The percolation behaviour of grain-boundary networks was characterized in two- and three-dimensional lattices with circular macroscale cross-sections that corresponded to nuclear fuel elements. The percolation of gas bubbles on grain boundaries, and the subsequent percolation of grain boundary networks was the primary mechanism of fission gas release from nuclear fuels. Both radial cracks and radial gradients in grain boundary property distributions were correlated with the fraction of grain boundaries vented to free surfaces. The results showed that cracks surprisingly did not significantly increase the percolation of uniform grain boundary networks. However, for networks with radial gradients in boundary properties, the cracks could considerably increase the vented grain boundary content. The above percolation modelling, although rather simple to implement, provided interesting insight into the FGR mechanism. Most notably, the presence of long radial cracks made little difference in grain boundary percolation for uniform distributions of so-called open grain boundaries. On the other hand, the radial cracks made a significant difference for radial gradients in distributions of open grain boundaries if they extended into regions above the percolation threshold. During reactor operation, fuel pellets experienced steep temperature gradients, and hence consideration of gradients in grain-boundary bubble percolation was certainly pertinent. However, uniform temperature gradients were also relevant for post-irradiation fuel studies (such as post-irradiation annealing) and fuel storage, in which FGR was of interest. Although this study provided important information, further developments could make the model more comparable to experimental studies. Principally, this would involve incorporating the time-scale of grain-boundary bubble growth and percolation as a function of temperature, grain boundary type, grain size and gas production rate. Meso-scale phase-field modelling was being used to characterize these dependencies. In addition, the percolation of bubbles on triple junction lines had been assumed to play an important role in long-range gas migration. Triple junctions did not exist in the three-dimensional cubic lattice considered here. However, they could be incorporated as individual entities in tetrakaidecahedral lattices, where unique percolation rates could conceivably be applied to each triple-junction line. Experimental validation of the present conclusion that radial cracks were only relevant to FGR with temperature gradients would be an important objective. Such a study could be realized using fuel samples that were irradiated (and therefore cracked) and then annealed in uniform and non-uniform temperature fields.

Percolation on Grain Boundary Networks: Application to Fission Gas Release in Nuclear Fuels. P.C.Millett: Computational Materials Science, 2012, 53[1], 31-6