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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

王坤 乔英杰 张晓红 王晓东 郑婷 白成英 张一鸣 都时禹

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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

王坤, 乔英杰, 张晓红, 王晓东, 郑婷, 白成英, 张一鸣, 都时禹

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

Wang Kun, Qiao Ying-Jie, Zhang Xiao-Hong, Wang Xiao-Dong, Zheng Ting, Bai Cheng-Ying, Zhang Yi-Ming, Du Shi-Yu
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  • 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.
    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.
      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.
      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).
    [1]

    Miao Y B, Harp J, Mo K, Kim Y S, Zhu S, Yacout A M 2018 J. Nucl. Mater. 503 314Google Scholar

    [2]

    Srinivasu K, Modak B, Ghanty T K 2018 J. Nucl. Mater. 510 360Google 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 106Google Scholar

    [5]

    Beeler B, Baskes M, Andersson D, Cooper M W D, Zhang Y F 2017 J. Nucl. Mater. 495 267Google Scholar

    [6]

    Kim Y S 2012 Comprehensive Nuclear Materials (Oxford: Elsevier) pp391–422

    [7]

    Birtcher R C, Wang L M 2011 MRS Proceedings 235 467Google Scholar

    [8]

    Rest J 1997 J. Nucl. Mater. 240 205Google Scholar

    [9]

    Yao T K, Gong B W, He L F, Harp J, Tonks M, Lian J 2018 J. Nucl. Mater. 498 169Google Scholar

    [10]

    Carvajal-Nunez U, Saleh T A, White J T, Maiorov B, Nelson A T 2018 J. Nucl. Mater. 498 438Google Scholar

    [11]

    Jossou E, Eduok U, Dzade N Y, Szpunar B, Szpunar J A 2018 Phys. Chem. Chem. Phys. 20 4708Google 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 194Google Scholar

    [13]

    Noordhoek M J, Besmann T M, Andersson D, Middleburgh S C, Chernatynskiy A 2016 J. Nucl. Mater. 479 216Google Scholar

    [14]

    Chattaraj D, Majumder C 2018 J. Alloy. Compd. 732 160Google Scholar

    [15]

    Liu H, Claisse A, Middleburgh S C, Olsson P 2019 J. Nucl. Mater. 527 151828Google Scholar

    [16]

    Remschnig K, Le Bihan T, Noël H, Rogl P 1992 J. Solid State Chem. 97 391Google Scholar

    [17]

    Miyadai T, Mori H, Oguchi T, Tazuke Y, Amitsuka H, Kuwai T, Miyako Y 1992 J. Magn. Magn. Mater. 104–107 47Google 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 409Google Scholar

    [19]

    Roundy D, Krenn C R, Cohen M L, Morris J W 1999 Phys. Rev. Lett. 82 2713Google Scholar

    [20]

    Roundy D, Krenn C R, Cohen M L, Morris J W 2001 Philos. Mag. A 81 1725Google Scholar

    [21]

    Ogata S, Li J, Hirosaki N, Shibutani Y, Yip S 2004 Phys. Rev. B 70 104104Google 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 B864Google Scholar

    [24]

    Kohn W, Sham L J 1965 Phys. Rev. 140 A1133Google Scholar

    [25]

    Kresse G G, Furthmüller J J 1996 Phys. Rev. B 54 11169Google Scholar

    [26]

    Kresse G, Hafner J 1993 Phys. Rev. B Condens. Matter. 47 558Google Scholar

    [27]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [28]

    Liechtenstein A I, Anisimov V V, Zaanen J 1995 Phys. Rev. B 52 R5467Google Scholar

    [29]

    Sarma D D, Krummacher S, Hillebrecht F U, Koelling D D 1988 Phys. Rev. B: Condens. Matter. 38 1Google Scholar

    [30]

    Shih B C, Zhang Y B, Zhang W Q, Zhang P H 2012 Phys. Rev. B 85 045132Google Scholar

    [31]

    Szpunar B 2012 J. Phys. Chem. Solids 73 1003Google Scholar

    [32]

    Setyawan W, Curtarolo S 2010 Comput. Mater. Sci. 49 299Google Scholar

    [33]

    Mei Z G, Miao Y B, Liang L Y, Yacout A M 2019 J. Nucl. Mater. 513 192Google 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 104229Google Scholar

    [35]

    Zachariasen W H 1949 Acta Crystallogr. 2 94Google Scholar

    [36]

    Smirnov M B, Kazimirov V Y, Rita B H, Smirnov K S, Pereira-Ramos J P 2014 J. Phys. Chem. Solids 75 115Google Scholar

    [37]

    Manikandan M, Rajeswarapalanichamy R, Iyakutti K 2017 Philos. Mag. 98 1Google Scholar

    [38]

    M I, T L, Bihan, S H, J R 2004 Phys. Rev. B 70 014113Google Scholar

    [39]

    Dubois S M M, Rignanese G M, Pardoen T, Charlier J C 2006 Phys. Rev. B 74 235203Google Scholar

  • 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].

    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.

    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.

    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.

    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.

    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.

    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.

    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.

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

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

    Comp-
    ound
    C11C12C13C33C44C66EBGB/GυRefs.
    U3Si21554750142654613983571.460.22[13]
    1494948139634681531.53[14]
    1674653205677416392681.360.2[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
    acV3dU-UdSi-SidU-SiRefs.
    U3Si27.424.03221.813.3752.3962.909Present
    7.483.98222.583.3862.4322.930[2]
    7.454.03223.26[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 314Google Scholar

    [2]

    Srinivasu K, Modak B, Ghanty T K 2018 J. Nucl. Mater. 510 360Google 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 106Google Scholar

    [5]

    Beeler B, Baskes M, Andersson D, Cooper M W D, Zhang Y F 2017 J. Nucl. Mater. 495 267Google Scholar

    [6]

    Kim Y S 2012 Comprehensive Nuclear Materials (Oxford: Elsevier) pp391–422

    [7]

    Birtcher R C, Wang L M 2011 MRS Proceedings 235 467Google Scholar

    [8]

    Rest J 1997 J. Nucl. Mater. 240 205Google Scholar

    [9]

    Yao T K, Gong B W, He L F, Harp J, Tonks M, Lian J 2018 J. Nucl. Mater. 498 169Google Scholar

    [10]

    Carvajal-Nunez U, Saleh T A, White J T, Maiorov B, Nelson A T 2018 J. Nucl. Mater. 498 438Google Scholar

    [11]

    Jossou E, Eduok U, Dzade N Y, Szpunar B, Szpunar J A 2018 Phys. Chem. Chem. Phys. 20 4708Google 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 194Google Scholar

    [13]

    Noordhoek M J, Besmann T M, Andersson D, Middleburgh S C, Chernatynskiy A 2016 J. Nucl. Mater. 479 216Google Scholar

    [14]

    Chattaraj D, Majumder C 2018 J. Alloy. Compd. 732 160Google Scholar

    [15]

    Liu H, Claisse A, Middleburgh S C, Olsson P 2019 J. Nucl. Mater. 527 151828Google Scholar

    [16]

    Remschnig K, Le Bihan T, Noël H, Rogl P 1992 J. Solid State Chem. 97 391Google Scholar

    [17]

    Miyadai T, Mori H, Oguchi T, Tazuke Y, Amitsuka H, Kuwai T, Miyako Y 1992 J. Magn. Magn. Mater. 104–107 47Google 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 409Google Scholar

    [19]

    Roundy D, Krenn C R, Cohen M L, Morris J W 1999 Phys. Rev. Lett. 82 2713Google Scholar

    [20]

    Roundy D, Krenn C R, Cohen M L, Morris J W 2001 Philos. Mag. A 81 1725Google Scholar

    [21]

    Ogata S, Li J, Hirosaki N, Shibutani Y, Yip S 2004 Phys. Rev. B 70 104104Google 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 B864Google Scholar

    [24]

    Kohn W, Sham L J 1965 Phys. Rev. 140 A1133Google Scholar

    [25]

    Kresse G G, Furthmüller J J 1996 Phys. Rev. B 54 11169Google Scholar

    [26]

    Kresse G, Hafner J 1993 Phys. Rev. B Condens. Matter. 47 558Google Scholar

    [27]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [28]

    Liechtenstein A I, Anisimov V V, Zaanen J 1995 Phys. Rev. B 52 R5467Google Scholar

    [29]

    Sarma D D, Krummacher S, Hillebrecht F U, Koelling D D 1988 Phys. Rev. B: Condens. Matter. 38 1Google Scholar

    [30]

    Shih B C, Zhang Y B, Zhang W Q, Zhang P H 2012 Phys. Rev. B 85 045132Google Scholar

    [31]

    Szpunar B 2012 J. Phys. Chem. Solids 73 1003Google Scholar

    [32]

    Setyawan W, Curtarolo S 2010 Comput. Mater. Sci. 49 299Google Scholar

    [33]

    Mei Z G, Miao Y B, Liang L Y, Yacout A M 2019 J. Nucl. Mater. 513 192Google 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 104229Google Scholar

    [35]

    Zachariasen W H 1949 Acta Crystallogr. 2 94Google Scholar

    [36]

    Smirnov M B, Kazimirov V Y, Rita B H, Smirnov K S, Pereira-Ramos J P 2014 J. Phys. Chem. Solids 75 115Google Scholar

    [37]

    Manikandan M, Rajeswarapalanichamy R, Iyakutti K 2017 Philos. Mag. 98 1Google Scholar

    [38]

    M I, T L, Bihan, S H, J R 2004 Phys. Rev. B 70 014113Google Scholar

    [39]

    Dubois S M M, Rignanese G M, Pardoen T, Charlier J C 2006 Phys. Rev. B 74 235203Google Scholar

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出版历程
  • 收稿日期:  2022-06-20
  • 修回日期:  2022-07-18
  • 上网日期:  2022-11-09
  • 刊出日期:  2022-11-20

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