理想拉伸/剪切应变对U<sub>3</sub>Si<sub>2</sub>化学键键长及电荷密度分布影响的第一性原理研究

王坤; 乔英杰; 张晓红; 王晓东; 郑婷; 白成英; 张一鸣; 都时禹

doi:10.7498/aps.71.20221210

摘要

2011年福岛核事故之后, U₃Si₂作为可代替UO₂的核燃料被预测为重要的耐事故燃料. 近年来的研究结果表明, U₃Si₂作为耐事故燃料的候选材料, 其在微观尺度上进行的模拟还不够深入. 在宏观尺度上不足以建立燃料数据库和模型来有效预测U₃Si₂的一些性能. 因此, 采用第一性原理计算U₃Si₂核燃料的一些物理化学数据受到了广泛关注. 在之前的工作中, 我们采用第一性原理计算拉伸/剪切实验 (FPCTT/FPCST) 的方法预测了U₃Si₂在几个低指数晶面/晶向上的理想强度. 然而, 并未对U₃Si₂的断裂行为进行过多的解释. 因此, 本论文通过论述理想拉伸/剪切应变对U₃Si₂化学键键长及电荷密度分布影响, 分析了U₃Si₂在这几个低指数晶面/晶向上的断裂行为. 结果表明: U₃Si₂在理想拉伸应变的作用下, 晶体的破坏主要受化学键变化的影响, 而在剪切应变的作用下应变能或应力的突然下降, 可能与U₃Si₂的应变诱导结构相变有关.

关键词:

Abstract

After the Fukushima nuclear accident in 2011, U₃Si₂ was predicted to be an important accident tolerant fuel that can replace UO₂. The results of recent studies have shown that the simulation at the micro-scale of U₃Si₂ serving as a candidate for accident tolerant fuel is not deep enough. It is not sufficient to build fuel databases and models at a macro-scale to effectively predict some properties of U₃Si₂. Therefore, employing the first principles to calculate some physicochemical data of U₃Si₂ nuclear fuel has received extensive attention. In previous work, we predicted the ideal strength of U₃Si₂ in several low-index crystal planes/directions by the first-principles computational tensile/shear test (FPCTT/FPCST) approach. However, the fracture behavior of U₃Si₂ has not been explained much. Therefore, in this work, the effects of ideal tensile/shear strain on the chemical bond length and charge density distribution of U₃Si₂ are discussed to analyze the fracture behaviors of U₃Si₂ in these low-index crystal planes/directions. The effect of strain is achieved by using the incremental simulation elements in the specified crystal plane/direction. The crystal structures of U₃Si₂ under different strains are optimized by using the first principles based on density functional theory. The variation ranges of chemical bond length and the charge density distributions of U₃Si₂ under different ultimate strains are summarized and calculated respectively. The results show that the elongation of the U—U bond is the main contributor to the tensile deformation of U₃Si₂ in the [100] crystal direction under tensile load. The toughness of U₃Si₂ in the [001] crystal direction is mainly due to the elongation of the U—Si bond and U—U bond. However, the tensile deformation produced in the [110] crystal direction of U₃Si₂ is mainly related to the elongation of the Si—Si bond. In the (100)[010] slip system, U₃Si₂ has great deformation and the crystal breaks when the Si—Si bond length reaches a limit of 3.038 Å. For the (001)[100], (110)[$ \bar 1 $10] and (001)[110] slip systems of U₃Si₂, the crystal is broken under small shear deformation, and the change of its bond length is not obvious, reflecting that the sudden decrease of the strain energy or stress in these several slip systems may be related to the strain-induced structural phase transition of U₃Si₂.

Keywords:

作者及机构信息

1.
哈尔滨工程大学材料科学与化学工程学院, 哈尔滨　150001

2.
中国科学院宁波材料技术与工程研究所先进能源材料工程实验室, 宁波　315201

通信作者: 张晓红, zhangxiaohong0451@hrbeu.edu.cn ; 都时禹, dushiyu@hrbeu.edu.cn

基金项目: 国家重点研发计划重点专项(批准号: 2016YFB0700100)和浙江省自然科学基金(批准号: LY18F020025)资助的课题.

Authors and contacts

1.
College of Material Science and Chemical Engineering, Harbin Engineering University, Harbin 150001, China

2.
Engineering Laboratory of Advanced Energy Materials, Ningbo Institute of Materials Engineering and Technology, Chinese Academy of Sciences, Ningbo 315201, China

Corresponding author: Zhang Xiao-Hong, zhangxiaohong0451@hrbeu.edu.cn ; Du Shi-Yu, dushiyu@hrbeu.edu.cn

Funds: Project supported by the National Key Research and Development Project, China (Grant No. 2016YFB0700100) and the Natural Science Foundation of Zhejiang province, China (Grant No. LY18F020025).

文章全文 : translate this paragraph

参考文献

[1]	Miao Y B, Harp J, Mo K, Kim Y S, Zhu S, Yacout A M 2018 J. Nucl. Mater. 503 314 Google Scholar
[2]	Srinivasu K, Modak B, Ghanty T K 2018 J. Nucl. Mater. 510 360 Google Scholar
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[4]	Liu R, Zhou W Z, Cai J J 2018 Nucl. Eng. Des. 330 106 Google Scholar
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[6]	Kim Y S 2012 Comprehensive Nuclear Materials (Oxford: Elsevier) pp391–422
[7]	Birtcher R C, Wang L M 2011 MRS Proceedings 235 467 Google Scholar
[8]	Rest J 1997 J. Nucl. Mater. 240 205 Google Scholar
[9]	Yao T K, Gong B W, He L F, Harp J, Tonks M, Lian J 2018 J. Nucl. Mater. 498 169 Google Scholar
[10]	Carvajal-Nunez U, Saleh T A, White J T, Maiorov B, Nelson A T 2018 J. Nucl. Mater. 498 438 Google Scholar
[11]	Jossou E, Eduok U, Dzade N Y, Szpunar B, Szpunar J A 2018 Phys. Chem. Chem. Phys. 20 4708 Google Scholar
[12]	Wang T, Qiu N X, Wen X D, Tian Y H, He J, Luo K, Zha X H, Zhou Y H, Huang Q, Lang J J, Du S Y 2016 J. Nucl. Mater. 469 194 Google Scholar
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[16]	Remschnig K, Le Bihan T, Noël H, Rogl P 1992 J. Solid State Chem. 97 391 Google Scholar
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[19]	Roundy D, Krenn C R, Cohen M L, Morris J W 1999 Phys. Rev. Lett. 82 2713 Google Scholar
[20]	Roundy D, Krenn C R, Cohen M L, Morris J W 2001 Philos. Mag. A 81 1725 Google Scholar
[21]	Ogata S, Li J, Hirosaki N, Shibutani Y, Yip S 2004 Phys. Rev. B 70 104104 Google Scholar
[22]	Li X Q, Schönecker S, Zhao J J, Johansson B, Vitos L 2014 Phys. Rev. B 87 291
[23]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864 Google Scholar
[24]	Kohn W, Sham L J 1965 Phys. Rev. 140 A1133 Google Scholar
[25]	Kresse G G, Furthmüller J J 1996 Phys. Rev. B 54 11169 Google Scholar
[26]	Kresse G, Hafner J 1993 Phys. Rev. B Condens. Matter. 47 558 Google Scholar
[27]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[28]	Liechtenstein A I, Anisimov V V, Zaanen J 1995 Phys. Rev. B 52 R5467 Google Scholar
[29]	Sarma D D, Krummacher S, Hillebrecht F U, Koelling D D 1988 Phys. Rev. B: Condens. Matter. 38 1 Google Scholar
[30]	Shih B C, Zhang Y B, Zhang W Q, Zhang P H 2012 Phys. Rev. B 85 045132 Google Scholar
[31]	Szpunar B 2012 J. Phys. Chem. Solids 73 1003 Google Scholar
[32]	Setyawan W, Curtarolo S 2010 Comput. Mater. Sci. 49 299 Google Scholar
[33]	Mei Z G, Miao Y B, Liang L Y, Yacout A M 2019 J. Nucl. Mater. 513 192 Google Scholar
[34]	Yang X Y, Korzhavyi P A, Liu Y, Wei Q L, Arslanov T R, Wärnå J P A, Yang Y, Zhang P 2022 Prog. Nucl. Energy 148 104229 Google Scholar
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[36]	Smirnov M B, Kazimirov V Y, Rita B H, Smirnov K S, Pereira-Ramos J P 2014 J. Phys. Chem. Solids 75 115 Google Scholar
[37]	Manikandan M, Rajeswarapalanichamy R, Iyakutti K 2017 Philos. Mag. 98 1 Google Scholar
[38]	M I, T L, Bihan, S H, J R 2004 Phys. Rev. B 70 014113 Google Scholar
[39]	Dubois S M M, Rignanese G M, Pardoen T, Charlier J C 2006 Phys. Rev. B 74 235203 Google Scholar

施引文献

图 1 U₃Si₂在几个低指数晶面/晶向上的应力-应变关系^[18]

Fig. 1. The stress-strain curves of U₃Si₂ in several low-index crystal planes/orientations^[18].

下载: 全尺寸图片幻灯片

图 2 不同基矢方向的U₃Si₂模型　(a) [100], [010]和[001]基矢方向; (b) [110], [$\bar 1$10]和[001]基矢方向

Fig. 2. The model of U₃Si₂ with the different basis vector directions: (a) [100], [010] and [001] vector directions; (b) [110], [$\bar 1$10] and [001] vector directions.

下载: 全尺寸图片幻灯片

图 3 U₃Si₂在不同切面上的电荷密度

Fig. 3. The charge density of U₃Si₂ on the different planes.

下载: 全尺寸图片幻灯片

图 4 U₃Si₂在不同切面上的差分电荷密度

Fig. 4. The differential charge density of U₃Si₂ on the different planes.

下载: 全尺寸图片幻灯片

图 5 U₃Si₂沿不同晶向拉伸过程中各化学键键长的变化情况:　(a) 沿[100]晶向拉伸; (b) 沿[001]晶向拉伸; (c) 沿[110]晶向拉伸

Fig. 5. Variation of the bond length of each chemical bond during the stretching of U₃Si₂ along with different crystal directions: (a) [100] crystal direction; (b) [001] crystal direction; (c) [110] crystal direction.

下载: 全尺寸图片幻灯片

图 6 U₃Si₂沿不同晶向拉伸时电荷密度的变化:　(a) 沿[100]晶向拉伸; (b) 沿[001]晶向拉伸; (c) 沿[110]晶向拉伸

Fig. 6. Variation of charge density when U₃Si₂ is stretched along with crystal directions: (a) [100] crystal direction; (b) [001] crystal direction; (c) [110] crystal direction.

下载: 全尺寸图片幻灯片

图 7 在剪切应变的作用下U₃Si₂键长的变化:　(a) (100)[010]滑移系; (b) (001)[100]滑移系; (c) (110)[$\bar 1$10]滑移系; (d) (001)[110]滑移系

Fig. 7. Variation of the chemical bond length of U₃Si₂ under shear strain: (a) (100)[010] slip system; (b) (001)[100] slip system; (c) (110)[$\bar 1$10] slip system; (d) (001)[110] slip system.

下载: 全尺寸图片幻灯片

图 8 U₃Si₂在不同剪切应变的作用下电荷密度的变化:　(a) (100)[010]滑移系; (b) (001)[100]滑移系; (c) (110)[$\bar 1$10]滑移系; (d) (001)[110]滑移系

Fig. 8. Variation of charge density of U₃Si₂ under shear strain: (a) (100)[010] slip system; (b) (001)[100] slip system; (c) (110)[$\bar 1$10] slip system; (d) (001)[110] slip system.

下载: 全尺寸图片幻灯片

表 1 U₃Si₂的弹性常数C_ij, 弹性模量E, B和G (单位: GPa), B/G以及泊松比υ

Table 1. The elastic constants C_ij, elastic moduli E, B and G (unit: GPa), B/G and Poisson’s ratio υ of U₃Si₂.

Comp-
ound C₁₁ C₁₂ C₁₃ C₃₃ C₄₄ C₆₆ E B G B/G υ Refs.

U₃Si₂ 155 47 50 142 65 46 139 83 57 1.46 0.22 [13]
149 49 48 139 63 46 — 81 53 1.53 — [14]
167 46 53 205 67 74 163 92 68 1.36 0.2 [12]

下载: 导出CSV

表 2 铁磁性条件下采用DFT+U计算得到U₃Si₂晶格常数及化学键长信息

Table 2. The lattice constants and chemical bond length of U₃Si₂ obtained by DFT+U calculation under ferromagnetic conditions.

Comp-
ound a/Å c/Å V/Å³ d_U-U/Å d_Si-Si/Å d_U-Si/Å Refs.

U₃Si₂ 7.42 4.03 221.81 3.375 2.396 2.909 Present
7.48 3.98 222.58 3.386 2.432 2.930 [2]
7.45 4.03 223.26 — — — [33]

下载: 导出CSV

[1]	Miao Y B, Harp J, Mo K, Kim Y S, Zhu S, Yacout A M 2018 J. Nucl. Mater. 503 314 Google Scholar
[2]	Srinivasu K, Modak B, Ghanty T K 2018 J. Nucl. Mater. 510 360 Google Scholar
[3]	Zhang Y F, Andersson A D R 2017 A Thermal Conductivity Model for USi Compounds. United States: N.p.2017
[4]	Liu R, Zhou W Z, Cai J J 2018 Nucl. Eng. Des. 330 106 Google Scholar
[5]	Beeler B, Baskes M, Andersson D, Cooper M W D, Zhang Y F 2017 J. Nucl. Mater. 495 267 Google Scholar
[6]	Kim Y S 2012 Comprehensive Nuclear Materials (Oxford: Elsevier) pp391–422
[7]	Birtcher R C, Wang L M 2011 MRS Proceedings 235 467 Google Scholar
[8]	Rest J 1997 J. Nucl. Mater. 240 205 Google Scholar
[9]	Yao T K, Gong B W, He L F, Harp J, Tonks M, Lian J 2018 J. Nucl. Mater. 498 169 Google Scholar
[10]	Carvajal-Nunez U, Saleh T A, White J T, Maiorov B, Nelson A T 2018 J. Nucl. Mater. 498 438 Google Scholar
[11]	Jossou E, Eduok U, Dzade N Y, Szpunar B, Szpunar J A 2018 Phys. Chem. Chem. Phys. 20 4708 Google Scholar
[12]	Wang T, Qiu N X, Wen X D, Tian Y H, He J, Luo K, Zha X H, Zhou Y H, Huang Q, Lang J J, Du S Y 2016 J. Nucl. Mater. 469 194 Google Scholar
[13]	Noordhoek M J, Besmann T M, Andersson D, Middleburgh S C, Chernatynskiy A 2016 J. Nucl. Mater. 479 216 Google Scholar
[14]	Chattaraj D, Majumder C 2018 J. Alloy. Compd. 732 160 Google Scholar
[15]	Liu H, Claisse A, Middleburgh S C, Olsson P 2019 J. Nucl. Mater. 527 151828 Google Scholar
[16]	Remschnig K, Le Bihan T, Noël H, Rogl P 1992 J. Solid State Chem. 97 391 Google Scholar
[17]	Miyadai T, Mori H, Oguchi T, Tazuke Y, Amitsuka H, Kuwai T, Miyako Y 1992 J. Magn. Magn. Mater. 104–107 47 Google Scholar
[18]	Wang K, Qiao Y J, Zhang X H, Wang X D, Zhang Y M, Wang P, Du S Y 2021 Eur. Phys. J. Plus 136 409 Google Scholar
[19]	Roundy D, Krenn C R, Cohen M L, Morris J W 1999 Phys. Rev. Lett. 82 2713 Google Scholar
[20]	Roundy D, Krenn C R, Cohen M L, Morris J W 2001 Philos. Mag. A 81 1725 Google Scholar
[21]	Ogata S, Li J, Hirosaki N, Shibutani Y, Yip S 2004 Phys. Rev. B 70 104104 Google Scholar
[22]	Li X Q, Schönecker S, Zhao J J, Johansson B, Vitos L 2014 Phys. Rev. B 87 291
[23]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864 Google Scholar
[24]	Kohn W, Sham L J 1965 Phys. Rev. 140 A1133 Google Scholar
[25]	Kresse G G, Furthmüller J J 1996 Phys. Rev. B 54 11169 Google Scholar
[26]	Kresse G, Hafner J 1993 Phys. Rev. B Condens. Matter. 47 558 Google Scholar
[27]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[28]	Liechtenstein A I, Anisimov V V, Zaanen J 1995 Phys. Rev. B 52 R5467 Google Scholar
[29]	Sarma D D, Krummacher S, Hillebrecht F U, Koelling D D 1988 Phys. Rev. B: Condens. Matter. 38 1 Google Scholar
[30]	Shih B C, Zhang Y B, Zhang W Q, Zhang P H 2012 Phys. Rev. B 85 045132 Google Scholar
[31]	Szpunar B 2012 J. Phys. Chem. Solids 73 1003 Google Scholar
[32]	Setyawan W, Curtarolo S 2010 Comput. Mater. Sci. 49 299 Google Scholar
[33]	Mei Z G, Miao Y B, Liang L Y, Yacout A M 2019 J. Nucl. Mater. 513 192 Google Scholar
[34]	Yang X Y, Korzhavyi P A, Liu Y, Wei Q L, Arslanov T R, Wärnå J P A, Yang Y, Zhang P 2022 Prog. Nucl. Energy 148 104229 Google Scholar
[35]	Zachariasen W H 1949 Acta Crystallogr. 2 94 Google Scholar
[36]	Smirnov M B, Kazimirov V Y, Rita B H, Smirnov K S, Pereira-Ramos J P 2014 J. Phys. Chem. Solids 75 115 Google Scholar
[37]	Manikandan M, Rajeswarapalanichamy R, Iyakutti K 2017 Philos. Mag. 98 1 Google Scholar
[38]	M I, T L, Bihan, S H, J R 2004 Phys. Rev. B 70 014113 Google Scholar
[39]	Dubois S M M, Rignanese G M, Pardoen T, Charlier J C 2006 Phys. Rev. B 74 235203 Google Scholar

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理想拉伸/剪切应变对U₃Si₂化学键键长及电荷密度分布影响的第一性原理研究