Mechanical and thermal properties of phosphorene under shear deformation

Li Ting; Bi Xiao-Yue; Kong Jing-Wen

doi:10.7498/aps.72.20230084

Abstract

Phosphorene, a new two-dimensional material beyond graphene, has received increasing attention in recent years owing to its superior physical properties of significant utility. Herein we carry out molecular dynamics simulations to systematically study the mechanical and thermal properties of phosphorene under shear loadings. It is found that the shear modulus of phosphorene is about 22 GPa in both the armchair direction and zigzag direction. The fracture strength and ultimate strain of phosphorene can be significantly reduced owing to stronger thermal vibrations of atoms at a higher temperature. The thermal conductivity of pristine phosphorene at room temperature is obtained, specifically, it is 18.57 W·m^–1·K^–1 along the armchair direction and 52.52 W·m^–1·K^–1 in the zigzag direction. When either an armchair- or a zigzag-oriented shear strain is applied, the armchair-oriented thermal conductivity decreases monotonically with the strain increasing. Whereas the zigzag-oriented thermal conductivity exhibits a non-monotonic behavior. The strain-induced redshift occurs in the high-frequency phonons of out-of-plane flexural modes in the phonon density of states of the sheared phosphorene. In addition, the buckled structure of phosphorene will lead the deformation characteristics under the shear strain differ from those of the planar structure such as graphene, which has a significant influence on the lattice anharmonicity and phonon scattering. It is believed that the interplay between the shift of phonon density of states and the change of phonon scattering channels results in the unique thermal transport behavior of phosphorene under shear deformation. The findings provide an insight into the understanding of the mechanical and thermal properties of phosphorene, and have significance for the future applications in phosphorene-based novel devices.

Keywords:

Authors and contacts

School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China

Corresponding author: Li Ting, tingli430@lnnu.edu.cn

Funds: Project supported by the Science Foundation for Doctoral Research of the Department of Science and Technology of Liaoning Province, China (Grant No. 2021-BS-200), the Dalian Technological Innovation Fund Project, China (Grant No. 2022JJ12GX023), and the Liaoning Normal University 2022 Outstanding Research Achievements Cultivation Fund, China (Grant No. 22GDL002).

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References

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Cited By

图 1 磷烯的原子结构　(a) 侧视图; (b) 俯视图

Figure 1. Atomic configuration of phosphorene: (a) Side view; (b) top view.

DownLoad: Full-Size Img PowerPoint

图 2 不同温度下磷烯的剪切应力-应变曲线　(a)扶手椅方向; (b)锯齿方向

Figure 2. Stress-strain curves of phosphorene at different temperatures for shear deformation: (a) Armchair direction; (b) zigzag direction

DownLoad: Full-Size Img PowerPoint

图 3 不同温度下磷烯的剪切性能　(a)断裂强度随温度的变化; (b) 极限应变随温度的变化

Figure 3. Shear properties of phosphorene at different temperatures: (a) Fracture strength versus temperature; (b) ultimate strain versus temperature.

DownLoad: Full-Size Img PowerPoint

图 4 磷烯沿扶手椅和锯齿方向上的热导率　(a) 热导率随长度的变化; (b) 热导率倒数与长度倒数之间的关系

Figure 4. Thermal conductivities of phosphorene in the armchair or zigzag directions: (a) Thermal conductivities versus length; (b) inverse of thermal conductivities as a function of inverse of length.

DownLoad: Full-Size Img PowerPoint

图 5 (a) 磷烯沿扶手椅方向的热导率与剪切应变的关系; (b) 磷烯沿锯齿方向的热导率与剪切应变的关系

Figure 5. Thermal conductivities of phosphorene in the (a) armchair and (b) zigzag directions under shear strain.

DownLoad: Full-Size Img PowerPoint

图 6 剪切形变下磷烯的面内(上图)与面外(下图)声子态密度　(a) 扶手椅方向; (b)锯齿方向

Figure 6. In-plane (upper panel) and out-of-plane (lower panel) phonon density of states of phosphorene under shear deformation: (a) Armchair direction; (b) zigzag direction.

DownLoad: Full-Size Img PowerPoint

表 1 磷烯的剪切力学性能

Table 1. Mechanical properties of phosphorene under shear loading.

文献	剪切模量/GPa	断裂强度/GPa	极限应变	计算方法
Wei和Peng^[31]	41	—	—	第一性原理
Yang等^[32]	22.1^a, 19.8^z	1.7^a, 1.4^z	0.14^a, 0.14^z	分子动力学
Gamil等^[33]	22.4^a	1.6^a	0.138^a	分子动力学
Hatam-Lee等^[34]	33.9^a, 32.5^z	2.5^a, 2.3^z	0.127^a, 0.118^z	分子动力学
本文	22.20^a, 22.34^z	2.45^a, 2.08^z	0.119^a, 0.126^z	分子动力学
注: 上标a代表扶手椅方向的结果, 上标z代表锯齿方向的结果.

DownLoad: CSV

[1]	Geim A K 2009 Science 324 1530 Google Scholar
[2]	Xu M, Liang T, Shi M, Chen H 2013 Chem. Rev. 113 3766 Google Scholar
[3]	Cai Z, Liu B, Zou X, Cheng H M 2018 Chem. Rev. 118 6091 Google Scholar
[4]	Lin Y, Connellb J W 2012 Nanoscale 4 6908 Google Scholar
[5]	Manzeli S, Ovchinnikov D, Pasquier D, Yazyev O V, Kis A 2017 Nat. Rev. Mater. 2 17033 Google Scholar
[6]	Balendhran S, Walia S, Nili H, Sriram S, Bhaskaran M 2015 Small 11 640 Google Scholar
[7]	Carvalho A, Wang M, Zhu X, Rodin A S, Su H, Neto A H C 2016 Nat. Rev. Mater. 1 16061 Google Scholar
[8]	Batmunkh M, Bat-Erdene M, Shapter J G 2016 Adv. Mater. 28 8586 Google Scholar
[9]	Akinwande D, Petrone N, Hone J 2014 Nat. Commun. 5 5678 Google Scholar
[10]	Novoselov K S, Mishchenko A, Carvalho A, Neto A H C 2016 Science 353 aac9439 Google Scholar
[11]	Bonaccorso F, Colombo L, Yu G, Stoller M, Tozzini V, Ferrari A C, Ruoff R S, Pellegrini V 2015 Science 347 1246501 Google Scholar
[12]	Jia P Z, Xie Z X, Deng Y X, Zhang Y, Tang L M, Zhou W X, Chen K Q 2022 Appl. Phys. Lett. 121 043901 Google Scholar
[13]	Zhou W X, Cheng Y, Chen K Q, Xie G, Wang T, Zhang G 2020 Adv. Funct. Mater. 30 1903829 Google Scholar
[14]	Liu H, Neal A T, Zhu Z, Luo Z, Xu X, Tománek D, Ye P D 2014 ACS Nano 8 4033 Google Scholar
[15]	Khandelwal A, Mani K, Karigerasi M H, Lahiri I 2017 Mater. Sci. Eng. B 221 17 Google Scholar
[16]	Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H, Feng D, Chen X H, Zhang Y 2014 Nat. Nanotech. 9 372 Google Scholar
[17]	Fei R, Faghaninia A, Soklaski R, Yan J A, Lo C, Yang L 2014 Nano Lett. 14 6393 Google Scholar
[18]	Qiao J, Kong X, Hu Z X, Yang F, Ji W 2014 Nat. Commun. 5 4475 Google Scholar
[19]	Tran V, Soklaski R, Liang Y, Yang L 2014 Phys. Rev. B 89 235319 Google Scholar
[20]	Jiang J W, Park H S 2014 J. Phys. D:Appl. Phys. 47 385304 Google Scholar
[21]	Sha Z D, Pei Q X, Ding Z, Jiang J W, Zhang Y W 2015 J. Phys. D: Appl. Phys. 48 395303 Google Scholar
[22]	Sha Z D, Pei Q X, Zhang Y Y, Zhang Y W 2016 Nanotech. 27 315704 Google Scholar
[23]	Li L, Yang J 2017 Nanotech. 28 475701 Google Scholar
[24]	Qin G, Hu M 2018 Small 14 1702465 Google Scholar
[25]	Hong Y, Zhang J, Zeng X C 2018 Chin. Phys. B 27 036501 Google Scholar
[26]	Qin G, Yan Q B, Qin Z, Yue S Y, Hu M, Su G 2015 Phys. Chem. Chem. Phys. 17 4854 Google Scholar
[27]	Hong Y, Zhang J, Huang X, Zeng X C 2015 Nanoscale 7 18716 Google Scholar
[28]	Ong Z Y, Cai Y, Zhang G, Zhang Y W 2014 J. Phys. Chem. C 118 25272 Google Scholar
[29]	Zhang Y Y, Pei Q X, Jiang J W, Wei N, Zhang Y W 2016 Nanoscale 8 483 Google Scholar
[30]	Liu B, Bai L, Korznikova E A, Dmitriev S V, Law A W K, Zhou K 2017 J. Phys. Chem. C 121 13876 Google Scholar
[31]	Wei Q, Peng X 2014 Appl. Phys. Lett. 104 251915 Google Scholar
[32]	Yang Z, Zhao J, Wei N 2015 Appl. Phys. Lett. 107 023107 Google Scholar
[33]	Gamil M, Zeng Q H, Zhang Y Y 2020 Phys. Lett. A 384 126784 Google Scholar
[34]	Hatam-Lee S M, Peer-Mohammadi H, Rajabpour A 2021 Mater. Today Commun. 26 101796 Google Scholar
[35]	Mahnama M, Meshkinghalam M, Ozmaian M 2022 J. Phys.: Condens. Matter 34 075403 Google Scholar
[36]	Li T 2021 Physica E 131 114761 Google Scholar
[37]	Plimpton S 1995 J. Comput. Phys. 117 1 Google Scholar
[38]	Jiang J W 2015 Nanotech. 26 315706 Google Scholar
[39]	Kheirkhah A H, Iranizad E S, Raeisi M, Rajabpour A 2014 Solid State Commun. 177 98 Google Scholar
[40]	Zhang C, Hao X L, Wang C X, Wei N, Rabczuk T 2017 Sci. Rep. 7 41398 Google Scholar
[41]	Zhao J, Jiang J W, Rabczuk T 2013 Appl. Phys. Lett. 103 231913 Google Scholar
[42]	Li T, Tang Z, Huang Z, Yu J 2017 Physica E 85 137 Google Scholar
[43]	Xu K, Fan Z, Zhang J, Wei N, Ala-Nissila T 2018 Modell. Simul. Mater. Sci. Eng. 26 085001 Google Scholar
[44]	Smith B, Vermeersch B, Carrete J, Ou E, Kim J, Mingo N, Akinwande D, Shi L 2017 Adv. Mater. 29 1603756 Google Scholar
[45]	Hu M, Zhang X, Poulikakos D 2013 Phys. Rev. B 87 195417 Google Scholar

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