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High-pressure gaseous hydrogen storage is an important way of hydrogen energy storage and transport at present, while high-strength steel material is one of the main materials used for hydrogen storage vessels. However, their internal doping elements and inherent defects often lead their mechanical properties to decrease, thus reducing the pressure-bearing capability and storage life of the vessel. At present, the mechanism of doping elements influencing the mechanical properties of high-strength steels is still unclear. In this work, a first-principles approach is used to study the influence of elemental doping (Cr, Mn, Mo, As, Sb, Bi, Sn, Pb) on the mechanical properties of Fe single crystals and Fe-C systems. The results show that among the above elements, Mn doping can increase the elastic modulus, bulk modulus, and shear modulus compared with those of pure Fe, while the doping by remaining elements will reduce the three moduli above, with the non-transition metal elements having a greater effect on the three moduli than the transition metal elements. Electronic structure analysis shows that the transition metal elements have better compatibility with the Fe lattice. Molecular dynamics results further show that the injection of H atoms significantly disrupts the lattice ordering of the Fe polycrystalline doped by C, Cr, and Mn elements, while the doping of Cr elements can significantly enhance the dislocation density of the system. The effects of doping elements on the mechanical properties of single-crystal and polycrystalline Fe, which are studied in this work, are of great significance in guiding the mechanistic study of the effects of doping and defects on the strength of Fe-based materials.
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Keywords:
- first-principles /
- molecular dynamics /
- mechanical properties /
- crystal defects
[1] Zhou X Y, Yang X S, Zhu J H, Xing F 2020 Int. J. Hydrog. Energy 45 3294
Google Scholar
[2] Xing X, Chen W X, Zhang H 2017 Int. J. Hydrog. Energy 42 4571
Google Scholar
[3] Zafra A, Peral L B, Belzunce J, Rodríguez C 2018 Int. J. Hydrog. Energy 43 9068
Google Scholar
[4] Bechtle S, Kumar M, Somerday B P, Launey M E, Ritchie R O 2009 Acta Mater. 57 4148
Google Scholar
[5] Ye T Z, Wang Z T, Wu Y W, Zhang J, Chen P, Wang M J, Tian W X, Su G H, Qiu S Z 2023 J. Mater. Res. 38 828
Google Scholar
[6] Chen K, Xu Y W, Song S H 2019 Results Phys. 13 102208
Google Scholar
[7] 周华生, 曹燕, 章小峰, 吴迪, 赵鑫磊, 邢梅, 林方敏, 江雅 2024 材料导报 38 22110194
Zhou H S, Cao Y, Zhang X F, Wu D, Zhao X L, Xing M, Lin F M, Jiang Y 2024 Mater. Rep. 38 22110194
[8] Chatterjee S, Ghosh S, Saha-Dasgupta T 2021 Minerals 11 258
Google Scholar
[9] Xiong X L, Ma H X, Zhang L N, Song K K, Yan Y, Qian P, Su Y J 2023 Comput. Mater. Sci. 216 111854
Google Scholar
[10] 文平, 李春福, 赵毅, 张凤春, 童丽华 2014 63 197101
Google Scholar
Wen P, Li C F, Zhao Y, Zhang F C, Tong L H 2014 Acta Phys. Sin. 63 197101
Google Scholar
[11] 王明军, 李春福, 文平, 张凤春, 王垚, 刘恩佐 2016 65 037101
Google Scholar
Wang M J, Li C F, Wen P, Zhang F C, Wang Y, Liu E Z 2016 Acta Phys. Sin. 65 037101
Google Scholar
[12] Zhou X Y, Zhu J H, Wu H H 2021 Int. J. Hydrog. Energy 46 5842
Google Scholar
[13] Hafner J, Kresse G 1997 Properties of Complex Inorganic Solids (Boston: Springer) pp69–82
[14] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[15] Thompson A P, Aktulga H M, Berger R, et al. 2022 Comput. Phys. Commun. 271 108171
Google Scholar
[16] Liu Z R, Yao B N, Zhang R F 2022 Comput. Mater. Sci. 210 111027
Google Scholar
[17] Starikov S, Smirnova D, Pradhan T, Gordeev I, Drautz R, Mrovec M 2022 Phys. Rev. Mater. 6 043604
Google Scholar
[18] Hepburn D J, Ackland G J 2008 Phys. Rev. B 78 165115
Google Scholar
[19] Kim Y M, Shin Y H, Lee B J 2009 Acta Mater. 57 474
Google Scholar
[20] Evans D J, Holian B L 1985 J. Chem. Phys. 83 4069
Google Scholar
[21] Stukowski A 2010 Modell. Simul. Mater. Sci. Eng. 18 015012
Google Scholar
[22] Zhao Y J, Zunger A 2004 Phys. Rev. B 69 075208
Google Scholar
[23] 刘柏年, 马颖, 周益春 2010 59 3377
Google Scholar
Liu B N, Ma Y, Zhou Y C 2010 Acta Phys. Sin. 59 3377
Google Scholar
[24] Lee H S, Mizoguchi T, Yamamoto T, Kang S J L, Ikuhara Y 2007 Acta Mater. 55 6535
Google Scholar
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图 1 (a) 5%浓度的替换掺杂的BCC单晶Fe超胞模型; (b)边长为150 Å的多晶Fe模型, 不同颜色用来区分晶粒内部和晶界处的原子
Figure 1. (a) Fe supercell of BCC single crystal, 5% substitutional solution; (b) a polycrystalline Fe model with a side length of 150 Å, where different colours indicate atoms at the boundary and inside grains.
图 2 (a)—(d) Fe-M体系、(e)—(h) Fe-C-M体系不同M种类及浓度下的弹性模量、体模量、剪切模量和泊松比, 虚线表示纯铁体系对应的数值
Figure 2. Young’s moduli, bulk moduli, shear moduli and Poisson’s ratio for (a)–(d) Fe-M systems and (e)–(h) Fe-C-M systems with different M species and concentrations. Dotted line represents moduli and Poisson’s ratio of pure Fe systems.
图 3 (a)—(d) Fe-Mn, Fe-Mo, Fe-As以及Fe-Pb体系的分波态密度; (e)—(h) Fe-C-Mn, Fe-C-Mo, Fe-C-As以及Fe-C-Pb体系的分波态密度
Figure 3. PDOS of (a) Fe-Mn, (b) Fe-Mo, (c) Fe-As, (d) Fe-Pb, (e) Fe-C-Mn, (f) Fe-C-Mo, (g) Fe-C-As, (h) Fe-C-Pb systems.
图 4 (a)—(d) 不同H浓度下Fe-C-H体系的分波态密度
Figure 4. (a)–(d) PDOS of Fe-C-H systems under different H concentrations.
图 5 (a) Fe-H, (b) Fe-C, (c) Fe-Cr以及(d) Fe-Mn多晶体系的杨氏模量随掺杂元素种类及含量的变化
Figure 5. Young’s moduli of (a) Fe-H, (b) Fe-C, (c) Fe-Cr, (d) Fe-Mn polycrystalline systems with various doping element content.
图 6 (a) Fe-H, (b) Fe-C, (c) Fe-Cr以及(d) Fe-Mn二元体系和(e) Fe-C-Cr, (f) Fe-C-Mn三元体系在不同掺杂浓度下的拉伸应力-应变曲线
Figure 6. Tensile stress-strain curves at different doping concentrations: (a) Fe-H, (b) Fe-C, (c) Fe-Cr and (d) Fe-Mn binary system; (e) Fe-C-Cr, (f) Fe-C-Mn ternary system.
图 7 (a)—(f) H, C, Cr, Mn元素对多晶体Fe最大应力和屈服强度的影响
Figure 7. Influences of (a)–(f) H, C, Cr and Mn on maximum strength and yield strength of Fe polycrystal.
图 8 (a)—(f) Fe-H体系、Fe-C体系、Fe-C-H体系、Fe-Cr体系、Fe-Cr-H体系及Fe-Mn体系在拉伸初始条件下的晶格取向模型; (g)—(l) Fe-H体系、Fe-C体系、Fe-C-H体系、Fe-Cr体系、Fe-Cr-H体系及Fe-Mn体系在拉伸过程4 ps到达最大应变时的晶体取向模型, 不同颜色代表晶体的不同取向
Figure 8. (a)–(f) Lattice orientation models of Fe-H, Fe-C, Fe-C-H, Fe-Cr, Fe-Cr-H and Fe-Mn systems under fully relaxed conditions; (g)–(l) crystal orientation models of Fe-H, Fe-C, Fe-C-H, Fe-Cr, Fe-Cr-H and Fe-Mn systems at maximum strain during stretching. Different colours indicate different orientations of crystals.
图 9 (a)—(f) Fe-H体系、Fe-C体系、Fe-C-H体系、Fe-Cr体系、Fe-Cr-H体系及Fe-Mn体系在拉伸初始条件下的位错线分布对比图
Figure 9. (a)–(f) Dislocation configurations of Fe-H, Fe-C, Fe-C-H, Fe-Cr, Fe-Cr-H and Fe-Mn systems after relaxation.
表 1 Fe-M体系的晶格参数a, b和c, 以及Fe-M体系和Fe-C-M掺杂体系的形成能$ \Delta {H_{{\text{D,q}}}} $和$ \Delta {H_{{\text{C,D,q}}}} $
Table 1. Lattice parameters of Fe-M systems, and formation energy of Fe-M and Fe-C-M systems.
掺杂/% a/Å b/Å c/Å ΔHD,q
/eVΔHC,D,q
/eVCr 1 2.831 2.831 2.831 –0.168 0.565 3 2.834 2.835 2.835 –0.456 0.690 5 2.838 2.837 2.838 –0.721 0.863 Mo 1 2.834 2.834 2.834 0.001 0.738 3 2.841 2.842 2.841 0.009 1.174 5 2.849 2.848 2.850 –0.003 1.603 Mn 1 2.830 2.830 2.830 0.232 0.964 3 2.829 2.830 2.829 0.756 1.307 5 2.829 2.829 2.828 0.993 1.711 As 1 2.832 2.832 2.832 –0.387 0.335 3 2.837 2.837 2.836 –1.173 0.023 5 2.842 2.843 2.842 –1.983 –0.269 Sb 1 2.836 2.836 2.836 0.433 1.169 3 2.851 2.850 2.849 1.233 3.165 5 2.864 2.868 2.863 1.807 4.969 Bi 1 2.839 2.839 2.839 2.125 2.864 3 2.862 2.859 2.858 6.156 7.641 5 2.878 2.885 2.878 9.758 11.807 Sn 1 2.836 2.836 2.836 0.613 1.357 3 2.851 2.850 2.850 1.663 3.181 5 2.864 2.868 2.864 2.452 4.797 Pb 1 2.839 2.839 2.839 2.233 2.976 3 2.860 2.857 2.858 6.412 7.613 5 2.875 2.880 2.877 10.206 11.695 
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[1] Zhou X Y, Yang X S, Zhu J H, Xing F 2020 Int. J. Hydrog. Energy 45 3294
Google Scholar
[2] Xing X, Chen W X, Zhang H 2017 Int. J. Hydrog. Energy 42 4571
Google Scholar
[3] Zafra A, Peral L B, Belzunce J, Rodríguez C 2018 Int. J. Hydrog. Energy 43 9068
Google Scholar
[4] Bechtle S, Kumar M, Somerday B P, Launey M E, Ritchie R O 2009 Acta Mater. 57 4148
Google Scholar
[5] Ye T Z, Wang Z T, Wu Y W, Zhang J, Chen P, Wang M J, Tian W X, Su G H, Qiu S Z 2023 J. Mater. Res. 38 828
Google Scholar
[6] Chen K, Xu Y W, Song S H 2019 Results Phys. 13 102208
Google Scholar
[7] 周华生, 曹燕, 章小峰, 吴迪, 赵鑫磊, 邢梅, 林方敏, 江雅 2024 材料导报 38 22110194
Zhou H S, Cao Y, Zhang X F, Wu D, Zhao X L, Xing M, Lin F M, Jiang Y 2024 Mater. Rep. 38 22110194
[8] Chatterjee S, Ghosh S, Saha-Dasgupta T 2021 Minerals 11 258
Google Scholar
[9] Xiong X L, Ma H X, Zhang L N, Song K K, Yan Y, Qian P, Su Y J 2023 Comput. Mater. Sci. 216 111854
Google Scholar
[10] 文平, 李春福, 赵毅, 张凤春, 童丽华 2014 63 197101
Google Scholar
Wen P, Li C F, Zhao Y, Zhang F C, Tong L H 2014 Acta Phys. Sin. 63 197101
Google Scholar
[11] 王明军, 李春福, 文平, 张凤春, 王垚, 刘恩佐 2016 65 037101
Google Scholar
Wang M J, Li C F, Wen P, Zhang F C, Wang Y, Liu E Z 2016 Acta Phys. Sin. 65 037101
Google Scholar
[12] Zhou X Y, Zhu J H, Wu H H 2021 Int. J. Hydrog. Energy 46 5842
Google Scholar
[13] Hafner J, Kresse G 1997 Properties of Complex Inorganic Solids (Boston: Springer) pp69–82
[14] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[15] Thompson A P, Aktulga H M, Berger R, et al. 2022 Comput. Phys. Commun. 271 108171
Google Scholar
[16] Liu Z R, Yao B N, Zhang R F 2022 Comput. Mater. Sci. 210 111027
Google Scholar
[17] Starikov S, Smirnova D, Pradhan T, Gordeev I, Drautz R, Mrovec M 2022 Phys. Rev. Mater. 6 043604
Google Scholar
[18] Hepburn D J, Ackland G J 2008 Phys. Rev. B 78 165115
Google Scholar
[19] Kim Y M, Shin Y H, Lee B J 2009 Acta Mater. 57 474
Google Scholar
[20] Evans D J, Holian B L 1985 J. Chem. Phys. 83 4069
Google Scholar
[21] Stukowski A 2010 Modell. Simul. Mater. Sci. Eng. 18 015012
Google Scholar
[22] Zhao Y J, Zunger A 2004 Phys. Rev. B 69 075208
Google Scholar
[23] 刘柏年, 马颖, 周益春 2010 59 3377
Google Scholar
Liu B N, Ma Y, Zhou Y C 2010 Acta Phys. Sin. 59 3377
Google Scholar
[24] Lee H S, Mizoguchi T, Yamamoto T, Kang S J L, Ikuhara Y 2007 Acta Mater. 55 6535
Google Scholar
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