Abstract
Elastic models of defects in two-dimensional (2D) crystals are presented in terms of continuum mechanics. The models are based on the classification of defects, which is founded on the dimensionality of the specification region of their self-distortions, i.e., lattice distortions associated with the formation of defects. The elastic field of an infinitesimal dislocation loop in a film is calculated for the first time. The fields of the center of dilatation, dislocation, disclination, and circular inclusion in planar 2D elastic media, namely, nanofilms and graphenes, are considered. Elastic fields of defects in 2D and 3D crystals are compared.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. USA 102, 10451 (2005).
M. I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, New York, 2012).
H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, Nature (London) 318, 162 (1985).
J. Baggott, Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene (Oxford University Press, Oxford, 1995).
W. F. Harris and L. E. Scriven, Nature (London) 228, 827 (1970).
F. R. N. Nabarro and W. F. Harris, Nature (London) 232, 423 (1971).
M. Kleman, Points, Lines and Walls (Wiley, New York, 1983).
M. Kleman and J. Friedel, Rev Mod. Phys. 80, 61 (2008).
H. Träuble and U. Essmann, J. Appl. Phys. 39(9), 4052 (1968).
A. L. Kolesnikova and A. E. Romanov, Phys. Solid State 40(6), 1075 (1998).
B. I. Yakobson and F. Ding, ACS Nano 5, 1569 (2011).
J. Zhang and J. Zhao, Carbon 55, 151 (2013).
O. V. Yazyev, Solid State Commun. 152, 1431 (2012).
L. Tapaszto, P. Nemes-Incze, G. Dobrik, K. Yoo Jae, C. Hwang, and L. P. Biro, Appl. Phys. Lett. 100, 053114 (2012).
A. E. Romanov, A. L. Kolesnikova, T. S. Orlova, I. Hussainova, V. E. Bougrov, and R. Z. Valiev, Carbon (2014) (in press).
T. Mura, Micromechanics of Defects in Solids (Martinus Nijhoff, Dordrecht, 1987).
R. De Vit, Continuum Theory of Disclinations (Mir, Moscow, 1977) [in Russian].
J. D. Eshelby, Proc. R. Soc. London, Ser. A 241, 376 (1957).
A. L. Kolesnikova, R. M. Soroka, and A. E. Romanov, Mater. Phys. Mech. 17(1), 71 (2013).
F. Kroupa, in Theory of Crystal Defects: Proceedings of the Summer School (Academia, Prague, 1966), p. 276.
C. Somigliana, Atti. Accad. Naz. Lincei, Cl. Sci. Fis., Mat. Nad., Rend. 24, 655 (1915).
A. L. Kolesnikova and A. E. Romanov, Preprint No. 1019, FTI (Ioffe Physical-Technical Institute, Academy of Sciences of the USSR, Leningrad, 1986).
A. L. Kolesnikova and A. E. Romanov, Phys. Solid State 45(9), 1706 (2003).
V. Volterra, Ann. Sci. Ec. Norm. Super. 24(4), 401 (1907).
J. P. Hirth and J. Lothe, Theory of Dislocations (Wiley, New York, 1982).
T. Mura, in Advanced in Materials Research, Ed. by H. Herman (Interscience, New York, 1968), Vol. 3, p. 1.
A. L. Kolesnikova and A. E. Romanov, Sov. Tech. Phys. Lett. 13(6), 272 (1987).
A. L. Kolesnikova and A. E. Romanov, Dislocation Models of Inclusions (1990) (unpublished).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.L. Kolesnikova, T.S. Orlova, I. Hussainova, A.E. Romanov, 2014, published in Fizika Tverdogo Tela, 2014, Vol. 56, No. 12, pp. 2480–2485.
Rights and permissions
About this article
Cite this article
Kolesnikova, A.L., Orlova, T.S., Hussainova, I. et al. Elastic models of defects in two-dimensional crystals. Phys. Solid State 56, 2573–2579 (2014). https://doi.org/10.1134/S1063783414120166
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063783414120166