LAUSR

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 ~ -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 is the H-W attraction and the lower is the H solution/trapping energy. Furthermore, taking the V_9^m cluster as an example, it is observed that the multiple H atoms form a multilayer nested cage configuration at VCs surface initially, and then the stable H2 molecules form in the center of VCs. Interestingly, the pre-existed H atoms in VCs inner surface has a shielding effect on the H-W interaction, decreasing the electron density of the central region of VCs and facilitating the formation of H2 molecules. Moreover, the desorption temperatures of H in VCs are also predicted based on the Polanyi-Wigner equation, which 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.