Hydrogen and vacancy concentrations in [formula omitted]-iron under high hydrogen gas pressure and external stress: A first-principles neural network simulation study

Abstract

The metal-hydrogen-vacancy interaction in α-iron is crucial for understanding hydrogen embrittlement behavior and developing reliable materials for green gaseous hydrogen applications; however, it remains underexplored, particularly in contexts involving external stress and high hydrogen gas pressure. In this study, we performed quantitative analyses of metal-vacancy–hydrogen interactions in α-iron, measured by hydrogen solubility and the thermodynamics of vacancy–hydrogen complexes, under such challenging conditions using a reliable first-principles neural network potential. High hydrogen gas pressures reaching up to 2 GPa were investigated. As the atomic concentration surpasses approximately 0.01, hydrogen solubility is dominated by hydrogen-induced lattice distortion (primarily volumetric expansion) and the interactions between hydrogen atoms within the metal matrix, resulting in significant deviations from Sieverts’ law. Our results reveal a significant effect of shear stress on hydrogen solubility, deviating from previously used equations. Moreover, the influence of external stress on the thermodynamics of the vacancy–hydrogen complex, particularly vacancy formation free energy, is uniquely characterized by hydrogen solubility, regardless of the external stress magnitude. It thereby offers a rapid method to estimate the vacancy properties under external stress based on readily accessible external-stress-free data.