1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
f
Molecular dynamics simulations of single-layer molybdenum disulphide (MoS2): Stillinger-Weber parametrization, mechanical properties, and thermal conductivity
Rent:
Rent this article for
Access full text Article
/content/aip/journal/jap/114/6/10.1063/1.4818414
1.
1. A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 (2007).
http://dx.doi.org/10.1038/nmat1849
2.
2. D. Li and R. B. Kaner, Science 320, 1170 (2008).
http://dx.doi.org/10.1126/science.1158180
3.
3. A. K. Geim, Science 324, 1530 (2009).
http://dx.doi.org/10.1126/science.1158877
4.
4. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
http://dx.doi.org/10.1103/RevModPhys.81.109
5.
5. C. N. R. Rao, A. K. Sood, K. S. Subrahmanyam, and A. Govindaraj, Angew. Chem., Int. Ed. 48, 7752 (2009).
http://dx.doi.org/10.1002/anie.200901678
6.
6. A. A. Balandin, Nature Mater. 10, 569 (2011).
http://dx.doi.org/10.1038/nmat3064
7.
7. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. 102, 10451 (2005).
http://dx.doi.org/10.1073/pnas.0502848102
8.
8. K. K. Kam and B. A. Parkinson, J. Phys. Chem. 86, 463 (1982).
http://dx.doi.org/10.1021/j100393a010
9.
9. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 105, 136805 (2010).
http://dx.doi.org/10.1103/PhysRevLett.105.136805
10.
10. V. M. Pereira and A. H. Castro Neto, Phys. Rev. Lett. 103, 046801 (2009).
http://dx.doi.org/10.1103/PhysRevLett.103.046801
11.
11. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature 438, 197 (2005).
http://dx.doi.org/10.1038/nature04233
12.
12. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Nat. Nanotechnol. 7, 699 (2012).
http://dx.doi.org/10.1038/nnano.2012.193
13.
13. M. Chhowalla, H. S. Shin, G. Eda, L. Li, K. P. Loh, and H. Zhang, Nat. Chem. 5, 263 (2013).
http://dx.doi.org/10.1038/nchem.1589
14.
14. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, Nat. Nanotechnol. 6, 147 (2011).
http://dx.doi.org/10.1038/nnano.2010.279
15.
15. P. Joensen, E. D. Crozier, N. Alberding, and R. F. Frindt, J. Phys. C 20, 4043 (1987).
http://dx.doi.org/10.1088/0022-3719/20/26/009
16.
16. S. Helveg, J. V. Lauritsen, E. Lgsgaard, I. Stensgaard, J. K. Nrskov, B. S. Clausen, H. Topsoe, and F. Besenbacher, Phys. Rev. Lett. 84, 951 (2000).
http://dx.doi.org/10.1103/PhysRevLett.84.951
17.
17. C. Lee, H. Yan, L. E. Brus, T. F. Heinz, J. Hone, and S. Ryu, ACS Nano 4, 26952700 (2010).
http://dx.doi.org/10.1021/nn1003937
18.
18. I. Popov, G. Seifert, and D. Tománek, Phys. Rev. Lett. 108, 156802 (2012).
http://dx.doi.org/10.1103/PhysRevLett.108.156802
19.
19. C. Ataca, H. Sahin, E. Aktürk, and S. Ciraci, J. Phys. Chem. C 115, 39343941 (2011).
http://dx.doi.org/10.1021/jp1115146
20.
20. A. Molina-Sánchez and L. Wirtz, Phys. Rev. B 84, 155413 (2011).
http://dx.doi.org/10.1103/PhysRevB.84.155413
21.
21. S. Sahoo, A. P. S. Gaur, M. Ahmadi, M. J.-F. Guinel, and R. S. Katiyar, J. Phys. Chem. C 117, 90429047 (2013); e-print: arxiv.org.
http://dx.doi.org/10.1021/jp402509w
22.
22. Z. Yin, H. Li, H. Li, L. Jiang, Y. Shi, Y. Sun, G. Lu, Q. Zhang, X. Chen, and H. Zhang, ACS Nano 6, 74 (2012).
http://dx.doi.org/10.1021/nn2024557
23.
23. K. Chang and W. Chen, J. Mater. Chem. 21, 17175 (2011).
http://dx.doi.org/10.1039/c1jm12942b
24.
24. C. Ataca and S. Ciraci, J. Phys. Chem. C 115, 13303 (2011).
http://dx.doi.org/10.1021/jp2000442
25.
25. B. Radisavljevic, M. B. Whitwick, and A. Kis, Appl. Phys. Lett. 101, 043103 (2012).
http://dx.doi.org/10.1063/1.4738986
26.
26. A. Castellanos-Gomez, M. Barkelid, A. M. Goossens, V. E. Calado, H. S. J. van der Zant, and G. A. Steele, Nano Lett. 12, 31873192 (2012).
http://dx.doi.org/10.1021/nl301164v
27.
27. J. N. Coleman, M. Lotya, A. ONeill, S. D. Bergin, P. J. King, U. Khan, K. Young, A. Gaucher, S. De, R. J. Smith, I. V. Shvets, S. K. Arora, G. Stanton, H.-Y. Kim, K. Lee, G. T. Kim, G. S. Duesberg, T. Hallam, J. J. Boland, J. J. Wang, J. F. Donegan, J. C. Grunlan, G. Moriarty, A. Shmeliov, R. J. Nicholls, J. M. Perkins, E. M. Grieveson, K. Theuwissen, D. W. McComb, P. D. Nellist, and V. Nicolosi, Science 331, 568 (2011).
http://dx.doi.org/10.1126/science.1194975
28.
28. K.-K. Liu, W. Zhang, Y.-H. Lee, Y.-C. Lin, M.-T. Chang, C.-Y. Su, C.-S. Chang, H. Li, Y. Shi, H. Zhang, C.-S. Lai, and L.-J. Li, Nano Lett. 12, 1538 (2012).
http://dx.doi.org/10.1021/nl2043612
29.
29. D. Le, D. Sun, W. Lu, L. Bartels, and T. S. Rahman, Phys. Rev. B 85, 075429 (2012).
http://dx.doi.org/10.1103/PhysRevB.85.075429
30.
30. J. Brivio, D. T. L. Alexander, and A. Kis, Nano Lett. 11, 51485153 (2011).
http://dx.doi.org/10.1021/nl2022288
31.
31. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).
http://dx.doi.org/10.1021/nl0731872
32.
32. D. L. Nika, E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, Phys. Rev. B 79, 155413 (2009).
http://dx.doi.org/10.1103/PhysRevB.79.155413
33.
33. D. L. Nika, S. Ghosh, E. P. Pokatilov, and A. A. Balandin, Appl. Phys. Lett. 94, 203103 (2009).
http://dx.doi.org/10.1063/1.3136860
34.
34. J.-W. Jiang, J.-S. Wang, and B. Li, Phys. Rev. B 79, 205418 (2009).
http://dx.doi.org/10.1103/PhysRevB.79.205418
35.
35. W. Huang, H. Da, and G. Liang, J. Appl. Phys. 113, 104304 (2013).
http://dx.doi.org/10.1063/1.4794363
36.
36. J.-W. Jiang, X.-Y. Zhuang, and T. Rabczuk, Sci. Rep. 3, 2209 (2013); e-print: arxiv.org.
37.
37. V. Varshney, S. S. Patnaik, C. Muratore, A. K. Roy, A. A. Voevodin, and B. L. Farmer, Comput. Mater. Sci. 48, 101 (2010).
http://dx.doi.org/10.1016/j.commatsci.2009.12.009
38.
38. N. Wakabayashi, H. G. Smith, and R. M. Nicklow, Phys. Rev. B 12, 659 (1975).
http://dx.doi.org/10.1103/PhysRevB.12.659
39.
39. S. Jimenez Sandoval, D. Yang, R. F. Frindt, and J. C. Irwin, Phys. Rev. B 44, 3955 (1991).
http://dx.doi.org/10.1103/PhysRevB.44.3955
40.
40. E. Dobardzic, I. Milosevic, B. Dakic, and M. Damnjanovic, Phys. Rev. B 74, 033403 (2006).
http://dx.doi.org/10.1103/PhysRevB.74.033403
41.
41. M. Damnjanovic, E. Dobardzic, I. Miloeevic, M. Virsek, and M. Remskar, Mater. Manuf. Processes 23, 579 (2008).
http://dx.doi.org/10.1080/10426910802160361
42.
42. T. Liang, S. R. Phillpot, and S. B. Sinnott, Phys. Rev. B 79, 245110 (2009).
http://dx.doi.org/10.1103/PhysRevB.79.245110
43.
43. D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, J. Phys.: Condens. Matter 14, 783 (2002).
http://dx.doi.org/10.1088/0953-8984/14/4/312
44.
44. J. A. Stewart and D. E. Spearot, Modell. Simul. Mater. Sci. Eng. 21, 045003 (2013).
http://dx.doi.org/10.1088/0965-0393/21/4/045003
45.
45. J. Tersoff, Phys. Rev. Lett. 56, 632 (1986).
http://dx.doi.org/10.1103/PhysRevLett.56.632
46.
46. J. Tersoff, Phys. Rev. B 37, 6991 (1988).
http://dx.doi.org/10.1103/PhysRevB.37.6991
47.
47. J. Tersoff, Phys. Rev. B 38, 9902 (1988).
http://dx.doi.org/10.1103/PhysRevB.38.9902
48.
48. J. Tersoff, Phys. Rev. Lett. 61, 2879 (1988).
http://dx.doi.org/10.1103/PhysRevLett.61.2879
49.
49. J. Tersoff, Physical Review B 39, 5566 (1989).
http://dx.doi.org/10.1103/PhysRevB.39.5566
50.
50. F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985).
http://dx.doi.org/10.1103/PhysRevB.31.5262
51.
51. P. Y. Yu, Fundamentals of Semiconductors (Springer, New York, 2010).
52.
52. J. D. Gale, J. Chem. Soc., Faraday Trans. 93, 629 (1997).
http://dx.doi.org/10.1039/a606455h
54.
54. F. F. Abraham and I. P. Batra, Surf. Sci. 209, L125 (1989).
http://dx.doi.org/10.1016/0039-6028(89)90053-8
55.
55. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, Oxford, 1995).
56.
56. A. Kokalj, Comput. Mater. Sci. 28, 155 (2003).
http://dx.doi.org/10.1016/S0927-0256(03)00104-6
57.
57. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, Oxford, 1954).
58.
58. R. C. Cooper, C. Lee, C. A. Marianetti, X. Wei, J. Hone, and J. W. Kysar, Phys. Rev. B 87, 035423 (2013).
http://dx.doi.org/10.1103/PhysRevB.87.035423
59.
59. R. C. Cooper, C. Lee, C. A. Marianetti, X. Wei, J. Hone, and J. W. Kysar, Phys. Rev. B 87, 079901 (2013).
http://dx.doi.org/10.1103/PhysRevB.87.079901
60.
60. S. Bertolazzi, J. Brivio, and A. Kis, ACS Nano 5, 9703 (2011).
http://dx.doi.org/10.1021/nn203879f
61.
61. S. Y. Kim and H. S. Park, Nano Lett. 9, 969 (2009).
http://dx.doi.org/10.1021/nl802853e
62.
62. J.-W. Jiang, J. Chen, J.-S. Wang, and B. Li, Phys. Rev. B 80, 052301 (2009).
http://dx.doi.org/10.1103/PhysRevB.80.052301
63.
63. C. D. Reddy, A. Ramasubramaniam, V. B. Shenoy, and Y. Zhang, Appl. Phys. Lett. 94, 101904 (2009).
http://dx.doi.org/10.1063/1.3094878
64.
64. J.-W. Jiang and J.-S. Wang, J. Appl. Phys. 111, 054314 (2012).
http://dx.doi.org/10.1063/1.3691958
65.
65. V. B. Shenoy, C. D. Reddy, A. Ramasubramaniam, and Y. W. Zhang, Phys. Rev. Lett. 101, 245501 (2008).
http://dx.doi.org/10.1103/PhysRevLett.101.245501
66.
66. H. Zhao, K. Min, and N. R. Aluru, Nano Lett. 9, 3012 (2009).
http://dx.doi.org/10.1021/nl901448z
67.
67. T. Ikeshoji and B. Hafskjold, Mol. Phys. 81, 251 (1994).
http://dx.doi.org/10.1080/00268979400100171
68.
68. X. Zhang, D. O. Hayward, and D. M. P. Mingos, Chem. Commun. 1999, 975.
69.
69. A. Stukowski, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).
http://dx.doi.org/10.1088/0965-0393/18/1/015012
70.
70. J.-W. Jiang, J.-S. Wang, and B. Li, J. Appl. Phys. 109, 014326 (2011).
http://dx.doi.org/10.1063/1.3531573
71.
71. N. Wei, L. Xu, H.-Q. Wang, and J.-C. Zheng, Nanotechnology 22, 105705 (2011).
http://dx.doi.org/10.1088/0957-4484/22/10/105705
72.
72.See supplementary material at http://dx.doi.org/10.1063/1.4818414 for the Stillinger-Weber potential script for LAMMPS and the modified source file for LAMMPS. [Supplementary Material]
http://aip.metastore.ingenta.com/content/aip/journal/jap/114/6/10.1063/1.4818414
Loading

Figures

Image of FIG. 1.

Click to view

FIG. 1.

Configuration of single-layer MoS. (a) Top view. The unit cell is highlighted by a parallelogram. (b) The viewing direction is slightly changed to display the intra-layer structure. (c) Each Mo atom is surrounded by six S atoms, while each S atom is connected to three FNN Mo neighbors. Springs illustrate the five interaction terms: two angle bending terms and three bond bending terms.

Image of FIG. 2.

Click to view

FIG. 2.

Phonon spectrum for SLMoS along the ΓM direction in the Brillouin zone. The results from the SW potential (blue lines) are fitted to the experiment data (gray pentagons) from Ref. . We note the energy gap around 250 cm and the crossover between the two highest-frequency spectra.

Image of FIG. 3.

Click to view

FIG. 3.

Eigenvectors for the nine phonon modes at the Γ point in SLMoS. (a) Three acoustic phonon modes. (b) Two intra-layer shearing modes, with the two S atomic layers undergoing out-of-phase shearing. (c) Another two intra-layer shearing modes, with the outer two S atomic layers undergoing in-phase shearing. (d) Two intra-layer breathing modes.

Image of FIG. 4.

Click to view

FIG. 4.

Phonon spectrum for bulk MoS along the ΓM direction in the Brillouin zone. The results from the SW potential (blue lines) are compared with the experiment data (gray pentagons) from Ref. . We note the agreement between the SW results and the experiment for the two low-frequency optical modes at the Γ point (inter-layer shearing and breathing modes).

Image of FIG. 5.

Click to view

FIG. 5.

The eigenvectors for the two inter-layer shearing modes and the inter-layer breathing mode. (a) and (b) are the two shearing modes with degenerate frequency. (c) The inter-layer breathing mode. Numbers are the frequency calculated from the SW potential, which is compared with the experiment data in parentheses.

Image of FIG. 6.

Click to view

FIG. 6.

Size-dependent Young's modulus for armchair and zigzag SLMoS nanoribbons (i.e., with free boundary conditions). The length of the SLMoS is 5 nm. Both curves converge to the same value of 229.0 GPa, which coincides with the Young's modulus of SLMoS with PBCs.

Image of FIG. 7.

Click to view

FIG. 7.

Temperature profile at 300 K for armchair SLMoS with PBC. The current ratio and the relaxation time of the heat bath is . The top left inset shows the linear fitting for the profile in , giving a temperature gradient . The right inset shows the linear fitting for the profile in , giving a temperature gradient . These two temperature gradients ( and ) are averaged in the calculation of the thermal conductivity using the Fourier law.

Image of FIG. 8.

Click to view

FIG. 8.

Temperature gradients from the calculation with different simulation parameters in armchair SLMoS with PBC. (a) The relaxation time τ has almost no effect on the simulation result. The current ratio . (b) The temperature gradient increases linearly with increasing current ratio in small α region. The increasing deviates obviously from linear for . The relaxation time .

Image of FIG. 9.

Click to view

FIG. 9.

Melting of armchair SLMoS with PBCs at 300 K with a large current ratio of . (a) The hot atom number to the total atom number ratio. Hot atoms are those with temperature above the melting point . The melting process begins around 0.16 ns and ends quickly. A large current ratio leads to high temperature in the hot temperature-controlled region, resulting in higher melting possibility. (b) Snap-shots for initial stages of the melting process. The melting starts from some atoms in the hot temperature-controlled region, and propagates to the two cold temperature-controlled regions. (c) Snap-shots for the final stages of the melting process. The SLMoS fractures, followed by evaporation of most of the atoms. Finally, the remaining atoms aggregate into a spherical nano-particle. The size of the resulting nano-particle is stabilized through exchanging surface atoms with the evaporated atoms. Color in (b) and (c) is with respect to the temperature.

Image of FIG. 10.

Click to view

FIG. 10.

Temperature dependence for the thermal conductivity. The chirality does not appear to significantly affect the thermal conductivity. The armchair MoS nanoribbon with free edges (FBCs) has a much lower thermal conductivity than that without free edges.

Image of FIG. 11.

Click to view

FIG. 11.

The melting process in the armchair SLMoS with free edges at 300 K. (a) The hot atom number to the total atom number ratio. The whole melting process is completed rapidly. (b) The melting process starts from the free edge, which possess some edge modes as shown in figure. The edge modes cause serve damage to the free edges, inducing the induction of the melting phenomenon. An obvious nano-particle is also generated as the outcome of the melting phenomenon.

Image of FIG. 12.

Click to view

FIG. 12.

One edge mode in the armchair SLMoS with free edges. Left and right are the top and side views, respectively.

Image of FIG. 13.

Click to view

FIG. 13.

Strain effect on the thermal conductivity at 300 K of the armchair SLMoS with PBC.

Tables

Generic image for table

Click to view

Table I.

The two-body (bond bending) SW potential parameters for GULP. The expression is . Energy parameters are in the unit of eV. Length parameters are in the unit of Å.

Generic image for table

Click to view

Table II.

Three-body (angle bending) SW potential parameters for GULP. The expression is . Energy parameters are in the unit of eV. Length parameters are in the unit of Å. Mo-S-S indicates the bending energy for the angle with Mo as the apex.

Generic image for table

Click to view

Table III.

SW potential parameters for LAMMPS. The two-body potential expression is . The three-body potential expression is . tol in the last column is a controlling parameter in LAMMPS. Note that the last two lines only contribute to the two-body (bond bending) interaction, where the three-body interactions are zero ( ). Hence, the other three-body parameters (γ and ) in the last two lines can be set arbitrarily. Energy parameters are in the unit of eV. Length parameters are in the unit of Å.

Generic image for table

Click to view

Table IV.

The Lennard-Jones potential parameters for the inter-layer coupling between two neighboring S atomic layers from Ref. . The expression is . The cut-off is 10.0 Å.

Loading

Article metrics loading...

/content/aip/journal/jap/114/6/10.1063/1.4818414
2013-08-12
2014-04-24

Abstract

We present a parameterization of the Stillinger-Weber potential to describe the interatomic interactions within single-layer MoS (SLMoS). The potential parameters are fitted to an experimentally obtained phonon spectrum, and the resulting empirical potential provides a good description for the energy gap and the crossover in the phonon spectrum. Using this potential, we perform classical molecular dynamics simulations to study chirality, size, and strain effects on the Young's modulus and the thermal conductivity of SLMoS. We demonstrate the importance of the free edges on the mechanical and thermal properties of SLMoS nanoribbons. Specifically, while edge effects are found to reduce the Young's modulus of SLMoS nanoribbons, the free edges also reduce the thermal stability of SLMoS nanoribbons, which may induce melting well below the bulk melt temperature. Finally, uniaxial strain is found to efficiently manipulate the thermal conductivity of infinite, periodic SLMoS.

Loading

Full text loading...

/deliver/fulltext/aip/journal/jap/114/6/1.4818414.html;jsessionid=2fh84srtku2ax.x-aip-live-03?itemId=/content/aip/journal/jap/114/6/10.1063/1.4818414&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/jap
true
true
This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Molecular dynamics simulations of single-layer molybdenum disulphide (MoS2): Stillinger-Weber parametrization, mechanical properties, and thermal conductivity
http://aip.metastore.ingenta.com/content/aip/journal/jap/114/6/10.1063/1.4818414
10.1063/1.4818414
SEARCH_EXPAND_ITEM