Solubility of Hydrogen and Vacancy Concentration in Nickel from First Principles Calculations
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Solubility of Hydrogen and Vacancy Concentration in Nickel from First Principles Calculations Arnaud Metsue, Abdelali Oudriss and Xavier Feaugas Laboratoire des Sciences de l’Ingénieur pour l’Environnement, UMR CNRS 7356 Université de La Rochelle , Avenue Michel Crépeau, 17000 La Rochelle, France ABSTRACT The hydrogen solubility and the vacancy concentration in Ni single crystals at thermal equilibrium with a H2 gas have been determined from a combination of first principles calculations and statistical mechanics up to the melting point. We show that the H solubility increases and the vacancy formation is promoted at high PH2. The apparent solution enthalpy and entropy are extracted from the fit of the solubility with the Sieverts’s law. We show that our results are in good agreement with previous experimental data at PH2=1 bar. The vacancy concentration increases with PH2 whatever the temperature but the effect of H is more significant at low temperature. However, the vacancy concentration and the H solubility in single crystals remain small and a comparison with the experimental data on polycrystals indicates that the grain boundaries may play the most important source of superabundant vacancies and preferential sites for H incorporation. INTRODUCTION The incorporation of hydrogen in metals can strongly affect the physical properties of the host matrix and can lead to irreversible damages. Therefore, the solubility of hydrogen in metals is a fundamental data to design new protections preventing hydrogen embrittlement and safety materials. However, the apparent H solubility can be influenced by the presence of crystalline defects such as point defects, dislocations or grain boundaries. In particular, it has been suggested that hydrogen promotes the formation of vacancies, called “superabundant vacancies” which participate extensively to the mechanisms of degradation of metals [1-3]. In this study, we determine the vacancy concentration and the hydrogen solubility in nickel single crystals at thermodynamic equilibrium with a H2 gas up to the melting temperature from a combination of first principles calculations and statistical mechanics. Hydrogen is incorporated in the interstitial sites of a perfect crystal but also in the sites inside and around the vacancy core delimited by the first shell of atoms around the center of the defect. Finally, we discuss the contribution of hydrogen to the formation of vacancies. THEORY The H solubility and the total vacancy concentration have been calculated from the minimization of the free energy J of the crystal in the grand canonical ensemble containing hydrogen atoms, vacancies and hydrogen-vacancy clusters:
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sol sol J = N octa × Gocta + N tetra × Gtetra {H −vac}
+
f f + N vac × Gvac ∑ N site−iH × Gsite−iH
(1)
−TS conf where Nocta,tetra
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