Molecular dynamics study of trapping and detrapping process of hydrogen in tungsten vacancy

Fu Bao-Qin; Hou Qing; Wang Jun; Qiu Ming-Jie; Cui Jie-Chao

doi:10.7498/aps.68.20190701

Abstract

Tungsten (W) alloys and W-based alloys are the primary candidate materials for plasma-facing components in future fusion reactors (e.g. ITER and CFETR). One of the critical issues still to be clarified in the design of the fusion reactor materials is the retention of hydrogen (H) isotopes in W, when the plasma-facing materials are supposed to sustain high-flux plasma and high-energy neutron. The dynamical behaviours of H in W with radiation defects (e.g. vacancy) are of serious concerns for understanding the mechanism of H capture, retention and permeation in W. In this work, a new model to extract the effective capture radius (ECR) and dissociation coefficient simultaneously is presented through coupling the trapping process and detrapping process of H in W vacancy. In the new model, the quantity ratio of vacancy to H atom in vacancy-H complex (VH_x+1) in the molecular dynamics (MD) simulations is described as a function of time, while the exact occurrence time of corresponding event is not required. This new model, combined with extensive MD calculations, enables the simultaneous determining of the ECR and dissociation coefficient of H in W vacancy. It is found that the parameters are dependent not only on the event type but also on temperature. The dissociation energy of H from vacancy-H complex decreases gradually with the increase of the trapped number of H atoms in the vacancy-H complex. It is also found that the common assumption (i.e. the ECR is equal to one lattice constant and the pre-exponential factor is equal to 10¹³ s^–1) in the long-term simulation methods (e.g. kinetic Monte Carlo and rate theory) is not always valid, since these calculated dynamical parameters are dispersive. The new model to obtain more reliable results with lower cost of computing resources can be easily extended into the other similar kinetic processes (e.g. H/He trapping and detrapping processes in other materials systems). These calculated dynamical parameters should be potentially helpful in supplying the initial input parameters for the long-term simulation methods.

Keywords:

Authors and contacts

Key Laboratory for Radiation Physics and Technology, Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, China

Corresponding author: Fu Bao-Qin, bqfu@scu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51501119)

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References

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[2]	李建刚, 宋云涛, 刘永, 汪小琳, 万元熙 2016 聚变工程试验堆装置主机设计 (北京: 科学出版社) 第250−252页 Li J G, Song Y T, Liu Y, Wang X L, Wan Y X 2016 Main Machine Design of Fusion Engineering Test Reactor (Beijing: Science Press) pp250−252 (in Chinese)
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Cited By

图 1 含有空位-H复合体(VH₂)的初始超胞, 其中红色点表示W原子, 蓝色球表示H原子

Figure 1. One simulation box with vacancy-H complex (VH₂), where red pots represent W atoms and blue spheres represent H atoms.

DownLoad: Full-Size Img PowerPoint

图 2 不同温度下, 空位-H复合体(VH_x₊₁)的含量(${y_{{\rm{V}}{{\rm{H}}_{x + 1}}}}\left( t \right) = {{{N_{{\rm{V}}{{\rm{H}}_{x + 1}}}}\left( t \right)} / {{N_{\rm{b}}}}}$)与时间(t)的变化, 其中曲线由 (10)式拟合

Figure 2. Ratio of VH_x₊₁ in the simulation (${y_{{\rm{V}}{{\rm{H}}_{x + 1}}}}\left( t \right) = {{{N_{{\rm{V}}{{\rm{H}}_{x + 1}}}}\left( t \right)} / {{N_{\rm{b}}}}}$) as function of time (t), where the curves are fitted by Eq. (10).

DownLoad: Full-Size Img PowerPoint

图 3 不同空位-H复合体(VH_x₊₁)的H解离系数(k_diss,_x₊₁)与温度(T)的变化, 其中曲线由公式lnk = lnν – E/k_B/T拟合

Figure 3. Dissociation coefficients (k_diss,_x₊₁) of H detrapping from various VH_x₊₁ complex as functions of temperature (T), where the curves are fitted by equation lnk = lnν – E/k_B/T.

DownLoad: Full-Size Img PowerPoint

图 4 新模型推导的解离能(a)和前因子(b)与前期模型^[26]计算值的比较, 其中虚线表示(E_new = E_old或ν_new = ν_old)

Figure 4. (a) Dissociation energies and (b) pre-exponential factors deduced by new model (present work) and old model ^[26], where the dash line means E_new = E_old or ν_new = ν_old.

DownLoad: Full-Size Img PowerPoint

图 5 新模型推导的有效捕获半径ECR_new与前期模型^[26] ECR_old计算值的比较, 其中虚线表示ECR_new = ECR_old

Figure 5. Effective capture radii deduced by new model (present work) and old model ^[26], where the dash line means ECR_new = ECR_old.

DownLoad: Full-Size Img PowerPoint

[1]	Lu G H, Zhou H B, Becquart C S 2014 Nucl. Fusion 54 086001 Google Scholar
[2]	李建刚, 宋云涛, 刘永, 汪小琳, 万元熙 2016 聚变工程试验堆装置主机设计 (北京: 科学出版社) 第250−252页 Li J G, Song Y T, Liu Y, Wang X L, Wan Y X 2016 Main Machine Design of Fusion Engineering Test Reactor (Beijing: Science Press) pp250−252 (in Chinese)
[3]	Jia Y Z, Liu W, Xu B, Luo G N, Li C, Fu B Q, de Temmerman G 2015 J. Nucl. Mater. 463 312 Google Scholar
[4]	Yi X, Jenkins M L, Hattar K, Edmondson P D, Roberts S G 2015 Acta Mater. 92 163 Google Scholar
[5]	Hu X, Koyanagi T, Fukuda M, Kumar N A P K, Snead L L, Wirth B D, Katoh Y 2016 J. Nucl. Mater. 480 235 Google Scholar
[6]	Fu B Q, Lai W S, Yuan Y, Xu H Y, Li C, Jia Y Z, Liu W 2013 Chinese Phys. B 22 126601 Google Scholar
[7]	Ye M Y 2005 Plasma Sci. Technol. 7 2828 Google Scholar
[8]	Fu B Q, Qiu M J, Zhai L, Yang A L, Hou Q 2019 Nucl. Instrum. Meth. B 450 220 Google Scholar
[9]	Oyaidzu M, Hayashi T, Alimov V K 2016 Nucl. Mater. Energy 9 93 Google Scholar
[10]	Jia Y Z, Liu W, Xu B, Qu S L, Shi L Q, Morgan T W 2017 Nucl. Fusion 57 034003 Google Scholar
[11]	Heinola K, Ahlgren T 2010 Phys. Rev. B 81 073409 Google Scholar
[12]	Frauenfelder R 1969 J. Vac. Sci. Technol. 6 388 Google Scholar
[13]	Qiu M J, Zhai L, Cui J C, Fu B Q, Li M, Hou Q 2018 Chin. Phys. B 27 073103 Google Scholar
[14]	Liu Y L, Zhang Y, Luo G N, Lu G H 2009 J. Nucl. Mater. 390/391 1032 Google Scholar
[15]	Jiang B, Wan F R, Geng W T 2010 Phys. Rev. B 81 134112
[16]	Liu Y L, Gao A Y, Lu W, Zhou H B, Zhang Y 2012 Chin. Phys. Lett. 29 077101
[17]	Guo W, Ge L, Yuan Y, Cheng L, Wang S, Zhang X, Lu G H 2019 Nucl. Fusion 59 026005 Google Scholar
[18]	Terentyev D, Dubinko V, Bakaev A, Zayachuk Y, van Renterghem W, Grigorev P 2014 Nucl. Fusion 54 042004 Google Scholar
[19]	Zhou H B, Liu Y L, Jin S, Zhang Y, Luo G N, Lu G H 2010 Nucl. Fusion 50 025016 Google Scholar
[20]	Wang X X, Niu L L, Wang S 2017 J. Nucl. Mater. 487 158 Google Scholar
[21]	Fu B Q, Xu B, Lai W S, Yuan Y, Xu H Y, Li C, Jia Y Z, Liu W 2013 J. Nucl. Mater. 441 24 Google Scholar
[22]	王欣欣, 张颖, 周洪波, 王金龙 2014 物理学报 63 046103 Google Scholar Wang X X, Zhang Y, Zhou H B, Wang J L 2014 Acta Phys. Sin. 63 046103 Google Scholar
[23]	汪俊, 张宝玲, 周宇璐, 侯氢 2011 物理学报 60 106601 Google Scholar Wang J, Zhang B L, Zhou Y L, Hou Q 2011 Acta Phys. Sin. 60 106601 Google Scholar
[24]	严六明, 朱素华 2013 分子动力学模拟的理论与实践 (北京: 科学出版社) 第6−12页 Yan L M, Zhu S H 2013 Theory and Practice of Molecular Dynamics Simulation (Beijing: Science Press) pp6−12 (in Chinese)
[25]	Hou Q, Li M, Zhou Y, Cui J, Cui Z, Wang J 2013 Comput. Phys. Commun. 184 2091 Google Scholar
[26]	Fu B Q, Qiu M J, Cui J C, Li M, Hou Q 2018 J. Nucl. Mater. 508 278 Google Scholar
[27]	Fu B Q, Qiu M J, Cui J C, Li M, Wang J, Hou Q 2019 Nucl. Instrum. Meth. B 452 21 Google Scholar
[28]	Zhou Y L, Wang J, Hou Q, Deng A H 2014 J. Nucl. Mater. 446 49 Google Scholar
[29]	Chandrasekhar S 1943 Rev. Mod. Phys. 15 1 Google Scholar
[30]	Fernandez N, Ferro Y, Kato D 2015 Acta Mater. 94 307 Google Scholar
[31]	Ahlgren T, Bukonte L 2016 J. Nucl. Mater. 479 195 Google Scholar
[32]	Bonny G, Grigorev P, Terentyev D 2014 J. Phys.-Condens. Mat. 26 485001 Google Scholar
[33]	Swope W C, Andersen H C, Berens P H, Wilson K R 1982 J. Chem. Phys. 76 637 Google Scholar
[34]	Fu B Q, Liu W, Li Z L 2009 Appl. Surf. Sci. 255 8511 Google Scholar
[35]	Marinica M C, Ventelon L, Gilbert M R, Proville L, Dudarev S L, Marian J, Bencteux G, Willaime F 2013 J. Phys.-Condens. Mat. 25 395502 Google Scholar
[36]	Stukowski A 2010 Model. Simul. Mater. Sci. 18 015012 Google Scholar
[37]	Cheng G J, Fu B Q, Hou Q, Zhou X S, Wang J 2016 Chinese Phys. B 25 076602 Google Scholar
[38]	Fu B Q, Fitzgerald S P, Hou Q, Wang J, Li M 2017 Nucl. Instrum. Meth. B 393 169 Google Scholar

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