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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.
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Keywords:
- phase field crystal /
- misorientation /
- grain boundary /
- dislocation
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图 1 单模近似下的二维相图
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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(°) A 0.285 –0.27 6 B 0.285 –0.27 7 C 0.285 –0.27 8 D 0.285 –0.27 9 
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[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. 779 175
Google 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. 35 512
Google Scholar
[3] Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys. Rev. Lett. 88 245701
Google Scholar
[4] Elder K R, Grant M 2004 Phys. Rev. E 70 051605
Google Scholar
[5] Elder K R, Provatas N, Berry J, Stefanovic P 2007 Phys. Rev. B 75 064107
Google Scholar
[6] Wang J, Yu L M, Huang Y, Li H J, Liu Y C 2019 Comput. Mater. Sci. 160 105
Google Scholar
[7] Zhao Y H, Zhang B, Hou H, Chen W P, Wang M 2019 J. Mater. Sci. Technol. 35 1044
Google Scholar
[8] Zhang B, Zhao Y H, Chen W P, Xu Q Y, Wang M, Hou H 2019 J. Cryst. Growth 522 183
Google Scholar
[9] Sun Y Y, Zhao Y H, Zhao B J, Yang W K, Li X L 2019 J. Mater. Sci. 54 11263
Google Scholar
[10] Fan D, Chen L Q 1997 Acta Mater. 45 611
Google 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 3000
Google Scholar
Sun Y Y, Zhao Y H, Hou H, Zheng X J, Guo H J 2018 Rare Metal Mat. Eng. 47 3000
Google Scholar
[12] 康永生, 赵宇宏, 侯华, 靳玉春, 陈利文 2016 物理学报 65 188102
Google Scholar
Kang Y S, Zhao Y H, Hou H, Jin Y C, Chen L W 2016 Acta Phys. Sin. 65 188102
Google Scholar
[13] 田晓林, 赵宇宏, 田晋忠, 侯华 2018 物理学报 67 230201
Google Scholar
Tian X L, Zhao Y H, Tian J Z, Hou H 2018 Acta Phys. Sin. 67 230201
Google 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 1793
Google Scholar
[15] 赵宝军, 赵宇宏, 孙远洋, 杨文奎, 侯华 2019 金属学报 55 593
Google Scholar
Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593
Google 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 44
Google Scholar
[18] Tian J Z, Zhao Y H, Wang B, Hou H, Zhang Y M 2018 Mater. Chem. Phys. 209 200
Google 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 86
Google Scholar
[20] Kuang W W, Wang H F, Li X, Zhang J B, Zhou Q, Zhao Y H 2018 Acta Mater. 159 16
Google Scholar
[21] 方辉, 薛桦, 汤倩玉, 张庆宇, 潘诗琰, 朱鸣芳 2019 物理学报 68 048102
Google Scholar
Fang H, Xue H, Tang Q Y, Zhang Q Y, Pan S Y, Zhu M F 2019 Acta Phys. Sin. 68 048102
Google Scholar
[22] Zhao Y H, Wang S, Zhang B, Yuan Y, Guo Q W, Hou H 2019 J. Solid State Chem. 276 232
Google Scholar
[23] Wu K A, Voorhees P W 2012 Acta Mater. 60 407
Google Scholar
[24] 祁科武, 赵宇宏, 郭慧俊, 田晓林, 侯华 2019 物理学报 68 170504
Google Scholar
Qi K W, Zhao Y H, Guo H J, Tian X L, Hou H 2019 Acta Phys. Sin. 68 170504
Google Scholar
[25] Olmsted D L, Buta D, Adland A, Foiles S M, Asta M, Karma A 2011 Phys. Rev. Lett. 106 046101
Google 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 106105
Google Scholar
Gao Y J, Qin H L, Zhou W Q, Deng Q Q, Luo Z R, Huang C G 2015 Acta Phys. Sin. 64 106105
Google Scholar
[27] Berry J, Elder K R, Grant M 2008 Phys. Rev. B 77 224114
Google Scholar
[28] Nourian A, Asadi E 2018 Comput. Mater. Sci. 145 224
Google Scholar
[29] ChanV W L, Pisutha-Arnond N, Thornton K 2017 Comput. Mater. Sci. 135 205
Google Scholar
[30] Asadi E, Zaeem M A 2015 Jom 67 186
Google Scholar
[31] Hu S, Xi W, Chen Z, Wang S, Zhang T H 2017 Comput. Mater. Sci. 132 125
Google Scholar
[32] Hu S, Wang S 2019 Phys. B 552 104
Google Scholar
[33] Gao Y J, Deng Q Q, Huang L L, Ye L, Wen Z C, Luo Z R 2017 Comput. Mater. Sci. 130 64
Google Scholar
[34] Greenwood M, Ofori-Opoku N, Rottler J, Provatas N 2011 Phys. Rev. B 84 064104
Google 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. 91 151
Google Scholar
[37] Lu G M, Lu Y L, Hu T T, Chen Z 2015 Comput. Mater. Sci. 106 170
Google 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. 129 163
Google Scholar
[39] Zhao Y H, Deng S J, Liu H, Zhang J X, Guo Z H, Hou H 2018 Comput. Mater. Sci. 154 365
Google Scholar
[40] Wen Z Q, Hou H, Tian J Z, Zhao Y H, Li H J, Han P D 2018 Intermetallics 92 15
Google Scholar
[41] Wen Z Q, Zhao Y H, Hou H, Wang B, Han P D 2017 Mater. Des. 114 398
Google Scholar
[42] Zhao Y H, Qi L, Jin Y C, Wang K, Tian J Z, Han P D 2015 J. Alloys Compd. 647 1104
Google Scholar
[43] Hirouchi T, Takaki T, Tomita Y 2009 Comput. Mater. Sci. 44 1192
Google Scholar
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