Phase-field modeling of irradiated void microstructure evolution of Fe-Cr alloy

Yang Hui; Feng Ze-Hua; Wang He-Ran; Zhang Yun-Peng; Chen Zheng; Xin Tian-Yuan; Song Xiao-Rong; Wu Lu; Zhang Jing

doi:10.7498/aps.70.20201457

Abstract

As cladding materials, Fe-Cr alloys are used in the extreme environments of high temperature, high pressure, and energetic particle radiation, thus generating irradiation defects such as vacancies and interstitials. The clustering of irradiation defects leads the voids or dislocation loops to form, resulting in irradiation swelling and lattice distortion, and further radiation hardening or softening, finally, material failure. It is beneficial to tailor desired microstructures and obtain stable service performances by understanding defects cluster and voids formation process. In this paper, the phase-field method is employed to study the evolution of voids of Fe-Cr alloy. In the model the temperature effects on point defects and generation/recombination of vacancies and interstitials are taken into consideration. The 400–800 K temperature range and 0–16 dpa radiation dose range are selected, in which the voids’ formation process including generation and recombination, as well as vacancy clustering caused by vacancy diffusion, is studied for Fe-Cr alloy. The nucleation rate of the void cluster shows a trend of first increasing and then decreasing with temperature increasing from 400 to 800 K. This phenomenon is related to complex interactions among defects concentration, atomic diffusion, recombination, nucleation, and growth conditions. At a given temperature, the average radius and the volume fraction of the voids grow bigger as the radiation dose increases. With the increase of irradiation dose, the cascade collision reaction is strengthened, and the number of Frenkel defect pairs is also increases. A large number of vacancies and interstitial atoms are generated, and the rapid diffusion and accumulation of vacancies in the Fe-Cr alloy at high temperature form a larger number and larger size of voids. The incubation period of vacancy clusters and voids are quite different due to the influence of irradiation temperature and dose. The higher the irradiation dose, the shorter the incubation period is. The relationship between the incubation period and temperature is more complicated. When the temperature is relatively low, the incubation period is shortened as the temperature increases, and as the temperature continues to increase to a higher temperature, the incubation period is extended. This relates to the increase in the concentration of vacancies, the recombination of vacancies and interstitials, and the increase of the critical nucleus radius for the growth of voids when the temperature increases.

Keywords:

Authors and contacts

1.
School of Material Science and Engineering, Xi’an University of Technology, Xi’an 710048, China
2.
School of Material Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China
3.
The First Sub-institute, Nuclear Power Institute of China, Chengdu 610005, China

Corresponding author: Zhang Jing, Jingzhang@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51704243, 51674205, 51601185), the National Defense Basic Scientific Research Program of China (Grant No. JCKY2017201C016), the China Postdoctoral Science Foundation (Grant No. 2015M582575), and the National Basic Research Program of China (Grant No. 2016YFB07001)

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References

[1]	Klueh R L, Nelson A T 2007 J. Nucl. Mater. 371 37 Google Scholar
[2]	Buongiorno J, Swindeman R, Corwin W, Rowchitte A, McDonald P, Was G, Mansur L, Wikon D, Nanstad R, Wright I 2003 Supercritical Water Reactor (SCWR) : Survey of Materials Experience and R&D Needs to Assess Viability, Idaho National EngineeringLaboratory Report INEEL/EXT-03-00693 (Rev. 1) Idaho September 2003
[3]	Sass S L, Eyre B L 1973 Philos. Mag. 27 1447 Google Scholar
[4]	Une K, Nogita K, Kashibe S, Imamura M 1992 J. Nucl. Mater. 188 65 Google Scholar
[5]	Nogita K, Une K 1993 J. Nucl. Mater. 91 301
[6]	Zacharie I, Lansiart S, Combette P, Trotabas M, Coster M, Groos M 1998 J. Nucl. Mater. 255 92 Google Scholar
[7]	Katsuyama K, Nagamine T, Matsumoto S, Ito M 2002 J. Nucl. Sci. Technol. 39 804 Google Scholar
[8]	张娜, 刘波, 林黎蔚 2020 69 016101 Google Scholar Zhang N, Liu B, Lin L W 2020 Acta Phys. Sin. 69 016101 Google Scholar
[9]	高云亮, 朱芫江, 李进平 2017 66 057104 Google Scholar Gao Y L, Zhu Y J, Li J P 2017 Acta Phys. Sin. 66 057104 Google Scholar
[10]	Lindhard J, Nielsen V, Scharff M, Thomsen P V 1963 Mat. Fys. Medd. Dan. Vid. Selsk. 33 706
[11]	郁金南 2007 核材料科学与工程——材料辐照效应 (北京: 化学工业出版社) 第198—203页 Yu J N 2007 Nuclear Materials Science and Engineering Radiation Effects of Materials (Beijing: Chemical Industry Press) pp198–203 (in Chinese)
[12]	Becker C H 1972 US Patent 3 657 707 [1972-4-18]
[13]	黄鹤飞, 李健健, 刘仁多, 陈怀灿, 闫隆 2014 金属学报 50 1189 Google Scholar Huang H F, Li J J, Liu R D, Chen H C, Yan L 2014 J. Acta Metall. Sin. 50 1189 Google Scholar
[14]	丁兆楠, 杨义涛, 宋银, 张丽卿, 缑洁, 张崇宏, 罗广南 2017 66 112501 Google Scholar Ding Z N, Yang Y T, Song Y, Zhang L Q, Gou J, Zhang C H, Luo G N 2017 Acta Phys. Sin. 66 112501 Google Scholar
[15]	Lambrecht M, Malerba L 2011 Acta Mater. 59 6547 Google Scholar
[16]	Reese E R, Almirall N, Yamamoto T 2018 Scr. Mater. 146 213 Google Scholar
[17]	Liu Y L, Zhang Y, Zhou H B 2009 Phys. Rev. B 79 172103 Google Scholar
[18]	Zhou H B, Liu Y L, Jin S 2010 Nucl. Fusi. 50 115010 Google Scholar
[19]	Alkhamees A, Liu Y L, Zhou H B 2009 J. Nucl. Mater. 393 508 Google Scholar
[20]	梁晋洁, 高宁, 李玉红 2020 69 116102 Google Scholar Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 116102 Google Scholar
[21]	朱琪, 王升涛, 赵福祺, 潘昊 2020 69 036201 Google Scholar Zhu Q, Wang S T, Zhao F Q, Pan H 2020 Acta Phys. Sin. 69 036201 Google Scholar
[22]	梁晋洁, 高宁, 李玉红 2020 69 036101 Google Scholar Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 036101 Google Scholar
[23]	梁林云, 吕广宏 2013 62 182801 Google Scholar Liang L Y, Lü G H 2013 Acta Phys. Sin. 62 182801 Google Scholar
[24]	李然然, 张一帆, 耿殿程, 张高伟, 渡边英雄, 韩文妥, 万发荣 2019 68 216101 Google Scholar Li R R, Zhang Y F, Geng D C, Zhang G W, Watanabe Hideo, Han W T, Wan F R 2019 Acta Phys. Sin. 68 216101 Google Scholar
[25]	Hu S Y, Henager C H, Heinisch H L 2009 J. Nucl. Mater. 392 292 Google Scholar
[26]	Rokkam S, El-Azab A, Millett P 2009 Model Simul. Mater.Sci. Eng. 17 064002 Google Scholar
[27]	Millett P C, Rokkam S, El-Azab A 2009 Model Simul. Mater. Sci. Eng. 17 064003 Google Scholar
[28]	Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593
[29]	Yan Z W, Shi S J, Li Y S, Chen J, Maqbool S 2020 Phys. Chem. Chem. Phys. 22 3611 Google Scholar
[30]	Provatas N, Elder K 2010 Phase-field Methods in Materials Science and Engineering (Germany: Weinheim Wiley-VCH) pp2−5
[31]	Hu S Y, Henager C H 2010 Acta Mater. 58 3230 Google Scholar
[32]	Li Y, Hu S, Sun X 2010 J. Nucl. Mater. 407 119 Google Scholar
[33]	Simeone D, Ribis J, Luneville L 2018 J. Mater. Res. 33 440 Google Scholar
[34]	Ortiz C J, Caturla M J 2007 Phys. Rev. B 75 184101 Google Scholar
[35]	Bacon D J, Gao F, Osetsky Y N 2000 J. Nucl. Mater. 276 1 Google Scholar
[36]	Souidi A, Becquart C S, Domain C 2006 J. Nucl. Mater. 355 89 Google Scholar
[37]	Boisse J, Domain C, Becquart C S 2014 J. Nucl. Mater. 455 10 Google Scholar
[38]	徐恒均 2009 材料科学基础(第一版)(北京: 北京工业大学出版社) 第205−214页 Xu H J 2009 Foundations of Materials Science (Vol.1) (Beijjing: Beijing University of Technology Press) pp205−214 (in Chinese)
[39]	Wong K L, Lee H J, Shim J H, Sadigh B, Wirth B D 2009 J. Nucl. Mater 386 227
[40]	Norris, D I R 1972 Radiation Effects 14 1 Google Scholar
[41]	Getto E, Jiao Z, Monterrosa A M 2015 J. Nucl.Mater. 462 458 Google Scholar
[42]	Toloczko M B, Garner F A, Voyevodin V N 2014 J. Nucl.Mater. 453 323 Google Scholar
[43]	Brailsford A D, Bullough R, Hayns M R 1978 J. Nucl. Mater. 60 246

Cited By

图 1 不同辐照温度和剂量下Fe-Cr合金中空洞形貌的变化

Figure 1. Morphology evolution of voids of Fe-Cr alloys at different irradiation temperature and dose.

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图 2 Fe-Cr合金空位及间隙原子扩散速度与温度的关系

Figure 2. The relationship between the diffusion rate of Fe-Cr alloy vacancies, the interstitial atoms and temperature.

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图 3 Fe-Cr合金中空位浓度、空位-间隙重组率与温度的关系

Figure 3. Relationship between vacancy concentration, vacancy-interstitial recombination rate, and temperature in Fe-Cr alloy.

DownLoad: Full-Size Img PowerPoint

图 4 Fe-Cr合金在700 K温度下0—16 dpa辐照剂量下空洞的平均半径演化

Figure 4. The average radius of the voids of Fe-Cr alloy suffer different irradiation doses at 700 K.

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图 5 Fe-Cr合金在700 K时0—16 dpa不同辐照剂量下空洞的数量演化

Figure 5. Void numbers of Fe-Cr alloy suffers different irradiation doses at 700 K.

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图 6 Fe-Cr合金在700 K时空洞数量与辐照剂量的关系

Figure 6. Relationship between the number of voids and irradiation dose in Fe-Cr alloy at 700 K.

DownLoad: Full-Size Img PowerPoint

图 7 Fe-Cr合金在700 K时空洞形貌随时间和辐照剂量的时间演化

Figure 7. Temporal evolution of void in the Fe-Cr alloy at 700 K as functions of time and irradiation dose.

DownLoad: Full-Size Img PowerPoint

图 8 Fe-Cr合金在辐照剂量为8 dpa时空洞数量与温度的关系

Figure 8. Relationship between the number of voids and temperature in Fe-Cr alloy irradiated at 8 dpa.

DownLoad: Full-Size Img PowerPoint

图 9 Fe-Cr合金在辐照剂量为8 dpa时400—800 K温度下的空洞数量

Figure 9. Comparison of the number of voids in Fe-Cr alloy at different irradiation temperatures of 8 dpa.

DownLoad: Full-Size Img PowerPoint

图 10 Fe-Cr合金在辐照剂量为8 dpa时400—800 K温度下的空洞体积分数

Figure 10. Comparison of the results of void volume fractions of Fe-Cr alloy at different irradiation temperatures at 8 dpa.

DownLoad: Full-Size Img PowerPoint

表 1 本文模拟使用的物性和模拟参数^[33]

Table 1. Physical properties and simulation parameters used in this paper^[33].

k_B/(eV·K^–1) a b₀ b₁ b₂ b₃ b₄ M_v M_i L k_cv k_ci

8.61733 × 10^–5 8.0 0.02 2.8 50.4 –105.4 52.2 1.0 1.0 1.0 1.0 1.0

DownLoad: CSV

map

[1]	Klueh R L, Nelson A T 2007 J. Nucl. Mater. 371 37 Google Scholar
[2]	Buongiorno J, Swindeman R, Corwin W, Rowchitte A, McDonald P, Was G, Mansur L, Wikon D, Nanstad R, Wright I 2003 Supercritical Water Reactor (SCWR) : Survey of Materials Experience and R&D Needs to Assess Viability, Idaho National EngineeringLaboratory Report INEEL/EXT-03-00693 (Rev. 1) Idaho September 2003
[3]	Sass S L, Eyre B L 1973 Philos. Mag. 27 1447 Google Scholar
[4]	Une K, Nogita K, Kashibe S, Imamura M 1992 J. Nucl. Mater. 188 65 Google Scholar
[5]	Nogita K, Une K 1993 J. Nucl. Mater. 91 301
[6]	Zacharie I, Lansiart S, Combette P, Trotabas M, Coster M, Groos M 1998 J. Nucl. Mater. 255 92 Google Scholar
[7]	Katsuyama K, Nagamine T, Matsumoto S, Ito M 2002 J. Nucl. Sci. Technol. 39 804 Google Scholar
[8]	张娜, 刘波, 林黎蔚 2020 69 016101 Google Scholar Zhang N, Liu B, Lin L W 2020 Acta Phys. Sin. 69 016101 Google Scholar
[9]	高云亮, 朱芫江, 李进平 2017 66 057104 Google Scholar Gao Y L, Zhu Y J, Li J P 2017 Acta Phys. Sin. 66 057104 Google Scholar
[10]	Lindhard J, Nielsen V, Scharff M, Thomsen P V 1963 Mat. Fys. Medd. Dan. Vid. Selsk. 33 706
[11]	郁金南 2007 核材料科学与工程——材料辐照效应 (北京: 化学工业出版社) 第198—203页 Yu J N 2007 Nuclear Materials Science and Engineering Radiation Effects of Materials (Beijing: Chemical Industry Press) pp198–203 (in Chinese)
[12]	Becker C H 1972 US Patent 3 657 707 [1972-4-18]
[13]	黄鹤飞, 李健健, 刘仁多, 陈怀灿, 闫隆 2014 金属学报 50 1189 Google Scholar Huang H F, Li J J, Liu R D, Chen H C, Yan L 2014 J. Acta Metall. Sin. 50 1189 Google Scholar
[14]	丁兆楠, 杨义涛, 宋银, 张丽卿, 缑洁, 张崇宏, 罗广南 2017 66 112501 Google Scholar Ding Z N, Yang Y T, Song Y, Zhang L Q, Gou J, Zhang C H, Luo G N 2017 Acta Phys. Sin. 66 112501 Google Scholar
[15]	Lambrecht M, Malerba L 2011 Acta Mater. 59 6547 Google Scholar
[16]	Reese E R, Almirall N, Yamamoto T 2018 Scr. Mater. 146 213 Google Scholar
[17]	Liu Y L, Zhang Y, Zhou H B 2009 Phys. Rev. B 79 172103 Google Scholar
[18]	Zhou H B, Liu Y L, Jin S 2010 Nucl. Fusi. 50 115010 Google Scholar
[19]	Alkhamees A, Liu Y L, Zhou H B 2009 J. Nucl. Mater. 393 508 Google Scholar
[20]	梁晋洁, 高宁, 李玉红 2020 69 116102 Google Scholar Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 116102 Google Scholar
[21]	朱琪, 王升涛, 赵福祺, 潘昊 2020 69 036201 Google Scholar Zhu Q, Wang S T, Zhao F Q, Pan H 2020 Acta Phys. Sin. 69 036201 Google Scholar
[22]	梁晋洁, 高宁, 李玉红 2020 69 036101 Google Scholar Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 036101 Google Scholar
[23]	梁林云, 吕广宏 2013 62 182801 Google Scholar Liang L Y, Lü G H 2013 Acta Phys. Sin. 62 182801 Google Scholar
[24]	李然然, 张一帆, 耿殿程, 张高伟, 渡边英雄, 韩文妥, 万发荣 2019 68 216101 Google Scholar Li R R, Zhang Y F, Geng D C, Zhang G W, Watanabe Hideo, Han W T, Wan F R 2019 Acta Phys. Sin. 68 216101 Google Scholar
[25]	Hu S Y, Henager C H, Heinisch H L 2009 J. Nucl. Mater. 392 292 Google Scholar
[26]	Rokkam S, El-Azab A, Millett P 2009 Model Simul. Mater.Sci. Eng. 17 064002 Google Scholar
[27]	Millett P C, Rokkam S, El-Azab A 2009 Model Simul. Mater. Sci. Eng. 17 064003 Google Scholar
[28]	Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593
[29]	Yan Z W, Shi S J, Li Y S, Chen J, Maqbool S 2020 Phys. Chem. Chem. Phys. 22 3611 Google Scholar
[30]	Provatas N, Elder K 2010 Phase-field Methods in Materials Science and Engineering (Germany: Weinheim Wiley-VCH) pp2−5
[31]	Hu S Y, Henager C H 2010 Acta Mater. 58 3230 Google Scholar
[32]	Li Y, Hu S, Sun X 2010 J. Nucl. Mater. 407 119 Google Scholar
[33]	Simeone D, Ribis J, Luneville L 2018 J. Mater. Res. 33 440 Google Scholar
[34]	Ortiz C J, Caturla M J 2007 Phys. Rev. B 75 184101 Google Scholar
[35]	Bacon D J, Gao F, Osetsky Y N 2000 J. Nucl. Mater. 276 1 Google Scholar
[36]	Souidi A, Becquart C S, Domain C 2006 J. Nucl. Mater. 355 89 Google Scholar
[37]	Boisse J, Domain C, Becquart C S 2014 J. Nucl. Mater. 455 10 Google Scholar
[38]	徐恒均 2009 材料科学基础(第一版)(北京: 北京工业大学出版社) 第205−214页 Xu H J 2009 Foundations of Materials Science (Vol.1) (Beijjing: Beijing University of Technology Press) pp205−214 (in Chinese)
[39]	Wong K L, Lee H J, Shim J H, Sadigh B, Wirth B D 2009 J. Nucl. Mater 386 227
[40]	Norris, D I R 1972 Radiation Effects 14 1 Google Scholar
[41]	Getto E, Jiao Z, Monterrosa A M 2015 J. Nucl.Mater. 462 458 Google Scholar
[42]	Toloczko M B, Garner F A, Voyevodin V N 2014 J. Nucl.Mater. 453 323 Google Scholar
[43]	Brailsford A D, Bullough R, Hayns M R 1978 J. Nucl. Mater. 60 246

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