We propose a method to evaluate the diffusion coefficient of vacancy-hydrogen clusters (${\mathrm{VH}}_n)$ in metals. The key is a good separation of time scales between H diffusion and the metal-vacancy exchange. The Ni-H system is investigated in details, using ab initio calculations, but the arguments can be transposed to other systems. It is shown that cluster diffusion can be treated as an uncorrelated random walk and that H is always in equilibrium before the vacancy-metal exchange. Then, the diffusion coefficient is a sum over jump paths of the equilibrium probability of being in a specific ${\mathrm{VH}}_n$ configuration times the corresponding activation terms. The influence of H on the energy barrier is well reproduced by effective pair interactions between the jumping Ni and the H atoms inside the vacancy. This model is motivated by an analysis of the electronic charge redistribution in key saddle configurations. The interaction is repulsive and decreases with distance. The model is used to find easy jump path, reduce the number of saddle searches, and provide an estimate of the error expected from this reduction. The application to the Ni-H system shows that vacancies are drastically slowed down by H. The effects of temperature and bulk H concentration are explored and the origin of the non-Arrhenius behavior is explained. At equilibrium, ${\mathrm{VH}}_n$ clusters always induce a speedup of metal diffusion. The implications concerning H induced damage, in particular in regards to Ni-Cr oxidation, are discussed.

• Received 25 June 2014
• Revised 17 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.094106