Consideration of grain size distribution in the diffusion of fission gas to grain boundaries

We analyze the accumulation of fission gas on grain boundaries in a polycrystalline microstructure with a distribution of grain sizes. The diffusion equation is solved throughout the microstructure to evolve the gas concentration in space and time. Grain boundaries are treated as infinite sinks for the gas concentration, and we monitor the cumulative gas inventory on each grain boundary throughout time. We consider two important cases: first, a uniform initial distribution of gas concentration without gas production (correlating with post-irradiation annealing), and second, a constant gas production rate with no initial gas concentration (correlating with in-reactor conditions). The results show that a single-grain-size model, such as the Booth model, over predicts the gas accumulation on grain boundaries compared with a polycrystal with a grain size distribution. Also, a considerable degree of scatter, or variability, exists in the grain boundary gas accumulation when comparing all of the grain boundaries in the microstructure.