Interactions between hydrogen impurities and vacancies in Mg and Al: A comparative analysis based on density functional theory

Using first-principles methods we have studied the interactions between hydrogen impurities and vacancies in hcp Mg and fcc Al. We find that single vacancies can, in principle, host up to 9 H atoms in Mg and 10 in Al, not 12 as recently reported in the case of Al. The difference between our results and the results in previous work is attributed to a more appropriate definition of the trapping energy of hydrogen impurities in vacancies. The concentration of hydrogen-vacancy complexes depends on the amount of hydrogen dissolved in the metal, which in turn is dictated by the hydrogen chemical potential ${\ensuremath{\mu}}_{\text{H}}$. We evaluated the concentration of all relevant hydrogen-vacancy complexes as a function of ${\ensuremath{\mu}}_{\text{H}}$, corresponding to different H loading conditions---ranging from low pressures to high pressures of ${\text{H}}_{2}$ gas, up to hydrogen plasma conditions. Our analysis reveals fundamental differences in the characteristics of the hydrogen-vacancy interaction between Mg and Al. In the case of Al, up to 15% of H atoms are trapped in single vacancies in the form of H-vacancy complexes even for very low values of ${\ensuremath{\mu}}_{\text{H}}$. The trapping effect slows down the diffusion of H atoms in Al by more than an order of magnitude. While interactions between vacancies and single hydrogen atoms are therefore clearly important, interactions with multiple H atoms and related mechanisms (such as hydrogen-induced superabundant vacancy formation) are predicted to occur in Al only at very high values of ${\ensuremath{\mu}}_{\text{H}}$. In the case of Mg, the effects of H trapping in single vacancies are negligible for low values of ${\ensuremath{\mu}}_{\text{H}}$ due to the relatively low formation energy of isolated interstitial H. However, vacancies containing multiple H atoms and related mechanisms such as hydrogen-induced superabundant vacancy formation are predicted to occur in Mg at much lower values of ${\ensuremath{\mu}}_{\text{H}}$ than in Al. We estimate that, at room temperature, the critical pressure of an ${\text{H}}_{2}$ gas to induce hydrogen-enhanced (superabundant) vacancy formation is $\ensuremath{\sim}1\text{ }\text{GPa}$ in Mg and $\ensuremath{\sim}10\text{ }\text{GPa}$ in Al.