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取向角对小角度非对称倾斜晶界位错运动影响的晶体相场模拟

祁科武 赵宇宏 田晓林 彭敦维 孙远洋 侯华

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取向角对小角度非对称倾斜晶界位错运动影响的晶体相场模拟

祁科武, 赵宇宏, 田晓林, 彭敦维, 孙远洋, 侯华

Phase field crystal simulation of effect of misorientation angle on low-angle asymmetric tilt grain boundary dislocation motion

Qi Ke-Wu, Zhao Yu-Hong, Tian Xiao-Lin, Peng Dun-Wei, Sun Yuan-Yang, Hou Hua
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  • 采用晶体相场法模拟纳米尺度下小角度非对称倾斜晶界结构和位错运动, 从外应力作用下晶界位错运动位置变化和晶体体系自由能变化角度, 分析取向角对小角度非对称倾斜晶界结构和晶界位错运动的影响规律. 研究表明, 不同取向角下组成小角度非对称倾斜晶界的位错对类型相同. 随取向角增大晶界位错对增加, 且晶界更易形成n1n2型和n4n5型位错对. 外应力作用下, 不同取向角晶界位错对初始运动状态均沿晶界进行攀移运动, 随体系能量积累, 取向角越大出现晶界位错对分解的个数越多, 且均为n1n2型和n4n5型位错对发生分解反应. 不同取向角下小角度非对称倾斜晶界体系自由能曲线都存在四个阶段, 分别对应位错对攀移、位错对滑移及分解、位错对反应抵消形成单晶和体系吸收能量自由能上升过程. 进一步对比发现随取向角增大, 晶界湮没形成的单晶体系所需时间增加.
    Grain boundary affects the microstructure of metal material, and thus further its macroscopic properties. As is well known, under the action of applied stress, the grain boundary migrates. The structures and arrangements of grain boundary dislocations at different misorientation angles are very different, which affects the macrophysical and chemical properties of metal crystal. Therefore, it is of great theoretical and practical significance to study the dislocation structure and reaction mechanism of grain boundary under different misorientations for further studying the material properties.The phase field crystal method is used to simulate the low-angle asymmetric tilt grain boundary structure and dislocation motion on a nanoscale. From the perspective of the change of the position of the grain boundary dislocation motion under the applied stress and the change of the free energy of the crystal system, the influences of the misorientation angle on the low-angle asymmetric tilt grain boundary structure and the motion of the grain boundary dislocation are analyzed. The results show that the types of dislocation pairs of low-angle asymmetric tilt grain boundaries at different misorientation angles are the same. With the increase of misorientation angle, the grain boundary dislocation pairs increase, and n1n2 and n4n5 type dislocation pairs are more easily formed at the grain boundaries. Under the action of applied stress, the initial movement states of the grain boundary dislocation pairs at different misorientation angles are all climbing along the grain boundaries. As the system energy accumulates, the larger the misorientation angle is, the more the number of decomposed grain boundary dislocation pairs decomposed will be, and only in the dislocation pairs of n1n2 and n4n5 type there occurs decomposition reaction. There are four stages in the free energy curve of the low-angle asymmetric tilt grain boundary system at different misorientation angles, which correspond to the dislocation pairs climbing, dislocation pairs sliding and decomposition, dislocation pairs reaction to form single crystal, and the free energy rising process of the system. Further research shows that as the misorientation angle increases, the time for the single crystal system formed by the dislocation of grain boundary pairs to annihilate is required to be long.
      通信作者: 赵宇宏, zhaoyuhong@nuc.edu.cn
    • 基金项目: 国家级-国家自然科学基金(51774254,51774253,51701187,51674226,51804279,51801189)
      Corresponding author: Zhao Yu-Hong, zhaoyuhong@nuc.edu.cn
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    Chen Y Y, Hu Z P, Xu Y F, Wang J Y, Schützendübe P, Huang Y, Liu Y C, Wang Z M 2019 J. Mater. Sci. Technol. 35 512Google Scholar

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    Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys. Rev. Lett. 88 245701Google Scholar

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    Elder K R, Grant M 2004 Phys. Rev. E 70 051605Google Scholar

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    Elder K R, Provatas N, Berry J, Stefanovic P 2007 Phys. Rev. B 75 064107Google Scholar

    [6]

    Wang J, Yu L M, Huang Y, Li H J, Liu Y C 2019 Comput. Mater. Sci. 160 105Google Scholar

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    Zhao Y H, Zhang B, Hou H, Chen W P, Wang M 2019 J. Mater. Sci. Technol. 35 1044Google Scholar

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    Zhang B, Zhao Y H, Chen W P, Xu Q Y, Wang M, Hou H 2019 J. Cryst. Growth 522 183Google Scholar

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    Sun Y Y, Zhao Y H, Zhao B J, Yang W K, Li X L 2019 J. Mater. Sci. 54 11263Google Scholar

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    Fan D, Chen L Q 1997 Acta Mater. 45 611Google Scholar

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    孙远洋, 赵宇宏, 侯华, 郑晓娟, 郭慧俊 2018 稀有金属材料与工程 47 3000Google Scholar

    Sun Y Y, Zhao Y H, Hou H, Zheng X J, Guo H J 2018 Rare Metal Mat. Eng. 47 3000Google Scholar

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    康永生, 赵宇宏, 侯华, 靳玉春, 陈利文 2016 物理学报 65 188102Google Scholar

    Kang Y S, Zhao Y H, Hou H, Jin Y C, Chen L W 2016 Acta Phys. Sin. 65 188102Google Scholar

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    田晓林, 赵宇宏, 田晋忠, 侯华 2018 物理学报 67 230201Google Scholar

    Tian X L, Zhao Y H, Tian J Z, Hou H 2018 Acta Phys. Sin. 67 230201Google Scholar

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    Zhao Y H, Tian X L, Zhao B J, Sun Y Y, Guo H J, Dong M Y, Liu H, Wang X J, Guo Z H, Umar A, Hou H 2018 Sci. Adv. Mater. 10 1793Google Scholar

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    赵宝军, 赵宇宏, 孙远洋, 杨文奎, 侯华 2019 金属学报 55 593Google Scholar

    Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593Google Scholar

    [16]

    孙远洋, 赵宇宏, 侯华, 靳玉春, 郑晓娟 2018 中国有色金属学报 28 71

    Sun Y Y, Zhao Y H, Hou H, Jin Y C, Zheng X J 2018 Chin. J. Nonferrous Met. 28 71

    [17]

    Tian J Z, Zhao Y H, Hou H, Han P D 2017 Solid State Commun. 268 44Google Scholar

    [18]

    Tian J Z, Zhao Y H, Wang B, Hou H, Zhang Y M 2018 Mater. Chem. Phys. 209 200Google Scholar

    [19]

    Zhang J B, Wang H F, Kuang W W, Zhang Y C, Li H, Zhao Y H, Herlach D 2018 Acta Mater. 148 86Google Scholar

    [20]

    Kuang W W, Wang H F, Li X, Zhang J B, Zhou Q, Zhao Y H 2018 Acta Mater. 159 16Google Scholar

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    方辉, 薛桦, 汤倩玉, 张庆宇, 潘诗琰, 朱鸣芳 2019 物理学报 68 048102Google Scholar

    Fang H, Xue H, Tang Q Y, Zhang Q Y, Pan S Y, Zhu M F 2019 Acta Phys. Sin. 68 048102Google Scholar

    [22]

    Zhao Y H, Wang S, Zhang B, Yuan Y, Guo Q W, Hou H 2019 J. Solid State Chem. 276 232Google Scholar

    [23]

    Wu K A, Voorhees P W 2012 Acta Mater. 60 407Google Scholar

    [24]

    祁科武, 赵宇宏, 郭慧俊, 田晓林, 侯华 2019 物理学报 68 170504Google Scholar

    Qi K W, Zhao Y H, Guo H J, Tian X L, Hou H 2019 Acta Phys. Sin. 68 170504Google Scholar

    [25]

    Olmsted D L, Buta D, Adland A, Foiles S M, Asta M, Karma A 2011 Phys. Rev. Lett. 106 046101Google Scholar

    [26]

    高英俊, 秦河林, 周文权, 邓芊芊, 罗志荣, 黄创高 2015 物理学报 64 106105Google Scholar

    Gao Y J, Qin H L, Zhou W Q, Deng Q Q, Luo Z R, Huang C G 2015 Acta Phys. Sin. 64 106105Google Scholar

    [27]

    Berry J, Elder K R, Grant M 2008 Phys. Rev. B 77 224114Google Scholar

    [28]

    Nourian A, Asadi E 2018 Comput. Mater. Sci. 145 224Google Scholar

    [29]

    ChanV W L, Pisutha-Arnond N, Thornton K 2017 Comput. Mater. Sci. 135 205Google Scholar

    [30]

    Asadi E, Zaeem M A 2015 Jom 67 186Google Scholar

    [31]

    Hu S, Xi W, Chen Z, Wang S, Zhang T H 2017 Comput. Mater. Sci. 132 125Google Scholar

    [32]

    Hu S, Wang S 2019 Phys. B 552 104Google Scholar

    [33]

    Gao Y J, Deng Q Q, Huang L L, Ye L, Wen Z C, Luo Z R 2017 Comput. Mater. Sci. 130 64Google Scholar

    [34]

    Greenwood M, Ofori-Opoku N, Rottler J, Provatas N 2011 Phys. Rev. B 84 064104Google Scholar

    [35]

    Greenwood M, Rottler J, Provatas N 2011 Phys. Rev. E 83 031601

    [36]

    Elder K R, Thornton K, Hoyt J J 2011 Philos. Mag. 91 151Google Scholar

    [37]

    Lu G M, Lu Y L, Hu T T, Chen Z 2015 Comput. Mater. Sci. 106 170Google Scholar

    [38]

    Guo H J, Zhao Y H, Sun Y Y, Tian J Z, Hou H, Qi K W, Tian X L 2019 Superlattices Microstruct. 129 163Google Scholar

    [39]

    Zhao Y H, Deng S J, Liu H, Zhang J X, Guo Z H, Hou H 2018 Comput. Mater. Sci. 154 365Google Scholar

    [40]

    Wen Z Q, Hou H, Tian J Z, Zhao Y H, Li H J, Han P D 2018 Intermetallics 92 15Google Scholar

    [41]

    Wen Z Q, Zhao Y H, Hou H, Wang B, Han P D 2017 Mater. Des. 114 398Google Scholar

    [42]

    Zhao Y H, Qi L, Jin Y C, Wang K, Tian J Z, Han P D 2015 J. Alloys Compd. 647 1104Google Scholar

    [43]

    Hirouchi T, Takaki T, Tomita Y 2009 Comput. Mater. Sci. 44 1192Google Scholar

  • 图 1  单模近似下的二维相图

    Fig. 1.  Two-dimensional phase diagram as calculated in a one-mode approximation.

    图 2  小角度非对称倾斜晶界结构

    Fig. 2.  Low-angle asymmetric tilt grain boundary structure.

    图 3  应力作用下θ = 8° 时晶界位错运动模拟图 (a) n = 400; (b) n = 11400; (c) n = 21200; (d) n = 21600; (e) n = 22000; (f) n = 22500; (g) n = 57050; (h) n = 57500

    Fig. 3.  Simulation diagram of grain boundary dislocation motion under stress with θ = 8°: (a) n = 400; (b) n = 11400; (c) n = 21200; (d) n = 21600; (e) n = 22000; (f) n = 22500; (g) n = 57050; (h) n = 57500

    图 4  (a)刃型位错类型; (b)位错对应的柏氏矢量类型

    Fig. 4.  (a) Edge dislocation types and (b) its corresponding Burgers vector types

    图 5  n1n2型位错对分解为n2n3型位错对和n1n6型位错对

    Fig. 5.  The n1n2 dislocation pairs is decomposed to n2n3 and n1n6 dislocation pairs.

    图 6  n4n5型位错对分解为n3n4型位错对和n5n6型位错对

    Fig. 6.  The n4n5 dislocation pairs is decomposed to n3n4 and n5n6 dislocation pairs.

    图 7  应力作用下θ = 6° 时晶界位错运动模拟图 (a) n = 9500; (b) n = 18500; (c) n = 20600; (d) n = 21500; (e) n = 23500; (f) n = 31100; (g) n = 31800; (h) n = 37500

    Fig. 7.  Simulation diagram of grain boundary dislocation motion under stress with θ = 6°: (a) n = 9500; (b) n = 18500; (c) n = 20600; (d) n = 21500; (e) n = 23500; (f) n = 31100; (g) n = 31800; (h) n = 37500

    图 9  应力作用下θ = 9° 时晶界位错运动模拟图 (a) n = 10850; (b) n = 18750; (c) n = 21600; (d) n = 22550; (e)n = 24350; (f) n = 27000; (g) n = 54800; (h) n = 58000

    Fig. 9.  Simulation diagram of grain boundary dislocation motion under stress with θ = 9°: (a) n = 10850; (b) n = 18750; (c) n = 21600; (d) n = 22550; (e) n = 24350; (f) n = 27000; (g) n = 54800; (h) n = 58000

    图 8  应力作用下θ = 7° 时晶界位错运动模拟图 (a) n = 9100; (b) n = 12950; (c) n = 18500; (d) n = 22500; (e) n = 23200; (f) n = 24050; (g) n = 26450; (h)n = 39600

    Fig. 8.  Simulation diagram of grain boundary dislocation motion under stress with θ = 7°: (a) n = 9100; (b) n = 12950; (c) n = 18500; (d) n = 22500; (e) n = 23200; (f) n = 24050; (g) n = 26450; (h) n = 39600

    图 10  不同取向角下体系自由能变化曲线

    Fig. 10.  Free energy curve of system under different misorientations

    表 1  模拟所采用的参数

    Table 1.  Parameters used in the simulation.

    方案初始原子密度 ρ0温度相关参量 r取向角 θ(°)
    A0.285–0.276
    B0.285–0.277
    C0.285–0.278
    D0.285–0.279
    下载: 导出CSV
  • [1]

    Li X H, Wen X, Zhao H H, Ma Z Q, Yu L M, Li C, Liu C X, Guo Q Y, Liu Y C 2019 J. Alloys Compd. 779 175Google Scholar

    [2]

    Chen Y Y, Hu Z P, Xu Y F, Wang J Y, Schützendübe P, Huang Y, Liu Y C, Wang Z M 2019 J. Mater. Sci. Technol. 35 512Google Scholar

    [3]

    Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys. Rev. Lett. 88 245701Google Scholar

    [4]

    Elder K R, Grant M 2004 Phys. Rev. E 70 051605Google Scholar

    [5]

    Elder K R, Provatas N, Berry J, Stefanovic P 2007 Phys. Rev. B 75 064107Google Scholar

    [6]

    Wang J, Yu L M, Huang Y, Li H J, Liu Y C 2019 Comput. Mater. Sci. 160 105Google Scholar

    [7]

    Zhao Y H, Zhang B, Hou H, Chen W P, Wang M 2019 J. Mater. Sci. Technol. 35 1044Google Scholar

    [8]

    Zhang B, Zhao Y H, Chen W P, Xu Q Y, Wang M, Hou H 2019 J. Cryst. Growth 522 183Google Scholar

    [9]

    Sun Y Y, Zhao Y H, Zhao B J, Yang W K, Li X L 2019 J. Mater. Sci. 54 11263Google Scholar

    [10]

    Fan D, Chen L Q 1997 Acta Mater. 45 611Google Scholar

    [11]

    孙远洋, 赵宇宏, 侯华, 郑晓娟, 郭慧俊 2018 稀有金属材料与工程 47 3000Google Scholar

    Sun Y Y, Zhao Y H, Hou H, Zheng X J, Guo H J 2018 Rare Metal Mat. Eng. 47 3000Google Scholar

    [12]

    康永生, 赵宇宏, 侯华, 靳玉春, 陈利文 2016 物理学报 65 188102Google Scholar

    Kang Y S, Zhao Y H, Hou H, Jin Y C, Chen L W 2016 Acta Phys. Sin. 65 188102Google Scholar

    [13]

    田晓林, 赵宇宏, 田晋忠, 侯华 2018 物理学报 67 230201Google Scholar

    Tian X L, Zhao Y H, Tian J Z, Hou H 2018 Acta Phys. Sin. 67 230201Google Scholar

    [14]

    Zhao Y H, Tian X L, Zhao B J, Sun Y Y, Guo H J, Dong M Y, Liu H, Wang X J, Guo Z H, Umar A, Hou H 2018 Sci. Adv. Mater. 10 1793Google Scholar

    [15]

    赵宝军, 赵宇宏, 孙远洋, 杨文奎, 侯华 2019 金属学报 55 593Google Scholar

    Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593Google Scholar

    [16]

    孙远洋, 赵宇宏, 侯华, 靳玉春, 郑晓娟 2018 中国有色金属学报 28 71

    Sun Y Y, Zhao Y H, Hou H, Jin Y C, Zheng X J 2018 Chin. J. Nonferrous Met. 28 71

    [17]

    Tian J Z, Zhao Y H, Hou H, Han P D 2017 Solid State Commun. 268 44Google Scholar

    [18]

    Tian J Z, Zhao Y H, Wang B, Hou H, Zhang Y M 2018 Mater. Chem. Phys. 209 200Google Scholar

    [19]

    Zhang J B, Wang H F, Kuang W W, Zhang Y C, Li H, Zhao Y H, Herlach D 2018 Acta Mater. 148 86Google Scholar

    [20]

    Kuang W W, Wang H F, Li X, Zhang J B, Zhou Q, Zhao Y H 2018 Acta Mater. 159 16Google Scholar

    [21]

    方辉, 薛桦, 汤倩玉, 张庆宇, 潘诗琰, 朱鸣芳 2019 物理学报 68 048102Google Scholar

    Fang H, Xue H, Tang Q Y, Zhang Q Y, Pan S Y, Zhu M F 2019 Acta Phys. Sin. 68 048102Google Scholar

    [22]

    Zhao Y H, Wang S, Zhang B, Yuan Y, Guo Q W, Hou H 2019 J. Solid State Chem. 276 232Google Scholar

    [23]

    Wu K A, Voorhees P W 2012 Acta Mater. 60 407Google Scholar

    [24]

    祁科武, 赵宇宏, 郭慧俊, 田晓林, 侯华 2019 物理学报 68 170504Google Scholar

    Qi K W, Zhao Y H, Guo H J, Tian X L, Hou H 2019 Acta Phys. Sin. 68 170504Google Scholar

    [25]

    Olmsted D L, Buta D, Adland A, Foiles S M, Asta M, Karma A 2011 Phys. Rev. Lett. 106 046101Google Scholar

    [26]

    高英俊, 秦河林, 周文权, 邓芊芊, 罗志荣, 黄创高 2015 物理学报 64 106105Google Scholar

    Gao Y J, Qin H L, Zhou W Q, Deng Q Q, Luo Z R, Huang C G 2015 Acta Phys. Sin. 64 106105Google Scholar

    [27]

    Berry J, Elder K R, Grant M 2008 Phys. Rev. B 77 224114Google Scholar

    [28]

    Nourian A, Asadi E 2018 Comput. Mater. Sci. 145 224Google Scholar

    [29]

    ChanV W L, Pisutha-Arnond N, Thornton K 2017 Comput. Mater. Sci. 135 205Google Scholar

    [30]

    Asadi E, Zaeem M A 2015 Jom 67 186Google Scholar

    [31]

    Hu S, Xi W, Chen Z, Wang S, Zhang T H 2017 Comput. Mater. Sci. 132 125Google Scholar

    [32]

    Hu S, Wang S 2019 Phys. B 552 104Google Scholar

    [33]

    Gao Y J, Deng Q Q, Huang L L, Ye L, Wen Z C, Luo Z R 2017 Comput. Mater. Sci. 130 64Google Scholar

    [34]

    Greenwood M, Ofori-Opoku N, Rottler J, Provatas N 2011 Phys. Rev. B 84 064104Google Scholar

    [35]

    Greenwood M, Rottler J, Provatas N 2011 Phys. Rev. E 83 031601

    [36]

    Elder K R, Thornton K, Hoyt J J 2011 Philos. Mag. 91 151Google Scholar

    [37]

    Lu G M, Lu Y L, Hu T T, Chen Z 2015 Comput. Mater. Sci. 106 170Google Scholar

    [38]

    Guo H J, Zhao Y H, Sun Y Y, Tian J Z, Hou H, Qi K W, Tian X L 2019 Superlattices Microstruct. 129 163Google Scholar

    [39]

    Zhao Y H, Deng S J, Liu H, Zhang J X, Guo Z H, Hou H 2018 Comput. Mater. Sci. 154 365Google Scholar

    [40]

    Wen Z Q, Hou H, Tian J Z, Zhao Y H, Li H J, Han P D 2018 Intermetallics 92 15Google Scholar

    [41]

    Wen Z Q, Zhao Y H, Hou H, Wang B, Han P D 2017 Mater. Des. 114 398Google Scholar

    [42]

    Zhao Y H, Qi L, Jin Y C, Wang K, Tian J Z, Han P D 2015 J. Alloys Compd. 647 1104Google Scholar

    [43]

    Hirouchi T, Takaki T, Tomita Y 2009 Comput. Mater. Sci. 44 1192Google Scholar

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出版历程
  • 收稿日期:  2020-01-18
  • 修回日期:  2020-04-22
  • 上网日期:  2020-05-09
  • 刊出日期:  2020-07-20

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