First-principles study of  effect of ideal tensile/shear strain on  chemical bond length and charge density distribution of U<sub>3</sub>Si<sub>2</sub>

Wang Kun; Qiao Ying-Jie; Zhang Xiao-Hong; Wang Xiao-Dong; Zheng Ting; Bai Cheng-Ying; Zhang Yi-Ming; Du Shi-Yu

doi:10.7498/aps.71.20221210

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:

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).

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References

[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
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[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

Cited By

图 1 U₃Si₂在几个低指数晶面/晶向上的应力-应变关系^[18]

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 3 U₃Si₂在不同切面上的电荷密度

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

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图 4 U₃Si₂在不同切面上的差分电荷密度

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

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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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

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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]

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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]

DownLoad: 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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First-principles study of effect of ideal tensile/shear strain on chemical bond length and charge density distribution of U₃Si₂

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Authors and contacts

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

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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]

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]

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First-principles study of effect of ideal tensile/shear strain on chemical bond length and charge density distribution of U3Si2

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

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First-principles study of effect of ideal tensile/shear strain on chemical bond length and charge density distribution of U₃Si₂