Thermodynamic analysis of the interaction between metal vacancies and hydrogen in bulk Cu

Using grand canonical thermodynamic analysis with inputs from DFT calculations we calculated equilibrium molar fractions of copper vacancies (V_Cu), H interstitials (H_i) and their complexes in bulk Cu in a wide range of temperature and hydrogen pressure values. The results show that the equilibrium molar fractions of both V_Cu and H_i are low in most conditions of interest, in good agreement with available experimental data. Although H_i-V_Cu complexes have significantly lower formation energies than the isolated defects, the low molar fraction of H is predicted to have little impact on the rise in vacancy molar fraction for external hydrogen pressures below 100 bar. Only at relatively high hydrogen pressures exceeding 10 kbar in the presence of Cu vacancies, the H molar fraction was found to reach the same order of magnitude as the molar fraction of vacancies. These results put thermodynamic limits on the hydrogen-induced vacancy clustering and void formation in bulk Cu.