2$, with light grey ($\Psi \approx 1$) representing grains, dark grey ($\Psi \approx 0.5$) representing GBs and red-yellow ($\Psi<0.4$) representing bubbles.
• Figure 2: Comparison of our simulation results with experimental data and an analytical model (Eq. \ref{['Eq:White_Analytical']}) from White White_2004 for the bubble density $N$ versus mean bubble area $A$. Our simulation results without a FS at 1600 K are show for the 10-grain polycrystal with 320 and 160 initial bubbles and for the 100-grain polycrystal. We include the simulation data from Millet et al.Millet_2012_a and Prudil et al.PRUDIL2022153777 for reference.
• Figure 3: Evolution of 10-grain UO$_2$ polycrystals without a FS with $320$ initial bubbles at (a) 1200 K and (b) 1600 K. The top images are shaded by the function $\Psi=\sum_{i=1}^{N}\eta_{ui}^2$, with light gray ($\Psi \approx 1$) representing grains, dark gray ($\Psi \approx 0.5$) representing GBs and red-yellow ($\Psi<0.4$) representing bubbles. In the bottom images, the intergranular bubble contour ($\eta_{b0}=0.5$) is yellow, the initial GBs without bubbles are light gray, and the initial TJ lines without bubbles are red.
• Figure 4: Metrics evolution with time quantifying the microstructure evolution in the $10$-grain polycrystals without a FS, where (a) shows the number of intergranular bubbles, (b) number of grains, (c) $\langle s_{g}\rangle$, representing the volume-averaged number of Xe atoms reaching GBs and intergranular bubbles surfaces, calculated using Eq. \ref{['eq:av_sg']}, (d) GB fractional coverage, and (e) TJ fractional coverage.
• Figure 5: Evolution with time of 10-grain UO$_2$ polycrystals at 1600 with (a) 320 initial bubbles (same as Fig. \ref{['fig:evol_10gr_320_1600K']}) and (b) 160 initial bubbles. The top images are shaded by the function $\Psi=\sum_{i=1}^{N}\eta_{ui}^2$, with light gray ($\Psi \approx 1$) representing grains, dark gray ($\Psi \approx 0.5$) representing GBs and red-yellow ($\Psi<0.4$) representing bubbles.In the bottom images, the intergranular bubble contour ($\eta_{b0}=0.5$) is yellow, the initial GBs without bubbles are light gray, and the initial TJ lines without bubbles are red.