Article pubs.acs.org/JPCC
Failure Mechanism of Phosphorene by Nanoindentation Zhen-Dong Sha,† Qing-Xiang Pei,*,‡ Qiang Wan,*,§ and Zi-Shun Liu† †
International Center for Applied Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China ‡ Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore § Institute of System Engineering, China Academy of Engineering Physics, MianYang, SiChuan, 621900, China ABSTRACT: Phosphorene, a new two-dimensional material, has attracted tremendous attention in recent years due to its superior physical and electrical properties. Despite the fact that it may have a strong impact in future flexible electronics, there has been so far little or no atomic-level understanding of the failure process of phosphorene under nanoindentation. Here, we report a systematic study of the deformation and failure mechanism of phosphorene under nanoindentation by using molecular dynamics simulations. Three different regimes of deformation behaviors can be identified. The bump behavior in the first regime is different from that in the graphene and other 2D materials. Our simulations reveal the strong correlation between the normal load and the number of C−P pairs with repulsive force across the contact interface. Furthermore, the failure mechanism does not change with increasing tip size or defect concentration. However, it is found that the failure load decreases by 30% even though the defect concentration is 0.5%. It is rationalized that crack nucleates from the defect located at the contact area and hence the failure load significantly degrades. Our present work provides significant insights into atomic-scale understanding of the mechanical properties and failure mechanisms of phosphorene under nanoindentation.
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INTRODUCTION Since graphene was discovered in 2004,1 two-dimensional (2D) materials have gained considerable interest as they have extraordinary physical and electrical properties associated with their reduced dimensionality.2−5 For example, graphene has ultrahigh electron mobility due to its massless charge carriers.5−8 The lack of band gap in graphene, however, has motivated a surge of works on other 2D materials, such as monolayer MoS2, boron nitride, and silicene. Recently, single-layer black phosphorus or phosphorene has been successfully isolated by mechanical exfoliation in experiment and immediately becomes the new focus of scientific research.9−14 Phosphorene is a semiconductor with a large direct band gap of 1.5 eV with relatively high charge carrier mobility of up to 10000 cm2 V−1 s−1.10 In addition, phosphorene exhibits a high on/off current ratio over 104.9 Remarkably, its electronic and optical properties can be tuned by applying mechanical strain.9,12,15,16 In Cakir et al.’s firstprinciples calculations, it has been shown that tensile strain can significantly enhance electron transport along the zigzag direction of phosphorene.15 Rodin et al.’s work demonstrated that an out-of-plane strain can tune the band gap of phosphorene in a wide range.16 Furthermore, Hu et al. reported that an in-plane stress can change phosphorene from a semiconductor to a metal.12 © XXXX American Chemical Society
Previous studies on phosphorene have mostly focused on its deformation under tensile loading.12,15,16 There has been so far little or no atomic-level understanding of its deformation process under nanoindentation. Nanoindentation has been widely used to measure the mechanical properties of 2D materials. For example, atomic force microscopy (AFM) nanoindentation has been successfully used to measure Young’s modulus and fracture strength of graphene in experiment.17,18 Very recently, the mechanical properties of phosphorene nanoribbons suspended on narrow grooves have been quantitatively investigated with the AFM nanoindentation method.19 In addition, the environmental effects on mechanical properties of few-layer black phosphorus were characterized by nanoindentation using an AFM tip.20 2D materials can also have a strong impact in future flexible electronics; therefore, an atomic-level understanding of the deformation and failure process of phosphorene under nanoindentation is of both scientific interest and technological significance. In the present work, we comprehensively evaluate the mechanical behavior of phosphorene. We employ the molecular dynamics (MD) simulations of nanoindentation to characterize Received: December 29, 2016 Revised: February 8, 2017 Published: February 13, 2017 A
DOI: 10.1021/acs.jpcc.6b13071 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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is first relaxed at 0 K to minimize its total energy. Subsequently the tip is gradually heated to and equilibrated at 300 K. The top 1.0 nm of the tip is rigidly held during MD simulations of nanoindentation. For the rectangle phosphorene substrate shown in Figure 1, it contains ∼300000 atoms and has dimensions of 110.4 nm (x) × 95.6 nm (y). Similarly, the phosphorene sample is statically relaxed at 0 K, and gradually heating to and equilibrating at 300 K. The edge of the phosphorene with length of 2 nm is rigidly held during MD simulations of nanoindentation. The nanoindentation simulations are performed at 300 K. The diamond tip is driven toward the phosphorene substrate at a speed of 0.5 Å/ps, which is slow enough to allow the decay of most transients.30 Periodic boundary conditions (PBCs) are applied in all three directions. A vacuum gap of 200 Å is placed below the phosphorene sheet, so that the atoms do not interact across the periodic boundary in the z direction. A time step of 0.5 fs is used for the integration of the equations of atomic motion in the MD simulations.
the deformation and failure mechanics of phosphorene sheet as a function of loading speed, tip size, and defect concentration. Our observations are compared with those from previous experimental and MD simulations results on graphene and other 2D materials under tensile loading and nanoindentation. Finally, our study provides significant insights into the atomic understanding of the deformation and failure mechanisms of phosphorene by nanoindentation.
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MODEL AND METHOD MD simulations are performed using the large-scale atomic/ molecular massively parallel simulator (LAMMPS) code.21 The Tersoff22 and Stillinger−Weber (SW) potentials23 are used to describe the interatomic interactions for diamond tip and phosphorene substrate, respectively. The cutoff distance in the SW potential for phosphorene is set at 2.79 Å.24 It was shown that this SW potential could accurately predict the phonon spectrum and mechanical behavior of phosphorene.23,25 In addition, the van der Waals (vdW) potential is employed to model the interatomic interaction between diamond tip and phosphorene substrate, due to the nonbonded interactions at the contact interface:22,26 EijvdW = 4ε[(σ /rij)12 − (σ /rij)6 ]
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RESULTS AND DISCUSSION The obtained normal load vs indentation depth (d) relation is shown in Figure 2. The normal load is calculated as the sum of
(1)
where rij is the interatomic distance, and σ and ε are parameters equal to 2.807 Å and 2.22 meV for the C−P interaction, respectively.27 In the present MD simulations, both the diamond tip and the phosphorene substrate are allowed to deform.28,29 The tip has a height of 10 nm and radius of 10 nm, as shown in Figure 1. The tip is prepared by cutting from a bulk diamond sample. The tip
Figure 2. Obtained normal load vs indentation depth (d) curve. Three different regimes of deformation behaviors can be identified.
the average normal forces exerted on the diamond tip by the phosphorene substrate.22,26,28,29 The indentation depth is defined as the difference between the lowest point of the tip and the initial position of the phosphorene substrate.30 The failure load of phosphorene is found to be ∼12 nN, which is much smaller than that for graphene. 22 As a result, phosphorene has relatively low fracture strength in comparison with graphene, which is consistent with experimental and recent MD simulation results on phosphorene under tensile loading.25 Meanwhile, three different regimes of deformation behaviors can be identified from the normal load vs indentation depth curve depicted in Figure 2. In the first regime, there is a bump. Such bump behavior is caused by that the tip is wrapped by the soft phosphorene sheet at the initial process of indentation. The detailed physical mechanism of this bump phenomenon will be discussed in Figures 3-4. It should be emphasized that the first regime observed for phosphorene is quite different from that in the graphene and other 2D materials under indentation22as well as tensile loading,31 where the slope of the normal load vs indentation depth curve increases, arising from erasing the wrinkle in a thin membrane structure.31 In the second regime, the normal load becomes linearly dependent on the indentation depth. In the third
Figure 1. Atomistic model for nanoindentation test with the diamond tip and the rectangle phosphorene substrate, as seen from (a) top and (b) 3D views. The tip has a height of 10 nm and radius of 10 nm. The top 1.0 nm of the tip (colored by dark blue) and the edge of the phosphorene sheet with length of 2.0 nm (dotted line) are held rigidly during simulations of nanoindentation. B
DOI: 10.1021/acs.jpcc.6b13071 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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A quantitative measure of the number of C−P pairs with distance short than 2.807 Å as a function of indentation depth is shown in Figure 4. Three different regimes also can be identified, suggesting the strong correlation between the normal load and the number of C−P pairs within the distance of 2.807 Å. Initially, the number of C−P pairs with distance short than 2.807 Å increases rapidly, indicating that there is strong repulsive force between the tip and substrate. In the second regime, the number of C−P pairs with distance short than 2.807 Å increases gradually as the indentation depth increases. In the third regime, the number of C−P pairs keeps on increasing to the maximum value and the phosphorene sheet fails due to fracture. Our MD simulation results in Figures 3 and 4 reveal that due to its softness, the phosphorene sheet undergoes the large material deformation rather than the geometry deformation at the initial process of indentation. The tip then can be wrapped by the soft phosphorene sheet, simultaneously many C−P pairs and strong repulsive force between tip and substrate. Accordingly, the bump phenomenon is observed in the curve of normal load versus indentation depth. Furthermore, it should be emphasized that there is no direct causal relationship between this bump phenomenon and the vdW potential chose to model the nonbonded interactions at the contact interface. This is mainly due to the fact that the physical mechanism of the bump phenomenon originates from the large deformation of the soft phosphorene sheet, instead of the interactions between tip and substrate. We further examine the deformation process of phosphorene by nanoindentation in the second and third regimes, as shown in Figure 5. As the indentation depth increases, the stress
Figure 3. (a, b) Sequence of snapshots capturing deformation process of phosphorene in the first regime at different indentation depths, as seen from top view. For clarity, the indenter tip is not shown. Atoms are colored according to their von Mises stresses. (c) Side and (d) bottom views of the interatomic interaction between C−P pairs at the indentation depth of 35 Å, respectively. The red color represents the C−P pairs with interaction distance short than 2.807 Å, indicating strong repulsive force.
Figure 4. Number of C−P pairs with interaction distance short than 2.807 Å vs indentation depth (d) curve. A strong correlation between the normal load and the number of C−P pairs with interaction distance short than 2.807 Å is observed.
regime, the normal load quickly increases as the indentation depth increases until the failure of phosphorene sheet. To reveal the physical mechanism of the bump phenomenon observed in the first regime, parts a and b of Figure 3 show a sequence of snapshots capturing deformation process of phosphorene. For clarity, the indenter tip is not shown. Atoms are colored according to their von Mises stresses. It is found that the tip is wrapped by the phosphorene sheet at the initial process of indentation. This is because the phosphorene sheet is quite soft. Furthermore, parts c and d of Figure 3 demonstrate the interatomic interaction between C−P pairs. The red color indicates the C−P pairs with distance less than 2.807 Å, which is the distance where the potential energy of the C−P pair is zero.27 When the distance of C−P pairs is shorter than 2.807 Å, the force between C−P pairs is repulsive. In Figure 3d, the bottom view of interaction between C−P pairs is essentially consistent with previous studies demonstrating that at nanoscale the real contact area is linear with the number of substrate atoms within the interaction range from the tip atoms, and is different from the contact area defined by the edge of the contact zone in continuum mechanics.26,28,29
Figure 5. Sequence of snapshots capturing the deformation process of phosphorene in the second and third regimes at different indentation depths, as seen from the top view.
concentration in contact area becomes more apparent. Typically, a crack initiated at the indentation location is observed in the third regime. Then the crack grows through the whole sheet with no plastic deformation, indicating brittle fracture. To further study the deformation and failure mechanism of phosphorene, a series of MD simulations have been carried out with different loading speeds and indenter radii. Figure 6 depicts the normal load vs indentation depth (d) curves as a function of loading speed ranging from 0.5 to 2.0 Å/ps. With C
DOI: 10.1021/acs.jpcc.6b13071 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 6. Normal load vs indentation depth (d) curves as a function of loading speed.
the increase of loading speed, the change of the maximum load is not that obvious, while the critical indentation depth for the phosphorene failure decreases. This is because that at a higher loading speed it takes less time to go through the phosphorene sheet, resulting in a decreased indentation depth. More interestingly, our results reveal that the bump in the first regime disappears with increasing loading speed, indicating the change in the failure mechanism caused by the loading speed. For example, when the loading speed increases to 2.0 Å/ps, the normal load is nearly linear with the indentation depth. Parts a and b of Figure 7 show a sequence of snapshots capturing
Figure 8. (a) Top and (b) 3D views of the nanoindentation test with the diamond tip and the rectangle phosphorene substrate, respectively. The tip has a radius of 20 nm, and its height is kept at 10 nm. The nanoindentation simulation is carried out at the loading speed of 0.5 Å/ps.
Figure 9. Normal load vs indentation depth curves as a function of tip radius. Figure 7. Sequence of snapshots capturing deformation process of phosphorene at the loading speeds of (a) 1.0 and (b) 2.0 Å/ps, respectively.
the failure mechanism of phosphorene, which is different from the observations on the effect of loading speed. However, the maximum load for the tip radius of 20 nm is ∼1.7 times larger than that for the tip radius of 10 nm. Figure 10 shows a sequence of snapshots capturing deformation process of phosphorene with tip radius of 20 nm at different indentation depths. With the increase of the indenter radius, the contact
deformation process of phosphorene at the loading speed of 1.0 and 2.0 Å/ps, respectively. Apparently, the stress concentration at the contact area increases rapidly with increasing loading speed, causing the fast fracture of phosphorene. Hence, the slow loading speed of 0.5 Å/ps is chosen for the investigation of the failure mechanism of phosphorene in our MD simulations. To study the effect of tip size on the deformation and failure mechanism of phosphorene, a large tip radius (r) of 20 nm is used. Note that the tip size is similar to that used in recent nanoindentation experiments.17,18,32,33 Parts a and b of Figure 8 show the top and 3D views of the nanoindentation test with the diamond tip and the rectangle phosphorene substrate, respectively. The tip has a radius of 20 nm, and its height is kept at 10 nm. The equivalent radius (R) of the rectangular phosphorene sheet is calculated to be ∼58 nm. The nanoindentation simulation is carried out at the loading speed of 0.5 Å/ps. The normal load vs indentation depth curves as a function of tip radius are shown in Figure 9. It has been reported that when r/R > 0.1, the tip radius has a significant influence on the load−indentation depth curve.34,35 Our results reveal that increasing the tip radius does not change
Figure 10. Sequence of snapshots capturing the deformation process of phosphorene with the indenter tip radius of 20 nm at different indentation depths, as seen from top view. The indenter tip is not shown. Atoms are colored according to their von Mises stresses. D
DOI: 10.1021/acs.jpcc.6b13071 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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the mechanical properties of phosphorene sheet. Figure 13 shows a sequence of snapshots capturing crack initiation and
area increases and the stress is more uniform in the middle of the phosphorene sheet, so that the failure load increases and the critical indentation depth for the phosphorene failure also becomes greater. This is consistent with previous MD simulations on graphene by nanoindentation.22,34 Because of low formation energies, it is very easy to create atomic defects (such as vacancies and other point defects) in phosphorene during its fabrication process.36 Therefore, it is very important and necessary to investigate the effect of defect concentration on the failure mechanism of phosphorene. In our previous studies on phosphorene under tensile loading, it is found that atomic vacancies significantly degrade the mechanical properties of phosphorene.36 In the present work, we further investigate the effect of defect concentration on the deformation and failure mechanism of phosphorene by nanoindentation. Figure 11 shows the bottom view of the
Figure 13. Sequence of snapshots capturing crack initiation and propagation in phosphorene substrate with defect concentration of 4% at different indentation depths, as seen from bottom view.
propagation in phosphorene substrate. The local stress concentration is clearly observed especially in the defect regions located at the contact area. Upon further indentation, a crack initiates from one of the defects located at the contact area, and then propagates to the neighboring defects. Our MD simulation results in Figures 12 and 13 clearly show that the vacancy-induced stress concentration causes crack formation at the contact area, and therefore significantly degrades the mechanical properties of phosphorene.
Figure 11. Bottom view of the nanoindentation test with 4% defect concentration at the phosphorene substrate. The close-up view clearly shows the randomly distributed monovacancies at phosphorene substrate.
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CONCLUSIONS In conclusion, we have performed systemic MD simulations to investigate the deformation and failure mechanism of phosphorene by nanoindentation with focus on the effects of loading speed, tip size, and defect concentration. From the normal load vs indentation depth curve, our simulations reveal three different regimes of deformation behaviors. The bump behavior in the first regime caused by the tip wrapped by the soft phosphorene sheet is different from that in the graphene and other 2D materials under indentation as well as tensile loading. Our simulations further reveal that the number of C−P pairs with repulsive force across the contact interface correlates well with the normal load. In addition, the loading speed, tip size, and defect concentration are found to have significant influences on the failure load and the failure mechanism. The failure mechanism changes with increasing loading speed from 0.5 to 2.0 Å/ps, while the failure load remains unchanged. In contrast, increasing the tip radius from 10 to 20 nm does not change the failure mechanism, but the failure load increases. Furthermore, the effect of defect on the deformation behavior of phosphorene is discussed, with results suggesting that the defect does not alter the failure mechanism but significantly degrades the failure load of phosphorene. The crack is observed to nucleate from the defect located at the contact area and then propagates to the neighboring defects, causing the material failure. It is found that our simulations results of nanoindentation in phosphorene are in good agreement with observations on phosphorene under tensile loading. Our simulations provide significant insights into atomic-scale understanding of the deformation and failure mechanisms of phosphorene by nanoindentation.
nanoindentation test with 4% defect concentration at the phosphorene substrate. The close-up view clearly shows the randomly distributed monovacancies at phosphorene substrate. Figure 12 depicts the normal load vs indentation depth curves
Figure 12. Normal load vs indentation depth curves as a function of defect concentration ranging from 0% to 4%.
as a function of defect concentration ranging from 0% to 4%. Three different regimes of deformation behaviors also can be identified from the curves of normal load vs indentation depth, indicating that monovacancies do not change the failure mechanism of phosphorene. However, it is found that the maximum load is decreased by ∼30% even though the defect concentration is just 0.5%. With increasing defect concatenation, the failure load continues to decrease. Our findings are essentially consistent with recent MD simulations on phosphorene under tensile loading,36 which demonstrates that atomic vacancies may cause a significant degradation of E
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AUTHOR INFORMATION
Corresponding Authors
*(Q.-X.P.) E-mail:
[email protected]. *(Q.W.) E-mail:
[email protected]. ORCID
Qing-Xiang Pei: 0000-0001-8711-2854 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful for the support from the National Natural Science Foundation of China through Grant Nos. 11402189, 11372295, and 11372236. Z.-D.S. and Q.W. would also like to acknowledge the support from the key subject “Computational Solid Mechanics” of the China Academy of Engineering Physics. This work was partially supported by a grant from the Science and Engineering Research Council, A*STAR, Singapore (152-70-00017).
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