High-throughput calculation of interfacial friction of two-dimensional material

Cui Zi-Chun; Yang Mo-Han; Ruan Xiao-Peng; Fan Xiao-Li; Zhou Feng; Liu Wei-Min

doi:10.7498/aps.72.20221676

Abstract

Friction generally occurs in the relative motion or the contact interface with the trend of relative motion, which impedes the relative motion and produces energy loss. Micro-scale friction is different from the macro-scale friction due to surface effects and other factors. It is necessary to study the friction behavior on a nano-scale. First-principles method is an important way to study and understand friction on a nano-scale. Nevertheless, the constructing of nearly a thousand models and the processing of a large number of data are very time consuming. In this paper, we establish a high-throughput computational program based on the first-principles method to study the interfacial friction of two-dimensional materials. The program realizes modeling, submitting computation tasks, multi-task concurrent calculation, data collection and processing, and image rendering of calculation results. All of these are done in batch automatically, which greatly saves researchers’ time. In this work, this program is used to simulate the normal load by changing the distance between layers and calculate the potential energy surface of BN/BN and graphene/graphene bilayer sliding systems at a series of interlayer distances, as well as the interlayer friction forces and friction coefficients. The study finds that with the decrease of the interlayer distance, the averaged friction force at BN/BN interface increases approximately linearly, and the friction coefficient is in a range of 0.11–0.17. The friction force at graphene/graphene interface first increases, then decreases, and increases again. The friction coefficient reaches a minimum value (0.014) under a load of 12 nN, and these results are consistent with the previous results, verifying the reliability of the calculation program. In addition, we investigate the effect of surface hydrogenation and fluorination on the tribological property of the BN bilayer and find that the friction at the fluorinated BN/BN interface decreases, which is attributed to the smaller charge transfer at interface. Although the high-throughput calculation method realizes the automation and high-throughput calculation of tribological property at solid interface, there are still some limitations. Firstly, the effect of interlaminar bending is not considered in the process of interlaminar relative sliding. Secondly, the essence of the calculation result is static friction, rather than dynamic friction. In addition, the method does not consider the influence of temperature.

Keywords:

Authors and contacts

1.
Center of Advanced Lubrication and Seal Materials, School of Material Science and Engineering, Northwestern Polytechnic University, Xi’an 710072, China
2.
Queen Mary University of London Engineering School, Northwestern Polytechnical University, Xi’an 710072, China
3.
State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China

Corresponding author: Fan Xiao-Li, xlfan@nwpu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2018YFB0703800), the Key Project of Natural Science Fund of Shaanxi Province, China (Grant No. 2021JZ-07), and the Polymer Electromagnetic Functional Materials Innovation Team of Shaanxi Sanqin Scholars, China.

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References

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[41]	Kresse G 1995 J. Non-Cryst. Solids 193 222
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[43]	Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169 Google Scholar
[44]	Weinan E, Ren W Q, Vanden-Eijnden E 2002 Phys. Rev. B 66 052301
[45]	Zhong W, Tomanek D 1990 Phys. Rev. Lett. 64 3054 Google Scholar
[46]	Perdew J P, Burke K, Ernzerhof M 1997 Phys. Rev. Lett. 78 1396
[47]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[48]	Wang V, Xu N, Liu J C, Tang G, Geng W T 2021 Comput. Phys. Commun. 267 108033 Google Scholar
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[50]	Martin J M, Lemogne T, Chassagnette C, Gardos M N 1992 Tribol. T. 35 462 Google Scholar
[51]	Wang W, Xie G X, Luo J B 2018 Friction 6 116 Google Scholar
[52]	Zhang B Z, Zhang G G, Cheng Z W, Ma F, Lu Z B 2019 Appl. Surf. Sci. 483 742 Google Scholar
[53]	Fan K, Chen X Y, Wang X, Liu X K, Liu Y, Lai W C, Liu X Y 2018 Acs Appl. Mater. Interfaces 10 28828 Google Scholar
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Cited By

图 1 二维材料界面摩擦学特性高通量计算流程示意图

Figure 1. The schematic diagram showing the procedure of high-throughput calculation of the tribological property at the interface of two-dimensional materials.

DownLoad: Full-Size Img PowerPoint

图 2 BN/BN, H-BN/BN 和 F-BN/BN 双层体系原子结构的俯视图和侧视图　(a) Top和(b) Hollow位置BN/BN的俯视图和侧视图; (c) H-BN/BN和(d) F-BN/BN在Hollow位置的俯视图和侧视图

Figure 2. Top and side views for atomic structures of BN/BN, H-BN/BN, and F-BN/BN bilayer. Top and side views of BN/BN bilayer in (a) Top and (b) Hollow positions. Top and side views of (c) H-BN/BN and (d) F-BN/BN bilayers in Hollow position.

DownLoad: Full-Size Img PowerPoint

图 3 BN/BN位于Top位置的界面结合能和载荷随层间距的变化　(a) 结合能; (b) 载荷

Figure 3. The variation of interlayer binding energy ($ {E}_{\rm{b}} $) and load with interlayer distance for BN/BN bilayer at Top position: (a) $ {E}_{\rm{b}} $ and (b) load.

DownLoad: Full-Size Img PowerPoint

图 4 不同载荷下BN/BN的势能面　(a) 0 nN; (b) 1 nN; (c) 2 nN; (d) 3 nN; (e) 4 nN; (f) 5 nN; (g) 6 nN; (h) 7 nN; (i) 8 nN. T和H分别表示Top和Hollow位置, 白色带箭头线代表最小能量路径

Figure 4. Potential energy surface of BN/BN bilayer under normal load of (a) 0 nN, (b) 1 nN, (c) 2 nN, (d) 3 nN, (e) 4 nN, (f) 5 nN, (g) 6 nN, (h) 7 nN and (i) 8 nN. T and H present the Top and Hollow positions, respectively. The white lines with arrow represent the minimum energy path.

DownLoad: Full-Size Img PowerPoint

图 5 0—8 nN载荷下BN/BN最小能量路径上势能的变化

Figure 5. The variation of potential energy along the minimum energy path of BN/BN bilayer under 0–8 nN loads.

DownLoad: Full-Size Img PowerPoint

图 6 BN/BN, F-BN/BN, H-BN/BN的平均界面摩擦力($ {F}_{\rm{f}} $)和摩擦系数($ \mu $)随载荷的变化　(a)平均摩擦力; (b)摩擦系数

Figure 6. The variation of friction force at the interface of BN/BN, F-BN/BN, and H-BN/BN bilayers with respect to the normal load: (a) Averaged interfacial friction ($ {F}_{\rm{f}} $); (b) friction coefficient ($ \mu $).

DownLoad: Full-Size Img PowerPoint

图 7 不同载荷下Gr/Gr的势能面　(a) 1 nN; (b) 4 nN; (c) 7 nN; (d) 10 nN; (e) 12 nN; (f) 13.5 nN. (a)—(d)中的H/T对应最小/最大势能, 而(e), (f)中的H/T对应最大/最小势能

Figure 7. Potential energy surface of graphene/graphene (Gr/Gr) bilayer under normal load of (a) 1 nN, (b) 4 nN, (c) 7 nN, (d) 10 nN, (e) 12 nN, and (f) 13.5 nN. T and H present the top and hollow positions, respectively. H/T in (a)–(d) is the position of minimum/maximum potential energy, whereas, T/H in (e), (f) is the position of minimum/maximum potential energy.

DownLoad: Full-Size Img PowerPoint

图 8 Gr/Gr界面平均摩擦力和摩擦系数随载荷的变化　(a)平均摩擦力; (b)摩擦系数

Figure 8. The variation of friction force at the interface of graphene/graphene (Gr/Gr) bilayers with respect to the normal load: (a) Averaged interfacial friction and (b) friction coefficient.

DownLoad: Full-Size Img PowerPoint

图 9 BN/BN和F-BN/BN的最高和最低势能态在0 nN和8 nN载荷下的差分电荷密度　(a) BN/BN, 0 nN; (b) BN/BN, 8 nN; (c) F-BN/BN, 0 nN; (d) F-BN/BN, 8 nN. 黄色代表电子聚集, 蓝色代表电子损失; 左边和右边的图分别对应最高和最低势能态; 图(a)和(c)中的等值面设置为0.00006e/Bohr³; 图 (b) 和 (d) 中的等值面设置为0.0003e/Bohr³

Figure 9. Differential charge density of BN/BN and F-BN/BN bilayer at the highest and lowest potential energy state under 0 nN and 8 nN loads. BN/BN bilayer under (a) 0 nN and (b) 8 nN load, F-BN/BN bilayer under (c) 0 nN and (d) 8 nN loads. The yellow color represents electron aggregation, and the blue color represents electron dissipation. The isosurface value in figure (a) and (c) is set to 0.00006e/Bohr³; the isosurface value in figure (b) and (d) is set to 0.0003e/Bohr³.

DownLoad: Full-Size Img PowerPoint

map

[1]	Holmberg K, Andersson P, Nylund N O, Makela K, Erdemir A 2014 Tribol. Int. 78 94 Google Scholar
[2]	Carpick R W 2006 Science. 313 184 Google Scholar
[3]	Zhuang C Q, Liu L 2017 Aip Adv. 7 085103 Google Scholar
[4]	Berman D, Erdemir A, Sumant A V 2018 Acs Nano. 12 2122 Google Scholar
[5]	Yuan J H, Yang R, Zhang G Y 2022 Nanotechnology 33 102002 Google Scholar
[6]	Marchetto D, Feser T, Dienwiebel M 2015 Friction 3 161 Google Scholar
[7]	Kimura Y, Wakabayashi T, Okada K, Wada T, Nishikawa H 1999 Wear 232 199 Google Scholar
[8]	Dominguez-Meister S, Rojas T C, Brizuela M, Sanchez-Lopez J C 2017 Sci. Technol. Adv. Mat. 18 122 Google Scholar
[9]	Zhao X Y, Hamilton M, Sawyer W G, Perry S S 2007 Tribol. Lett. 27 113 Google Scholar
[10]	Schirmeisen A, Jansen L, Holscher H, Fuchs H 2006 Appl. Phys. Lett. 88 607
[11]	Tshiprut Z, Zelner S, Urbakh M 2009 Phys. Rev. Lett. 102 136102 Google Scholar
[12]	Weiss M, Majchrzycki L, Borkowska E, Cichomski M, Ptak A 2021 Tribol. Int. 162 107133 Google Scholar
[13]	Luan B Q, Robbins M O 2005 Nature 435 929 Google Scholar
[14]	Riedo E, Pallaci I, Boragno C, Brune H 2004 J. Phys. Chem. B 108 5324 Google Scholar
[15]	He X, Liu Z, Ripley L B, Swensen V L, Griffin-Wiesner I J, Gulner B R, McAndrews G R, Wieser R J, Borovsky B P, Wang Q J, Kim S H 2021 Tribol. Int. 155 106780 Google Scholar
[16]	Ru G L, Qi W H, Tang K W, Wei Y R, Xue T W 2020 Tribol. Int. 151 106483 Google Scholar
[17]	Ru G L, Qi W H, Wei Y R, Tang K W, Xue T W 2021 Tribol. Int. 159 106974 Google Scholar
[18]	Dong Y, Perez D, Gao H, Martini A 2012 J. Phys-Condens Mat. 24 265001 Google Scholar
[19]	Zworner O, Holscher H, Schwarz U D, Wiesendanger R 1998 Appl. Phys. A-Mater. 66 S263 Google Scholar
[20]	Fajardo O Y, Barel I, Urbakh M 2014 J. Phys-Condens Mat. 26 315002 Google Scholar
[21]	Mate C M, Mcclelland G M, Erlandsson R, Chiang S 1987 Phys. Rev. Lett. 59 1942 Google Scholar
[22]	Mo Y F, Turner K T, Szlufarska I 2009 Nature 457 1116 Google Scholar
[23]	An X H, Yao H J, Ma F, Lu Z B 2015 Rsc Adv. 5 106239 Google Scholar
[24]	Sun J H, Zhang Y N, Lu Z B, Li Q Y, Xue Q J, Du S Y, Pu J B, Wang L P 2018 J. Phys. Chem. Lett. 9 2554 Google Scholar
[25]	Cheng Z W, Sun J H, Zhang B Z, Lu Z B, Ma F, Zhang G A, Xue Q J 2020 J. Phys. Chem. Lett. 11 5815 Google Scholar
[26]	Wang K B, Li H, Guo Y F 2021 Materials 14 4717 Google Scholar
[27]	Wang J J, Wang F, Li J M, Wang S J, Song Y L, Sun Q, Jia Y 2012 Tribol. Lett. 48 255 Google Scholar
[28]	Gao W, Tkatchenko A 2015 Phys. Rev. Lett. 114 096101 Google Scholar
[29]	Zhuang C Q, Liu L 2015 J. Appl. Phys. 117 114302 Google Scholar
[30]	Ko J H, Kwon S, Byun I S, Choi J S, Park B H, Kim Y H, Park J Y 2013 Tribol. Lett. 50 137 Google Scholar
[31]	Qu C Y, Wang K Q, Wang J, Gongyang Y J, Carpick R W, Urbakh M, Zheng Q S 2020 Phys. Rev. Lett. 125 12
[32]	Ruan X, Shi J, Wang X, Wang W Y, Fan X, Zhou F 2021 ACS Appl. Mater. Interfaces 13 40901 Google Scholar
[33]	Liao M Z, Nicolini P, Du L J, Yuan J H, Wang S P, Yu H, Tang J, Cheng P, Watanabe K, Taniguchi T, Gu L, Claerbout V E P, Silva A, Kramer D, Polcar T, Yang R, Shi D X, Zhang G Y 2022 Nat. Mater. 21 47 Google Scholar
[34]	Li S Z, Li Q Y, Carpick R W, Gumbsch P, Liu X Z, Ding X D, Sun J, Li J 2016 Nature 539 541 Google Scholar
[35]	Filippov A E, Dienwiebel M, Frenken J W M, Klafter J, Urbakh M 2008 Phys. Rev. Lett. 100 046102 Google Scholar
[36]	Zhang J, Bai Y, An L, Zhang B, Zhang J, Yu Y, Wang C M 2019 J. Appl. Phys. 126 035104 Google Scholar
[37]	Cheng Z W, An X H, Wang J J, Zhang B Z, Lu Z B, Zhang G G 2020 Tribol. Int. 141 105961 Google Scholar
[38]	Wang J J, Li J M, Fang L L, Sun Q, Jia Y 2014 Tribol. Lett. 55 405 Google Scholar
[39]	Restuccia P, Levita G, Wolloch M, Losi G, Fatti G, Ferrario M, Righi M C 2018 Comp. Mater. Sci. 154 517 Google Scholar
[40]	Gonze X, Ghosez P, Godby R W 1997 Phys. Rev. Lett. 78 294 Google Scholar
[41]	Kresse G 1995 J. Non-Cryst. Solids 193 222
[42]	Kresse G, Furthmuller J 1996 Comp. Mater. Sci. 6 15 Google Scholar
[43]	Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169 Google Scholar
[44]	Weinan E, Ren W Q, Vanden-Eijnden E 2002 Phys. Rev. B 66 052301
[45]	Zhong W, Tomanek D 1990 Phys. Rev. Lett. 64 3054 Google Scholar
[46]	Perdew J P, Burke K, Ernzerhof M 1997 Phys. Rev. Lett. 78 1396
[47]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[48]	Wang V, Xu N, Liu J C, Tang G, Geng W T 2021 Comput. Phys. Commun. 267 108033 Google Scholar
[49]	Marom N, Bernstein J, Garel J, Tkatchenko A, Joselevich E, Kronik L, Hod O 2010 Phys. Rev. Lett. 105 046801 Google Scholar
[50]	Martin J M, Lemogne T, Chassagnette C, Gardos M N 1992 Tribol. T. 35 462 Google Scholar
[51]	Wang W, Xie G X, Luo J B 2018 Friction 6 116 Google Scholar
[52]	Zhang B Z, Zhang G G, Cheng Z W, Ma F, Lu Z B 2019 Appl. Surf. Sci. 483 742 Google Scholar
[53]	Fan K, Chen X Y, Wang X, Liu X K, Liu Y, Lai W C, Liu X Y 2018 Acs Appl. Mater. Interfaces 10 28828 Google Scholar
[54]	Cahangirov S, Ciraci S, Ozcelik V O 2013 Phys. Rev. B 87 205428 Google Scholar
[55]	Li Q Y, Liu X Z, Kim S P, Shenoy V B, Sheehan P E, Robinson J T, Carpick R W 2014 Nano Lett. 14 5212 Google Scholar
[56]	Wolloch M, Levita G, Restuccia P, Righi M C 2018 Phys. Rev. Lett. 121 026804

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