Physics of the Solid State

, Volume 56, Issue 4, pp 723–730 | Cite as

Misfit dislocation loops in composite core-shell nanoparticles

  • M. Yu. Gutkin
  • A. L. Kolesnikova
  • S. A. Krasnitsky
  • A. E. Romanov
Mechanical Properties, Physics of Strength, and Plasticity


The critical conditions have been calculated for the generation of circular prismatic loops of misfit dislocations at the interfaces in spherically symmetric composite core-shell nanoparticles. It has been shown that the formation of these loops becomes energetically favorable if the misfit parameter exceeds a critical value, which is determined by the geometry of the system. The most preferred position of the dislocation loop is in the equatorial plane of the nanoparticle. For a given radius of the nanoparticle, there is a minimum value of the critical misfit parameter below which the generation of a misfit dislocation is energetically unfavorable for any ratio of the core and shell radii. For a misfit parameter exceeding the minimum critical value, there are two critical values of the reduced radius of the particle core in the interval between which the generation of a dislocation loop is energetically favorable. This interval increases with increasing misfit parameter for a fixed particle size and decreases with decreasing particle size for a fixed misfit parameter.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. W. Cao and U. Banin, J. Am. Chem. Soc. 122, 9692 (2000).CrossRefGoogle Scholar
  2. 2.
    W. Schartl, Nanoscale 2(6), 829 (2010).ADSCrossRefGoogle Scholar
  3. 3.
    C. De Mello Donega, Chem. Soc. Rev. 40, 1512 (2011).CrossRefGoogle Scholar
  4. 4.
    D. V. Talapin, Jong-Soo Lee, M. V. Kovalenko, and E. V. Shevchenko, Chem. Rev. 110, 389 (2010).CrossRefGoogle Scholar
  5. 5.
    L. Zhang, W. F. Dong, and H. B. Sun, Nanoscale 5 (17), 7664 (2013).Google Scholar
  6. 6.
    M. D. Brown, M. M. Lee, H. J. Snaith, T. Suteewong, U. Wiesner, R. S. S. Kumar, V. D’Innocenzo, and A. Petrozza, Nano Lett. 11, 438 (2011).ADSCrossRefGoogle Scholar
  7. 7.
    S. Deng, K. C. Pingali, and D. A. Rockstraw, IEEE Sensors J. 8, 730 (2008).CrossRefGoogle Scholar
  8. 8.
    S. Wei, Q. Wang, J. Zhu, L. Sun, H. Lin, and Z. Guo, Nanoscale 3, 4474 (2011).ADSCrossRefGoogle Scholar
  9. 9.
    X. Teng, D. Black, N. J. Watkins, Y. Gao, and H. Yang, Nano Lett. 3, 261 (2003).ADSCrossRefGoogle Scholar
  10. 10.
    K. Wang, W. Tan, and X. He, in Proceedings of the 27th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE-EMBS-2005), Shanghai, China, September 1–4, 2005 (Shanghai, 2005), p. 717.Google Scholar
  11. 11.
    T. Mitsudome and K. Kaneda, ChemCatChem 5, 1681 (2013).CrossRefGoogle Scholar
  12. 12.
    L. B. Freund and S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University Press, Cambridge, 2003).Google Scholar
  13. 13.
    M. Yu. Gutkin, Strength and Plasticity of Nanocomposites (St. Petersburg State Polytechnical University, St. Petersburg, 2011) [in Russian].Google Scholar
  14. 14.
    L. I. Trusov, M. Yu. Tanakov, V. G. Gryaznov, A. M. Kaprelov, and A. E. Romanov, J. Cryst. Growth 114(1–2), 133 (1991).ADSCrossRefGoogle Scholar
  15. 15.
    V. Vitek, G. Gutekunst, J. Mayer, and M. Ruhle, Philos. Mag. A 71(6), 1219 (1995).ADSCrossRefGoogle Scholar
  16. 16.
    R. Popovitz-Biro, A. Kretinin, P. Von Huth, and H. Shtrikman, Cryst. Growth Des. 11, 3858 (2011).CrossRefGoogle Scholar
  17. 17.
    K. L. Kavanagh, I. Saveliev, M. Blumin, G. Swadener, and H. E. Ruda, J. Appl. Phys. 111, 044301 (2012).ADSCrossRefGoogle Scholar
  18. 18.
    M. Yu. Gutkin, Int. J. Eng. Sci. 61, 59 (2012).CrossRefGoogle Scholar
  19. 19.
    X. Chen, Y. Lou, A. C. Samia, and C. Burda, Nano Lett. 3, 799 (2003).ADSCrossRefGoogle Scholar
  20. 20.
    Y. Ding, F. Fan, Z. Tian, and Z. L. Wang, J. Am. Chem. Soc. 132, 12480 (2010).CrossRefGoogle Scholar
  21. 21.
    N. Bhattarai, G. Casillas, A. Ponce, and M. Jose-Yacaman, Surf. Sci. 609, 161 (2013).ADSCrossRefGoogle Scholar
  22. 22.
    Y. Ding, X. Sun, Z. L. Wang, and S. Sun, Appl. Phys. Lett. 100(11), 111603 (2012).ADSCrossRefGoogle Scholar
  23. 23.
    J. W. Matthews, in Dislocations in Solids, Ed. by F. R. N. Nabarro (North-Holland, Amsterdam, The Netherlands, 1979), Vol. 2, p. 461.Google Scholar
  24. 24.
    R. Bean, D. J. Dunstan, and P. J. Goodhew, Adv. Phys. 45, 87 (1996).ADSCrossRefGoogle Scholar
  25. 25.
    J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974).ADSCrossRefGoogle Scholar
  26. 26.
    M. Yu. Gutkin and A. E. Romanov, Phys. Status Solidi A 129, 117 (1992).ADSCrossRefGoogle Scholar
  27. 27.
    K. E. Aifantis, A. L. Kolesnikova, and A. E. Romanov, Philos. Mag. 87, 4731 (2007).ADSCrossRefGoogle Scholar
  28. 28.
    A. L. Kolesnikova and A. E. Romanov, Philos. Mag. Lett. 84(8), 501 (2004).ADSCrossRefGoogle Scholar
  29. 29.
    A. L. Kolesnikova, M. Yu. Gutkin, S. A. Krasnitckii, and A. E. Romanov, Int. J. Solids Struct. 50, 1839 (2013).CrossRefGoogle Scholar
  30. 30.
    T. Mura, in Advances in Materials Research, Ed. by H. Herman (Interscience, New York, 1968), Vol. 3, p. 1.Google Scholar
  31. 31.
    J. Dundurs and N. J. Salamon, Phys. Status Solidi B 50, 125 (1972).ADSCrossRefGoogle Scholar
  32. 32.
    A. L. Kolesnikova and A. E. Romanov, Preprint No. 1019, FTI im. A. F. Ioffe AN SSSR (Ioffe Physical-Technical Institute, Academy of Sciences of the Soviet Union, Leningrad, 1986).Google Scholar
  33. 33.
    G. Eason, B. Noble, and I. N. Sneddon, Philos. Trans. R. Soc. 247, 529 (1955).ADSCrossRefMATHMathSciNetGoogle Scholar
  34. 34.
    J. Hirth and J. Lothe, Theory of Dislocations (McGraw-Hill, New York, 1967; Atomizdat, Moscow, 1972).Google Scholar
  35. 35.
    L. M. Dorogin, S. Vlassov, A. L. Kolesnikova, I. Kink, R. Löhmus, and A. E. Romanov, Phys. Status Solidi B 247(2), 288 (2010).ADSCrossRefGoogle Scholar
  36. 36.
    M. Yu. Gutkin, I. A. Ovid’ko, and A. G. Sheinerman, J. Phys.: Condens. Matter 12, 5391 (2000).ADSGoogle Scholar
  37. 37.
    A. Braun, K. M. Briggs, and P. Boni, J. Cryst. Growth 241, 231 (2002).ADSCrossRefGoogle Scholar
  38. 38.
    R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, Adv. Comput. Math. 5, 329 (1996).CrossRefMATHMathSciNetGoogle Scholar
  39. 39.
    C. Wang, D. van der Vliet, K. L. More, N. J. Zaluzec, S. Peng, S. Sun, H. Daimon, G. Wang, J. Greeley, J. Pearson, A. P. Paulikas, G. Karapetrov, D. Strmcnik, N. M. Markovic, and V. R. Stamenkovic, Nano Lett. 11, 919 (2011).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • M. Yu. Gutkin
    • 1
    • 2
    • 3
  • A. L. Kolesnikova
    • 1
  • S. A. Krasnitsky
    • 2
  • A. E. Romanov
    • 3
    • 4
    • 5
  1. 1.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia
  2. 2.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  3. 3.St. Petersburg National Research University of Information Technologies, Mechanics and OpticsSt. PetersburgRussia
  4. 4.Ioffe Physical-Technical InstituteRussian Academy of SciencesSt. PetersburgRussia
  5. 5.Togliatti State UniversityTogliatti, Samara oblastRussia

Personalised recommendations