Thermodynamic vs. Kinetic Origin of Superabundant Vacancy Formation in Ni Single Crystals

The aim of this study is a clarification of the thermodynamic and/or kinetic origin of superabundant vacancies formation in nickel exposed to hydrogen ingress. Here, first-principles calculations within density functional theory have been conducted on the solubility and diffusion of H in Ni single crystals both in the bulk material and in the vicinity of a vacancy core up to P_H2 = 10 GPa. The calculations are performed up to 1,200 K where the Gibbs free energies of H solubility, H-vacancy clusters formation, and diffusion’s barriers are expressed as a sum of vibration and electronic contributions from the computation of the phonon dispersion curves and the electronic density of states. The first time, the total H solubility and the total vacancy concentration of H-free and H-decorated defects at thermodynamic equilibrium were determined from the minimization of the free energy of the system expressed in the grand-canonical ensemble. It was found that the total vacancy concentration at thermodynamic equilibrium is larger than the thermal defect concentration in H-free Ni and confirmed that H promotes the vacancy formation. However, the defect concentration at thermodynamic equilibrium remains too small compared to the concentrations observed experimentally. The second time, the H jump frequencies associated with the diffusion in the bulk lattice, the trapping and the detrapping of the solute into and out of the vacancy core, were calculated. These jump rates are implemented in a one-dimensional kinetic model to follow the evolution of mobile H concentrations and the formation of H-vacancy clusters during H diffusion. It was found that the H-vacancy clusters concentrations become larger than the values given by the stationary equilibrium condition. This result indicates that the system switches in out-of-equilibrium and may be responsible for the formation of superabundant vacancies. Therefore, it is suggested that the formation of superabundant vacancies in nickel has mainly a kinetic origin from the oversaturation of H-decorated defects during diffusion.