Strain Fields around Dislocation Cores Studied by Analyzing Coordinates of Discrete Atoms

Abstract:

Dislocation core structures in Au and Cu crystals are investigated by means of quasicontinuum simulations combined with the embedded atom method potentials. A dislocation pair in a graphene sheet, which is observed by Warner et al. experimentally, is also analyzed in the present work. The strain fields around these dislocations in Au, Cu, and graphene crystals are calculated by analyzing the coordinates of discrete atoms, which is a strain tensor calculation method proposed by Zimmerman et al., and compared with theoretical predictions based on Foreman dislocation model. It is shown that the strain fields given by Zimmerman theory are completely suitable for describing the dislocation core structures of Au, Cu and graphene crystals. However, compared with the results of Au and Cu, the Zimmerman strain field in the vicinity of graphene dislocation core is a little less accurate, possibly due to the effect of lattice symmetry of graphene, which needs to be clarified in the future study.

• Periodical: Materials Science Forum (Volume 817)
• Pages: 712-718
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.817.712
• Online since: April 2015
• Authors: Yu Fei Shao*, Xin Yang, Jiu Hui Li, Xing Zhao
• Keywords: Atomistic Simulation, Dislocation Core, Graphene, Strain Field

References

[1] J. P. Hirth,J. Lothe, Theory of dislocation. 1982, New York: Wiley.

[2] Z. W. Shan, J. M. K. Wiezorek, E. A. Stach, D. M. Follstaedt, J. A. Knapp, S. X. Mao, Dislocation Dynamics in Nanocrystalline Nickel, Phys. Rev. Lett. 98 (2007) 095502.

DOI: 10.1103/physrevlett.98.095502

[3] L. H. Wang, X. D. Han, P. Liu, Y. H. Yue, Z. Zhang, E. Ma, In Situ Observation of Dislocation Behavior in Nanometer Grains, Phys. Rev. Lett. 105 (2010) 135501.

DOI: 10.1103/physrevlett.105.135501

[4] G. Lu, N. Kioussis, V. V. Bulatov, E. Kaxiras, Dislocation core properties of aluminum: a first-principles study, Mater. Sci. Eng. A. 309-310 (2001) 142-147.

DOI: 10.1016/s0921-5093(00)01711-1

[5] G. Schoeck, The core structure of dislocations: Peierls model vs. atomic simulation, Acta Mater. 54 (2006) 4865-4870.

DOI: 10.1016/j.actamat.2006.06.023

[6] C. Woodward, D. R. Trinkle, L. G. Hector Jr, D. L. Olmsted, Prediction of Dislocation Cores in Aluminum from Density Functional Theory, Phys. Rev. Lett. 100 (2008) 045507.

DOI: 10.1103/physrevlett.100.045507

[7] E. Clouet, L. Ventelon, F. Willaime, Dislocation Core Energies and Core Fields from First Principles, Phys. Rev. Lett. 102 (2009) 055502.

DOI: 10.1103/physrevlett.102.055502

[8] R. Wang, S. F. Wang, X. Z. Wu, Edge dislocation core structures in FCC metals determined from ab initio calculations combined with the improved Peierls–Nabarro equation, Phys. Scr. 83 (2011) 045604.

DOI: 10.1088/0031-8949/83/04/045604

[9] C. W. Zhao, Y. M. Xing, C. E. Zhou, P. C. Bai, Experimental examination of displacement and strain fields in an edge dislocation core, Acta Mater. 56 (2008) 2570-2575.

DOI: 10.1016/j.actamat.2008.01.045

[10] C. W. Zhao, Y. M. Xing, P. C. Bai, Experimental verification of Foreman dislocation model, Chin. Phys. B. 18 (2009) 2464-2468.

[11] R. Peierls, The size of a dislocation, Proc. Phys. Soc. 52 (1940) 34.

[12] F. R. N. Nabarro, Dislocations in a simple cubic lattice Proc. Phys. Soc. 59 (1947) 256.

DOI: 10.1088/0959-5309/59/2/309

[13] A. J. Foreman, M. A. Jaswon, J. K. Wood, Factors Controlling Dislocation Widths, Proc. Phys. Soc. A. 64 (1951) 156-163.

DOI: 10.1088/0370-1298/64/2/307

[14] J. Zimmermann, Continuum and atomistic modelling of dislocation nucleation at crystal surface ledges. 1999: (Ph.D. Thesis) (Stanford University).

[15] M. J. Buehler, H. G. Gao, Y. G. Huang, Atomistic and continuum studies of stress and strain fields near a rapidly propagating crack in a harmonic lattice, Theor. Appl. Fract. Mec.,. 41 (2004) 21-42.

DOI: 10.1016/j.tafmec.2003.11.022

[16] E. B. Tadmor, M. Ortiz, R. Phillips, Quasicontinuum analysis of defects in solids, Philos. Mag. A. 73 (1996) 1529-1563.

DOI: 10.1080/01418619608243000

[17] E. B. Tadmor, R. Phillips, M. Ortiz, Mixed atomistic and continuum models of deformation in Solids, Langmuir. 12 (1996) 4529-4534.

DOI: 10.1021/la9508912

[18] M. S. Daw,M. I. Baskes, Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B. 29 (1984) 6443-6453.

DOI: 10.1103/physrevb.29.6443

[19] R. E. Miller,E. B. Tadmor, The Quasicontinuum Method: Overview, applications and current directions, J. Computer-Aided Mater. Design. 9 (2002) 203-239.

[20] E. B. Tadmor,R. E. Miller, The theory and implementation of the quasicontinuum method, in Handbook of Materials Modeling, Part A - Methods, S. Yip, Editor. 2005, Springer-Verlag: New York. pp.663-682.

DOI: 10.1007/978-1-4020-3286-8_34

[21] Y. Mishin, M. J. Mehl, D. A. Papaconstantopoulos, A. F. Voter, J. D. Kress, Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations, Phys. Rev. B. 63 (2001) 224106.

DOI: 10.1103/physrevb.63.224106

[22] G. Grochola, S. P. Russo, I. K. Snook, On fitting a gold embedded atom method potential using the force matching method, J. Chem. Phys. 123 (2005) 204719.

DOI: 10.1063/1.2124667

[23] Y. F. Shao, X. Yang, J. H. Li, X. Zhao, Atomistic simulation study on the local strain fields around an extended edge dislocation in copper, Acta Physica Sinica. 63 (2014) 076103.

DOI: 10.7498/aps.63.076103

[24] J. H. Warner, E. R. Margine, M. Mukai, A. W. Robertson, F. Giustino, A. I. Kirkland, Dislocation-Driven Deformations in Graphene, Science. 337 (2012) 209-211.

DOI: 10.1126/science.1217529