Molecular dynamics simulations for tensile behaviors of mono-layer MoS<sub>2</sub> with twin boundary

Shao Yu-Fei; Meng Fan-Shun; Li Jiu-Hui; Zhao Xing

doi:10.7498/aps.68.20182125

Abstract

Grain boundary (GB) plays a key role in determining the electrical and mechanical properties of mono-layer transition metal dichalcogenide (TMDC), however it is still a challenge to uncover the GB-mediated TMDC material experimentally. In this paper, the effect of twin boundary on the tensile behaviors of mono-layer MoS₂ is investigated by using the molecular dynamics simulation combined with the Stillinger-Weber potential. Mono-layer MoS₂ model under the varied size and temperature condition is adopted. Stress calculation is performed by using Virial theorem. The results are obtained as follows. 1) Twin boundary promotes the brittle fracture of an undefected mono-layer MoS₂ sheet by inducing the nucleation of the crack near boundaries, thus the fracture strength and strain are weakened. 2) Increasing the ambient temperature from 1 K to 600 K, the crack nucleation process near the twin boundary is intensely accelerated, and the fracture strength and strain are further declined. 3) Twin lamellar spacing also plays an important role in the tensile process of mono-layer MoS₂, and the specimen with dense twin boundary, especially with void, shows higher fracture strain. 4) Stress analysis at an atomic level outlines the stress concentration caused by voids and the shielding effect of twin boundary. Because of the interactions between voids and twin boundary, the fracture strength and strain of a voided mono-layer MoS₂ sheet can be greatly improved.

Keywords:

Authors and contacts

1.
Institute of Applied Physics and Technology, Liaoning Technical University, Huludao 125105, China
2.
College of Sciences, Liaoning University of Technology, Jinzhou 121001, China
3.
College of Materials Science and Engineering, Northeastern University, Shenyang 110819, China

Corresponding author: Shao Yu-Fei, yfshao@alum.imr.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51801091) and the Provincial Natural Science Foundation of Liaoning of China (Grant Nos. 201602360, 20180550484)

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References

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Geim A K, Novoselov K S 2007 Nat. Mater. 6 183 Google Scholar
[3]	Radisavljevic B, Radenovic A, Brivio J, Giacometti V, Kis A 2011 Nat. Nanotech. 6 147 Google Scholar
[4]	Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N, Strano M S 2012 Nat. Nanotech. 7 699 Google Scholar
[5]	Yin X B, Ye Z L, Chenet D A, Ye Y, Brien K O, Hone J C, Zhang X 2014 Science 344 488 Google Scholar
[6]	魏争, 王琴琴, 郭玉拓, 李佳蔚, 时东霞, 张广宇 2018 物理学报 67 128103 Google Scholar Wei Z, Wang Q Q, Guo Y T, Li J W, Shi D X, Zhang G Y 2018 Acta Phys. Sin. 67 128103 Google Scholar
[7]	吴木生, 徐波, 刘刚, 欧阳楚英 2012 物理学报 61 227102 Google Scholar Wu M S, Xu B, Liu G, Ouyang C Y 2012 Acta Phys. Sin. 61 227102 Google Scholar
[8]	Tao P, Guo H, Yang T, Zhang Z 2014 J. Appl. Phys. 115 054305 Google Scholar
[9]	Dang K Q, Spearot D E 2014 J. Appl. Phys. 116 013508 Google Scholar
[10]	Casillas G, Santiago U, Barron H, Alducin D, Ponce A, José-Yacamán M 2015 J. Phys. Chem. C 119 710 Google Scholar
[11]	李明林, 万亚玲, 胡建玥, 王卫东 2016 物理学报 65 176201 Google Scholar Li M L, Wan Y L, Hu J Y, Wang W D 2016 Acta Phys. Sin. 65 176201 Google Scholar
[12]	Wang W D, Li L L, Yang C G, Soler-Crespo R A, Meng Z X, Li M L, Zhang X, Keten S, Espinosa H D 2017 Nanotechnology 28 164005 Google Scholar
[13]	Wu J Y, Cao P Q, Zhang Z S, Ning F L, Zheng S S, He J Y, Zhang Z L 2018 Nano Lett. 18 1543 Google Scholar
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[16]	Yang Y, Li X, Wen M, Hacopian E, Chen W, Gong Y, Zhang J, Li B, Zhou W, Ajayan P M, Chen Q, Zhu T, Lou J 2017 Adv. Mater. 29 1604201 Google Scholar
[17]	Yun W S, Han S W, Hong S C, Kim I G, Lee J D 2012 Phys. Rev. B 85 033305 Google Scholar
[18]	Wang X, Tabarraei A, Spearot D E 2015 Nanotechnology 26 175703 Google Scholar
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[27]	Stillinger F H, Weber T A 1985 Phys. Rev. B 31 5262 Google Scholar
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[31]	Du L J, Yu H, Xie L, Wu S, Wang S, Lu X, Liao M, Meng J, Zhao J, Zhang J, Zhu J, Chen P, Wang G, Yang R, Shi D, Zhang G 2016 Crystals 6 115 Google Scholar
[32]	Dao M, Lu L, Asaro R J, De Hosson J T M, Ma E 2007 Acta Mater. 55 4041 Google Scholar
[33]	Wang S S, Qin Z, Jung G S, Martin-Martinez F J, Zhang K, Buehler M J, Warner J H 2016 ACS Nano 10 9831 Google Scholar
[34]	Peron-Luhrs V, Sansoz F, Noels L 2014 Acta Mater. 64 419 Google Scholar
[35]	Dang K Q, Simpsona J P, Spearot D E 2014 Scripta Mater. 76 41 Google Scholar
[36]	Lu L, Chen X, Huang X, Lu K 2009 Science 323 607 Google Scholar

Cited By

图 1 单层MoS₂的分子动力学模型　(a)含孪晶界; (b)不含孪晶界

Figure 1. Molecular dynamics model of mono-layer MoS₂: (a) With twin boundaries; (b) without twin boundary.

DownLoad: Full-Size Img PowerPoint

图 2 (a)应变能E; (b)应力σ, 其中ε表示应变

Figure 2. (a) Strain energy E and (b) stress σ, where ε denotes strain.

DownLoad: Full-Size Img PowerPoint

图 3 与拉伸曲线相对应的原子结构　(a)孪晶界, A点, ε = 27.74%; (b)孪晶界, B点, ε = 27.79%; (c)不含孪晶界, A点, ε = 28.94%; (d)不含孪晶界, B点, ε = 29.24%

Figure 3. Atomic structures corresponding to the tensile curves: (a) With twin boundary, point A, ε = 27.74%; (b) with twin boundary, point B, ε = 27.79%; (c) without twin boundary, point A, ε = 28.94%; (d) without twin boundary, point B, ε = 29.24%.

DownLoad: Full-Size Img PowerPoint

图 4 温度和孪晶界面间距的影响　(a)不同温度下的应变能; (b)不同温度下的应力; (c)不同孪晶片层间距下的应变能; (d)不同孪晶片层间距下的应力

Figure 4. Effects of temperature and the twin lamellar spacing: (a) Effect of temperature on strain energy; (b) effect of temperature on stress; (c) effect of twin lamellar spacing effect on strain energy; (d) effect of twin lamellar spacing effect on stress.

DownLoad: Full-Size Img PowerPoint

图 5 孔洞对拉伸应力的影响

Figure 5. Effect of a Mo₃S₂ void on the tensile stress of specimen

DownLoad: Full-Size Img PowerPoint

图 6 不含孪晶界的带孔洞的单层MoS₂　(a) ε = 0; (b) ε = 22.514%; (c) ε = 22.514%, 放大视图; (d) ε = 23.345%, 放大视图

Figure 6. Voided mono-layer MoS₂ without twin boundary: (a) ε = 0; (b) ε = 22.514%; (c) ε = 22.514%, enlarged view; (d) ε = 23.345%, enlarged view.

DownLoad: Full-Size Img PowerPoint

图 7 含孪晶界的带孔洞的单层MoS₂　(a) ε = 0; (b) ε = 19.971%; (c) ε = 19.971%, 放大视图; (d) ε = 20.779%, 放大视图

Figure 7. Voided mono-layer MoS₂ with twin boundaries: (a) ε = 0; (b) ε = 19.971%; (c) ε = 19.971%, enlarged view; (d) ε = 20.779%, enlarged view.

DownLoad: Full-Size Img PowerPoint

图 8 带孔洞的含孪晶界模型断裂前后应力分布状态　(a) ε = 14.34%; (b) ε = 16.92%; (c) ε = 18.25%; (d) ε = 20.87%

Figure 8. Distribution of tensile stress in the voided mono-layer MoS₂ sheet with twin boundaries: (a) ε = 14.34%; (b) ε = 16.92%; (c) ε = 18.25%; (d) ε = 20.87%.

DownLoad: Full-Size Img PowerPoint

图 9 断裂应变ε_A与孪晶片层间距D的关联

Figure 9. Correlation of the fracture strain ε_A and the twin lamellar spacing D.

DownLoad: Full-Size Img PowerPoint

表 1 模型平面内初始尺寸

Table 1. Initial in-plane size of model.

L_x/nm L_y/nm

含孪晶模型 25.96 5.70

不含孪晶模型 13.16 5.70

DownLoad: CSV

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Geim A K, Novoselov K S 2007 Nat. Mater. 6 183 Google Scholar
[3]	Radisavljevic B, Radenovic A, Brivio J, Giacometti V, Kis A 2011 Nat. Nanotech. 6 147 Google Scholar
[4]	Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N, Strano M S 2012 Nat. Nanotech. 7 699 Google Scholar
[5]	Yin X B, Ye Z L, Chenet D A, Ye Y, Brien K O, Hone J C, Zhang X 2014 Science 344 488 Google Scholar
[6]	魏争, 王琴琴, 郭玉拓, 李佳蔚, 时东霞, 张广宇 2018 物理学报 67 128103 Google Scholar Wei Z, Wang Q Q, Guo Y T, Li J W, Shi D X, Zhang G Y 2018 Acta Phys. Sin. 67 128103 Google Scholar
[7]	吴木生, 徐波, 刘刚, 欧阳楚英 2012 物理学报 61 227102 Google Scholar Wu M S, Xu B, Liu G, Ouyang C Y 2012 Acta Phys. Sin. 61 227102 Google Scholar
[8]	Tao P, Guo H, Yang T, Zhang Z 2014 J. Appl. Phys. 115 054305 Google Scholar
[9]	Dang K Q, Spearot D E 2014 J. Appl. Phys. 116 013508 Google Scholar
[10]	Casillas G, Santiago U, Barron H, Alducin D, Ponce A, José-Yacamán M 2015 J. Phys. Chem. C 119 710 Google Scholar
[11]	李明林, 万亚玲, 胡建玥, 王卫东 2016 物理学报 65 176201 Google Scholar Li M L, Wan Y L, Hu J Y, Wang W D 2016 Acta Phys. Sin. 65 176201 Google Scholar
[12]	Wang W D, Li L L, Yang C G, Soler-Crespo R A, Meng Z X, Li M L, Zhang X, Keten S, Espinosa H D 2017 Nanotechnology 28 164005 Google Scholar
[13]	Wu J Y, Cao P Q, Zhang Z S, Ning F L, Zheng S S, He J Y, Zhang Z L 2018 Nano Lett. 18 1543 Google Scholar
[14]	Zhang R, Koutsos V, Cheung R 2016 Appl. Phys. Lett. 108 042104 Google Scholar
[15]	Hao S, Yang B, Gao Y 2017 Appl. Phys. Lett. 110 153105 Google Scholar
[16]	Yang Y, Li X, Wen M, Hacopian E, Chen W, Gong Y, Zhang J, Li B, Zhou W, Ajayan P M, Chen Q, Zhu T, Lou J 2017 Adv. Mater. 29 1604201 Google Scholar
[17]	Yun W S, Han S W, Hong S C, Kim I G, Lee J D 2012 Phys. Rev. B 85 033305 Google Scholar
[18]	Wang X, Tabarraei A, Spearot D E 2015 Nanotechnology 26 175703 Google Scholar
[19]	Zhou W, Zou X, Najmaei S, Liu Z, Shi Y, Kong J, Lou J, Ajayan P M, Yakobson B I, Idrobo J C 2013 Nano Lett. 13 2615 Google Scholar
[20]	Lin Z, Carvalho B R, Kahn E, Lü R, Rao R, Terrones H, Pimenta M A, Terrones M 2016 2D Mater. 3 022002 Google Scholar
[21]	Ly T H, Chiu M H, Li M Y, Zhao J, Perello D J, Cichocka M O, Oh H M, Chae S H, Jeong, Hye Yun, Yao F, Li L J, Lee Y H 2014 ACS Nano 8 11401 Google Scholar
[22]	Cheng J, Jiang T, Ji Q, Zhang Y, Li Z, Shan Y, Zhang Y, Gong X, Liu W, Wu S 2015 Adv. Mater. 27 4069 Google Scholar
[23]	van der Zande A M, Huang P Y, Chenet D A, Berkelbach T C, You Y M, Lee G H, Heinz T F, Reichman D R, Muller D A, Hone J C 2013 Nat. Mater. 12 554 Google Scholar
[24]	Barja S, Wickenburg S, Liu Z F, Zhang Y, Ryu H, Ugeda M M, Hussain Z, Shen Z X, Mo S K, Wong E, Salmeron M B, Wang F, Crommie M F, Ogletree D F, Neaton J B, Weber-Bargioni A 2016 Nat. Phys. 12 751 Google Scholar
[25]	Hong J, Wang Y, Wang A, Lü D, Jin C, Xu Z, Probert M I J, Yuan J, Zhang Z 2017 Nanoscale 9 10312 Google Scholar
[26]	Jiang J W, Park H S, Rabczuk T 2013 J. Appl. Phys. 114 064307 Google Scholar
[27]	Stillinger F H, Weber T A 1985 Phys. Rev. B 31 5262 Google Scholar
[28]	Plimpton S 1995 J. Comp. Phys. 117 1 Google Scholar
[29]	Stukowski A 2010 Modelling Simul. Mater. Sci. Eng. 18 015012 Google Scholar
[30]	Xiong S, Cao G X 2015 Nanotechnology 26 185705 Google Scholar
[31]	Du L J, Yu H, Xie L, Wu S, Wang S, Lu X, Liao M, Meng J, Zhao J, Zhang J, Zhu J, Chen P, Wang G, Yang R, Shi D, Zhang G 2016 Crystals 6 115 Google Scholar
[32]	Dao M, Lu L, Asaro R J, De Hosson J T M, Ma E 2007 Acta Mater. 55 4041 Google Scholar
[33]	Wang S S, Qin Z, Jung G S, Martin-Martinez F J, Zhang K, Buehler M J, Warner J H 2016 ACS Nano 10 9831 Google Scholar
[34]	Peron-Luhrs V, Sansoz F, Noels L 2014 Acta Mater. 64 419 Google Scholar
[35]	Dang K Q, Simpsona J P, Spearot D E 2014 Scripta Mater. 76 41 Google Scholar
[36]	Lu L, Chen X, Huang X, Lu K 2009 Science 323 607 Google Scholar

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Molecular dynamics simulations for tensile behaviors of mono-layer MoS₂ with twin boundary

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Corresponding author: Shao Yu-Fei, yfshao@alum.imr.ac.cn

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	L_x/nm	L_y/nm
含孪晶模型	25.96	5.70
不含孪晶模型	13.16	5.70

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Molecular dynamics simulations for tensile behaviors of mono-layer MoS2 with twin boundary

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Corresponding author: Shao Yu-Fei, yfshao@alum.imr.ac.cn

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Molecular dynamics simulations for tensile behaviors of mono-layer MoS₂ with twin boundary