Journal of Statistical Physics

, Volume 145, Issue 4, pp 812–830 | Cite as

Combining Rare Events Techniques: Phase Change in Si Nanoparticles

  • Sergio Orlandini
  • Simone Meloni
  • Giovanni Ciccotti
Article

Abstract

We describe a combined Restrained MD/Parallel Tempering approach to study the difference in free energy as a function of a set of collective variables between two states in presence of metastabilities in the manifold orthogonal to the one spanned by the chosen collective variables. We illustrate the method by an extended study of the relative stability of the amorphous vs crystalline Si nanoparticles embedded in a-SiO2 of size ranging between 0.8 and 1.8 nm as a function of temperature [S. Orlandini, S. Meloni, and L. Colombo in Phys. Rev. B 83:235303, 2011]. The results show that the method permits to get over the hidden metastabilities. Finally, we try to identify the missing collective variables from the Restrained MD/Parallel Tempering trajectories and analyze whether the collective variable used to control the amorphous-to-crystalline transition is adequate to describe the mechanism of crystallization of some of the nanoparticles considered.

Keywords

Rare events Restrained MD Parallel Tempering Si nanoparticles Order-disorder phase transition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Maragliano, L., Vanden-Eijnden, E.: Chem. Phys. Lett. 426, 168 (2006) ADSCrossRefGoogle Scholar
  2. 2.
    Ciccotti, G., Meloni, S.: Phys. Chem. Chem. Phys. 13, 5952 (2011) CrossRefGoogle Scholar
  3. 3.
    Abrams, J.B., Tuckerman, M.E.: J. Phys. Chem. B 112, 15742 (2008) CrossRefGoogle Scholar
  4. 4.
    Laio, A., Parrinello, M.: Proc. Natl. Acad. Sci. USA 99, 12562 (2002) ADSCrossRefGoogle Scholar
  5. 5.
    Iannuzzi, M., Laio, A., Parrinello, M.: Phys. Rev. Lett. 90, 238302 (2003) ADSCrossRefGoogle Scholar
  6. 6.
    Tan, P.-N., Steinbach, M., Kumar, V.: Introduction to Data Mining. Addison-Wesley, Reading (2006). Chapter: Cluster analysis: basic concepts and algorithms Google Scholar
  7. 7.
    Daura, X., Gademann, K., Jaun, B., Seebach, D., van Gunsteren, W.F., Mark, A.E.: Angew. Chem., Int. Ed. Engl. 38, 236 (1999) CrossRefGoogle Scholar
  8. 8.
    Carter, E.A., Ciccotti, G., Hynes, J.T., Kapral, R.: Chem. Phys. Lett. 156, 472 (1989) ADSCrossRefGoogle Scholar
  9. 9.
    Swendsen, R.H., Wang, J.S.: Phys. Rev. Lett. 57, 2607 (1986) MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Geyer, C.J.: In: Computing Science and Statistics Proceedings of the 23rd Symposium on the Interface. p. 156. Am. Statist. Assoc., New York (1991) Google Scholar
  11. 11.
    Marinari, E., Parisi, G.: Europhys. Lett. 19, 451 (1992) ADSCrossRefGoogle Scholar
  12. 12.
    Sugita, Y., Okamoto, Y.: Chem. Phys. Lett. 314, 141 (1999) ADSCrossRefGoogle Scholar
  13. 13.
    Earl, D.J., Deem, M.W.: Phys. Chem. Chem. Phys. 7, 3910 (2005) CrossRefGoogle Scholar
  14. 14.
    Faller, R., Yan, Q., de Pablo, J.J.: J. Chem. Phys. 116, 5419 (2002) ADSCrossRefGoogle Scholar
  15. 15.
    Coluzza, I., Muller, H., Frenkel, D.: Phys. Rev. E 68, 1 (2003) CrossRefGoogle Scholar
  16. 16.
    Coluzza, I., Frenkel, D.: ChemPhysChem 6, 1779 (2005) CrossRefGoogle Scholar
  17. 17.
    Rick, S.W.: J. Chem. Theory Comput. 2(4), 939–946 (2006) MathSciNetCrossRefGoogle Scholar
  18. 18.
    Woods, C.J., Essex, J.W., King, M.: J. Phys. Chem. B 107, 13703 (2003) CrossRefGoogle Scholar
  19. 19.
    Kirkwood, J.G.: J. Chem. Phys. 3, 300 (1935) ADSCrossRefGoogle Scholar
  20. 20.
    Bussi, G., Gervasio, F.L., Laio, A., Parrinello, M.: J. Am. Chem. Soc. 128, 13435 (2006) CrossRefGoogle Scholar
  21. 21.
    Orlandini, S., Meloni, S., Colombo, L.: Phys. Rev. B 83, 235303 (2011) ADSCrossRefGoogle Scholar
  22. 22.
    Crespo, Y., Marinelli, F., Pietrucci, F., Laio, A.: Phys. Rev. E 81, 1 (2010) CrossRefGoogle Scholar
  23. 23.
    Kumar, S., Rosenberg, J.M., Bouzida, D., Swendsen, R.H., Kollman, P.A.: J. Comput. Chem. 13, 1011 (1992) CrossRefGoogle Scholar
  24. 24.
    Steinhardt, P.J., Nelson, D.R., Ronchetti, M.: Phys. Rev. B 28, 784 (1983) ADSCrossRefGoogle Scholar
  25. 25.
    Meloni, S., Rosati, M., Federico, A., Ferraro, L., Mattoni, A., Colombo, L.: Comput. Phys. Commun. 169, 462 (2005) ADSCrossRefGoogle Scholar
  26. 26.
    Meloni, S., Rosati, M., Colombo, L.: J. Chem. Phys. 126, 121102 (2007) ADSCrossRefGoogle Scholar
  27. 27.
    Billeter, S.R., Curioni, A., Fischer, D., Andreoni, W.: Phys. Rev. B 73, 155329 (2006); ADSCrossRefGoogle Scholar
  28. 28.
    Billeter, S.R., Curioni, A., Fischer, D., Andreoni, W.: Phys. Rev. B 79, 169904(E) (2009); ADSCrossRefGoogle Scholar
  29. 29.
    Fischer, D., Curioni, A., Billeter, S., Andreoni, W.: Appl. Phys. Lett. 88, 012101 (2006) ADSCrossRefGoogle Scholar
  30. 30.
    Ippolito, M., Meloni, S., Colombo, L.: Appl. Phys. Lett. 93, 153109 (2008) ADSCrossRefGoogle Scholar
  31. 31.
    Orlandini, S., Meloni, S., Ippolito, M., Colombo, L.: Phys. Rev. B 81, 014203 (2010) ADSCrossRefGoogle Scholar
  32. 32.
    Tuma, C., Curioni, A.: Appl. Phys. Lett. 96, 193106 (2010) ADSCrossRefGoogle Scholar
  33. 33.
    Daldosso, N., Luppi, M., Ossicini, S., Degoli, E., Magri, R., Dalba, G., Fornasini, P., Grisenti, R., Rocca, F., Pavesi, L., Boninelli, S., Priolo, F., Spinella, C., Iacona, F.: Phys. Rev. B 68, 085327 (2003) ADSCrossRefGoogle Scholar
  34. 34.
    Wakayama, Y., Inokuma, T., Hasegawa, S.: J. Cryst. Growth 183, 124 (1998) ADSCrossRefGoogle Scholar
  35. 35.
    Inokuma, T., Wakayama, Y., Muramoto, T., Aoki, R., Kurata, Y., Hasegawa, S.: J. Appl. Phys. 83, 2228 (1998) ADSCrossRefGoogle Scholar
  36. 36.
    Hadjisavvas, G., Kelires, P.C.: Phys. Rev. Lett. 93, 226104 (2004) ADSCrossRefGoogle Scholar
  37. 37.
    Iacona, F., Bongiorno, C., Spinella, C., Boninelli, S., Priolo, F.: J. Appl. Phys. 95, 3723 (2004) ADSCrossRefGoogle Scholar
  38. 38.
    Stenger, I., Gallas, B., Siozade, L.: Kao, C.-C., Chenot, S., Fisson, S., Vuye, G., Rivory, J.: J. Appl. Phys. 103, 114303 (2008) ADSCrossRefGoogle Scholar
  39. 39.
    Wang, Y.Q., Smirani, R., Ross, G.G.: J. Cryst. Growth 294, 486 (2006) ADSCrossRefGoogle Scholar
  40. 40.
    Boninelli, S., Iacona, F., Franzó, G., Bongiorno, C., Spinella, C., Priolo, F.: J. Phys., Condens. Matter 19, 225003 (2007) ADSCrossRefGoogle Scholar
  41. 41.
    Fischer, D., Curioni, A., Billeter, S., Andreoni, W.: Appl. Phys. Lett. 88, 12101 (2006) ADSCrossRefGoogle Scholar
  42. 42.
    Hadjisavvas, G., Kelires, P.C.: Phys. Rev. Lett. 93, 226104 (2004) ADSCrossRefGoogle Scholar
  43. 43.
    Kelton, K.F., Greer, A.L.: Nucleation in Condensed Matter. Elsevier, Amsterdam (2010) Google Scholar
  44. 44.
    ten Wolde, R.P., Ruiz-Montero, M.J., Frenkel, D.: J. Chem. Phys. 104, 9932 (1996) ADSCrossRefGoogle Scholar
  45. 45.
    Moroni, D., ten Wolde, P.R., Bolhuis, P.G.: Phys. Rev. Lett. 94, 235703 (2005) ADSCrossRefGoogle Scholar
  46. 46.
    Knuth, D.E.: The Art of Computer Programming, vol. 1. Addison-Wesley, Reading (1997) Google Scholar
  47. 47.
    Vanden-Eijnden, E.: Transition path theory. In: Ferrario, M., Ciccotti, G., Binder, K. (eds.) Computer Simulations in Condensed Matter: From Materials to Chemical Biology, vol. 5. Springer, Berlin (2006) Google Scholar
  48. 48.
    Maragliano, L., Fischer, A., Vanden-Eijnden, E., Ciccotti, G.: J. Chem. Phys. 125, 24106 (2006) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Sergio Orlandini
    • 2
    • 3
  • Simone Meloni
    • 1
    • 2
  • Giovanni Ciccotti
    • 1
    • 4
  1. 1.School of PhysicsUniversity College DublinDublin 4Ireland
  2. 2.Consorzio Interuniversitario per le Applicazioni di Supercalcolo Per Università e Ricerca (CASPUR)RomeItaly
  3. 3.Dipartimento di ChimicaUniversità “Sapienza”RomeItaly
  4. 4.Dipartimento di Fisica and CNISMUniversità “Sapienza”RomeItaly

Personalised recommendations