Fe-Cr合金晶界偏析及辐照加速晶界偏析的相场模拟

杨朝曦; 柳文波; 张璁雨; 贺新福; 孙正阳; 贾丽霞; 师田田; 恽迪

doi:10.7498/aps.70.20201840

摘要

基于WBM相场模型对热力学条件和辐照条件下Fe-Cr合金晶界处Cr元素偏析行为进行了模拟. 模拟结果表明温度对Fe-Cr合金晶界处Cr元素的偏析有很大影响: 当温度低于500 ℃时, 晶界处的偏析量很小; 而当温度高于500 ℃时晶界处的偏析量增加明显. 基体中Cr元素含量对晶界Cr元素的相对偏析量也有显著影响: 随着基体中Cr元素含量的增加, 相同模拟条件下晶界处Cr元素的相对浓度增量降低. 辐照条件下, 晶界处Cr元素的相对偏析量比热力学条件下的相对偏析量有明显增加; 随着辐照剂量率的提高, 晶界中心处Cr元素浓度增量变大; 相同辐照条件下, 随着Cr元素含量的增加, 晶界处Cr元素的相对浓度增量也降低.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
西安交通大学核科学与技术学院, 西安　710049

2.
清华大学材料学院, 北京　100084

3.
中国原子能科学研究院, 北京　102413

通信作者: 柳文波, liuwenbo@xjtu.edu.cn

基金项目: 国家自然科学基金青年科学基金(批准号: 11705137)、国家自然科学基金委员会-中国工程物理研究院联合基金(批准号: U1830124)、中国博士后科学基金(批准号: 2019M663738)、中国核工业集团有限公司领创科研项目和中央高校基本科研业务费专项资金资助的课题

Authors and contacts

1.
Institute of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China

2.
Institute of Materials Science, Tsinghua University, Beijing 100084, China

3.
China Institute of Atomic Energy, Beijing 102413, China

Corresponding author: Liu Wen-Bo, liuwenbo@xjtu.edu.cn

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11705137), the Joint Fund of the National Natural Science Foundation of China and The China Academy of Engineering Physics (Grant No. U1830124), the China Postdoctoral Science Foundation (Grant No. 2019M663738), the Innovative Scientific Program of CNNC, and the Fundamental Research Fund for the Central Universities, China

文章全文 : translate this paragraph

参考文献

[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

施引文献

图 1 相场变量ϕ和x的初始分布

Fig. 1. Initial distribution of phase field variable ϕ and x.

下载: 全尺寸图片幻灯片

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

Fig. 2. Evolution of Cr concentration at grain boundary in Fe-Cr alloys: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.

下载: 全尺寸图片幻灯片

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

Fig. 3. The curves of the phase field variables of Fe-Cr alloys with different compositions after 100 s at 500 ℃: (a) x; (b) ϕ.

下载: 全尺寸图片幻灯片

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

Fig. 4. The relationship between the relative change of Cr concentration at grain boundary and the bulk Cr concentration after 100 s at 500 ℃.

下载: 全尺寸图片幻灯片

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

Fig. 5. Distribution of Cr concentration at grain boundary with different temperatures: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

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

Fig. 8. Distribution of Cr concentration with different dose rates: (a) Fe-9Cr; (b) Fe-10Cr; (c) Fe-12Cr; (d) Fe-15Cr.

下载: 全尺寸图片幻灯片

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

Fig. 9. The relationship between the relative change of Cr concentration at grain boundary and the bulk Cr concentration at different dose rates at 450 ℃

下载: 全尺寸图片幻灯片

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

Fig. 10. Comparison of simulation results and experimental results when the dose rate is 1.2 × 10^–5 dpa/s.

下载: 全尺寸图片幻灯片

表 1 Fe-Cr合金的物理参数

Table 1. Physical parameters of Fe-Cr alloys.

物理参数	数值	参考文献
$ {\varepsilon }^{2} $/(J·m^–1)	$ 4\times {10}^{-10} $	[20]
$ {V}_{{\rm{m}}} $/(m³·mol^–1)	$ 7.0\times {10}^{-6} $	[20]
w/(J·m^-1)	$ 3\times {10}^{4} $	[20]
m	4.5	[28, 29]
σ/(J·m^–2)	0.3	[30]
R/(J·mol^-1·k^–1)	8.314

下载: 导出CSV

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} $

下载: 导出CSV

map

[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

[1]	程大钊, 刘彩艳, 张超然, 屈佳辉, 张静. 中子辐照奥氏体不锈钢晶内/晶间孔隙形貌演化的相场模拟. , 2024, 73(22): 224601. doi: 10.7498/aps.73.20241353
[2]	廖宇轩, 申文龙, 吴学志, 喇永孝, 柳文波. 陶瓷型复合燃料烧结过程的相场模拟研究. , 2024, 73(21): 210201. doi: 10.7498/aps.73.20241112
[3]	刘续希, 高士森, 喇永孝, 玉栋梁, 柳文波. Zr-2.5Sn合金高温腐蚀过程的相场模拟. , 2024, 73(14): 148201. doi: 10.7498/aps.73.20240393
[4]	史芳杰, 李南, 郭峻铭, 陈柏屹, 李飒腾, 刘浩良, 郭建业, 李乾武, 李烨飞, 肖冰. Fe-Cr二元合金微观组织演化的质量密度场耦合动力学Monte-Carlo模拟研究. , 2023, 72(13): 136401. doi: 10.7498/aps.72.20230291
[5]	姜彦博, 柳文波, 孙志鹏, 喇永孝, 恽迪. 外加应力作用下 UO₂ 中空洞演化过程的相场模拟. , 2022, 71(2): 026103. doi: 10.7498/aps.71.20211440
[6]	申天展, 宋海洋, 安敏荣. 孪晶界对Cr₂₆Mn₂₀Fe₂₀Co₂₀Ni₁₄高熵合金力学行为影响的分子动力学模拟. , 2021, 70(18): 186201. doi: 10.7498/aps.70.20210324
[7]	杨辉, 冯泽华, 王贺然, 张云鹏, 陈铮, 信天缘, 宋小蓉, 吴璐, 张静. Fe-Cr合金辐照空洞微结构演化的相场法模拟. , 2021, 70(5): 054601. doi: 10.7498/aps.70.20201457
[8]	刘迪, 王静, 王俊升, 黄厚兵. 相场模拟应变调控PbZr_(1–x)Ti_xO₃薄膜微观畴结构和宏观铁电性能. , 2020, 69(12): 127801. doi: 10.7498/aps.69.20200310
[9]	祁科武, 赵宇宏, 郭慧俊, 田晓林, 侯华. 温度对小角度对称倾斜晶界位错运动影响的晶体相场模拟. , 2019, 68(17): 170504. doi: 10.7498/aps.68.20190051
[10]	张军, 陈文雄, 郑成武, 李殿中. γ-α相变中不同晶界特征下铁素体生长形貌的相场模拟. , 2017, 66(7): 070701. doi: 10.7498/aps.66.070701
[11]	段培培, 邢辉, 陈志, 郝冠华, 王碧涵, 金克新. 镁基合金自由枝晶生长的相场模拟研究. , 2015, 64(6): 060201. doi: 10.7498/aps.64.060201
[12]	杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘林. 横向限制下凝固微观组织演化的相场法模拟. , 2013, 62(10): 106401. doi: 10.7498/aps.62.106401
[13]	潘诗琰, 朱鸣芳. 双边扩散枝晶生长的定量相场模型. , 2012, 61(22): 228102. doi: 10.7498/aps.61.228102
[14]	王明光, 赵宇宏, 任娟娜, 穆彦青, 王伟, 杨伟明, 李爱红, 葛洪浩, 侯华. 相场法模拟NiCu合金非等温凝固枝晶生长. , 2011, 60(4): 040507. doi: 10.7498/aps.60.040507
[15]	任秀, 王锦程, 杨玉娟, 杨根仓. 纯物质晶界结构及运动的晶体相场法模拟. , 2010, 59(5): 3595-3600. doi: 10.7498/aps.59.3595
[16]	王刚, 徐东生, 杨锐. Ti-6Al-4V合金中片层组织形成的相场模拟. , 2009, 58(13): 343-S348. doi: 10.7498/aps.58.343
[17]	龙文元, 蔡启舟, 魏伯康, 陈立亮. 相场法模拟多元合金过冷熔体中的枝晶生长. , 2006, 55(3): 1341-1345. doi: 10.7498/aps.55.1341
[18]	朱昌盛, 王智平, 荆涛, 肖荣振. 二元合金微观偏析的相场法数值模拟. , 2006, 55(3): 1502-1507. doi: 10.7498/aps.55.1502
[19]	赵代平, 荆涛, 柳百成. 相场方法模拟铝合金三维枝晶生长. , 2003, 52(7): 1737-1742. doi: 10.7498/aps.52.1737
[20]	万发荣, 褚武扬, 肖纪美, 高桥平七郎. Fe-10%Cr铁素体合金中氢对辐照诱起偏析的影响. , 1996, 45(3): 464-469. doi: 10.7498/aps.45.464

计量

文章访问数: 7564
PDF下载量: 188
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板