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

Abstract

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.

Relationship between the Behavior of Hydrogen and Hydrogen Bubble Nucleation in Vanadium

“…As shown in Figure 1a, in the case that two hydrogen atoms were placed initially at 1 and 2 Å, the final relaxed distance significantly increased due to the volatile initial configuration. Therefore, the equilibrium distances for two hydrogen atoms are longer than the bond length of hydrogen molecule of 0.74 Å, which means that two hydrogen atoms cannot be directly bonded to each other to form a hydrogen molecule in bcc V. The H-H binding energies are detailed in Figure 1b, and the H-H interaction in vanadium mainly includes two parts: one is the elastic interaction due to the lattice distortion by the interstitial hydrogen, and the other is electronic interaction arising from the change of the electronic structure states of the hydrogen [43]. Both electronic and elastic interaction decrease with increasing the H-H distance.…”

Irradiation hardening induced by blistering in tungsten due to low-energy high flux hydrogen plasma exposure

“…It is known that blister formation includes the nucleation of cavity/crack and growth of these nuclei. The nucleation mechanisms of cavities in recrystallized W are suggested as the dislocation loop punching initially from vacancies [12][13][14], dislocations [4,15,16], and H platelet aggregations [17], but not yet experimentally confirmed. While, the growth mechanisms of cavities are generally acknowledged as the plastic deformation [11,18,19], dislocation loop punching [20] and agglomeration of H-vacancy complexes [21,22].…”

Hydrogen Clustering in Bcc Metals: Atomic Origin and Strong Stress Anisotropy

“…This perspective, however, contradict with extensive experimental evidences where H was shown to induce damages even in metals with very low defect density. A typical example is H induced bubbling/blistering in well annealed pure W with coarse-grained or single crystal structure [30][31][32][33][34][35] , where influence of pre-existing defects is minimized, making H clustering a plausible mechanism.…”

“…To fundamentally understand such discrepancy, there have been a few atomistic studies that investigate the interaction between multiple H, and H clustering in non-hydride forming metals 35,36 . For instance, recent first-principles calculations have shown that H in tungsten (W) can form platelet-like self-clusters along {001} planes, with binding energy between H gradually increases as the self-cluster grows in size 35,36 .…”

“…To fundamentally understand such discrepancy, there have been a few atomistic studies that investigate the interaction between multiple H, and H clustering in non-hydride forming metals 35,36 . For instance, recent first-principles calculations have shown that H in tungsten (W) can form platelet-like self-clusters along {001} planes, with binding energy between H gradually increases as the self-cluster grows in size 35,36 . Further to those first-principles studies, large-scale atomistic simulations have also been conducted to examine H self-trapping in W 37 employing an interatomic potential fitted to reproduce H-H interactions from first-principles database 38 , demonstrating formation of platelet-like H self-clusters, induced by dislocations or homogeneous stresses, or at high H concentration 37 .…”