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“M-shape” nanoscale friction anisotropy of phosphorene
Computational Materials Science 150 (2018) 364–368
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Letter
“M-shape” nanoscale friction anisotropy of phosphorene a
b,⁎
c
d
Hanjun Gong , Pengzhe Zhu , Lina Si , Xiaoqing Zhang , Guoxin Xie
a,⁎
T
a
State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China School of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, China d School of Materials Science and Mechanical Engineering, Beijing Technology and Business University, Beijing 100048, China b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Phosphorene Friction anisotropy M-shape Molecular dynamics
In this work, molecular dynamics simulations are employed to explore the nanoscale friction anisotropy of phosphorene. We study the friction process of a diamond tip sliding against the phosphorene on the silicon substrate under different sliding directions. The results show that there exists a significant anisotropy in the friction force along different lattice orientations of phosphorene. The friction force exhibits “M-shape” which means the friction force is locally maximum along the 15° and 75° directions relative to the zigzag direction of phosphorene. It is proposed that this “M-shape” friction anisotropy is due to the difference of potential energy among different orientations arising from the unique structure of phosphorene and heterogeneous interaction with the substrate.
1. Introduction Black phosphorus is a natural p-type semiconductor in which each layer is vertically stacked by the van der Waals force. As shown in Fig. 1, black phosphorus has a pleated honeycomb crystal structure which is different from other two-dimensional materials such as graphene and molybdenum disulfide. The interlayer distance of the adjacent two layers of black phosphorus is 5.25 Å. The lattice constants of black phosphorus are about 3.31 Å and 4.38 Å [1] along the x- and yaxis, which correspond to the zigzag and armchair directions, respectively. Black phosphorus can be exfoliated down to a single layer by various methods, referred to as phosphorene [2–4]. Phosphorene has become one of the most promising materials in different areas because of its unique physical properties e.g., limited and direct bandgap, excellent room temperature carrier mobility and on/off ratio, high optical and UV absorption [5–8]. It has been shown theoretically that the bandgap decreases from 1.51 eV to 0.59 eV when phosphorene is reduced from five-layer to single-layer. The monolayer is exceptional in having an extremely high hole mobility and anomalous elastic properties which reverse the anisotropy, making few-layer phosphorene a very appealing candidate material for future applications in electronics and optoelectronics [5]. Besides, phosphorenebased field-effect transistors exhibited ambipolar behavior in the dark state and the response to excitation wavelengths from the visible up to 940 nm and rise time of about 1 ms upon illumination. The ambipolar behavior coupled to the fast and broadband photodetection showed the
⁎
Corresponding authors. E-mail addresses: [email protected] (P. Zhu), [email protected] (G. Xie).
https://doi.org/10.1016/j.commatsci.2018.04.013 Received 4 January 2018; Received in revised form 19 March 2018; Accepted 8 April 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.
potential of phosphorene as active material for high-speed NIR detectors [6]. Among the unique physical properties, anisotropy is the most fascinating characteristic of phosphorene. Unique angle-dependent properties of phosphorene allow a new degree of freedom for designing conceptually new optoelectronic and electronic devices, which are not possible by using other two dimensional materials [7]. It was found that phosphorene showed substantial anisotropy in the transport behavior, which was associated with the unique ridge structure of the layers [9]. The mechanical properties have also been confirmed to be anisotropic. For instance, the Young’s modulus of phosphorene with few layers has been measured to be 58.6 and 27.2 GPa in the zigzag and armchair directions respectively [10] and the dependences on size, chirality, temperature and vacancy defects are also anisotropic [11,12], making it an alternative material for applications in flexible electronics, straindependent optoelectronics and electromechanical nano-devices. Recently, both experiments and molecular dynamics (MD) simulations have found that friction of phosphorene exhibits atomic-level anisotropy, and more specifically the friction force is larger along the armchair direction than that along the zigzag direction [13,14]. However, at present the researches mainly focused on the friction behaviors of phosphorene along the armchair and zigzag directions. A systematic study of the friction properties, especially the friction anisotropy, of phosphorene is still lacking. An in-depth study of nanoscale friction properties of phosphorene can not only shed light on the friction mechanisms of phosphorene, but also can guide the design and precision control of phosphorene-based micro- and nano-mechanical systems.
Computational Materials Science 150 (2018) 364–368
H. Gong et al.
Fig. 1. Crystal structure of black phosphorus (a) side view of black phosphorus lattice; (b) top view of monolayer black phosphorus lattice.
Second Law imitate the true atomic dynamic behavior. The MD simulations are performed using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator), which is an open source program developed at the Sandia National Laboratory, USA [17]. The interaction between phosphorene atoms is described by the Stillinger-Weber (SW) potentials [18]. The Tersoff potential is used to evaluate the interatomic interactions for the diamond tip and the amorphous silicon substrate [19]. Besides, the Lennard-Jones (LJ) potential is employed to model the non-bonded interaction between dissimilar atoms, which takes the form of
As the friction experiment of single-layer phosphorene is still very difficult, molecular dynamic (MD) simulation is often adopted in the study of nanoscale friction since it can provide direct information about the buried interface during the nanoscale sliding process. In this work, the friction force along various lattice orientations of phosphorene were simulated and analyzed in great detail to explore the anisotropy of friction behavior of phosphorene.
2. Simulation method
E = 4ε [(σ / r )12−(σ / r )6]
The MD model, as illustrated in Fig. 2, consists of three parts, i.e., the substrate, the phosphorene and the tip. The substrate is made up of amorphous silicon, which is obtained by rapid quenching of the fused silicon [15]. A diamond tip with a hemispherical geometry is created from a perfect cube diamond crystal slides against the phosphorene on the substrate with a thickness of 18 Å. In the simulation, the top layers of tip are set as a rigid body and a constant external normal load Fn is applied. The periodic boundary conditions are imposed in the x and y directions to remove the edge effect. The size of phosphorene and amorphous silicon substrate is 20 nm × 20 nm along the x and y directions. The atoms in the bottom layers of amorphous silicon substrate with a thickness of about 4 Å are fixed as boundary layer to restrain the free motion of substrate. The atoms next to the boundary atoms with a thickness of 5 Å are the thermostat layer. The height of the tip is 2 nm and it is divided into boundary layer, thermostat layer and Newtonian layer from top to bottom with thicknesses of 2.4, 4 and 12.2 Å, respectively. The atoms in thermostat layer are kept at the constant temperature and act as a medium for the thermal diffusion of the Newtonian layer during the simulation. The friction process is conducted at 10 K and the temperature of thermostat layer is maintained by the velocity scale method [16]. Meanwhile, the Newtonian atoms which follow Newton’s
(1)
where E is the potential energy. The expression has two independent parameters: the minimum energy ε and the zero crossing distance σ . The standard geometric combination rules are used to extract the parameters. εbp − c = 8.19 meV and σbp − c = 3.410 Å are employed to calculate the interaction strengths between diamond and phosphorene. εbp − si = 16.67 meV and σbp − si = 3.632 Å are for the interaction between silicon and phosphorene. εsi − c = 8.56 meV and σsi − c = 3.604 Å are for the interaction between diamond and silicon [20,21]. The cutoff distance and the time step are set as10 Å and 1 fs. In order to investigate the anisotropy in the nano-friction behavior of phosphorene in depth, the friction forces of multiple sliding angles are measured in the present study. Assuming that sliding angle is 0° along the x-axis, we perform seven simulations with angles of θ = 0°, 15°, 30°, 45°, 60°, 75° and 90° between the zigzag direction and the sliding direction for the tip radius ranging from 2 to 4 nm, as shown in Fig. 1. In the simulation, the diamond tip slides at a constant speed of 10 m/s. In this paper, the arithmetic mean of forces along the sliding diN rection, which is calculated by Ff = ∑i = 1 Fi / N (N is the number of data points), is taken as the friction force. 3. Result and discussion Fig. 3(a) shows the typical friction force curve in the sliding process. It can be seen that the friction force shows a stick-slip pattern and fluctuates with the period of lattice constant. We further evaluate the influence of tip radius on the friction anisotropy of phosphorene, as shown in Fig. 3(b). It confirms that the friction force increases with tip radius under the similar stress condition. The stress σ is roughly estimated:
σ = W / Areal
(2)
Areal = N ·Aatom
(3)
where W is the normal load, Areal is the real contact area, N is the number of phosphorene atoms in contact with the tip and Aatom is the average surface area per atom. The tips with the radii of 2, 3 and 4 nm slide along various lattice orientations of phosphorene under loads of 7, 15 and 25 nN, respectively. In the present simulation, it is interesting to find that friction force does not gradually increase with the sliding
Fig. 2. A snapshot of the molecular dynamics model. The inset shows the sliding direction in the simulations, and the sliding angles between zigzag direction and sliding direction are θ = 0°, 15°, 30°, 45°, 60°, 75° and 90°, respectively. 365
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Fig. 3. The variation of friction force in the sliding process. (a) Friction curves of phosphorene with a tip of 3 nm in radius under a load of 15 nN and the red dotted lines represent the friction forces calculated by arithmetic mean along the sliding angles of 15°, 45° and 75°. (b) The friction forces at different angles between the zigzag direction and the sliding direction: 0°, 15°, 30°, 45°, 60°, 75° and 90°. The loads of 7, 15 and 25 nN are applied when the radii of tip are 2, 3 and 4 nm, respectively. The friction anisotropy with a tip of 2 nm is amplified in the inset. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
observed that the number of contact atoms, which reflects the size of the contact area, increases with the tip size. It can well explain the increase of friction force with the tip size for phosphorene, which is due to the increase in the real contact area. Moreover, the existence of slight wear on the surface of phosphorene is found when the tip radius increases to 4 nm. In order to further explore the occurrence condition of the “M-shape” friction
angle from 0° to 90°. In contrast, two peaks appear near the sliding angles of 15° and 75°, giving rise to “M-shape” friction force variation with sliding angle. The relationship between friction force and tip radius is consistent with the previous research [22]. From the inset in Fig. 4(a), the number of phosphorene atoms N in contact with the tip under different tip radii along the zigzag direction is calculated with a cutoff of 5 Å. It can be
Fig. 4. (a) The number of phosphorene atoms N in contact with the tip (3 nm in radius) along different sliding angles from 0° to 90°. The inset shows the number of phosphorene atoms under different tip radii of 2, 3, 4 nm along the zigzag direction. N is calculated with a cutoff of 5 Å. (b) Friction anisotropy of phosphorene with a tip of 4 nm in radius under a load of 10 nN. (c) The potential profiles with 3 nm tip along the sliding angles of 15°, 45° and 75°.
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H. Gong et al.
Fig. 5. The numerical simulation results of two-dimensional Tomlinson model along various lattice orientations of phosphorene. (a) θ = 0°; (b) θ = 24°; (c) θ = 45°; (d) θ = 63°; (e) θ = 75°; (f) θ = 90°.
The unique friction anisotropic effect of phosphorene is quite different from other two-dimensional materials such as graphene and molybdenum disulfide [25,26]. Fig. 4(c) shows the potential profiles along 15°, 45° and 75° directions by scanning the surface of phosphorene, calculating the interaction energy between the tip and the phosphorene. The local amplitude of the curves indicates the height of energy barrier. It can be seen that the energy barrier along the 45° direction is smaller than that along the 15° and 75° directions. The higher the energy barrier, the more resistance (friction force) the tip needs to overcome. Hence, it is not difficult to understand that the variation of energy barrier is consistent with that of the friction force. In order to further explore the mechanism of sliding angle dependence of friction anisotropy, a two-dimensional Tomlinson model [26] is adopted for the numerical simulation:
Fig. 6. The numerical simulation results of angle-dependent friction anisotropy of phosphorene.
m x x¨t = k x (xM −x t )−∂V (x t ,yt )/ ∂x t −γx x ṫ
(4)
m y y¨t = k y (yM −yt )−∂V (x t ,yt )/ ∂yt −γy yṫ
(5)
where x t , k x and xM are the actual position, the elasticity and the equilibrium position of the tip, respectively. So are yt , k y and yM . The effective masses of the system m x and m y are both, 10−12 kg, and the damping constants of the system γx and γy are both 10−3 Ns [14]. The initial interaction potential of tip-sample E0 [27],
phenomenon, a low-load simulation is carried out, as shown in Fig. 4(b). The wear of phosphorene is not found under the load of 10 nN and the “M- shape” is still observed. Fig. 4(a) also shows that the friction anisotropy with sliding angle is independent of contact area. The number of contact atoms has no obvious fluctuation along different lattice orientations at the same radius. The animation of the sliding friction process confirms that the slight increase in contact atoms at 75° sliding angle is due to local wear of phosphorene. Besides, it has been found that the maximum Young’s modulus of phosphorene is in the third principle direction which is equivalent to the sliding angle of 42° in the present study [23]. For twodimensional materials, the thinner the layers, the more easily the surface is wrinkled (out-of-plane deformation) to adhere to the tip, resulting in the increases of contact area and friction force. If the tip slides along the direction with a higher Young’s modulus, puckering effect of phosphorene will be weakened, giving rise to the trough of friction force [24]. Nevertheless, the Young's modulus gradually decreases with the increase or decrease of the sliding angle, indicating the existence of other friction mechanisms.
E0 = (aFLmax )/ π FLmax
(6)
are the periodicity of the atomic structure along the where a and sliding direction and the maximum friction force, respectively. In this work, due to the difference of the lattice constants along the armchair and zigzag directions, a is 3.31, 10.85, 18.65, 14.71, 14.14 and 4.38 Å along the sliding angles of 0° (zigzag), 24°, 45°, 63°, 75° and 90° (armchair). For the image to be more intuitive, FLmax is multiplied by a fixed value, without affecting the analysis of friction anisotropy. The simulation results of the two-dimensional Tomlinson model are displayed in Fig. 5. Half of the area between the forward and the backward scan curves represents the magnitude of the friction force. Specifically, the ratios of the friction force are 2.6, 4.3, 1, 1.3, 4.9 and 1.5 along various lattice orientations from zigzag to armchair in Fig. 6, also forming an “M-shape”. The consistency of MD simulations and twodimensional Tomlinson model simulations indicates that the friction 367
Computational Materials Science 150 (2018) 364–368
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Acknowledgments
anisotropy is due to the difference of energy barriers of tip-sample interaction during the sliding process along different lattice orientations (sliding angles) and the energy barriers can be divided into two parts. The first part comes from the atomic structure of phosphorene. In order to achieve minimal energy dissipation, the tip atoms do not move along a straight line at the nanoscale. Instead, the tip will jump from an interstitial site to another corresponding to a stick-slip jump and the path is probably polyline [26]. For the sliding directions that are compliant with or close to the interstitial site and stable position such as the 0°, 45° and 90° directions [14], the sliding process is easy to carry out and the friction force is low. However, the atoms make “long detours” corresponding to larger stick-slip jumps and higher energy barriers when other lattice orientations are set, especially along the 15° and 75° directions. Furthermore, the significant stick-slip is attributed to the well-ordered motion path experienced by the tip. When the atomic contact interface configurations between the diamond tip and phosphorene vary, the periodicity consistent with the lattice constant disappears. It can be found that several different periods appear in the friction force versus sliding distance curve where friction force is higher, suggesting a more complex internal mechanism. Previous research showed that an offset modulation of friction force was caused by the orientation-dependent mismatch between sample and the substrate [28,29]. Fig. 4(c) underpins the existence of periodic energy barrier on the contact surface and it is consistent with the “M-shape”. Therefore, it is considered one of the reasons for friction anisotropy. The energy barrier is derived from heterogeneous interaction between substrate and phosphorene and depends on the sliding path. The atomic configuration rearrangement of the interface between diamond and phosphorene brings transformation of interfacial potential amplitude and period causing high energy dissipation and friction force.
This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51775044, 51605008 and 51405337) and Beijing Natural Science Foundation of China (Grant No. 3182010). Conflict of interest The authors declare no conflict of interest. References [1] A. Brown, S. Rundqvist, Acta Crystallogr. A 19 (1965) 684. [2] J.R. Brent, N. Savjani, E.A. Lewis, S.J. Haigh, D.J. Lewis, P. O'Brien, Chem. Commun. 50 (2014) 13338. [3] D. Hanlon, C. Backes, E. Doherty, C.S. Cucinotta, N.C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q.M. Ramasse, N. McEvoy, W.J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D.D. O'Regan, G.S. Duesberg, V. Nicolosi, J.N. Coleman, Nat. Commun. 6 (2015) 8563. [4] A. Castellanos-Gomez, L. Vicarelli, E. Prada, J.O. Island, K.L. Narasimha-Acharya, S.I. Blanter, D.J. Groenendijk, M. Buscema, G.A. Steele, J.V. Alvarez, H.W. Zandbergen, J.J. Palacios, H.S.J. van der Zant, 2D Mater. 1 (2014) 025001. [5] J. Qiao, X. Kong, Z.X. Hu, F. Yang, W. Ji, Nat. Commun. 5 (2014) 4475. [6] M. Buscema, D.J. Groenendijk, S.I. Blanter, G.A. Steele, H.S. van der Zant, A. Castellanos-Gomez, Nano Lett. 14 (2014) 3347. [7] F. Xia, H. Wang, Y. Jia, Nat. Commun. 5 (2014) 4458. [8] D. Warschauer, J. Appl. Phys. 34 (1963) 1853. [9] H. Liu, A.T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, P.D. Ye, ACS Nano 8 (2014) 4033. [10] J. Tao, W. Shen, S. Wu, L. Liu, Z. Feng, C. Wang, C. Hu, P. Yao, H. Zhang, W. Pang, X. Duan, J. Liu, C. Zhou, D. Zhang, ACS Nano 9 (2015) 11362. [11] W.H. Chen, C.F. Yu, I.C. Chen, H.C. Cheng, Comput. Mater. Sci. 133 (2017) 35. [12] B. Liu, L. Bai, E.A. Korznikova, S.V. Dmitrievet, A.W. Law, K. Zhou, J. Phys. Chem. C 121 (2017) 13876. [13] L. Bai, B. Liu, N. Srikanth, Y. Tian, K. Zhou, Nanotechnology 28 (2017) 355704. [14] Z. Cui, G. Xie, F. He, W. Wang, D. Guo, W. Wang, Adv. Mater. Interfaces 4 (2017) 1700998. [15] M.D. Kluge, J.R. Ray, A. Rahman, Phys. Rev. B 36 (1987) 4234. [16] J.M. Haile, I. Johnston, A.J. Mallinckrodt, S. McKay, Comput. Phys. 7 (1993) 625. [17] S. Plimpton, J. Comput. Phys. 117 (1995) 1. [18] J.W. Jiang, Nanotechnology 26 (2015) 315706. [19] J. Tersoff, Phys. Rev. B 39 (1989) 5566. [20] J.W. Jiang, H.S. Park, J. Appl. Phys. 117 (2015) 124304. [21] H.Y. Song, X.W. Zha, Physica B 393 (2007) 217. [22] E.-S. Yoon, R.A. Singh, H.-J. Oh, H. Kong, Wear 259 (2005) 1424. [23] J.W. Jiang, Physics (2015). [24] Q. Li, C. Lee, R.W. Carpick, J. Hone, Phys. Status Solidi (B) 247 (2010) 2909. [25] J.S. Choi, J.-S. Kim, I.-S. Byun, D.H. Lee, M.J. Lee, B.H. Park, C. Lee, D. Yoon, H. Cheong, K.H. Lee, Y.-W. Son, J.Y. Park, M. Salmeron, Science 333 (2011) 607. [26] M. Li, J. Shi, L. Liu, P. Yu, N. Xi, Y. Wang, Sci. Technol. Adv. Mater. 17 (2016) 189. [27] A. Socoliuc, R. Bennewitz, E. Gnecco, E. Meyer, Phys. Rev. Lett. 92 (2004) 134301. [28] N. Chan, S.G. Balakrishna, A. Klemenz, M. Moseler, P. Egberts, R. Bennewitz, Carbon 113 (2017) 132. [29] J. Liu, S. Zhang, Q. Li, X.Q. Feng, Z.F. Di, C. Ye, Y. Dong, Carbon 125 (2017) 76.
4. Conclusions In conclusion, an “M-shape” friction anisotropy of phosphorene at the nanoscale is observed using MD simulations. The anisotropic behavior of friction is independent of contact area and still maintains even if wear of phosphorene occurs. The novel friction characteristic is considered to be the coupling effect of the special honeycomb structure of phosphorene and heterogeneous interaction between the sample and substrate, which are confirmed by the calculation of two-dimension Tomlinson model and the potential profiles along different lattice orientations. The present work not only gives deep insights into the fundamental mechanical properties of phosphorene, but also suggests the possible applications of phosphorene as solid lubricants and smart materials in the ultrahigh precision positioning area.
368
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Letter
“M-shape” nanoscale friction anisotropy of phosphorene a
b,⁎
c
d
Hanjun Gong , Pengzhe Zhu , Lina Si , Xiaoqing Zhang , Guoxin Xie
a,⁎
T
a
State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China School of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, China d School of Materials Science and Mechanical Engineering, Beijing Technology and Business University, Beijing 100048, China b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Phosphorene Friction anisotropy M-shape Molecular dynamics
In this work, molecular dynamics simulations are employed to explore the nanoscale friction anisotropy of phosphorene. We study the friction process of a diamond tip sliding against the phosphorene on the silicon substrate under different sliding directions. The results show that there exists a significant anisotropy in the friction force along different lattice orientations of phosphorene. The friction force exhibits “M-shape” which means the friction force is locally maximum along the 15° and 75° directions relative to the zigzag direction of phosphorene. It is proposed that this “M-shape” friction anisotropy is due to the difference of potential energy among different orientations arising from the unique structure of phosphorene and heterogeneous interaction with the substrate.
1. Introduction Black phosphorus is a natural p-type semiconductor in which each layer is vertically stacked by the van der Waals force. As shown in Fig. 1, black phosphorus has a pleated honeycomb crystal structure which is different from other two-dimensional materials such as graphene and molybdenum disulfide. The interlayer distance of the adjacent two layers of black phosphorus is 5.25 Å. The lattice constants of black phosphorus are about 3.31 Å and 4.38 Å [1] along the x- and yaxis, which correspond to the zigzag and armchair directions, respectively. Black phosphorus can be exfoliated down to a single layer by various methods, referred to as phosphorene [2–4]. Phosphorene has become one of the most promising materials in different areas because of its unique physical properties e.g., limited and direct bandgap, excellent room temperature carrier mobility and on/off ratio, high optical and UV absorption [5–8]. It has been shown theoretically that the bandgap decreases from 1.51 eV to 0.59 eV when phosphorene is reduced from five-layer to single-layer. The monolayer is exceptional in having an extremely high hole mobility and anomalous elastic properties which reverse the anisotropy, making few-layer phosphorene a very appealing candidate material for future applications in electronics and optoelectronics [5]. Besides, phosphorenebased field-effect transistors exhibited ambipolar behavior in the dark state and the response to excitation wavelengths from the visible up to 940 nm and rise time of about 1 ms upon illumination. The ambipolar behavior coupled to the fast and broadband photodetection showed the
⁎
Corresponding authors. E-mail addresses: [email protected] (P. Zhu), [email protected] (G. Xie).
https://doi.org/10.1016/j.commatsci.2018.04.013 Received 4 January 2018; Received in revised form 19 March 2018; Accepted 8 April 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.
potential of phosphorene as active material for high-speed NIR detectors [6]. Among the unique physical properties, anisotropy is the most fascinating characteristic of phosphorene. Unique angle-dependent properties of phosphorene allow a new degree of freedom for designing conceptually new optoelectronic and electronic devices, which are not possible by using other two dimensional materials [7]. It was found that phosphorene showed substantial anisotropy in the transport behavior, which was associated with the unique ridge structure of the layers [9]. The mechanical properties have also been confirmed to be anisotropic. For instance, the Young’s modulus of phosphorene with few layers has been measured to be 58.6 and 27.2 GPa in the zigzag and armchair directions respectively [10] and the dependences on size, chirality, temperature and vacancy defects are also anisotropic [11,12], making it an alternative material for applications in flexible electronics, straindependent optoelectronics and electromechanical nano-devices. Recently, both experiments and molecular dynamics (MD) simulations have found that friction of phosphorene exhibits atomic-level anisotropy, and more specifically the friction force is larger along the armchair direction than that along the zigzag direction [13,14]. However, at present the researches mainly focused on the friction behaviors of phosphorene along the armchair and zigzag directions. A systematic study of the friction properties, especially the friction anisotropy, of phosphorene is still lacking. An in-depth study of nanoscale friction properties of phosphorene can not only shed light on the friction mechanisms of phosphorene, but also can guide the design and precision control of phosphorene-based micro- and nano-mechanical systems.
Computational Materials Science 150 (2018) 364–368
H. Gong et al.
Fig. 1. Crystal structure of black phosphorus (a) side view of black phosphorus lattice; (b) top view of monolayer black phosphorus lattice.
Second Law imitate the true atomic dynamic behavior. The MD simulations are performed using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator), which is an open source program developed at the Sandia National Laboratory, USA [17]. The interaction between phosphorene atoms is described by the Stillinger-Weber (SW) potentials [18]. The Tersoff potential is used to evaluate the interatomic interactions for the diamond tip and the amorphous silicon substrate [19]. Besides, the Lennard-Jones (LJ) potential is employed to model the non-bonded interaction between dissimilar atoms, which takes the form of
As the friction experiment of single-layer phosphorene is still very difficult, molecular dynamic (MD) simulation is often adopted in the study of nanoscale friction since it can provide direct information about the buried interface during the nanoscale sliding process. In this work, the friction force along various lattice orientations of phosphorene were simulated and analyzed in great detail to explore the anisotropy of friction behavior of phosphorene.
2. Simulation method
E = 4ε [(σ / r )12−(σ / r )6]
The MD model, as illustrated in Fig. 2, consists of three parts, i.e., the substrate, the phosphorene and the tip. The substrate is made up of amorphous silicon, which is obtained by rapid quenching of the fused silicon [15]. A diamond tip with a hemispherical geometry is created from a perfect cube diamond crystal slides against the phosphorene on the substrate with a thickness of 18 Å. In the simulation, the top layers of tip are set as a rigid body and a constant external normal load Fn is applied. The periodic boundary conditions are imposed in the x and y directions to remove the edge effect. The size of phosphorene and amorphous silicon substrate is 20 nm × 20 nm along the x and y directions. The atoms in the bottom layers of amorphous silicon substrate with a thickness of about 4 Å are fixed as boundary layer to restrain the free motion of substrate. The atoms next to the boundary atoms with a thickness of 5 Å are the thermostat layer. The height of the tip is 2 nm and it is divided into boundary layer, thermostat layer and Newtonian layer from top to bottom with thicknesses of 2.4, 4 and 12.2 Å, respectively. The atoms in thermostat layer are kept at the constant temperature and act as a medium for the thermal diffusion of the Newtonian layer during the simulation. The friction process is conducted at 10 K and the temperature of thermostat layer is maintained by the velocity scale method [16]. Meanwhile, the Newtonian atoms which follow Newton’s
(1)
where E is the potential energy. The expression has two independent parameters: the minimum energy ε and the zero crossing distance σ . The standard geometric combination rules are used to extract the parameters. εbp − c = 8.19 meV and σbp − c = 3.410 Å are employed to calculate the interaction strengths between diamond and phosphorene. εbp − si = 16.67 meV and σbp − si = 3.632 Å are for the interaction between silicon and phosphorene. εsi − c = 8.56 meV and σsi − c = 3.604 Å are for the interaction between diamond and silicon [20,21]. The cutoff distance and the time step are set as10 Å and 1 fs. In order to investigate the anisotropy in the nano-friction behavior of phosphorene in depth, the friction forces of multiple sliding angles are measured in the present study. Assuming that sliding angle is 0° along the x-axis, we perform seven simulations with angles of θ = 0°, 15°, 30°, 45°, 60°, 75° and 90° between the zigzag direction and the sliding direction for the tip radius ranging from 2 to 4 nm, as shown in Fig. 1. In the simulation, the diamond tip slides at a constant speed of 10 m/s. In this paper, the arithmetic mean of forces along the sliding diN rection, which is calculated by Ff = ∑i = 1 Fi / N (N is the number of data points), is taken as the friction force. 3. Result and discussion Fig. 3(a) shows the typical friction force curve in the sliding process. It can be seen that the friction force shows a stick-slip pattern and fluctuates with the period of lattice constant. We further evaluate the influence of tip radius on the friction anisotropy of phosphorene, as shown in Fig. 3(b). It confirms that the friction force increases with tip radius under the similar stress condition. The stress σ is roughly estimated:
σ = W / Areal
(2)
Areal = N ·Aatom
(3)
where W is the normal load, Areal is the real contact area, N is the number of phosphorene atoms in contact with the tip and Aatom is the average surface area per atom. The tips with the radii of 2, 3 and 4 nm slide along various lattice orientations of phosphorene under loads of 7, 15 and 25 nN, respectively. In the present simulation, it is interesting to find that friction force does not gradually increase with the sliding
Fig. 2. A snapshot of the molecular dynamics model. The inset shows the sliding direction in the simulations, and the sliding angles between zigzag direction and sliding direction are θ = 0°, 15°, 30°, 45°, 60°, 75° and 90°, respectively. 365
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Fig. 3. The variation of friction force in the sliding process. (a) Friction curves of phosphorene with a tip of 3 nm in radius under a load of 15 nN and the red dotted lines represent the friction forces calculated by arithmetic mean along the sliding angles of 15°, 45° and 75°. (b) The friction forces at different angles between the zigzag direction and the sliding direction: 0°, 15°, 30°, 45°, 60°, 75° and 90°. The loads of 7, 15 and 25 nN are applied when the radii of tip are 2, 3 and 4 nm, respectively. The friction anisotropy with a tip of 2 nm is amplified in the inset. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
observed that the number of contact atoms, which reflects the size of the contact area, increases with the tip size. It can well explain the increase of friction force with the tip size for phosphorene, which is due to the increase in the real contact area. Moreover, the existence of slight wear on the surface of phosphorene is found when the tip radius increases to 4 nm. In order to further explore the occurrence condition of the “M-shape” friction
angle from 0° to 90°. In contrast, two peaks appear near the sliding angles of 15° and 75°, giving rise to “M-shape” friction force variation with sliding angle. The relationship between friction force and tip radius is consistent with the previous research [22]. From the inset in Fig. 4(a), the number of phosphorene atoms N in contact with the tip under different tip radii along the zigzag direction is calculated with a cutoff of 5 Å. It can be
Fig. 4. (a) The number of phosphorene atoms N in contact with the tip (3 nm in radius) along different sliding angles from 0° to 90°. The inset shows the number of phosphorene atoms under different tip radii of 2, 3, 4 nm along the zigzag direction. N is calculated with a cutoff of 5 Å. (b) Friction anisotropy of phosphorene with a tip of 4 nm in radius under a load of 10 nN. (c) The potential profiles with 3 nm tip along the sliding angles of 15°, 45° and 75°.
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Fig. 5. The numerical simulation results of two-dimensional Tomlinson model along various lattice orientations of phosphorene. (a) θ = 0°; (b) θ = 24°; (c) θ = 45°; (d) θ = 63°; (e) θ = 75°; (f) θ = 90°.
The unique friction anisotropic effect of phosphorene is quite different from other two-dimensional materials such as graphene and molybdenum disulfide [25,26]. Fig. 4(c) shows the potential profiles along 15°, 45° and 75° directions by scanning the surface of phosphorene, calculating the interaction energy between the tip and the phosphorene. The local amplitude of the curves indicates the height of energy barrier. It can be seen that the energy barrier along the 45° direction is smaller than that along the 15° and 75° directions. The higher the energy barrier, the more resistance (friction force) the tip needs to overcome. Hence, it is not difficult to understand that the variation of energy barrier is consistent with that of the friction force. In order to further explore the mechanism of sliding angle dependence of friction anisotropy, a two-dimensional Tomlinson model [26] is adopted for the numerical simulation:
Fig. 6. The numerical simulation results of angle-dependent friction anisotropy of phosphorene.
m x x¨t = k x (xM −x t )−∂V (x t ,yt )/ ∂x t −γx x ṫ
(4)
m y y¨t = k y (yM −yt )−∂V (x t ,yt )/ ∂yt −γy yṫ
(5)
where x t , k x and xM are the actual position, the elasticity and the equilibrium position of the tip, respectively. So are yt , k y and yM . The effective masses of the system m x and m y are both, 10−12 kg, and the damping constants of the system γx and γy are both 10−3 Ns [14]. The initial interaction potential of tip-sample E0 [27],
phenomenon, a low-load simulation is carried out, as shown in Fig. 4(b). The wear of phosphorene is not found under the load of 10 nN and the “M- shape” is still observed. Fig. 4(a) also shows that the friction anisotropy with sliding angle is independent of contact area. The number of contact atoms has no obvious fluctuation along different lattice orientations at the same radius. The animation of the sliding friction process confirms that the slight increase in contact atoms at 75° sliding angle is due to local wear of phosphorene. Besides, it has been found that the maximum Young’s modulus of phosphorene is in the third principle direction which is equivalent to the sliding angle of 42° in the present study [23]. For twodimensional materials, the thinner the layers, the more easily the surface is wrinkled (out-of-plane deformation) to adhere to the tip, resulting in the increases of contact area and friction force. If the tip slides along the direction with a higher Young’s modulus, puckering effect of phosphorene will be weakened, giving rise to the trough of friction force [24]. Nevertheless, the Young's modulus gradually decreases with the increase or decrease of the sliding angle, indicating the existence of other friction mechanisms.
E0 = (aFLmax )/ π FLmax
(6)
are the periodicity of the atomic structure along the where a and sliding direction and the maximum friction force, respectively. In this work, due to the difference of the lattice constants along the armchair and zigzag directions, a is 3.31, 10.85, 18.65, 14.71, 14.14 and 4.38 Å along the sliding angles of 0° (zigzag), 24°, 45°, 63°, 75° and 90° (armchair). For the image to be more intuitive, FLmax is multiplied by a fixed value, without affecting the analysis of friction anisotropy. The simulation results of the two-dimensional Tomlinson model are displayed in Fig. 5. Half of the area between the forward and the backward scan curves represents the magnitude of the friction force. Specifically, the ratios of the friction force are 2.6, 4.3, 1, 1.3, 4.9 and 1.5 along various lattice orientations from zigzag to armchair in Fig. 6, also forming an “M-shape”. The consistency of MD simulations and twodimensional Tomlinson model simulations indicates that the friction 367
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Acknowledgments
anisotropy is due to the difference of energy barriers of tip-sample interaction during the sliding process along different lattice orientations (sliding angles) and the energy barriers can be divided into two parts. The first part comes from the atomic structure of phosphorene. In order to achieve minimal energy dissipation, the tip atoms do not move along a straight line at the nanoscale. Instead, the tip will jump from an interstitial site to another corresponding to a stick-slip jump and the path is probably polyline [26]. For the sliding directions that are compliant with or close to the interstitial site and stable position such as the 0°, 45° and 90° directions [14], the sliding process is easy to carry out and the friction force is low. However, the atoms make “long detours” corresponding to larger stick-slip jumps and higher energy barriers when other lattice orientations are set, especially along the 15° and 75° directions. Furthermore, the significant stick-slip is attributed to the well-ordered motion path experienced by the tip. When the atomic contact interface configurations between the diamond tip and phosphorene vary, the periodicity consistent with the lattice constant disappears. It can be found that several different periods appear in the friction force versus sliding distance curve where friction force is higher, suggesting a more complex internal mechanism. Previous research showed that an offset modulation of friction force was caused by the orientation-dependent mismatch between sample and the substrate [28,29]. Fig. 4(c) underpins the existence of periodic energy barrier on the contact surface and it is consistent with the “M-shape”. Therefore, it is considered one of the reasons for friction anisotropy. The energy barrier is derived from heterogeneous interaction between substrate and phosphorene and depends on the sliding path. The atomic configuration rearrangement of the interface between diamond and phosphorene brings transformation of interfacial potential amplitude and period causing high energy dissipation and friction force.
This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51775044, 51605008 and 51405337) and Beijing Natural Science Foundation of China (Grant No. 3182010). Conflict of interest The authors declare no conflict of interest. References [1] A. Brown, S. Rundqvist, Acta Crystallogr. A 19 (1965) 684. [2] J.R. Brent, N. Savjani, E.A. Lewis, S.J. Haigh, D.J. Lewis, P. O'Brien, Chem. Commun. 50 (2014) 13338. [3] D. Hanlon, C. Backes, E. Doherty, C.S. Cucinotta, N.C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q.M. Ramasse, N. McEvoy, W.J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D.D. O'Regan, G.S. Duesberg, V. Nicolosi, J.N. Coleman, Nat. Commun. 6 (2015) 8563. [4] A. Castellanos-Gomez, L. Vicarelli, E. Prada, J.O. Island, K.L. Narasimha-Acharya, S.I. Blanter, D.J. Groenendijk, M. Buscema, G.A. Steele, J.V. Alvarez, H.W. Zandbergen, J.J. Palacios, H.S.J. van der Zant, 2D Mater. 1 (2014) 025001. [5] J. Qiao, X. Kong, Z.X. Hu, F. Yang, W. Ji, Nat. Commun. 5 (2014) 4475. [6] M. Buscema, D.J. Groenendijk, S.I. Blanter, G.A. Steele, H.S. van der Zant, A. Castellanos-Gomez, Nano Lett. 14 (2014) 3347. [7] F. Xia, H. Wang, Y. Jia, Nat. Commun. 5 (2014) 4458. [8] D. Warschauer, J. Appl. Phys. 34 (1963) 1853. [9] H. Liu, A.T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, P.D. Ye, ACS Nano 8 (2014) 4033. [10] J. Tao, W. Shen, S. Wu, L. Liu, Z. Feng, C. Wang, C. Hu, P. Yao, H. Zhang, W. Pang, X. Duan, J. Liu, C. Zhou, D. Zhang, ACS Nano 9 (2015) 11362. [11] W.H. Chen, C.F. Yu, I.C. Chen, H.C. Cheng, Comput. Mater. Sci. 133 (2017) 35. [12] B. Liu, L. Bai, E.A. Korznikova, S.V. Dmitrievet, A.W. Law, K. Zhou, J. Phys. Chem. C 121 (2017) 13876. [13] L. Bai, B. Liu, N. Srikanth, Y. Tian, K. Zhou, Nanotechnology 28 (2017) 355704. [14] Z. Cui, G. Xie, F. He, W. Wang, D. Guo, W. Wang, Adv. Mater. Interfaces 4 (2017) 1700998. [15] M.D. Kluge, J.R. Ray, A. Rahman, Phys. Rev. B 36 (1987) 4234. [16] J.M. Haile, I. Johnston, A.J. Mallinckrodt, S. McKay, Comput. Phys. 7 (1993) 625. [17] S. Plimpton, J. Comput. Phys. 117 (1995) 1. [18] J.W. Jiang, Nanotechnology 26 (2015) 315706. [19] J. Tersoff, Phys. Rev. B 39 (1989) 5566. [20] J.W. Jiang, H.S. Park, J. Appl. Phys. 117 (2015) 124304. [21] H.Y. Song, X.W. Zha, Physica B 393 (2007) 217. [22] E.-S. Yoon, R.A. Singh, H.-J. Oh, H. Kong, Wear 259 (2005) 1424. [23] J.W. Jiang, Physics (2015). [24] Q. Li, C. Lee, R.W. Carpick, J. Hone, Phys. Status Solidi (B) 247 (2010) 2909. [25] J.S. Choi, J.-S. Kim, I.-S. Byun, D.H. Lee, M.J. Lee, B.H. Park, C. Lee, D. Yoon, H. Cheong, K.H. Lee, Y.-W. Son, J.Y. Park, M. Salmeron, Science 333 (2011) 607. [26] M. Li, J. Shi, L. Liu, P. Yu, N. Xi, Y. Wang, Sci. Technol. Adv. Mater. 17 (2016) 189. [27] A. Socoliuc, R. Bennewitz, E. Gnecco, E. Meyer, Phys. Rev. Lett. 92 (2004) 134301. [28] N. Chan, S.G. Balakrishna, A. Klemenz, M. Moseler, P. Egberts, R. Bennewitz, Carbon 113 (2017) 132. [29] J. Liu, S. Zhang, Q. Li, X.Q. Feng, Z.F. Di, C. Ye, Y. Dong, Carbon 125 (2017) 76.
4. Conclusions In conclusion, an “M-shape” friction anisotropy of phosphorene at the nanoscale is observed using MD simulations. The anisotropic behavior of friction is independent of contact area and still maintains even if wear of phosphorene occurs. The novel friction characteristic is considered to be the coupling effect of the special honeycomb structure of phosphorene and heterogeneous interaction between the sample and substrate, which are confirmed by the calculation of two-dimension Tomlinson model and the potential profiles along different lattice orientations. The present work not only gives deep insights into the fundamental mechanical properties of phosphorene, but also suggests the possible applications of phosphorene as solid lubricants and smart materials in the ultrahigh precision positioning area.
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