Effect of uniaxial pre-strain on H adsorption and diffusion on C-doped Fe (110) surface

CAI Yiquan; YIN Yihui; LI Jicheng

doi:10.7498/aps.74.20250107

Abstract

In order to further investigate and improve the mechanism of the interaction between pre-strain/pre-stress and hydrogen-adsorbed steel (Fe-C alloy) surface at the microstructural level, the first-principles calculations method is used to study the effects of uniaxial pre-strain on hydrogen adsorption and diffusion on C-doped Fe(110) surface. The influence of pre-strain on hydrogen adsorption and permeation is investigated from three aspects: surface atomic spatial configuration, binding energy (E_b), and electronic structure. The diffusion energy barriers for hydrogen permeation are calculated in both doped and undoped C atoms. The results demonstrate that doped C atoms induce octahedral lattice distortion in Fe crystals in different directions, creating “distortion” on the Fe(110) surface. Variations in distortion degree (D_Δ) at different sites and their distances from C atom lead to inconsistent trends in adsorption configurations (H adsorption height d and unit surface area S_Δ) and binding energy (E_b) under pre-strain. For adsorption configurations, d is coupled by ε and C atom effects: at the TF_pure site (non-C-doped site ), d decreases as S_Δ increases; under compression (ε decreases from 0% to –5%) at TF (C-doped site with C atom directly beneath the site), TF_S (C-doped site located closer to the maximally distorted atom Fe₁₃₅) and TF_L sites (C-doped site located farther from the maximally distorted atom Fe₁₃₅), d positively correlates with D_Δ, while under tension (ε increases from 0% to 5%), d negatively correlates with S_Δ. As ε increases from –5% to 5%, E_b peaks at TF_pure then declines, whereas E_b at TF decreases initially before rising, and E_b at TF_S/TF_L monotonically increases. The analysis hows that E_b at TF_S/TF_L positively is correlated with the standard deviation (S_α) of the three internal angles in the triangular unit. The trend of diffusion energy barrier (E_∆) is opposite to that of E_b. When H is adsorbed at C-doped sites, the adsorption configuration and binding energy calculations indicate that H tends to diffuse inward more readily. However, electronic structure analysis reveals repulsion between C and H atoms, accompanied by increased diffusion barriers compared with the scenarios in the undoped cases, causing H atoms to accumulate around C atoms rather than penetrate the bulk phase, thereby leading hydrogen atoms to embrittle. The calculations of adsorption configuration, binding energy, and diffusion barrier indicate that at doped sites (TF_S site), increasing tensile strain can contribute to H diffusion into the steel microstructure, whereas compressive strain hinders it. This explains the engineering phenomenon where “higher carbon content exacerbates hydrogen embrittlement tendency under equivalent stress” on an atomic scale. This work elucidates the mechanism of H adsorption on pre-strained Fe-C alloy surfaces from an electronic structure perspective, providing theoretical ideas for studying hydrogen embrittlement.

Keywords:

Authors and contacts

1.
China Academy of Engineering Physics, Institute of Systems Engineering, Mianyang 621900, China
2.
Key Laboratory of Engineering Materials and Structural Shock Vibration in Sichuan Province, Mianyang 621999, China

Corresponding author: YIN Yihui, yinyh@caep.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12072333).

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References

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Cited By

图 1 Fe(110)表面原子排列和吸附位点, H吸附位点分别为长桥位点(LB)、短桥位点(SB)、准三重位点(TF)和顶部位点(OP), 最近的两个Fe原子之间的距离为2.48 Å; LB, SB, TF位点到OT位点的侧向距离分别为2.02, 1.24, 1.52 Å

Figure 1. Atom arrangement and symmetry sites on Fe(110). The H adsorption sites are long bridge site (LB), short bridge site (SB), quasi triple site (TF) and top site (OP), respectively; the distance between the nearest two Fe atoms is 2.48 Å, the lateral distances from LB, SB, TF sites to OT sites are 2.02, 1.24, 1.52 Å, respectively.

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图 2 晶体模型　(a) 3×3×4扩胞; (b)切(110)面; (c)纯铁晶体模型; (d) 3×3×4扩胞; (e)切(110)面; (f) 中碳钢晶体模型; 绿色面为(110)面, 粉色面为切割面, 以此为界将晶体模型切割, 后续计算将在切割面上添加真空层

Figure 2. Crystal model: (a) 3 × 3 × 4 cell expansion; (b) cut (110) face; (c) pure iron crystal model; (d) 3 × 3 × 4 cell expansion; (e) cut (110) face; (f) crystal model of medium carbon steel. The green surface is (110) side, the pink surface is the cutting surface, which is used as the boundary to cut the crystal model, subsequent calculations will add a vacuum layer on the cutting surface.

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图 3 基底模型　(a)未掺杂模型; (b) 掺杂模型; 掺杂时, 第135号Fe原子(Fe₁₃₅)为表面上最大畸变原子

Figure 3. Substrate model: (a) None-doped model; (b) doped model. When doped, the 135th Fe atom (Fe₁₃₅) is the largest distorted atom on the surface.

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图 4 掺杂吸附模型, 图中蓝色原子表示体心原子; 掺杂时, 整个表面都发生畸变, 以离C原子最近的吸附位点为研究对象: OP位点位于Fe₄₇顶部, COP位点位于Fe₁₃₅顶部, SB位点位于Fe₄₇和Fe₁₃₅之间, LB位点位于Fe₄₇和Fe₅₀之间, TF位点位于Fe₄₇, Fe₅₀, Fe₁₃₅组成的三角形区域

Figure 4. H-adsorption model (C-doped). Blue atoms represent body centered atoms; when doped, the whole surface is distorted, the adsorption site nearest to the C atom is taken as the research object: OP site is at the top of Fe₄₇, COP site is at the top of Fe₁₃₅, SB site is between Fe₄₇ and Fe₁₃₅, LB site is between Fe₄₇ and Fe₅₀, TF site is in the triangular region composed of Fe₄₇, Fe₅₀ and Fe₁₃₅.

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图 5 表面Fe原子空间位置分布情况　(a) ε = –5%; (b) ε = –2.5%; (c) ε = 0%; (d) ε = 2.5%; (e) ε = 5%

Figure 5. Spatial distribution of surface Fe atoms: (a) ε = –5%; (b) ε = –2.5%; (c) ε = 0%; (d) ε = 2.5%; (e) ε = 5%.

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图 6 ε = 0%时OP (a)和COP (b)位点差分电荷差分电荷密度空间分布(黄色区域代表得电子, 表示高电子密度; 蓝色区域代表失电子, 表示低电子密度)

Figure 6. Differential charge space distribution of OP (a) and COP (b) at ε = 0%. The yellow area represents electrons, indicating high electron density, and the blue area represents electron loss, indicating low electron density.

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图 7 不稳定点吸附结过示意图(掺杂C), 虚圆代表氢原子起始位点, 位于OP位点的H原子在应变为–5%和5%的作用下迁移至TF₁位点, 在–2.5%, 0%, 2.5%的情况下迁移至TF₂位点; 位于SB位点的H原子迁移至TF_S位点; 位于LB位点的氢原子迁移至TF_L位点

Figure 7. Adsorption results of unstable site (C-doped). The dotted circles represent the starting site of hydrogen atom, the H atom at the OP site migrates to the TF₁ site at the strain of –5% and 5%, and to the TF₂ site at the strain of –2.5%, 0%, 2.5%, the H atom located at the SB site migrates to the TF_S site, H atom at LB site migrates to TF_L site.

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图 8 H吸附的几何参数　(a) aob平面; (b) aoc平面

Figure 8. Geometric parameters for H adsorption: (a) aob plane; (b) aoc plane.

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图 9 H原子吸附结果　(a) TF_pure (未掺杂); (b) TF_S (掺杂C原子); (c) TF_L (掺杂C原子); (d) TF (掺杂C原子)

Figure 9. Adsorption results of H atom: (a) TF_pure (none-doped); (b) TF_S (C-doped); (c) TF_L (C-doped); (d) TF (C-doped).

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图 10 结合能分析　(a)预应变-结合能-标准差; (b) 标准差-结合能

Figure 10. Analysis of bonding energy: (a) Strain-binding energy-standard deviation; (b) standard deviation- binding energy.

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图 11 扩散分析　(a)吸附结构与结合能; (b)态密度; (c)扩散路径; (d)扩散能垒

Figure 11. Diffusion analysis: (a) Adsorption structure and binding energy; (b) density of state; (c) diffusion path; (d) diffusion activation energy.

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图 12 TF_S位点态密度和Bader电荷, 其中右图黄色字体为H原子上的电荷, 蓝色字体为3个配位Fe原子的电荷, 虚线框内为H, Fe原子得失总电荷以及它们的差值(红色字体)

Figure 12. State density and Bader charge of TF_S site. The charge on the H atom is shown in the right panel by the yellow font, the charge on the three coordinated Fe atoms by the blue font, and the total charge gain or loss of the H and Fe atoms as well as their difference (shown in red type) is included in the dashed box.

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图 13 TF_S位点电荷密度

Figure 13. Charge density of TFs site.

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表 1 基底表面畸变处参数

Table 1. Parameters of the substrate model at the distortion.

应变ε/%	未掺杂					掺杂
应变ε/%	d_SB	d_LB	d_z	l_Fe47/50-O	l_Fe135-O	d_SB	d_LB	d_z	l_Fe47/50-C	l_Fe135-C
–5.0	2.426	2.665	2.044	1.962	1.438	2.731	2.677	2.482	1.915	1.811
–2.5	2.426	2.735	2.016	1.973	1.421	2.761	2.762	2.447	1.935	1.802
0.0	2.423	2.805	1.994	1.985	1.404	2.773	2.826	2.418	1.952	1.789
2.5	2.434	2.875	1.978	2.002	1.393	2.772	2.884	2.421	1.963	1.789
5.0	2.442	2.946	1.952	2.018	1.379	2.806	2.958	2.446	1.976	1.794
注: d_SB为短桥距离, 为Fe₄₇和Fe₁₃₅之间的距离; d_LB为长桥距离, 为Fe₄₇和Fe₅₀之间的距离; d_z为最大畸变的Fe原子(Fe₁₃₅)到次表面Fe原子之间的平均垂直距离, l_Fe-C为C原子与配位Fe原子之间的键长; l_Fe-O为Fe原子到八面体中心之间的距离; 以上长度单位均为Å.

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表 2 结合能E_b (单位为eV)

Table 2. Binding energy E_b (Unit: eV).

ε/%	未掺杂					掺杂
ε/%	OP	COP	SB	LB	TF	OP	COP	SB	LB	TF
–5	–2.419	–2.421	–2.911	–2.901	–3.040	–3.105^*	–2.438	–2.993^*	–3.002^*	–2.736
–2.5	–2.360	–2.358	–2.850	–2.853	–2.979	–3.083^*	–2.436	–2.985^*	–2.962^*	–2.961
0	–2.360	–2.361	–2.829	–2.893	–2.969	–3.059^*	–2.419	–2.975^*	–2.941^*	–2.671
2.5	–2.369	–2.367	–2.841	–2.937	–2.990	–3.051^*	–2.389	–2.949^*	–2.921^*	–2.656
5	–2.387	–2.388	–2.849	–1.411	–3.002	–3.120^*	–2.290	–2.847^*	–2.840^*	–2.560
注: ^*表示位点不稳定, 最终吸附位点为附近的准三重位点.

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表 3 H吸附后单元表面积S_∆L

Table 3. Unit surface area of H-adsorption S_∆L.

ε/%	S_∆L/Å²
ε/%	TF_pure	TF_S	TF_L	TF
–5	2.715	2.909	2.751	2.936
–2.5	2.759	2.954	2.797	2.998
0	2.746	2.988	2.83	3.03
2.5	2.812	3.048	2.829	3.047
5	2.856	3.069	2.858	3.061

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[1]	Teng Y, Wang Z D, Li Y, Ma Q, Hui Q, Li S B 2019 Csee J. Power Energy 5 266 Google Scholar
[2]	张博, 万宏, 徐可忠, 李雪静, 魏寿祥 2017 国际石油经济 25 65 Google Scholar Zhang B, Wan H, Xu K Z, Li X J, Wei S X 2017 Int. Pet. Econ. 25 65 Google Scholar
[3]	Dodds P E, Mcdowall W 2013 Energy Policy 60 305 Google Scholar
[4]	Buzzard R W, Cleaves H E 1951 Hydrogen Embrittlement of Steel-Review of Literature (United States: National Bureau of Standards) p36
[5]	刘松, 王寅岗 2015 中国有色金属学 25 3100 Google Scholar Liu S, Wang M G 2015 Trans. Nonferrous Met. Soc. China 25 3100 Google Scholar
[6]	胡世威, 梁浩, 徐兵 2019 航空学报 40 278 Google Scholar Hu S W, Liang H, Xu B 2019 Acta Aeronaut. Astronaut. Sin. 40 278 Google Scholar
[7]	Cheng A K, Chen N Z 2017 Int. J. Fatigue 96 152 Google Scholar
[8]	Cheng A K, Chen N Z 2017 Ocean Eng. 142 10 Google Scholar
[9]	Meda U S, Bhat N, Pandey A, Subramanya K N, Lourdu Antony Raj M A 2023 Int. J. Hydrogen Energ. 48 17894 Google Scholar
[10]	Nanninga N, Grochowsi J, Heldt L, Rundman K 2009 Corros. Sci. 52 1237 Google Scholar
[11]	Nanninga N E, Levy Y S, Drexler E S, Condon R T, Stevenson A E, Slifka A J 2012 Corros. Sci. 59 1 Google Scholar
[12]	Zhou C S, Ye B G, Song Y Y, Cui T C, Xu P, Zhang L 2019 Int. J. Hydrogen Energ. 44 22547 Google Scholar
[13]	Toofan J, Watson P R 1998 Surf. Sci. 401 162 Google Scholar
[14]	Russell B C, Castell M R 2008 Phys. Rev. B 77 245414 Google Scholar
[15]	Lord M A, Evans E J, Barnett J C, Allen W M, Barron R A, Wilks P S 2017 J. Phys. Condens. Mat. 29 384001 Google Scholar
[16]	李守英, 胡瑞松, 赵卫民, 李贝贝王勇 2020 表面技术 49 15 Google Scholar Li S Y, Hu R S, Zhao W M, Li B B, Wang Y 2020 Surf. Technol. 49 15 Google Scholar
[17]	胡庭赫, 李直昊, 张千帆 2024 物理学报 73 067101 Google Scholar Hu T H, Li Z H, Zhang Q F 2024 Acta Phys. Sin. 73 067101 Google Scholar
[18]	赵巍, 汪家道, 刘峰斌, 陈大融 2009 物理学报 58 3352 Google Scholar Zhao W, Wang J D, Liu F B, Chen D R 2009 Acta Phys. Sin. 58 3352 Google Scholar
[19]	Yoshida K 1980 Jpn. J. Appl. Phys. 19 1873 Google Scholar
[20]	唐秀艳 2016 硕士学位论文(青岛: 中国石油大学(华东)) Tang X Y 2016 M. S. Thesis (Qingdao: China University of Petroleum (East China)
[21]	Savoie J, Ray R K, Butron-Guillen M P, Jonas J J 1994 Acta Metall. Mater. 42 2511 Google Scholar
[22]	Cremaschi P, Yang H, Whitten J L 1995 Surf. Sci. 330 255 Google Scholar
[23]	Bozso F, Ertl G, Grunze M, Weiss M 1977 Appl. of Surf. Sci. 1 103 Google Scholar
[24]	Baró A M, Erley W 1981 Surf. Sci. 112 L759 Google Scholar
[25]	Xie W W, Peng L, Peng D L, Gu F L, Liu J 2014 Appl. Surf. Sci. 296 47 Google Scholar
[26]	Eder M, Terakura K, Hafner J 2001 Phys. Rev. B 64 115426 Google Scholar
[27]	Raeker J T, DePristo E A 1990 Surf. Sci. 235 84 Google Scholar
[28]	Chohan K U, Jimenez M E, Koehler P K S 2016 Appl. Surf. Sci. 387 385 Google Scholar
[29]	Xu L, Kirvassilis D, Bai Y, Mavrikakis M 2018 Surf. Sci. 667 54 Google Scholar
[30]	Richard T, Zihan X, Balachandran R, Donald W, Wenhao S, Kristin A P, Ping O S 2016 Sci. Data 3 160080 Google Scholar
[31]	Sheikhzadeh A, Liu J, Zeng Y M, Zhang H 2024 Int. J. Hydrogen Energ. 81 727 Google Scholar
[32]	李守英, 赵卫民, 乔建华, 王勇 2019 物理学报 68 217103 Google Scholar Li S Y, Zhao W M, Qiao J H, Wang Y 2019 Acta Phys. Sin. 68 217103 Google Scholar
[33]	Li S Y, Zhao W M, Wang Y 2020 Chin. J. Struc. Chem. 39 443 Google Scholar
[34]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758 Google Scholar
[35]	Kresse G, Hafner J 1993 Phys. Rev. B 47 558 Google Scholar
[36]	Blochl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[37]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[38]	Liu X W, Huo C F, Li Y W, Wang J G, Jiao H J 2012 Surf. Sci. 606 733 Google Scholar
[39]	Jiang D E, Carter A E 2005 Phys. Rev. B 71 045402 Google Scholar
[40]	Dong N, Zhang C, Liu H, Li J, Wu X L 2014 Comp. Mater. Sci. 90 137 Google Scholar
[41]	Stibor A, Kresse G, Eichler A, Hafner J 2002 Surf. Sci. 507 99 Google Scholar
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