Skip to main content
Log in

Solidification of 2D simple monatomic system: molecular dynamics simulations

  • Regular Article - Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Solidification of the melted two-dimensional square lattice structure forming system is studied using molecular dynamics simulations. The initial model of 6400 atoms interacting via the square potential proposed by Rechstmann et al. (Phys. Rev. E, 73:011406, 2006) is cooled down from the melt at two different cooling rates. The research reveals the differences in the evolution of structure and thermodynamics of the system upon cooling from the melt. At the cooling rate of \({10}^{-7}\) per MD step, the phase transition temperature is found to be \({T}_{C}=0.50\), while it is \({T}_{g}=0.43\) at the cooling rate of \({10}^{-5}\) per MD step. Atomic mechanism of solidification of the system is analyzed via studying of the occurrence and growth of solid-like atoms upon cooling from the melt. Three characteristic temperatures of solidification are proposed. There is an evidence of the first-order phase transition behavior of the crystallization of the 2D melt.

Graphical abstract

T/TX dependence of the fraction of solid-like atoms (NS is the number of solid-like atoms, N is the total number of atoms in the system, T is temperature, TX is equal to Tg = 0.43 or TC = 0.50 depending on the cooling rate)

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability statement

The data supporting to this study’s findings cannot be openly available due to the rules of the funding foundation and are available from the corresponding author upon request.

References

  1. M. Rechtsman, F. Stillinger, S. Torquato, Phys. Rev. E 73, 011406 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  2. G. Algara-Siller, O. Lehtinen, F.C. Wang, R.R. Nair, U. Kaiser, H.A. Wu, I.V. Grigorieva, A.K. Geim, Nature 519, 443 (2015)

    Article  ADS  Google Scholar 

  3. J. Chen, G. Schusteritsch, C.J. Pickard, C.G. Salzmann, A. Michaelides, Phys. Rev. Lett. 116, 025501 (2016)

    Article  ADS  Google Scholar 

  4. H. Ohnishi, Y. Kondo, T. Kunio, Nature 395, 780 (1998)

    Article  ADS  Google Scholar 

  5. M.J. Lagos, F. Sato, D.S. Galvão, D. Ugarte, Phys. Rev. Lett. 106, 055501 (2011)

    Article  ADS  Google Scholar 

  6. J. Zhao, Q. Deng, A. Bachmatiuk, G. Sandeep, A. Popov, J. Eckert, M.H. Rümmeli, Science 343, 1228 (2014)

    Article  ADS  Google Scholar 

  7. Y. Shao, R. Pang, X. Shi, J. Phys. Chem. C. 119, 22954 (2015)

    Article  Google Scholar 

  8. V. van Hoang, N.T. Hieu, J. Phys. Chem. C 120, 18340 (2016)

    Article  Google Scholar 

  9. P. Wang, H. Wang, W. Yang, RSC Adv. 4, 17008 (2014)

    Article  ADS  Google Scholar 

  10. M.R. Thomsen, S.J. Brun, T.G. Pedersen, Phys. Rev. B 91, 125439 (2015)

    Article  ADS  Google Scholar 

  11. H. Zhang, Y.M. Dai, L.M. Liu, Comp. Mater. Sci. 101, 255 (2015)

    Article  Google Scholar 

  12. K. Takahashi, T. Hussain, L. Takahashi, J.D. Baran, Cryst. Growth Des. 16(3), 1746 (2016)

    Article  Google Scholar 

  13. A. Quandt, M.P. Teter, Phys. Rev. B 59(13), 8586 (1999)

    Article  ADS  Google Scholar 

  14. A. Jain, J.R. Errington, T.M. Truskett, Phys. Rev. X. 4, 031049 (2014)

    Google Scholar 

  15. T. Kawasaki, H. Tanaka, PNAS 107(32), 14036 (2010)

    Article  ADS  Google Scholar 

  16. P. Tan, N. Xu, L. Xu, Nat. Phys. 10, 73 (2013)

    Article  Google Scholar 

  17. E. Sanz, C. Valeriani, Nat. Mater. 14, 15 (2015)

    Article  ADS  Google Scholar 

  18. W. Qi, Y. Peng, Y. Han, R.K. Bowles, M. Dijkstra, Phys. Rev. Lett. 115, 185701 (2015)

    Article  ADS  Google Scholar 

  19. T.A. Weber, F.H. Stillinger, Phys. Rev. E 48, 4351 (1993)

    Article  ADS  Google Scholar 

  20. M. Engel, H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007)

    Article  ADS  Google Scholar 

  21. W. Humphrey, A. Dalke, K. Schulten, J. Mol. Graph. 14, 33 (1996)

    Article  Google Scholar 

  22. D.E. Dudalov, E.N. Tsiok, Y.D. Fomin, V.N. Ryzhov, J. Chem. Phys. 141, 18C522 (2014)

    Article  Google Scholar 

  23. V. van Hoang, V. Teboul, T. Odagaki, J. Phys. Chem. B 119, 15752 (2015)

    Article  Google Scholar 

  24. J.J. Gilvarry, Phys. Rev. 102(2), 308 (1956)

    Article  ADS  Google Scholar 

  25. F.H. Stillinger, T.A. Weber, Phys. Rev. B 22(8), 3790 (1980)

    Article  ADS  Google Scholar 

  26. R. Agrawal, D.A. Kofke, Mol. Phys. 85, 43 (1995)

    Article  ADS  Google Scholar 

  27. P.G. Bolhuis, D.A. Kofke, Phys. Rev. E 54(1), 634 (1996)

    Article  ADS  Google Scholar 

  28. D.A. Kofke, P.G. Bolhuis, Phys. Rev. E 59(1), 618 (1999)

    Article  ADS  Google Scholar 

  29. C. Chakravarty, J. Chem. Phys. 116, 8938 (2002)

    Article  ADS  Google Scholar 

  30. Z. Wang, A.M. Alsayed, A.G. Yodh, Y. Han, J. Chem. Phys. 132, 154501 (2010)

    Article  ADS  Google Scholar 

  31. P. Dillmann, G. Maret, P. Keim, J. Phys. Condens. Mat. 20, 404216 (2008)

    Article  Google Scholar 

  32. R. Ravinder, R. Kumar, M. Agarwal, N.M.A. Krishnan, Sci. Rep. 9, 4517 (2019)

    Article  ADS  Google Scholar 

  33. V.V. Hoang, T. Odagaki, J. Phys. Chem. B 115, 6946 (2011)

    Article  Google Scholar 

  34. S. Tang, M. Wu, S. Bai, D. Luo, J. Zhang, D. Wan, X. Li, J. Mater. Chem. C 10, 16116 (2022)

    Article  Google Scholar 

  35. S. Ono, Sci. Reports 10, 11810 (2020)

    ADS  Google Scholar 

  36. V.V. Hoang, T.N. Thanh-Thuy, N.H. Giang, T.Q. Dong, Comp. Mater. Sci. 181, 109730 (2020)

    Article  Google Scholar 

  37. K. Binder, S. Sengupta, P. Nielaba, J. Phys.: Condens. Matter 14, 2323 (2002)

    ADS  Google Scholar 

  38. K.J. Strandburg, Rev. Mod. Phys. 60, 161 (1988)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number VL2020-20-01.

Author information

Authors and Affiliations

Authors

Contributions

This article is written by NTN (PhD student) based on the idea and supervision of Prof. VVH.

Corresponding author

Correspondence to Nguyen To Nga.

Ethics declarations

Conflict of interest

The authors declare no competing financial interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nga, N.T., Van Hoang, V. Solidification of 2D simple monatomic system: molecular dynamics simulations. Eur. Phys. J. B 96, 82 (2023). https://doi.org/10.1140/epjb/s10051-023-00554-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-023-00554-7

Navigation