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.
Effect of carbon on hydrogen behaviour in tungsten: first-principle calculations