Skip to main content
SpringerLink
Log in

Nanowire size-effect on the equilibrium positions of a dislocation dipole

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The stability of a dipole of edge dislocations embedded in a cylindrical nanowire of infinite length has been theoretically investigated from a Peach–Koehler (PK) force analysis. Calculating both gliding and climbing components of the PK force, the stable and unstable equilibrium positions of the dislocations have been characterized when the two dislocations, symmetrically displayed with respect to the nanowire center, have the same Burgers vector and when the Burgers vectors are of opposite signs. The size effect of the nanowire on the stability of the dislocations and their relative position to each other are finally discussed and compared to the case where the dislocations are embedded in an infinite-size solid.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Agiasofitou, E., Lazar, M.: Micromechanics of dislocations in solids: J-, M-, and L-integrals and their fundamental relations. Int. J. Eng. Sci. 114, 16–40 (2017)

    Article  MathSciNet  Google Scholar 

  2. Chen, K.X., Dai, Q., Lee, W., Kim, J.K., Schubert, E.F., Grandusky, J., Mendrick, M., Li, X., Smart, J.A.: Effect of dislocations on electrical and optical properties of n-type A\(\text{ l}_{0.34}\)G\(\text{ a}_{0.66}\)N. Appl. Phys. Lett. 93, 192108 (2008)

    Article  ADS  Google Scholar 

  3. Chernakov, A.P., Kolesnikova, A.L., Gutkin, M.Y., Romanov, A.E.: Periodic array of misfit dislocation loops and stress relaxation in core-shell nanowires. Int. J. Eng. Sci. 156, 103367 (2020)

    Article  MathSciNet  Google Scholar 

  4. Colin, J., Grilhé, J.: Dipole of misfit dislocations in axially symmetric structures. Philos. Mag. Lett. 82, 125–132 (2002)

    Article  ADS  CAS  Google Scholar 

  5. Cui, Y., Toku, Y., Kimura, Y., Ju, Y.: The deformation mechanism in cold-welded gold nanowires due to dislocation emission. Comput. Mater. Sci. 188, 110214 (2021)

    Article  CAS  Google Scholar 

  6. Deb Nath, S.K.: Elastic, elastic-plastic properties of Ag, Cu and Ni nanowires by the bending test using molecular dynamics simulations. Comput. Mater. Sci. 87, 138–144 (2014)

    Article  CAS  Google Scholar 

  7. Dundurs, J., Gangadhlaran, A.C.: Edge dislocation near an inclusion with a slipping interface. J. Mech. Phys. 17, 459–471 (1969)

    Article  ADS  Google Scholar 

  8. Dundurs, J., Mura, T.: Interaction between an edge dislocation and a circular inclusion. J. Mech. Phys. 12, 177–189 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  9. Dundurs, J., Sendeckyj, G.P.: Edge dislocation inside a circular inclusion. J. Mech. Phys. 13, 141–147 (1965)

    Article  ADS  Google Scholar 

  10. Fang, Q.H., Liu, Y.W., Jin, B., Wen, P.H.: Effect of interface stresses on the image force and stability of an edge dislocation inside a nanoscale cylindrical inclusion. Int. J. Solids Struct. 46, 1413–1422 (2009)

    Article  Google Scholar 

  11. Fang, Q.H., Liu, Y.W., Wen, P.H.: Dipole of edge misfit dislocations and critical radius conditions for buried strained cylindrical inhomogeneity. Philos. Mag. 89(20), 1585–1595 (2009)

    Article  ADS  CAS  Google Scholar 

  12. Freund, L., Suresh, S.: Thin Film Materials. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  13. Giaremis, S., Komninou, P., Belabbas, I., J, C., Kioseoglou, J.: Structural and electronic properties of a-edge dislocations along \(<\)1–100\(>\) in GaN. J. Appl. Phys. 123, 244301 (2018)

  14. Gutkin, M.Y., Ovid’ko, I.A., Sheinerman, A.G.: Misfit dislocations in wire composite solids. J. Phys. Condens. Matter. 12, 5391–5401 (2000)

    Article  ADS  CAS  Google Scholar 

  15. Gutkin, M.Y., Rezazadeh Kalehbasti, S., Shodja, H.M.: Surface/interface effects on elastic behavior of an edge dislocation in the shell of a core-shell nanowire. Eur. J. Mech. A/Solids 41, 86–100 (2013)

    Article  ADS  Google Scholar 

  16. Gutkin, M.Y., Romanov, A.E.: On the stand-off positions of misfit dislocations. Phys. Status Solidi (a) 144, 39–57 (1994)

    Article  ADS  CAS  Google Scholar 

  17. Hirth, J.P., Lothe, J.: Theory of Dislocations. John Wiley Sons, Interscience Publication, New-York, USA (1982)

    Google Scholar 

  18. Hou, Z.Y., Li, C., Liu, L.X., Gao, Q.H., Wang, J.G., Liu, R.S., Tian, Z.A., Dong, K.J.: Three-dimensional topological structures and formation processes of dislocations in Au nanowire under tension loading. Comput. Mater. Sci. 197, 110639 (2021)

    Article  CAS  Google Scholar 

  19. Hull, D.: Introduction to dislocations, 2nd edn. International series on materials science and technology, Vol. 16, Pergamon Press Inc., New-York, USA (1975)

  20. Jung, D., Herrick, R., Norman, J., Turnlund, K., Jan, C., Feng, K., Gossard, A.C., Bowers, J.E.: Impact of threading dislocation density on the lifetime of InAs quantum dot lasers on Si. Appl. Phys. Lett. 112(15), 153507 (2018)

    Article  ADS  Google Scholar 

  21. Kolesnikova, A.L., Chernakov, A.P., Gutkin, M.Y., Romanov, A.E.: Misfit strain induced out-of-interface prismatic dislocation loops in axially inhomogeneous hybrid nanowires. Extrem. Mech. Lett. 56, 101861 (2022)

    Article  Google Scholar 

  22. Krasnitckii, S.A., Smirnov, A.M., Gutkin, M.Y.: Axial misfit stress relaxation in core-shell nanowires with polyhedral cores through the nucleation of misfit prismatic dislocation loops. J. Mater. Sci. 55, 9198–9210 (2020)

    Article  ADS  CAS  Google Scholar 

  23. Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Pergamon Press Ltd., Oxford (1970)

    Google Scholar 

  24. Liang, Y., Nix, D.-W., Griffin, P.B., Plummer, D.: Critical thickness enhancement of epitaxial SiGe films grown on small structures. J. Appl. Phys. 97, 043519 (2005)

    Article  ADS  Google Scholar 

  25. Lubarda, V.A.: Image force on a straight dislocation emitted from a cylindrical void. Int. J. Solids Struct. 48, 648–660 (2011)

    Article  Google Scholar 

  26. Lubarda, V.A.: Dislocation burgers vector and the peach-koehler force: a review. J. Mater. Res. Technol. 8, 1550–1565 (2019)

    Article  Google Scholar 

  27. Luo, H., Li, J., Yang, G., Zhu, R., Zhang, Y., Wang, R., Yang, D., Pi, X.: Electronic and optical properties of threading dislocations in n-type 4H-SiC. Appl. Electron. Mater. 4, 1678–1683 (2022)

    Article  CAS  Google Scholar 

  28. Luo, H.A., Chen, Y.: An edge dislocation in a three-phase composite cylinder model. J. Appl. Mech. 58, 75–86 (1991)

    Article  ADS  Google Scholar 

  29. Ovid’ko, I.A., Sheinerman, A.G.: Misfit dislocation loops in composite nanowires. Philos. Mag. 84, 2103–2118 (2004)

    Article  ADS  Google Scholar 

  30. Ovid’ko, I.A., Sheinerman, A.G.: Misfit dislocation loops in cylindrical quantum dots. J. Phys. Condens. Matter. 16, 7225–7232 (2004)

    Article  ADS  Google Scholar 

  31. Peach, M., Koehler, J.S.: The forces exerted on dislocations and the stress fields produced by them. Phys. Rev. 80, 436–439 (1950)

    Article  ADS  MathSciNet  Google Scholar 

  32. Romanov, A.E., Kolesnikova, A.L., Gutkin, M.Y.: Internal stresses and structural defects in nanowires. Mech. Solids 57, 1987–2004 (2022)

    Article  ADS  Google Scholar 

  33. Sheinerman, A.G., Gutkin, M.Y.: Misfit disclinations and dislocation walls in a two-phase cylindrical composite. Phys. Status Solidi A 184, 485–505 (2001)

    Article  ADS  CAS  Google Scholar 

  34. Shi, B., Li, Q., Lau, K.M.: Self-organized InAs/InAlGaAs quantum dots as dislocation filters for InP films on \((001)\) Si. J. Cryst. Growth 464(4), 28–32 (2017)

    Article  ADS  CAS  Google Scholar 

  35. Shilkrot, L.E., Srolovitz, D.J.: Elastic analysis of finite stiffness bimaterial interfaces: application to dislocation-interface interactions. Acta Mater. 46, 3063–3075 (1998)

    Article  ADS  CAS  Google Scholar 

  36. Smirnov, A.M., Krasnitckii, S.A., Gutkin, M.Y.: Generation of misfit dislocations in a core-shell nanowire near the edge of prismatic core. Acta Mater. 186, 494–510 (2020)

    Article  ADS  CAS  Google Scholar 

  37. Smirnov, A.M., Krasnitckii, S.A., Rochas, S., Gutkin, M.Y.: Critical conditions of dislocation generation in core-shell nanowires: a review. Rev. Adv. Mater. Technol. 2, 19–43 (2020)

    Article  Google Scholar 

  38. Smirnov, A.M., Krasnitckii, S.A., Rochas, S.S., Gutkin, M.Y.: Critical conditions of dislocation generation in core-shell nanowires: a review. Rev. Adv. Mater. Technol. 2, 19–43 (2020)

    Article  Google Scholar 

  39. Termentzidis, K., Isaiev, M., Salnikova, A., Belabbas, I., Lacroix, D., Kioseoglou, J.: Impact of screw and edge dislocations on the thermal conductivity of individual nanowires and bulk GaN: a molecular dynamics study. Phys. Chem. Chem. Phys. 20, 5159–5172 (2018)

    Article  CAS  PubMed  Google Scholar 

  40. Timoshenko, S., Goodier, J.N.: Theory of Elasticity. Mc Graw-Hill Book Company Inc., New-York, USA (1952)

    Google Scholar 

  41. Weertman, J.: The Peach-Koehler equation for the force on a dislocation modified for hydrostatic pressure. Philos. Mag. 11, 1217–1223 (1965)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work pertains to the French Government program “Investissements d’Avenir” (EUR INTREE, reference ANR-18-EURE-0010).

Author information

Authors and Affiliations

  1. Institut Pprime, UPR 3346 CNRS, Université de Poitiers-ENSMA-CNRS, Poitiers, France

    Jérôme Colin

Authors
  1. Jérôme Colin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jérôme Colin.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Colin, J. Nanowire size-effect on the equilibrium positions of a dislocation dipole. Arch Appl Mech 94, 683–693 (2024). https://doi.org/10.1007/s00419-024-02545-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-024-02545-1

Keywords

Search

Navigation