Hydrogen bubble nucleation by self-clustering: density functional theory and statistical model studies using tungsten as a model system

Low-energy, high-flux hydrogen irradiation is known to induce bubble formation in tungsten, but its atomistic mechanisms remain little understood. Using first-principles calculations and statistical models, we studied the self-clustering behaviour of hydrogen in tungsten. Unlike previous speculations that the hydrogen self-clusters are energetically unstable owing to the general repulsion between two hydrogen atoms, we found that 2D platelet-like hydrogen self-clusters could form at high hydrogen concentrations. The attractive binding energy of the hydrogen self-cluster becomes larger as the cluster size increases and plateaus at 0.38 eV/H around size of 40. We found that hydrogen atoms would form 2D platelet-like structures along planes. These hydrogen self-clustering behaviours can be quantitatively understood by the competition between long-ranged elastic attraction and local electronic repulsion among hydrogens. Further analysis showed hydrogen self-clusters to be kinetically feasible and thermodynamically stable above a critical hydrogen concentration. Based on this critical hydrogen concentration, we predicted the hydrogen irradiation condition required for the formation of hydrogen self-clusters. Our predictions showed excellent agreement with the experimental results of hydrogen bubble formation in tungsten exposed to low-energy hydrogen irradiation. Finally, we proposed a possible mechanism for the hydrogen bubble nucleation via hydrogen self-clustering. This work provides mechanistic insights and quantitative models towards understanding of plasma-induced hydrogen bubble formation in plasma-facing tungsten.