Abstract
Plasticity in nanocrystals is observed to be dominated by dislocation nucleation, as these volumes are typically too small to support a significant population of defects. Thus, it is imperative that accurate models of dislocation nucleation be developed to predict the strength of these novel structures. In this chapter, a set of multiscale models are introduced to address dislocation nucleation that spans both length- and time scales. Atomistic models are used to parameterize the activation energy associated with dislocation nucleation as a function of stress and/or strain. These results can be combined with transition state theory to predict dislocation nucleation with relative accuracy as a function of both temperature and time. Continuum models of dislocation nucleation can also be used, in conjunction with parameters from atomistic simulations, to extend the atomistic results to addition geometries, sizes, and materials. These models can then be integrated into mesoscale models of plasticity, such as dislocation dynamics, that are able to evolve the dislocation structures providing a complete picture of plasticity in these materials.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
S. Aubry, K. Kang, S. Ryu, W. Cai, Energy barrier for homogeneous nucleation: Comparing atomistic and continuum models. Scr. Mater. 64, 1043 (2011)
S. Brochard, P. Hirel, L. Pizzagalli, J. Godet, Elastic limit for surface step dislocation nucleation in face-centered cubic metals: temperature and step height dependence. Acta Mater. 58, 4182–4190 (2010)
A. Cao, E. Ma, Sample shape and temperature strongly influence the yield strength of metallic nanopillars. Acta Mater. 56 (17), 4816–4828 (2008)
A. Cao, Y. Wei, Atomistic simulations of the mechanical behavior of fivefold twinned nanowires. Phys. Rev. B 74, 214108 (2006)
J. Diao, K. Gall, M. Dunn, Surface-stress-induced phase transformation in metal nanowires. Nat. Mater. 2, 656–660 (2003)
J. Diao, K. Gall, M. Dunn, Surface stress driven reorientation of gold nanowires. Phys. Rev. B 70, 075413 (2004)
J. Diao, K. Gall, M. Dunn, Yield strength asymmetry in metal nanowires. Nano Lett. 4 (10), 1863–1867 (2004)
J. Diao, K. Gall, M. Dunn, J. Zimmerman, Atomistic simulations of the yielding of gold nanowires. Acta Mater. 54, 643–653 (2006)
R. Farraro, R.B. Mclellan, Temperature dependence of the young’s modulus and shear modulus of pure nickel, platinum, and molybdenum. Metall. Trans. A 8 (10), 1563–1565 (1977)
K. Gall, J. Diao, M. Dunn, The strength of gold nanowires. Nano Lett. 4 (12), 2431–2436 (2004)
J. Greer, J.D. Hosson, Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect. Prog. Mater. Sci. (2011). doi:10.1016/j.pmatsci.2011.01.005
J.R. Greer, W.C. Oliver, W.D. Nix, Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients. Acta Mater. 52, 1821–1830 (2005)
M.E. Gurtin, A.I. Murdoch, Surface stress in solids. Int. J. Solids Struct. 14 (6), 431–440 (1978)
P. Hänggi, P. Talkner, M. Borkovec, Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62 (2), 251 (1990)
S. Hara, S. Izumi, S. Sakai, Reaction pathway analysis for dislocation nucleation from a Ni surface step. J. Appl. Phys. 106, 093507 (2009)
K.G. Harold Park, J. Zimmerman, Deformation of FCC nanowires by twinning and slip. J. Mech. Phys. Solids 54, 1862–1881 (2006)
G. Henkelman, H. Jónsson, Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 113, 9978–9985 (2000)
G. Henkelman, G. Johannesson, H. Jónsson, Methods for finding saddle points and minimum energy paths, in Progress on Theoretical Chemistry and Physics, ed. by S.D. Schwartz (Kluwer Academics, Dordrecht, 2000), pp. 269–300
P. Hirel, J. Godet, S. Brochard, L. Pizzagalli, P. Beauchamp, Determination of activation parameters for dislocation formation from a surface in fcc metals by atomistic simulations. Phys. Rev. B 78, 064109 (2008)
J. Hirth, J. Lothe, Theory of Dislocations (Krieger, Malabar, FL, 1982)
A.T. Jennings, J. Li, J.R. Greer, Emergence of strain-rate sensitivity in Cu nanopillars: transition from dislocation multiplication to dislocation nucleation. Acta Materialia 59 (14), 5627–5637 (2011)
A.T. Jennings, C.R. Weinberger, S.W. Lee, Z.H. Aitken, L. Meza, J.R. Greer, Modeling dislocation nucleation strengths in pristine metallic nanowires under experimental conditions. Acta Mater. 61 (6), 2244–2259 (2013)
C. Ji, H.S. Park, Geometric effects on the inelastic deformation of metal nanowires. Appl. Phys. Lett. 89, 181916 (2006)
C. Ji, H.S. Park, The coupled effects of geometry and surface orientation on the mechanical properties of metal nanowires. Nanotechnology 18 (30), 305704 (2007)
C. Ji, H. Park, The effect of defects on the mechanical behavior of silver shape memory nanowires. J. Comput. Theor. Nanosci. 4 (3), 578 (2007)
J.W. Jiang, A.M. Leach, K. Gall, H.S. Park, T. Rabczuk, A surface stacking fault energy approach to predicting defect nucleation in surface-dominated nanostructures. J. Mech. Phys. Solids 61 (9), 1915–1934 (2013)
K. Kang, Atomistic modeling of fracture mechanisms in semiconductor nanowires under tension. Ph.D. Thesis, Stanford University, 2010
K. Kang, W. Cai, Brittle and ductile fracture of semiconductor nanowires–molecular dynamics simulations. Philos. Mag. 87 (14–15), 2169–2189 (2007)
C.L. Kelchner, S.J. Plimpton, J.C. Hamilton, Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085–11088 (1998)
J.Y. Kim, J.R. Greer, Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale. Acta Mater. 57 (17), 5245–5253 (2009)
U.F. Kocks, A.S. Argon, M.F. Ashby, Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19, 1–289 (1975)
J. Kollar, L. Vitos, J.M. Osorio-Guillen, R. Ahuja, Calculation of surface stress for fcc transition metals. Phys. Rev. B 68, 245417 (2003)
O. Kraft, P.A. Gruber, R. Monig, D. Weygand, Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40, 293–317 (2010)
A. Leach, M. McDowell, K. Gall, Deformation of top-down and bottom-up silver nanowires. Adv. Funct. Mater. 17, 43–53 (2007)
C. Li, G. Xu, Critical conditions for dislocation nucleation at surface steps. Philos. Mag. 86, 2957–2970 (2007)
W. Liang, M. Zhou, Response of copper nanowires in dynamic tensile deformation. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 218 (6), 599–606 (2004)
W. Liang, M. Zhou, Atomistic simulations reveal shape memory of fcc metal nanowires. Phys. Rev. B 73, 115409 (2006)
Y. Lu, C. Peng, Y. Ganesan, J.Y. Huang, J. Lou, Quantitative in situ TEM tensile testing of an individual nickel nanowire. Nanotechnology 22 (35), 355702 (2011)
Y. Lu, J. Song, J.Y. Huang, J. Lou, Fracture of sub-20 nm ultrathin gold nanowires. Adv. Funct. Mater. 21, 3982–3989 (2011)
J. Marian, J. Knap, Breakdown of self-similar hardening behavior in au nanopillar microplasticity. Int. J. Multiscale Comput. Eng. 5, 287–294 (2007)
R.J. Needs, M.J. Godfrey, M. Mansfield, Theory of surface stress and surface reconstruction. Surf. Sci. 242, 215–221 (1991)
J. Neighbours, G. Alers, Elastic constants of silver and gold. Phys. Rev. 111 (3), 707 (1958)
A. Ngan, L. Zhuo, P. Wo, Size dependence and stochastic nature of yield strength of micron-sized crystals: a case study on Ni3Al. Proc. R. Soc. 462, 1661 (2006)
L. Nguyen, D. Warner, Improbability of void growth in aluminum via dislocation nucleation under typical laboratory conditions. Phys. Rev. Lett. 108 (3), 035501 (2012)
L. Nguyen, K. Baker, D. Warner, Atomistic predictions of dislocation nucleation with transition state theory. Phys. Rev. B 84 (2), 024118 (2011)
W. Overton Jr., J. Gaffney, Temperature variation of the elastic constants of cubic elements. i. Copper. Phys. Rev. 98 (4), 969 (1955)
H.S. Park, J.A. Zimmerman, Modeling inelasticity and failure in gold nanowires. Phys. Rev. B 72, 054106 (2005)
H. Park, K. Gall, J. Zimmerman, Shape memory and pseudoelasticity in metal nanowires. Phys. Rev. Lett. 95 (25), 255504 (2005)
P. Pechukas, Transition state theory. Annu. Rev. Phys. Chem. 32 (1), 159–177 (1981)
E. Rabkin, H. Nam, D. Srolovitz, Atomistic simulation of the deformation of gold nanopillars. Acta Mater. 55 (6), 2085–2099 (2007)
G. Richter, K. Hillerich, D. Gianola, R. Monig, O. Kraft, C. Volkert, Ultrahigh strength single crystalline nanowhiskers grown by physical vapor deposition. Nano Lett. 9, 3048–3052 (2009)
S. Ryu, K. Kang, W. Cai, Entropic effect on the rate of dislocation nucleation. Proc. Natl. Acad. Sci. USA 108, 5174 (2011)
S. Ryu, K. Kang, W. Cai, Predicting the dislocation nucleation rate as a function of temperature and stress. J. Mater. Res. 26 (18), 2335–2354 (2011)
E. Schmid, W. Boas, Plasticity of Crystals (F. A. Hughes Co., London, 1950)
A. Sedlmayr, E. Bitzek, D.S. Gianola, G. Richter, R. Mönig, O. Kraft, Existence of two twinning-mediated plastic deformation modes in au nanowhiskers. Acta Mater. 60 (9), 3985–3993 (2012)
J.H. Seo, Y. Yoo, N.Y. Park, S.W. Yoon, H. Lee, S. Han, S.W. Lee, T.Y. Seong, S.C. Lee, K.B. Lee et al., Superplastic deformation of defect-free au nanowires via coherent twin propagation. Nano Lett. 11 (8), 3499–3502 (2011)
J.H. Seo, H.S. Park, Y. Yoo, T.Y. Seong, J. Li, J.P. Ahn, B. Kim, I.S. Choi, Origin of size dependency in coherent-twin-propagation-mediated tensile deformation of noble metal nanowires. Nano Lett. 13, 5112–5116 (2013)
J. Tallon, A. Wolfenden, Temperature dependence of the elastic constants of aluminum. J. Phys. Chem. Solids 40 (11), 831–837 (1979)
M.D. Uchic, P.A. Shade, D. Dimiduk, Plasticity of micrometer-scale single crystals in compression. Annu. Rev. Mater. Res. 39, 361–386 (2009)
J. Wang, H. Huang, Novel deformation mechanism of twinned nanowires. Appl. Phys. Lett. 88, 203112 (2006)
J. Wang, F. Sansoz, J. Huang, Y. Liu, S. Sun, Z. Zhang, S.X. Mao, Near-ideal theoretical strength in gold nanowires containing angstrom scale twins. Nat. Commun. 4, 1742 (2013)
E. Weinan, W. Ren, E. Vanden-Eijnden, Simplified and improved string method for computing the minimum energy paths in barrier-crossing events. J. Chem. Phys. 126, 164103 (2007)
C.R. Weinberger, The fundamentals of plastic deformation: several case studies of plasticity in confined volumes. Sandia Report 7736 (2012)
C.R. Weinberger, W. Cai, Plasticity in metallic nanowires. J. Mater. Chem. 22, 3277 (2012)
C.R. Weinberger, A.T. Jennings, K. Kang, J.R. Greer, Atomistic simulations and continuum modeling of dislocation nucleation and strength in gold nanowires. J. Mech. Phys. Solids 60 (1), 84–103 (2012)
Y. Xiang, H. Wei, P. Ming, W. E,: A generalized Peierls-Nabarro model for curved dislocations and cores structures of dislocation loops in Al and Cu. Acta Mater. 56, 1447–1460 (2008)
G. Xu, A.S. Argon, Homogeneous nucleation of dislocation loops under stress in perfect crystals. Philos. Mag. Lett. 80, 605 (2000)
G. Xu, C. Zhang, Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model. J. Mech. Phys. Solids 51, 1371–1394 (2003)
L. Zepeda-Ruiz, B. Sadigh, J. Biener, A. Hodge, A. Hamza, Mechanical response of freestanding au nanopillars under compression. Appl. Phys. Lett. 91, 101907 (2007)
Y. Zhang, H. Huang, Do twin boundaries always strengthen metal nanowires? Nanoscale Res. Lett. 4, 34–38 (2009)
H. Zheng, A. Cao, C.R. Weinberger, J.Y. Huang, K. Du, J. Wang, Y. Ma, Y. Xia, S.X. Mao, Discrete plasticity in sub-10 nm au crystals. Nat. Commun. 1, 144 (2010)
T. Zhu, J. Li, A. Samanta, A. Leach, K. Gall, Temperature and strain-rate dependence of surface dislocation nucleation. Phys. Rev. Lett. 100, 025502 (2008)
Y. Zhu, Q. Qin, F. Xu, F. Fan, Y. Ding, T. Zhang, B.J. Wiley, Z.L. Wang, Size effects on elasticity, yielding, and fracture of silver nanowires. Phys. Rev. B 85, 045443 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Guziewski, M., Yu, H., Weinberger, C.R. (2016). Modeling Dislocation Nucleation in Nanocrystals. In: Weinberger, C., Tucker, G. (eds) Multiscale Materials Modeling for Nanomechanics. Springer Series in Materials Science, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-33480-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-33480-6_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33478-3
Online ISBN: 978-3-319-33480-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)