  Low-energy hydrogen irradiation is known to induce bubble formation in
tungsten, while its atomistic mechanisms remain little understood. Using
first-principles calculations and statistical models, we studied the
self-clustering behavior of hydrogen in tungsten. Unlike previous speculations
that hydrogen self-clusters are energetically unstable owing to the general
repulsion between two hydrogens, we demonstrated that hydrogen self-cluster
becomes more favorable as the cluster size increases. We found that hydrogen
atoms would form two-dimensional platelet-like structures along {100} planes.
These hydrogen self-clustering behaviors can be quantitative understood by the
competition between long-ranged elastic attraction and local electronic
repulsion. Further statistical analysis showed that there exists a critical
hydrogen concentration above which hydrogen self-clusters are thermodynamically
stable and kinetically feasible. Based on this critical hydrogen concentration,
the plasma loading conditions under which hydrogen self-clusters form were
predicted. Our predictions showed excellent agreement with 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.
