Trapping/detrapping kinetic rates of hydrogen around a vacancy in nickel and some consequences on the hydrogen-vacancy clusters thermodynamic equilibrium

Abstract

The jump rates of H in the interstitial sites of a perfect crystal and in the vicinity of a vacancy in nickel have been determined accurately from ab initio calculations up to 1200 K. The migration free energy of H implemented in the Wert and Zener theory for interstitial diffusion is expressed as a sum of static energy, thermal expansion, vibration and electronic contributions. We show that the thermal expansion and the vibrations of the lattice are the major corrections to the migration energy at finite temperature. The computation of the jump rates indicates that the ratio between the trapping and the detrapping frequencies decrease from ∼104 at 300 K to ∼100 at 1200 K. The effects of the elastic displacement field induced by the vacancy on the jump kinetic rates are minor and the solute diffuses similarly to the perfect crystal out of the vacancy core. Finally, we implement a macroscopic rate equation model to evaluate the concentration of mobile and trapped hydrogen atoms as function of time in a one-dimension sample of 1 μm. The comparison of the H-vacancy cluster concentrations formed during H diffusion with the concentrations given by the quasi-equilibrium condition indicates that the system can develop internal stresses at low temperature due to an oversaturation of H-poor defects. These internal stress fields may be associated with the formation of superabundant vacancies and voids implied on the H embrittlement processes.