First-principles study of boron segregation in fcc-Fe grain boundaries and its influence on interface adhesive strength

Xu Pan-Pan; Han Pei-De; Zhang Zhu-Xia; Zhang Cai-Li; Dong Nan; Wang Jian

doi:10.7498/aps.70.20210361

Abstract

Boron, a commonly used microalloying element in steel, is distributed mainly at the grain boundary of stainless steel and plays an important role in regulating the mechanical, corrosion resistance and grain boundary structure of stainless steel. Owing to the small amount of boron added into the steel, it is difficult experimentally to detect the traces of boron segregation at the grain boundary, not to mention analyzing the structural characteristics of the boron segregation grain boundary. First-principles density functional theory (DFT) provides convenience in analyzing the existence mode and mechanism of boron in austenitic steel from the atomic level. Combining with the actual grain boundary structure types in austenitic stainless steel, Fcc-Fe Σ3(112), Σ5(210), Σ5(310), Σ9(114), Σ9(221) and Σ11(113) symmetric tilt grain boundaries are constructed based on DFT, and the segregation behaviors of boron atoms at the six grain boundaries are studied to reveal the segregation mechanism from the atomic and electronic level. The results show that boron segregation occurs mostly at Σ5(210), Σ5(310) and Σ9(114) grain boundaries, while a relatively weak segregation tendency is observed at Σ9(221), Σ3(112) and Σ11(113) grain boundaries; boron atom preferentially occupies the pentahedral or hexahedral segregation position with the largest coordination number; the interface adhesive strength at grain boundaries is improved by the segregation of boron according to the tensile test, which complies with the calculation results of Rice-Wang thermodynamic model; the chemical effect caused by the increase of local charge density after boron segregation at Σ9(114) grain boundary outstrips the adverse effect of structural changes, and the strong interaction between B-p electrons and Fe-s electrons improves the interface adhesive strength. The results provide a reference for using boron to optimize the interface structure of austenitic stainless-steel.

Keywords:

Authors and contacts

1.
College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2.
College of Aeronautics and Astronautics, Taiyuan University of Technology, Jinzhong 030600, China

Corresponding author: Han Pei-De, hanpeide@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51871159, U1860204) and the Natural Science Foundation of Shanxi Province, China (Grant No. 201801D221125)

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References

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图 1 fcc-Fe的　(a) Σ3(112), (b) Σ5(210), (c) Σ5(310), (d) Σ9(114), (e) Σ9(221), (f) Σ11(113)晶界和(g) B所处间隙位的模型图

Figure 1. Schematic illustration showing (a) Σ3(112), (b) Σ5(210), (c) Σ5(310), (d) Σ9(114), (e) Σ9(221), (f) Σ11(113) grain boundaries and (g) polyhedron interstices where B located.

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图 2 B在6个晶界中不同间隙位置的溶解能

Figure 2. The solution energies for B at different interstitial sites in the six studied grain boundaries.

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图 3 B原子在6个晶界中最稳定的偏析位点上的偏析能

Figure 3. The segregation energies for B at the most stable segregation sites of the six studied grain boundaries.

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图 4 B原子在6个晶界稳定偏析位的强化能

Figure 4. The strengthening energies for B at the stable segregation sites of the six studied grain boundaries.

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图 5 添加B原子前后6个晶界的抗拉强度曲线

Figure 5. Tensile strength curves of the six studied grain boundaries without and with B.

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图 6 添加B原子前后, Σ9(114)晶界体系(a)未形变及(b)均匀拉伸12%变形量后的电荷密度图

Figure 6. The charge density of (a) undeformed and (b) 12% tensile deformed Σ9(114) grain boundary without and with B

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图 7 (a)未添加B原子和(b)添加B原子Σ9(114)晶界的总态密度图, 以及B原子附近Fe₁, Fe₂和B原子的分波态密度图

Figure 7. The total density of states (TDOS) of Σ9(114) grain boundary without and with B atom, correspond to (a) and (b) respectively, and the projected density of states (PDOS) of Fe atoms in the vicinity of B atom (Fe₁ and Fe₂)and B atom.

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表 1 fcc-Fe的CSL晶界的结构特性

Table 1. Structural characteristics of calculated grain boundaries

Grain boundaries	γ_GB/(J·m^–2)	ΔV/(Å³·Å^–2)	Angle/(°)	Numbers of atomes	Supercell dimensions/(Å × Å × Å)	S/Å²
∑3(112)[110]	0.341	0.207	109.47	48	4.86 × 5.955 × 17.037	28.94
∑5(210)[001]	1.661	0.762	53.13	76	6.873 × 7.685 × 15.37	52.82
∑5(310)[001]	1.925	0.543	36.87	78	5.434 × 6.873 × 21.736	37.35
∑9(114)[110]	1.546	0.771	141.06	68	4.86 × 10.31 × 14.58	52.54
∑9(221)[110]	1.716	1.143	38.94	68	4.86 × 7.29 × 20.62	35.43
∑11(113)[110]	0.559	0.499	129.52	88	4.86 × 8.06 × 23.296	39.17

DownLoad: CSV

表 2 B原子在各晶界最佳偏析位的多面体结构模型、添加B原子前后的多面体的体积和体积增量、B原子与近邻Fe原子的键长, 以及引起晶界能的变化量

Table 2. The local atomic configurations of the stable segregation sites, the volume and volume increment of the polyhedron without and with B, the bond length between B and neighboring Fe atoms, and the change of grain boundary energy caused by B segregation when B at the stable segregation sites.

		Σ3(112)	Σ5(210)	Σ5(310)	Σ9(221)	Σ9(114)	Σ11(113)
Polyhedron of favorable interstitial sites
Volume of polyhedron/Å³	V_{pure Fe}	5.80	4.73	5.41	5.03	13.90	6.01
	V_{with B}	7.67	4.91	5.75	5.16	15.09	6.06
	V_{with B}-V_{pure Fe}	1.88	0.18	0.34	0.13	1.20	0.04
Bond length of Fe-B/Å	Fe₁-B	2.04	2.17	2.15	2.13	2.09	1.98
Bond length of Fe-B/Å	Fe₂-B	2.84	2.03	2.06	2.02	2.22	1.95
The change of grain boundary energy /(mJ·m^–2)		–14.90	–8.72	–11.50	–31.10	–25.00	–5.02

DownLoad: CSV

map

[1]	Ma S, Pan W, Xing J, et al. 2017 Mater. Chem. Phys. 199 356 Google Scholar
[2]	Naderi M, Ketabchi M, Abbasi M, et al. 2010 Steel Res. Int. 81 216 Google Scholar
[3]	Ghali S N, El-Faramawy H S, Eissa M M 2012 J. Miner. Mater. Char. Eng. 11 995
[4]	Jones R B, Younes C M, Heard P J, et al. 2002 Acta Mater. 50 4395 Google Scholar
[5]	Zarandi F, Yue S 2006 Metall. Mater. Trans. A 37 2316 Google Scholar
[6]	López-Chipres E, Mejía I, Maldonado C, et al. 2007 Mater. Sci. Eng. A-Struct 460/461 464 Google Scholar
[7]	Mejía I, Bedolla-Jacuinde A, Maldonado C, et al. 2011 Mater. Sci. Eng. A-Struct 528 4468 Google Scholar
[8]	Deva A, Jha B K, Mishra N S 2011 Mater. Sci. Eng. A-Struct 528 7375 Google Scholar
[9]	Takahashi J, Ishikawa K, Kawakami K, et al. 2017 Acta Mater. 133 41 Google Scholar
[10]	Li Y, Ponge D, Choi P, Raabe D 2015 Scripta Mater. 96 13 Google Scholar
[11]	王博, 张建民, 路彦冬, 等 2011 60 016601 Google Scholar Wang B, Zhang J M, Lu Y D, et al. 2011 Acta Phys. Sin. 60 016601 Google Scholar
[12]	孟凡顺, 李久会, 赵星 2014 63 237102 Google Scholar Meng F S, Li J H, Zhao X 2014 Acta Phys. Sin. 63 237102 Google Scholar
[13]	Li Y, Korzhavyi P A, Sandström R, et al. 2017 Phys. Rev. Mater. 1 070602 Google Scholar
[14]	Huang Z, Chen F, Shen Q, et al. 2018 Acta Mater. 148 110 Google Scholar
[15]	Huang Z, Chen F, Shen Q, et al. 2019 Acta Mater. 166 113 Google Scholar
[16]	Du Y A, Ismer L, Rogal J, et al. 2011 Phys. Rev. B 84 144121 Google Scholar
[17]	Wang J, Janisch R, Madsen G K H, et al. 2016 Acta Mater. 115 259 Google Scholar
[18]	Razumovskiy V I, Lozovoi A Y, Razumovskii I M 2015 Acta Mater. 82 369 Google Scholar
[19]	Bentria E L T, Lefkaier I K, Bentria B 2013 Mater. Sci. Eng. A-Struct 577 197 Google Scholar
[20]	Wu R, Freeman A J, Olson G B 1994 Science 265 376 Google Scholar
[21]	Shang J X, Wang C Y 2001 J. Phys.-Condens. Mat. 13 9635 Google Scholar
[22]	He B, Xiao W, Hao W, et al. 2013 J. Nucl. Mater. 441 301 Google Scholar
[23]	Li Y, Han C, Zhang C, et al. 2016 Comp. Mater. Sci. 115 170 Google Scholar
[24]	Rice J R, Wang J S 1989 Mater. Sci. Eng. A-Struct 107 23 Google Scholar
[25]	张颖, 吕广宏, 邓胜华 2006 55 2901 Google Scholar Zhang Y, Lü G H, Deng S H 2006 Acta Phys. Sin. 55 2901 Google Scholar
[26]	王晓中, 林理彬, 何捷, 等 2011 60 077104 Google Scholar Wang X Z, Lin L B, He J, et al. 2011 Acta Phys. Sin. 60 077104 Google Scholar
[27]	Zhou H, Jin S, Zhang Y, Lu G 2011 Prog. Nat. Sci. 21 240 Google Scholar
[28]	Shi F, Tian P C, Jia N, et al. 2016 Corros. Sci. 107 49 Google Scholar
[29]	Mahjoub R, Laws K J, Stanford N, Ferry M 2018 Acta Mater. 158 257 Google Scholar
[30]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[31]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[32]	Häglund J, Guillermet A F, Grimvall G, et al. 1993 Phys. Rev. B 48 11685 Google Scholar
[33]	Jiang D E, Carter E A 2003 Phys. Rev. B 67 214103 Google Scholar
[34]	Basinski Z S, Hume-Rothery W, Sutton A L 1955 Proc. R. Soc. Lond. A 229 459 Google Scholar
[35]	Bean J J, McKenna K P 2016 Acta Mater. 110 246 Google Scholar
[36]	Tran R, Xu Z, Zhou N, et al. 2016 Acta Mater. 117 91 Google Scholar
[37]	Yang Y, Ding J, Zhang P, et al. 2019 Nucl. Instrum. Meth. B 456 7 Google Scholar
[38]	Lejcek P 2010 Grain Boundary Segregation in Metals (Berlin: Springer Science & Business Media) p51
[39]	Zhang S, Kontsevoi O Y, Freeman A J, et al. 2011 Acta Mater. 59 6155 Google Scholar
[40]	Wu X, You Y W, Kong X S, et al. 2016 Acta Mater. 120 315 Google Scholar
[41]	Tian Z X, Yan J X, Xiao W, et al. 2009 Phys. Rev. B 79 144114 Google Scholar
[42]	Yamaguchi M, Shiga M, Kaburaki H 2005 Science 307 393 Google Scholar
[43]	Rose J H, Smith J R, Ferrante J 1983 Phys. Rev. B 28 1835
[44]	Warrington D H 1975 J. Phys. Colloques 36 C4-87
[45]	Brokman A, Balluffi R W 1981 Acta Metall. 29 1703 Google Scholar
[46]	Scholz F 1997 J Solid State Electrochem 1 117 Google Scholar
[47]	Zheng H, Li X, Tran R, et al. 2020 Acta Mater. 186 40 Google Scholar
[48]	Hatcher N, Madsen G K H, Drautz R 2014 J. Phys. Condens. Mat. 26 145502 Google Scholar
[49]	Rhodes N R, Tschopp M A, Solanki K N 2013 Model. Simul. Mater. Sc. 21 035009 Google Scholar
[50]	Bai J, Cui Y, Wang J, et al. 2018 Metals 8 497 Google Scholar

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