Characterization of the energetics and configurations of hydrogen in vacancy clusters in tungsten

We have explored the retention of hydrogen (H) in tungsten (W) by investigating its dissolution and aggregation in vacancy clusters (VCs) using a first-principles method and thermodynamic models. The solution energy of a single H in the VCs is in the range of -0.99 to -0.64 eV, much lower than that at a mono-vacancy (∼ -0.37 eV) and interstitial site (∼1.01 eV) in W. Such a remarkable discrepancy is rationalized on the electronic interaction of H with its neighboring W atoms, which varies from repulsion to attraction with H moving from perfect crystal to vacancy/VCs. Specifically, the solution/trapping energies of H in VCs can be well categorized by the coordination number of its neighboring W atoms, i.e. the lower the coordination number of W, the stronger the H-W attraction and the lower the H solution/trapping energy. Furthermore, taking the cluster as an example, it is observed that the multiple H atoms form a multilayer nested cage configuration at the VC surface initially, and then the stable H₂ molecules form in the center of the VCs. Interestingly, the pre-existing H atoms in the VC inner surface have a shielding effect on the H-W interaction, decreasing the electron density of the central region of the VCs and facilitating the formation of H₂ molecules. Moreover, the desorption temperatures of H in the VCs are also predicted based on the Polanyi-Wigner equation, and are in good agreement with the available thermal desorption spectroscopy experiments. Our calculations provide a good reference to understand the influence of VCs on the retention and evolution of H in W.