Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 18
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Gao, Yanfei and Bei, Hongbin 2016. Strength statistics of single crystals and metallic glasses under small stressed volumes. Progress in Materials Science, Vol. 82, p. 118.

    Guziewski, Matthew Yu, Hang and Weinberger, Christopher R. 2016. Multiscale Materials Modeling for Nanomechanics.

    Kotrechko, S. Ovsjannikov, O. Stetsenko, N. Mikhailovskij, I. Mazilova, T. and Starostenkov, M. 2016. Yield strength temperature dependence of tungsten nanosized crystals: experiment and simulation. Philosophical Magazine, Vol. 96, Issue. 5, p. 473.

    Ramachandramoorthy, Rajaprakash Gao, Wei Bernal, Rodrigo and Espinosa, Horacio 2016. High Strain Rate Tensile Testing of Silver Nanowires: Rate-Dependent Brittle-to-Ductile Transition. Nano Letters, Vol. 16, Issue. 1, p. 255.

    Ryu, Ill Cai, Wei Nix, William D. and Gao, Huajian 2016. Anisotropic Size-Dependent Plasticity in Face-Centered Cubic Micropillars Under Torsion. JOM, Vol. 68, Issue. 1, p. 253.

    Saroukhani, S. Nguyen, L.D. Leung, K.W.K. Singh, C.V. and Warner, D.H. 2016. Harnessing atomistic simulations to predict the rate at which dislocations overcome obstacles. Journal of the Mechanics and Physics of Solids, Vol. 90, p. 203.

    Chen, Lisa Y. He, Mo-rigen Shin, Jungho Richter, Gunther and Gianola, Daniel S. 2015. Measuring surface dislocation nucleation in defect-scarce nanostructures. Nature Materials, Vol. 14, Issue. 7, p. 707.

    Ryu, Ill Cai, Wei Nix, William D. and Gao, Huajian 2015. Stochastic behaviors in plastic deformation of face-centered cubic micropillars governed by surface nucleation and truncated source operation. Acta Materialia, Vol. 95, p. 176.

    Vigonski, Simon Djurabekova, Flyura Veske, Mihkel Aabloo, Alvo and Zadin, Vahur 2015. Molecular dynamics simulations of near-surface Fe precipitates in Cu under high electric fields. Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue. 2, p. 025009.

    Uranagase, Masayuki and Matsumoto, Ryosuke 2014. Thermal activation analysis of enthalpic and entropic contributions to the activation free energy of basal and prismatic slips in Mg. Physical Review B, Vol. 89, Issue. 22,

    Jennings, Andrew T. Weinberger, Christopher R. Lee, Seok-Woo Aitken, Zachary H. Meza, Lucas and Greer, Julia R. 2013. Modeling dislocation nucleation strengths in pristine metallic nanowires under experimental conditions. Acta Materialia, Vol. 61, Issue. 6, p. 2244.

    Sandoval, Luis A. Surh, Michael P. Chernov, Alexander A. and Richards, David F. 2013. Growth of deformation twins in tantalum via coherent twin boundary migration. Journal of Applied Physics, Vol. 114, Issue. 11, p. 113511.

    Wen, Mao Li, Zhiyuan and Barnoush, Afrooz 2013. Atomistic Study of Hydrogen Effect on Dislocation Nucleation at Crack Tip. Advanced Engineering Materials, Vol. 15, Issue. 11, p. 1146.

    Filleter, Tobin Ryu, Seunghwa Kang, Keonwook Yin, Jie Bernal, Rodrigo A. Sohn, Kwonnam Li, Shuyou Huang, Jiaxing Cai, Wei and Espinosa, Horacio D. 2012. Nucleation-Controlled Distributed Plasticity in Penta-twinned Silver Nanowires. Small, Vol. 8, Issue. 19, p. 2986.

    Han, Jing Fang, Liang Sun, Jiapeng Han, Ying and Sun, Kun 2012. Length-dependent mechanical properties of gold nanowires. Journal of Applied Physics, Vol. 112, Issue. 11, p. 114314.

    Nordlund, K. and Djurabekova, F. 2012. Defect model for the dependence of breakdown rate on external electric fields. Physical Review Special Topics - Accelerators and Beams, Vol. 15, Issue. 7,

    Pohjonen, Aarne S. Djurabekova, Flyura Kuronen, Antti Fitzgerald, Steven P. and Nordlund, Kai 2012. Analytical model of dislocation nucleation on a near-surface void under tensile surface stress. Philosophical Magazine, Vol. 92, Issue. 32, p. 3994.

    Weinberger, Christopher R. and Cai, Wei 2012. Plasticity of metal nanowires. Journal of Materials Chemistry, Vol. 22, Issue. 8, p. 3277.


Predicting the dislocation nucleation rate as a function of temperature and stress

  • Seunghwa Ryu (a1), Keonwook Kang (a2) and Wei Cai (a3)
  • DOI:
  • Published online: 05 October 2011

Predicting the dislocation nucleation rate as a function of temperature and stress is crucial for understanding the plastic deformation of nanoscale crystalline materials. However, the limited time scale of molecular dynamics simulations makes it very difficult to predict the dislocation nucleation rate at experimentally relevant conditions. We recently develop an approach to predict the dislocation nucleation rate based on the Becker–Döring theory of nucleation and umbrella sampling simulations. The results reveal very large activation entropies, which originated from the anharmonic effects, that can alter the nucleation rate by many orders of magnitude. Here we discuss the thermodynamics and algorithms underlying these calculations in greater detail. In particular, we prove that the activation Helmholtz free energy equals the activation Gibbs free energy in the thermodynamic limit and explain the large difference in the activation entropies in the constant stress and constant strain ensembles. We also discuss the origin of the large activation entropies for dislocation nucleation, along with previous theoretical estimates of the activation entropy.

Corresponding author
a)Address all correspondence to this author. e-mail:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.X. Li , Y. Wei , L. Lu , K. Lu , and H. Gao : Dislocation nucleation governed softening and maximum strength in nano-twinned metals. Nature 464, 877 (2010).

4.J. Li , K.J. Van Vliet , T. Zhu , S. Yip , and S. Suresh : Atomistic mechanisms governing elastic limit and incipient plasticity in crystals. Nature 418, 307 (2002).

5.C.A. Schuh , J.K. Mason , and A.C. Lund : Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments. Nature Mater. 4, 617 (2005).

6.P. Schall , I. Cohen , D.A. Weitz , and F. Spaepen : Visualizing dislocation nucleation by indenting colloidal crystals. Nature 440, 319 (2006).

7.W.D. Nix , J.R. Greer , G. Feng , and E.T. Lilleodden : Deformation at the nanometer and micrometer length scales: Effects of strain gradients and dislocation starvation. Thin Solid Films 515, 315 (2007).

8.S. Izumi , H. Ohta , C. Takahashi , T. Suzuki , and H. Saka : Shuffle-set dislocation nucleation in semiconductor silicon device. Philos. Mag. Lett. 90, 707 (2010).

9.G. Xu , A.S. Argon , and M. Ortiz : Critical configurations for dislocation nucleation from crack tips. Philos. Mag. A 75, 341 (1997).

10.F. Frank : Symposium on the Plastic Deformation of Crystalline Solids; Carnegie Institute of Technology and Office of Naval Research, Pittsburgh, PA, 1950; p. 89.

11.S. Aubry , K. Kang , S. Ryu , and W. Cai : Energy barrier for homogeneous dislocation nucleation: Comparing atomistic and continuum models. Scripta Mater. 64, 1043 (2011).

12.M.A. Tschopp , D.E. Spearot , and D.L. McDowell : Atomistic simulations of homogeneous dislocation nucleation in single crystal copper. Model. Simul. Mater. Sci. Eng. 15, 693 (2007).

13.E.M. Bringa , K. Rosolankova , R.E. Rudd , B.A. Remington , J.S. Wark , M. Duchaineau , D.H. Kalantar , J. Hawreliak , and J. Belak : Shock deformation of face-centered-cubic metals on subnanosecond timescales. Nat. Mater. 5, 805 (2006).

14.T. Zhu , J. Li , A. Samanta , A. Leach , and K. Gall : Temperature and strain-rate dependence of surface dislocation nucleation. Phys. Rev. Lett. 100, 025502 (2008).

15.P. Hanggi , P. Talkner , and M. Borkovec : Reaction-rate theory: Fifty years after Kramers. Rev. Mod. Phys. 62, 251 (1990).

18.G.H. Vineyard : Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solids 3, 121 (1957).

19.H. Jónsson , G. Mills , and K.W. Jacobsen : Nudged elastic band method for finding minimum energy paths of transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations; B.J. Berne , G. Ciccotti , and D.F. Coker , Eds.; World Scientific: New York; 1998; pp. 385404.

20.A.F. Voter : Introduction to the kinetic Monte Carlo Metho; Springer: New York; 2007.

21.C. Jin , W. Ren , and Y. Xiang : Computing transition rates of thermally activated events in dislocation dynamics. Script. Mater. 62, 206 (2010).

23.W. E. Ren and E. Vanden-Eijnden : String method for the study of rare events. Phys. Rev. B 66, 052301 (2002).

24.W. E. Ren and E. Vanden-Eijnden : Finite temperature string method for the study of rare events. J. Phys. Chem. B 109, 6688 (2005).

25.S. Ryu , K. Kang , and W. Cai : Entropic effect on the rate of dislocation nucleation. Proc. Natl. Acad. Sci. USA 108, 5174 (2011).

26.D. Frenkel and B. Smit : Understanding Molecular Simulation: From Algorithms to Applications, Academic Press: San Diego, CA; 2002.

29.H. Xiao , O.T. Bruhns , and A. Meyers : Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mech. 124, 89105 (1997).

32.M.L. Tonnet and E. Whalley : Effect of pressure on the alkaline hydrolysis of ethyl acetate in acetone–water solutions. Parameters of activation at constant volume. Can. J. Chem. 53, 3414 (1975).

33.W.C. Overton Jr. and J. Gaffney : Temperature variation of the elastic constants of cubic elements. I. Copper. Phys. Rev. 98, 969 (1955).

34.J.W. Cahn and F.R.N. Nabarro : Thermal activation under shear. Philos. Mag. A 81, 1409 (2001).

35.A.H. Cottrell : Thermally activated plastic glide. Philos. Mag. Lett. 82, 65 (2002).

36.Y. Mishin , M.R. Sorensen , and A.F. Voter : Calculation of point-defect entropy in metals. Philos. Mag. A 81, 2591 (2001).

39.A.S. Argon , R.D. Andrews , J.A. Godrick , and W. Whitney : Plastic deformation bands in glassy polystyrene. J. Appl. Phys. 39, 1899 (1968).

40.R.J. DiMelfi , W.D. Nix , D.M. Barnett , J.H. Holbrook , and G.M. Pound : An analysis of the entropy of thermally activated dislocation motion based on the theory of thermoelasticity. Phys. Status Solidi B 75, 573 (1976).

41.R.J. DiMelfi , W.D. Nix , D.M. Barnett , and G.M. Pound : The equivalence of two methods for computing the activation entropy for dislocation motion. Acta Mater. 28, 231 (1980).

42.G. Kemeny and B. Rosenberg : Compensation law in thermodynamics and thermal death. Nature 243, 400 (1973).

43.A. Yelon , M. Movagha , and H.M. Branz : Origin and consequences of the compensation (Meyer–Neldel) law. Phys. Rev. B 46, 12243 (1992).

44.M. Born : Thermodynamics of crystals and melting. J. Chem. Phys. 7, 591 (1939).

45.S. Brochard , P. Hirel , L. Pizzagalli , and J. Godet : Elastic limit for surface step dislocation nucleation in face-centered cubic metals: Temperature and step height dependence. Acta Mater. 58, 4182 (2010).

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

48.J.P. Hirth and J. Lothe : Theory of Dislocations; Krieger: New York; 1992.

49.M. Parrinello and A. Rahman : Crystal structure and pair potentials: A molecular dynamics study. Phys. Rev. Lett. 45, 1196 (1980).

50.H.C. Anderson : Molecular dynamics at constant pressure and/or temperature. J. Chem. Phys. 72, 2384 (1980).

51.W.G. Hoover : Canonical dynamics: Equilibrium phase space distribution. Phys. Rev. A 31, 1695 (1985).

52.T. Zhu , J. Li , K.J. Van Vliet , S. Ogata , S. Yip , and S. Suresh : Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper. J. Mech. Phys. Sol. 52, 691 (2004).

53.A.H.W. Ngan , L. Zuo , and P.C. Wo : Size dependence and stochastic nature of yield strength of micron-sized crystals: A case study on Ni3Al. Proc. Royal Soc. A 462, 1661 (2006).

54.S. Ryu and W. Cai : Validity of classical nucleation theory for Ising models. Phys. Rev. E 81, 030601(R) (2010).

55.T. Zhu , J. Li , A. Samanta , H.G. Kim , and S. Suresh : Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals. Proc. Natl. Acad. Sci. USA 104, 3031 (2007).

56.S.M. Foiles : Evaluation of harmonic methods for calculating the free energy of defects in solids. Phys. Rev. B 49, 14930 (1994).

57.M. de Koning , C.R. Miranda , and A. Antonelli : Atomistic prediction of equilibrium vacancy concentraions in Ni3Al. Phys. Rev. B 66, 104110 (2002).

58.S. Ryu and W. Cai : Comparison of thermal properties predicted by interatomic potential models. Model. Simul. Mater. Sci. Eng. 16, 085005 (2008).

59.A. Yelon , B. Movaghar , and R.S. Crandall : Multi-exitation entropy: Its role in thermodynamics and kinetics. Rep. Prog. Phys. 69, 1145 (2006).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *