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Ferritic/martensitic steel, with Cr atomic content in a range of 7%–15%, is a promising candidate for advanced nuclear power systems, due to its swelling resistance and creep fracture resistance under irradiation. Under thermodynamic conditions, Cr segregation usually occurs at grain boundary (GB) in Fe-Cr alloys. However, irradiation can greatly accelerate this process. The enrichment of Cr at GB will enhance precipitation, resulting in embrittlement; while the depletion of Cr at GB may greatly weaken the corrosion resistance properties. In the present work, thermodynamic segregation and radiation-enhanced segregation of Cr element at GB in Fe-Cr alloy is investigated by using the Wheeler-Boettinger-McFadden (WBM) phase-field model. The simulation results show that temperature has a great influence during thermodynamic segregation of Cr at the GB without radiation: when the temperature is lower than 500 ℃ the segregation amount of Cr at the GB is relatively small; when the temperature is higher than 500 ℃ the Cr concentration at GB increases significantly. In addition, as the concentration of Cr in the matrix increases, the amount of relative increase of Cr concentration at GB decreases. However, the Cr concentration at GB under irradiation is significantly enhanced, compared with the counterpart without irradiation. With the increase of dose rate, the Cr concentration in the center of GB also increases. Moreover, with the increase of Cr concentration in the matrix, the relative increase of the Cr concentration at the GB weakens.
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Keywords:
- phase-field simulation /
- Fe-Cr alloys /
- grain boundary segregation /
- radiation-enhanced diffusion
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Liu T, Yang M, Wang G, Wang L, Xu D S 2020 Rare Metal Mater. Eng. 56 1114
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Google Scholar
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Zhu L L 2014 M. S. Thesis (Wuhan: Central China Normal University) (in Chinese)
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Google Scholar
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[13] 柯常波, 周敏波, 张新平 2014 金属学报 50 294
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Ke C B, Zo H M, Zhang X P 2014 Acta Metall. Sin. 50 294
Google Scholar
[14] Wheeler A A, Boettinger W J, McFadden G B 1992 Phys. Rev. A 45 7424
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[37] McLean D 1957 Grain Boundaries in Metals (London: Oxford at the Clarendon Press) p1
[38] Seah M P 1980 J. Phys. F: Met. Phys. 10 1063
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图 1 相场变量ϕ和x的初始分布
Figure 1. Initial distribution of phase field variable ϕ and x.
图 2 Fe-Cr合金中晶界处Cr元素浓度的变化曲线 (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr
Figure 2. Evolution of Cr concentration at grain boundary in Fe-Cr alloys: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.
图 3 500 ℃模拟100 s后不同成分的Fe-Cr合金的相场变量 (a) x; (b) ϕ
Figure 3. The curves of the phase field variables of Fe-Cr alloys with different compositions after 100 s at 500 ℃: (a) x; (b) ϕ.
图 4 500 ℃下100 s后晶界处的相对Cr浓度增量和基体中Cr浓度的关系曲线
Figure 4. The relationship between the relative change of Cr concentration at grain boundary and the bulk Cr concentration after 100 s at 500 ℃.
图 5 不同温度下晶界处Cr元素的浓度分布 (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr
Figure 5. Distribution of Cr concentration at grain boundary with different temperatures: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.
图 6 450 ℃辐照剂量率为10–4 dpa/s下晶界处Cr元素的浓度分布 (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr
Figure 6. Concentration distribution of Cr element at GB at a dose rate of 10–4 dpa/s at 450 ℃: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.
图 7 450 ℃辐照剂量率为10–5 dpa/s下晶界处Cr元素浓度的变化曲线 (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr
Figure 7. Evolution of Cr concentration at grain boundary with a dose rate of 10–5 dpa/s at 450 ℃: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.
图 8 不同辐照剂量率下晶界处Cr元素浓度的分布 (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr
Figure 8. Distribution of Cr concentration with different dose rates: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.
图 9 450 ℃时不同剂量率下晶界处的相对Cr浓度增量和初始Cr浓度的关系曲线
Figure 9. The relationship between the relative change of Cr concentration at grain boundary and the bulk Cr concentration at different dose rates at 450 ℃
图 10 辐照剂量率为1.2 × 10–5 dpa/s时模拟结果与实验结果对比
Figure 10. Comparison of simulation results and experimental results when the dose rate is 1.2 × 10–5 dpa/s.
表 2 Fe-Cr合金辐照加速扩散模型的参数
Table 2. Parameters of radiation enhanced diffusion model of Fe-Cr alloys.
物理参数 数值 参考文献 d/m $ 2.49\times {10}^{-10} $ k/(J·K–1) $ 1.38\times {10}^{-23} $ $ {r}_{\rm{c}}/{\rm{m}} $ $ 3\times {10}^{-10} $ [26] ξ 0.33 [31] $ {V}_{{\rm{a}}} $/m3 $ 1.18\times {10}^{-29} $ $ {E}_{{\rm{m}}} $/eV 1.1 [32] $ {S}_{{\rm{d}}} $/m–2 $ 1.0\times {10}^{-13} $ $ {R}_{\rm{r}} $/m $ 5.7\times {10}^{-10} $ [23] $ {R}_{\rm{t}} $/m $ 5.7\times {10}^{-10} $ [23] $ {H}_{\rm{b}} $/eV 0.094 [33] $ {S}_{{\rm{s}}{\rm{a}}{\rm{t}}} $/m–2 $ 3.0\times {10}^{-15} $ 
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[1] Yvon P, Le F M, Cabet C, Seran J L 2015 Nucl. Eng. Des. 294 161
Google Scholar
[2] Zinkle S J, Busby J T 2009 Mater. Today 385 217
Google Scholar
[3] Yvon P, Carré F 2009 J. Nucl. Mater. 385 217
Google Scholar
[4] Lucas G E 2002 J. Nucl. Mater. 302 232
Google Scholar
[5] 刘涛, 杨梅, 王刚, 王璐, 徐东生 2020 稀有金属材料与工程 56 1114
Liu T, Yang M, Wang G, Wang L, Xu D S 2020 Rare Metal Mater. Eng. 56 1114
[6] Nastar M, Soisson F 2012 Compr. Nucl. Mater. 1 471
Google Scholar
[7] Wharry J P, Was G S 2013 J. Nucl. Mater. 442 7
Google Scholar
[8] Faulkner R G 1997 J. Nucl. Mater. 251 269
Google Scholar
[9] Terentyev D, He X, Zhurkin E, Bakaev A 2011 J. Nucl. Mater. 408 161
Google Scholar
[10] 朱陆陆 2014 硕士学位论文 (武汉: 华中师范大学)
Zhu L L 2014 M. S. Thesis (Wuhan: Central China Normal University) (in Chinese)
[11] Was G S, Wharry J P, Frisbie B, Wirth B D, Morgan D, Tucker J D, Allen T R 2011 J. Nucl. Mater. 411 41
Google Scholar
[12] Xia L D, Ji Y Z, Liu W B, Chen H, Yang Z G, Zhang C, Chen L Q 2020 Nucl. Eng. Technol. 52 148
Google Scholar
[13] 柯常波, 周敏波, 张新平 2014 金属学报 50 294
Google Scholar
Ke C B, Zo H M, Zhang X P 2014 Acta Metall. Sin. 50 294
Google Scholar
[14] Wheeler A A, Boettinger W J, McFadden G B 1992 Phys. Rev. A 45 7424
Google Scholar
[15] Kim S G, Kim W T, Suzuki T 1999 Phys. Rev. E 60 7186
Google Scholar
[16] Kim S G, Lee J S, Lee B J 2016 Acta Mater. 112 150
Google Scholar
[17] Badillo A, Bellon P, Averback R S 2015 Model. Simul. Mater. Sci. Eng. 23 035008
Google Scholar
[18] Piochaud J B, Nastar M, Soisson F, Thuinet L, Legris A 2016 Comput. Mater. Sci. 122 249
Google Scholar
[19] Grönhagen K, Ågren J 2007 Acta Mater. 55 955
Google Scholar
[20] Zhang C Y, Chen H, Zhu J N, Liu W B, Liu G, Zhang C, Yang Z G 2019 Scr. Mater. 162 44
Google Scholar
[21] Allen S M, Cahn J W 1979 Acta Metall. 27 1085
Google Scholar
[22] Cahn J W 1961 Acta Metall. 9 795
Google Scholar
[23] Odette G R, Yamamoto T, Klingensmith D 2005 Philos. Mag. 85 779
Google Scholar
[24] Ke H, Wells P, Edmondson P D, Almirall N, Barnard L, Odette G R, Morgan D 2017 Acta Mater. 138 10
Google Scholar
[25] Gamsjäger E, Svoboda J, Fischer F D 2005 Comput. Mater. Sci. 32 360
[26] Ke J H, Reese E R, Marquis E A, Odette G R, Morgan D 2019 Acta Mater. 164 586
Google Scholar
[27] Makin M J, Minter F J 1960 Acta Metall. 8 691
Google Scholar
[28] Enomoto M, White C L, Aaronson H I 1988 Metall. Trans. A 19A 1807
[29] Chen H, Zwaag S V D 2014 Acta Mater. 72 1
Google Scholar
[30] Zhu J N, Luo H W, Yang Z G, Zhang C, Zwaag S V D, Chen H 2017 Acta Mater. 133 258
Google Scholar
[31] Malerba L 2006 J. Nucl. Mater. 351 28
Google Scholar
[32] Martinez E, Senninger O, Fu C C 2012 Matter Mater. Phys. 86 1
Google Scholar
[33] Lavrentiev M Y, Nguyen-Manh D, Dudarev S L 2018 J. Nucl. Mater. 499 613
Google Scholar
[34] Moelans N, Blanpain B, Wollants P 2008 Calphad 32 268
Google Scholar
[35] Li J, Wang J, Yang G 2009 Acta Mater. 57 2108
Google Scholar
[36] 贾丽霞, 贺新福, 王东杰 2018 原子能科学技术 52 1040
Google Scholar
Jia L X, He X F, Wang D J 2018 Atomic Energy Science and Technology 52 1040
Google Scholar
[37] McLean D 1957 Grain Boundaries in Metals (London: Oxford at the Clarendon Press) p1
[38] Seah M P 1980 J. Phys. F: Met. Phys. 10 1063
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