Hydrogen concentration estimation in metals at finite temperature using first-principles calculations and vibrational analysis

• We provide a framework to calculate hydrogen concentrations in metals using DFT.
• Lattice vibration analysis is performed to take into account thermal effects.
• Interstitial sites and trap sites around vacancies are considered.
• We show that calculated concentrations agree with the experiments.
• Hydrogen concentrations in metals at a wide range of chemical potential are given.

In order to clarify hydrogen embrittlement mechanisms and to estimate structural strength of machine components under a hydrogen environment, it is essential to know the hydrogen concentration and its existing state in materials. Solute-hydrogen atoms change the behavior and stability of lattice defects and trigger strength degradation. This paper proposes a method for quantitatively evaluating hydrogen concentrations in metals under various conditions on the basis of first-principles calculations and lattice vibration analysis, to consider the influence of thermal vibrations. First, we give a formulation that yields the hydrogen concentration at interstitial sites and at vacancies and vacancy concentration. We then evaluate the influence of the hydrogen concentration at interstitial sites and sites around vacancies in α-Fe for the total hydrogen concentration. We show that the influence of the hydrogen around vacancies is small, and that the interstitial hydrogen concentration is the dominant influence when materials are well annealed. We also investigate hydrogen concentrations in various metals (Al, Ni, Cu, Pd, Mo, α-Ti, Mg, and α-Zr) and show that the calculated concentrations agree with the experimental data, given that interactions between solute-hydrogen atoms are not significant.