The second example demonstrates mesoscale KMC model simulations of the diffusion of silver (Ag) through the pyrolytic carbon and silicon carbide containment layers of a TRISO nuclear fuel particle. The model atomically resolves Ag, but provides a nonatomic, mesoscale medium of carbon and silicon carbide that includes a variety of defect features including grain boundaries, the carbon-silicon car­bide interfaces, cracks, precipitates, and nanocavities. These defect features can serve as either fast diffu — sional pathways or traps for the migrating silver. The model consists of a 2D slab geometry incorporating the pyrolytic carbon and silicon carbide layers, with incident silver atoms placed at the innermost pyro­lytic carbon layer, as described in more detail in Meric de Bellefon and Wirth.88

The key input parameters to the model (diffusion coefficients, trap binding energies, interface charac­teristics) are determined from available experimental data, or parametrically varied, until more precise values become available from lower length scale modeling. The predicted results, in terms of the time/temperature dependence of silver release dur­ing postirradiation annealing and the variability of silver release from particle to particle have been compared to available experimental data from the German High-Temperature Reactor (HTR) Fuel Program,89 as shown below in Figure 7, and studies performed by the Japan Atomic Energy Research Institute (JAERI).90

Figure 6 presents KMC simulation results, which shows the effect of different grain geometries in SiC on silver release during postirradiation annealing. In this model, the grains are considered to have a rect­angular geometry. The smaller dimension is parallel to the interfaces and has a fixed length of 1 pm. The longer dimension, parallel to the radial direction in a TRISO fuel particle, has a variable length that is uniformly distributed among grains over a range from 1 to 40 pm, as shown in the upper plot of Figure 6. Such a grain distribution mimics a highly columnar structure, as is often observed experimentally.91

The diffusion coefficient for silver transport within the grain boundaries has been assumed to be three orders of magnitude higher than in bulk SiC. As expected, within this model, the presence of grains provides fast diffusion paths for silver trans­port and accelerates the released fraction. Adding a

1

Decreasing grain width range

0.1

OPyC

0.001

columnar structure in those grains further increases the release of silver; the released fraction increases from 50 to 80% when the grain distribution shifts from an isotropic structure (grains are 1 mm squares) to a highly columnar structure (length of grains uni­formly distributed from 1 to 40 mm) after 270 h of heating at 1700 °C.

Figure 7 presents KMC simulation results of the transport of silver through a given PyC/SiC/PyC microstructure during postirradiation thermal an­nealing at 1600, 1700, and 1800 °C, as well as results from three German experimental release measure­ments performed at annealing temperatures of 1600, 1700, and 1800 °C. The simulated microstructures include reflective interfaces, trapping cavities, and a grain boundary structure in the SiC layer. The microstructures for the 1600 and 1700 °C simulations (particle 23 and 24) are identical and contain an isotropic grain geometry in SiC that consists of 1-mm long square grains with a grain boundary diffu — sivity 100x higher than in bulk. In the 1800 °C simu­lation (particle 25), the SiC grain characteristics are varied to match the measured release at 1800 °C. Faster transport through grain boundaries is required to match the experimental results, which is obtained by implementing a highly columnar structure in which the grains are 0.5 mm-wide and have a radial length between 10 and 40 mm into SiC, as well as a much higher grain boundary diffusivity that is 2000 times higher than in bulk.