Critical concentration for hydrogen bubble formation in metals

Employing a thermodynamic model with previously calculated first-principle energetics as inputs, we determined the hydrogen (H) concentration at the interstitial and monovacancy as well as its dependence on temperature and pressure in tungsten and molybdenum. Based on this, we predicted the critical H concentration for H bubble formation at different temperatures. The critical concentration, defined as the value when the concentration of H at a certain mH-vacancy complex first became equal to that of H at the interstitial, was 24 ppm/7.3 GPa and 410 ppm/4.7 GPa at 600 K in tungsten and molybdenum in the case of a monovacancy. Beyond the critical H concentration, numerous H atoms accumulated in the monovacancy, leading to the formation and rapid growth of H-vacancy complexes, which was considered the preliminary stage of H bubble formation. We expect that the proposed approach will be generally used to determine the critical H concentration for H bubble formation in metals.