Strain induced dislocation evolution at graphene grain boundary by three-mode phase-field crystal method

Gao Feng; Li Huan-Qing; Song Zhuo; Zhao Yu-Hong

doi:10.7498/aps.73.20241368

Abstract

The evolution law and mechanism of grain boundary structure in the deformation process of graphene are of great significance for understanding the deformation behavior of graphene and optimizing its mechanical properties. In this work, single-layer graphene is taken as the research object and a double crystalline graphene model is established by using the three-mode phase-field crystal method, thereby in depth ascertaining the evolution mechanism of dislocations at small-angle symmetrical tilt grain boundaries in graphene under strain. In view of the relaxation and deformation process, the relationship between the number of multiple dislocations and the grain boundary angle of graphene is studied on an atomic scale, and the deformation and failure mechanism of double crystalline graphene under tensile load are revealed, and also discussed from the perspective of the free energy.It is found that, after relaxation, with the increase of grain boundary angle, the density of dislocations at the grain boundary decreases, and the number of specific types of dislocations (5|8|7 and 5|7 dislocations) increases. Under stress loading parallel to the grain boundary, the changes of free energy of the systems containing grain boundaries with different angles show the same trend: at first, they fall to the inflection point and then rise abnormally, and the dislocation behavior cannot effectively alleviate the stress concentration caused by continuous loading in the system, leading to failure finally.Under tensile load, the free energy changes of the systems are divided into four stages, they being stage (I), in which the dislocations at grain boundaries are slightly deformed but do not change their structure, stage (II), in which dislocations at the grain boundaries are transformed into 5|7 or 5|9 dislocation due to C—C bond fracture or rotation, and the dislocations that are “incompatible” have higher energy, making them more conducive to improving the tensile properties of graphene, stage (III), in which the 5|7 and 5|9 dislocations begin to fail, and the free energy shows a tendency to decrease significantly, and stage (IV), in which the double crystalline graphene systems are completely in failure. The system with a grain boundary angle of 10° exhibits the most substantial deduction in free energy in stages (I), (II), and (III), and possesses the highest overall tensile strength.This work contributes to understanding the micromechanical behavior of graphene on an atomic scale.

Keywords:

Authors and contacts

1.
School of Materials Science and Engineering, North University of China, Taiyuan 030051, China
2.
Beijing Advanced Innovation Center for Materials Genome Engineering, University of Science and Technology Beijing, Beijing 100083, China
3.
Liaoning Laboratory of Materials, Institute of Materials Intelligence Technology, Shenyang 110004, China

Corresponding author: Zhao Yu-Hong, zhaoyuhong@nuc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52074246, 52275390, 52205429, 52201146), the National Defense Basic Scientific Research Program of China (Grant No. JCKY2020408B002), the Key Research and Development Program of Shanxi Province, China (Grant No. 202102050201011), and the Guiding Local Science and Technology Development Projects by the Central Government (Grant Nos. YDZJSX2022A025, YDZJSX2021A027).

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References

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[2]	Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385 Google Scholar
[3]	Cao K, Feng S Z, Han Y, Gao L B, Hue Ly T, Xu Z P, Lu Y 2020 Nat. Commun. 11 284 Google Scholar
[4]	Liu J, Hei L F, Song J H, Li C M, Tang W Z, Chen G C, Lu F X 2014 Diam. Relat. Mater. 46 42 Google Scholar
[5]	Huang P Y, Ruiz-Vargas C S, van der Zande A M, et al. 2011 Nature 469 389 Google Scholar
[6]	Hashimoto A, Suenaga K, Gloter A, Urita K, Iijima S 2004 Nature 430 870 Google Scholar
[7]	Meyer J C, Kisielowski C, Erni R, Rossell M D, Crommie M F, Zettl A 2008 Nano Lett. 8 3582 Google Scholar
[8]	He L C, Guo S S, Lei J C, Sha Z D, Liu Z H 2014 Carbon 75 124 Google Scholar
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[11]	Zhang J F, Zhao J J, Lu J P 2012 ACS Nano 6 2704 Google Scholar
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[13]	Grantab R, Shenoy V B, Ruoff R S 2010 Science 330 946 Google Scholar
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[17]	Zhao Y H, Tian X L, Zhao B J, et al. 2018 Sci. Adv. Mater. 10 1793 Google Scholar
[18]	Zhang J B, Wang H F, Kuang W W, Zhang Y C, Li S, Zhao Y H, Herlach D M 2018 Acta Mater. 148 86 Google Scholar
[19]	Guo Q W, Hou H, Wang K L, Li M X, Liaw P K, Zhao Y H 2023 npj Comput. Mater. 9 185 Google Scholar
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[25]	Zhao Y H, Xing H, Zhang L J, et al. 2023 Acta Metall. Sin. (Engl. Lett. ) 36 1749 Google Scholar
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[35]	Zhao Y H, Liu K X, Zhang H B, Tian X L, Jiang Q L, Murugadoss V, Hou H 2022 Adv. Compos. Hybrid Mater. 5 2546 Google Scholar
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[37]	Akhukov M A, Fasolino A, Gornostyrev Y N, Katsnelson M I 2012 Phys. Rev. B 85 115407 Google Scholar
[38]	Hirvonen P, Ervasti M M, Fan Z, et al. 2016 Phys. Rev. B 94 035414 Google Scholar
[39]	Guo H J, Zhao Y H, Sun Y Y, Tian J Z, Hou H, Qi K W, Tian X L 2019 Micro Nanostruct. 129 163 Google Scholar
[40]	Elder K R, Grant M 2004 Phys. Rev. E 70 051605 Google Scholar

Cited By

图 1 模拟结构示意图(${\theta _1}$为晶粒1取向角, ${\theta _2}$为晶粒2取向角)

Figure 1. Schematic diagram of simulation structure, ${\theta _1}$ is grain 1 orientation angle, ${\theta _2}$ is grain 2 orientation angle.

DownLoad: Full-Size Img PowerPoint

图 2 石墨烯气相结晶图(蓝、绿、黄色标记石墨烯的五角元胞、七角元胞、八角元胞)　(a)—(d)晶界角分别为4°, 6°, 8°, 10°, 其中黑框中为晶界处位错; (a1)—(a3), (b1)—(b3), (c1)—(c3), (d1)—(d3)是对应的放大图

Figure 2. Vapor crystallization diagram of graphene: (a)–(d) Grain boundary angles are 4°, 6°, 8° and 10°, respectively, dislocations at grain boundaries are shown in the black box; (a1)–(a3), (b1)–(b3), (c1)–(c3), (d1)–(d3) are the corresponding enlarged images. Blue, green, yellow labeled graphene pentagonal cells, heptagonal cells, octagonal cells

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图 3 双晶石墨烯体系中晶界处位错数目统计结果　(a) 晶界角为4°—10°的总位错数目; (b) 晶界角为4°—10°的各种位错数目

Figure 3. Statistical results of the number of dislocations at the grain boundaries in the double crystalline graphene system: (a) Total number of dislocations at grain boundary angles of 4°–10°; (b) number of various dislocations at grain boundary angles of 4°–10°.

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图 4 石墨烯晶界5|7位错在应变下的演化图　(A)—(C), (D)—(G), (H)—(I), (J)—(L)分别对应晶界角为4°, 6°, 8°, 10°的石墨烯晶界5|7位错在应变下的演化图; (a)—(c), (d)—(g), (h)—(i), (j)—(l)为对应的演化过程示意图; (A)—(C)的应变$\varepsilon $分别为0, 0.0297, 0.0352; (D)—(G) 的应变$\varepsilon $分别为0, 0.0286, 0.0308, 0.0352; (H), (I) 的应变$\varepsilon $分别为0, 0.0363; (J)—(L) 的应变$\varepsilon $分别为0, 0.0297, 0.0363 (演化过程示意图中标记的5, 7, 8, 9分别代表石墨烯五、七、八、九角元胞, 分别对应相应演化图中石墨烯蓝、绿、黄、红色标记的五、七、八、九角元胞, 图5—8中标记解释与此相同)

Figure 4. Evolution diagram of 5|7 dislocations at graphene grain boundaries under strain: (A)–(C), (D)–(G), (H)–(I), (J)–(L) are the evolution diagrams of 5|7 dislocations at graphene grain boundaries under strain for corresponding grain boundary angles of 4°, 6°, 8° and 10°; (a)–(c), (d)–(g), (h)–(i), (j)–(l) are the evolution process diagrams. The strains $\varepsilon $ of (A)–(C) are 0, 0.0297, 0.0352, (D)–(G) are 0, 0.0286, 0.0308, 0.0352, (H), (I) are 0, 0.0363, and (J)–(L) are 0, 0.0297, 0.0363. The 5, 7, 8, 9 marked in the evolution diagram represent the graphene pentagonal, heptagonal, octagonal, and nougonal cells respectively, corresponding to the pentagonal, heptagonal, octagonal, and nougonal cells marked in the corresponding evolution process diagram in blue, green, yellow, and red respectively. The explanations of labels in Figure 5-8 are the same as those in Figure 4.

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图 5 石墨烯晶界5|8|7位错在应变下的演化图　(A)—(D), (E)—(H), (I)—(K)分别对应晶界角为6°, 8°, 10°的石墨烯晶界5|8|7位错在应变下的演化图; (a)—(d), (e)—(h), (i)—(k)是对应的演化过程示意图; (A)—(D)的应变$\varepsilon $分别为0, 0.0209, 0.0352, 0.0407, (E)—(H) 的应变$\varepsilon $分别为0, 0.0209, 0.0429, 0.0473, (I)—(K) 的应变$\varepsilon $分别为0, 0.0165, 0.0319

Figure 5. Evolution diagram of 5|8|7 dislocations at graphene grain boundaries under strain: (A)–(D), (E)–(H), (I)–(K) are the evolution diagrams of 5|8|7 dislocations at graphene grain boundaries under strain for corresponding grain boundary angles of 6°, 8° and 10°; (a)–(d), (e)–(h), (i)–(k) are the corresponding evolution process diagrams; the strains $\varepsilon $ of (A)–(D) are 0, 0.0209, 0.0352, 0.0407, (E)–(H) are 0, 0.0209, 0.0429, 0.0473, (I)–(K) are 0, 0.0165, 0.0319.

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图 6 石墨烯晶界5|8|8|7位错在应变下的演化图　(A)—(C), (D)—(G), (H)—(J)分别对应晶界角为4°, 8°, 10°的石墨烯晶界5|8|8|7位错在应变下的演化图; (a)—(c), (d)—(g), (h)—(j)是对应的演化过程示意图; (A)—(C)的应变$\varepsilon $分别为0, 0.0165, 0.022, (D)—(G)的应变$\varepsilon $分别为0, 0.0253, 0.0363, 0.0473, (H)—(J)的应变$\varepsilon $分别为0, 0.0154, 0.0242

Figure 6. Evolution diagram of 5|8|8|7 dislocations at graphene grain boundaries under strain: (A)–(C), (D)–(G), (H)–(J) are the evolution diagrams of 5|8|8|7 dislocations at graphene grain boundaries under strain for corresponding grain boundary angles of 4°, 8° and 10°; (a)–(c), (d)–(g), (h)–(j) are the corresponding evolution process diagrams; the strains $\varepsilon $ of (A)–(C) are 0, 0.0165, 0.022, (D)–(G) are 0, 0.0253, 0.0363, 0.0473, (H)–(J) are 0, 0.0154, 0.0242.

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图 7 石墨烯晶界5|8|8|8|7位错在应变下的3种演化图　(A)—(C), (D)—(G), (H)—(M) 是晶界角为6°的石墨烯晶界5|8|8|8|7位错在应变下的3种演化图; (a)—(c), (d)—(g), (h)—(m)是对应的演化过程示意图; (A)—(C) 的应变$\varepsilon $分别为0, 0.0132, 0.0209, (D)—(G)的应变$\varepsilon $分别为0, 0.0132, 0.0242, 0.0297, (H)—(M)的应变$\varepsilon $分别为0, 0.099, 0.0187, 0.0264, 0.0407, 0.0462

Figure 7. Three evolution diagrams of 5|8|8|8|7 dislocations at graphene grain boundaries under strain: (A)–(C), (D)–(G), (H)–(M) are three evolution diagrams of 5|8|8|8|7 dislocations at graphene grain boundaries under strain for the grain boundary angle of 6°; (a)–(c), (d)–(g), (h)–(m) are the corresponding evolution process diagrams; the strains $\varepsilon $ of (A)–(C) are 0, 0.0132, 0.0209, (D)–(G) are 0, 0.0132, 0.0242, 0.0297, (H)–(M) are 0, 0.099, 0.0187, 0.0264, 0.0407, 0.0462.

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图 8 石墨烯晶界5|8|8|8|8|8|7位错在应变下的演化图　(A)—(G)晶界角为4°的石墨烯晶界5|8|8|8|8|8|7位错在应变下的演化图; (a)—(g)是演化过程示意图; (A)—(G)的应变$\varepsilon $分别为0, 0.0231, 0.0281, 0.0319, 0.0341, 0.0374, 0.0473

Figure 8. Evolution diagram of 5|8|8|8|8|8|7 dislocations at graphene grain boundaries under strain: (A)–(G) are the evolution diagrams of 5|8|8|8|8|8|7 dislocations at graphene grain boundaries under strain for grain boundary angles of 4°; (a)–(g) are the evolution process diagrams; the strains $\varepsilon $ of (A)–(G) are 0, 0.0231, 0.0281, 0.0319, 0.0341, 0.0374, 0.0473.

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图 9 晶界角为4°, 6°, 8°, 10°的石墨烯晶界各种位错的延伸率

Figure 9. Elongation of various dislocations of graphene grain boundaries with grain boundary angles of 4°, 6°, 8° and 10°

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图 10 变形过程中双晶石墨烯自由能-应变曲线　(a)—(d)晶界角分别为4°, 6°, 8°, 10°

Figure 10. Free energy curves of double crystalline graphene during deformation: (a)–(d) The grain boundary angles are 4°, 6°, 8°, 10°.

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表 1 施加应力应变的参数

Table 1. Parameters for applying stress and strain.

试样拉伸应
变方向晶粒取向角晶界角
$\theta $/(°)

${\theta _1}$/(°) ${\theta _2}$/(°)

A $y$ 2 –2 4

B $y$ 3 –3 6

C $y$ 4 –4 8

D $y$ 5 –5 10

DownLoad: CSV

[1]	林彰乾, 郑伟, 李浩, 王东君 2021 金属学报 57 111 Google Scholar Lin Z Q, Zhen W, Li H, Wang D J 2021 Acta. Metall. Sin. 57 111 Google Scholar
[2]	Lee C, Wei X, Kysar J W, Hone J 2008 Science 321 385 Google Scholar
[3]	Cao K, Feng S Z, Han Y, Gao L B, Hue Ly T, Xu Z P, Lu Y 2020 Nat. Commun. 11 284 Google Scholar
[4]	Liu J, Hei L F, Song J H, Li C M, Tang W Z, Chen G C, Lu F X 2014 Diam. Relat. Mater. 46 42 Google Scholar
[5]	Huang P Y, Ruiz-Vargas C S, van der Zande A M, et al. 2011 Nature 469 389 Google Scholar
[6]	Hashimoto A, Suenaga K, Gloter A, Urita K, Iijima S 2004 Nature 430 870 Google Scholar
[7]	Meyer J C, Kisielowski C, Erni R, Rossell M D, Crommie M F, Zettl A 2008 Nano Lett. 8 3582 Google Scholar
[8]	He L C, Guo S S, Lei J C, Sha Z D, Liu Z H 2014 Carbon 75 124 Google Scholar
[9]	周文权 2019 博士学位论文(西安: 西北工业大学) Zhou W Q 2019 Ph. D. Dissertation (Xi’an: Northwestern Polytechnical University
[10]	Shekhawat A, Ritchie R O 2016 Nat. Commun. 7 10546 Google Scholar
[11]	Zhang J F, Zhao J J, Lu J P 2012 ACS Nano 6 2704 Google Scholar
[12]	Heo J, Han J 2023 Nanotechnology 34 415704 Google Scholar
[13]	Grantab R, Shenoy V B, Ruoff R S 2010 Science 330 946 Google Scholar
[14]	Wei Y J, Wu J T, Yin H Q, Shi X H, Yang R G, Dresselhaus M 2012 Nat. Mater. 11 759 Google Scholar
[15]	Lehtinen O, Kurasch S, Krasheninnikov A V, Kaiser U 2013 Nat. Commun. 4 2098 Google Scholar
[16]	Liu Z, Suenaga K, Harris P J F, Iijima S 2009 Phys. Rev. Lett. 102 015501 Google Scholar
[17]	Zhao Y H, Tian X L, Zhao B J, et al. 2018 Sci. Adv. Mater. 10 1793 Google Scholar
[18]	Zhang J B, Wang H F, Kuang W W, Zhang Y C, Li S, Zhao Y H, Herlach D M 2018 Acta Mater. 148 86 Google Scholar
[19]	Guo Q W, Hou H, Wang K L, Li M X, Liaw P K, Zhao Y H 2023 npj Comput. Mater. 9 185 Google Scholar
[20]	Xin T Z, Zhao Y H, Mahjoub R, Jiang J X, Ferry M 2021 Sci. Adv. 7 eabf3039 Google Scholar
[21]	Xin T Z, Tang S, Ji F, Cui L Q, He B B, Lin X, Tian X L, Hou H, Zhao Y H, Ferry M 2022 Acta Mater. 239 118248 Google Scholar
[22]	Zhao Y H, Zhang B, Hou H, Chen W P, Wang M 2019 J. Mater. Sci. Technol. 35 1044 Google Scholar
[23]	Chen L Q, Zhao Y H 2022 Prog. Mater. Sci. 124 100868 Google Scholar
[24]	Zhao Y H, Xin T Z, Tang S, Wang H F, Fang X D, Hou H 2024 MRS Bull. 49 613 Google Scholar
[25]	Zhao Y H, Xing H, Zhang L J, et al. 2023 Acta Metall. Sin. (Engl. Lett. ) 36 1749 Google Scholar
[26]	Zhao Y H 2024 npj Comput. Mater. 2 e44 Google Scholar
[27]	Zhao Y H 2023 npj Comput. Mater. 9 94 Google Scholar
[28]	Kuang W W, Wang H F, Li X, Zhang J B, Zhou Q, Zhao Y H 2018 Acta Mater. 159 16 Google Scholar
[29]	Song Z, Li H Q, Wang X N, Tian X L, Hou H, Zhao Y H 2023 J. Mater. Res. Technol. 27 6501 Google Scholar
[30]	Zhong L, Gao H J, Li X Y 2020 Extreme Mech. Lett. 37 100699 Google Scholar
[31]	Meca E, Lowengrub J, Kim H, Mattevi C, Shenoy V B 2013 Nano Lett. 13 5692 Google Scholar
[32]	Li H Q, Wang X N, Zhang H B, Tian X L, Hou H, Zhao Y H 2022 Front. Mater. 9 875519 Google Scholar
[33]	Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys. Rev. Lett. 88 245701 Google Scholar
[34]	Tian X L, Zhao Y H, Gu T, Guo Y L, Xu F Q, Hou H 2022 Mater. Sci. Eng. 849 143485 Google Scholar
[35]	Zhao Y H, Liu K X, Zhang H B, Tian X L, Jiang Q L, Murugadoss V, Hou H 2022 Adv. Compos. Hybrid Mater. 5 2546 Google Scholar
[36]	Kim K, Lee Z, Regan W, Kisielowski C, Crommie M F, Zettl A 2011 ACS Nano 5 2142 Google Scholar
[37]	Akhukov M A, Fasolino A, Gornostyrev Y N, Katsnelson M I 2012 Phys. Rev. B 85 115407 Google Scholar
[38]	Hirvonen P, Ervasti M M, Fan Z, et al. 2016 Phys. Rev. B 94 035414 Google Scholar
[39]	Guo H J, Zhao Y H, Sun Y Y, Tian J Z, Hou H, Qi K W, Tian X L 2019 Micro Nanostruct. 129 163 Google Scholar
[40]	Elder K R, Grant M 2004 Phys. Rev. E 70 051605 Google Scholar

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Vol. 73, Issue 24 - 2024-12-20

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