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Acta Metall Sin  2026, Vol. 62 Issue (3): 489-496    DOI: 10.11900/0412.1961.2024.00240
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First-Principles Study on the Influence of Alloying Elements on the Dissolution and Diffusion of Hydrogen Atoms in α-Fe
BAO Ergen1,2, WANG Jiantao2,3, XU Wenjing2,3, MA Hui2,3(), CHEN Xing-qiu2,3
1.School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China
2.Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
3.School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China
Cite this article: 

BAO Ergen, WANG Jiantao, XU Wenjing, MA Hui, CHEN Xing-qiu. First-Principles Study on the Influence of Alloying Elements on the Dissolution and Diffusion of Hydrogen Atoms in α-Fe. Acta Metall Sin, 2026, 62(3): 489-496.

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Abstract  

Hydrogen embrittlement causes metals exposed to H-containing environments to become brittle and crack, posing serious risks to industries such as energy, manufacturing, transportation, and aerospace. Understanding the interaction between hydrogen and steel is crucial for addressing hydrogen embrittlement challenges. This study uses first-principles methods based on the density functional theory to examine how different alloying elements influence the dissolution of H atoms in α-Fe-based solid solutions, both with and without vacancy defects. The interactions between H atoms and alloying elements, as well as Fe atoms are analyzed using crystal orbital Hamilton populations. Additionally, the climbing image-nudged elastic band (CI-NEB) method was used to calculate the influence of the alloying elements on the diffusion of H atoms in α-Fe-based solid solutions. The results indicate that H atoms preferentially dissolve in the second and third nearest tetrahedral interstitial sites of alloy atoms. The solution enthalpy of H atoms is determined by the bond strength between the H atom and the nearest alloy atom as well as Fe atoms. For systems with vacancy defects after alloying, the solution enthalpies of H atoms at the first nearest vacancy for elements, such as Sc, V, Cr, Mn, Co, Ni, and Cu are lower than those at the tetrahedral interstitial sites of the complete α-Fe-based solid solutions. However, the opposite effect is observed for systems containing Al, Si, Ti, Zr, Nb, Eu, and W. Furthermore, alloying with Ti, Cu, Zr, Nb, and rare-earth elements increases the diffusion energy barriers for H atoms moving from the second nearest tetrahedral interstitial site to the third nearest site, while reducing diffusion energy barriers in the opposite direction. Conversely, the opposite effects are observed in α-Fe-based solid solutions containing Si, V, Cr, Mn, Co, Ni, Mo, and W.

Key words:  first-principles calculation      hydrogen embrittlement      steel      rare earth element      hydrogen diffusion     
Received:  17 July 2024     
ZTFLH:  TG131  
Fund: National Science and Technology Major Project(J2019-VI-0019-0134);Natural Science Foundation of Liaoning Province(2023-MS-017)
Corresponding Authors:  MA Hui, associate professor, Tel: (024)23971560, E-mail: hma@imr.ac.cn

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00240     OR     https://www.ams.org.cn/EN/Y2026/V62/I3/489

Fig.1  Crystal structures of α-Fe-based solid solutions
(a) the structure with a supercell and a substituted alloy atom (Purple and green balls represent Fe atoms and an alloy atom, respectively)
(b) the H atom dissolved in the tetrahedral interstitial site (Yellow ball represents the H atom)
(c) the H atom dissolved in the first, second, and third nearest neighbor tetrahedral interstitial sites around the alloy atom (View parallel to c-axis; the distances from the alloy atom to the H atom in the first, second, and third nearest neighbor positions are 0.167, 0.259, and 0.328 nm, respectively)
(d) the H atom dissolved in the first, second, and third nearest neighbor tetrahedral interstitial sites around the alloy atom (View parallel to b-axis)
(e) vacancy defects near the alloy atom (Two yellow balls represent the first and second nearest neighbor vacancies around the alloy atom, respectively)
(f) diffusion paths of the H atom (From the second nearest tetrahedral interstitial site to the third nearest tetrahedral interstitial site, and from the third nearest tetrahedral interstitial site to the fourth nearest tetrahedral interstitial site)
Fig.2  Solid solution enthalpies of alloying elements in α-Fe-based solid solutions
Fig.3  Charge density, electronic density of states (DOS), and projected crystal orbital Hamilton populations (pCOHP) of α-Fe containing H
(a) charge density on the (100) plane (The iso-surface value is set to 0.04 electrons/a03, where a0 is the Bohr radius)
(b1, b2) total electronic density of states (TDOS) and projected density of states of α-Fe-based solid solution containing H (b1) and negative pCOHP (-pCOHP) between H and the nearest, next-nearest Fe atoms (b2) (E—electron energy, EF—Fermi energy; 1NN and 2NN represent the nearest neighbors and next-nearest neighbors, respectively; “↑, ↓” represent spin-up and spin-down, respectively)
Fig.4  Solution enthalpies of H atoms in different tetrahedral interstitial sites within α-Fe-based solid solution (Gray dots, green triangles, and pink stars represent the cases where H atoms dissolve in the first, second, and third nearest tetrahedral interstitial sites of the alloy atoms, respectively; the dark green dashed line corresponds to the situation where H atoms dissolve in the interstitial sites of pure α-Fe, with an solid solution enthalpy of 0.42 eV)
Fig.5  Influence of alloying different elements on the integrated pCOHP (IpCOHP) between H and alloy atoms, as well as between H and the nearest Fe atoms (The green line represents the IpCOHP between H and the alloy atoms when H is dissolved in the second nearest tetrahedral interstitial site of the alloy atoms; the blue line represents the IpCOHP between H and the nearest Fe atoms when H is dissolved in the third nearest tetrahedral interstitial site of the alloy atoms; the purple dashed line corresponds to the IpCOHP between H and the next nearest Fe atoms when H is interstitially dissolved in pure α-Fe, which is -0.061 eV; the yellow dashed line corresponds to the IpCOHP between H and the nearest Fe atoms when H is interstitially dissolved in pure α-Fe, which is -0.478 eV)
Fig.6  Vacancy formation enthalpies at the first and second nearest sites of alloy atoms in α-Fe-based solid solutions (The black line and green line represent the first and second nearest vacancies of different alloy atoms, respectively; the dark green dashed line corresponds to the case of a single vacancy in pure Fe, with a formation enthalpy of 2.19 eV)
Fig.7  Solid solution enthalpies of H atoms at the first nearest vacancy of alloy atoms (Light blue dashed line corresponds to the solid solution enthalpy of H in the vacancy of pure α-Fe, which is 0.36 eV; dark green dashed line corresponds to the solid solution enthalpy of H in the tetrahedral interstitial site of complete pure α-Fe, which is 0.42 eV)
Fig.8  Transition state search for the diffusion of the H atom from the second nearest tetrahedral interstitial site to the third nearest tetrahedral interstitial site of different alloy atoms (Taking the energy of H atoms in the tetrahedral interstitial site of pure α-Fe as the reference)
(a) non-rare earth elements in solid solution
(b) rare earth elements in solid solution
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