Hydrogen solubility and vacancy concentration in nickel single crystals at thermal equilibrium: New insights from statistical mechanics and ab initio calculations

Abstract

The hydrogen solubility and the vacancy concentration in Ni single crystals at thermal equilibrium have been determined from a combination of mechanical statistics and ab initio calculations of the Gibbs free energy up to PH2 = 0.1 GPa and 1700 K. We consider that the H atoms can be located in the interstitial sites but also in the displacement field generated by a vacancy to create H-vacancy clusters. The solution and the H-vacancy clusters defect formation free energies are expressed as a sum of a vibration and an electronic contributions. We find that the H-vacancy interactions are significant inside the vacancy core and we show that the H-rich vacancy clusters have a negative free energy at high PH2, similarly to the case of fcc Fe. Then, we compute the H solubility and the vacancy concentration for a wide range of μH2. The calculated solubility at PH2 = 1 bar is in agreement with previous experimental data. Although the vibration contribution dominates the temperature dependence of the solution and formation free energies, the electronic excitations only can lead to a marked deviation of the solubility at high temperature. The vacancy formation is promoted at high PH2 with a significant contribution to the trapping of the H atoms inside the vacancy core at low temperature. However, the total number of vacancies remains too small and has a minor effect on the apparent solubility in single crystals up to PH2 = 0.1 GPa.