Skip to main content
    • Aa
    • Aa

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

  • Seunghwa Ryu (a1), Keonwook Kang (a2) and Wei Cai (a3)

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.

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).

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).

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).

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.

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

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).

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

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

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).

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).

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).

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? *