Using a dynamic point-source percolation model to simulate bubble growth

Accurate modeling of nucleation, growth and clustering of helium bubbles within metal tritide alloys is of high scientific and technological importance. Of interest is the ability to predict both the distribution of these bubbles and the manner in which these bubbles interact at a critical concentration of helium-to-metal atoms to produce an accelerated release of helium gas. One technique that has been used in the past to model these materials, and again revisited in this research, is percolation theory. Previous efforts have used classical percolation theory to qualitatively and quantitatively model the behavior of interstitial helium atoms in a metal tritide lattice; however, higher fidelity models are needed to predict the distribution of helium bubbles and include features that capture the underlying physical mechanisms present in these materials. In this work, we enhance classical percolation theory by developing the dynamic point-source percolation model. This model alters the traditionally binary character of site occupation probabilities by enabling them to vary depending on proximity to existing occupied sites, i.e. nucleated bubbles. This revised model produces characteristics for one and two dimensional systems that are extremely comparable with measurements from three dimensional physical samples. Future directions for continued development of the dynamic model are also outlined