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

Journal of Materials Research

Volumn 26, Issue 18, 2011, Pages 2335-2354

  Ryu, Seunghwa ^a   Kang, Keonwook ^b   Cai, Wei ^c  

^a STANFORD UNIVERSITY   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c Stanford University   (United States)

Author keywords

dislocations; ductility; simulation

Indexed keywords

ACTIVATION ENTROPIES; ANHARMONIC EFFECT; CONSTANT STRESS; DISLOCATION NUCLEATION; MOLECULAR DYNAMICS SIMULATIONS; NANO SCALE; NUCLEATION RATE; ORDERS OF MAGNITUDE; RING THEORY; SIMULATION; THERMODYNAMIC LIMITS; TIME-SCALES; UMBRELLA SAMPLING;

ACTIVATION ENERGY; CRYSTALLINE MATERIALS; ENTROPY; FORECASTING; FREE ENERGY; MOLECULAR DYNAMICS; THERMODYNAMICS;

NUCLEATION;

EID: 80053964435     PISSN: 08842914     EISSN: 20445326     Source Type: Journal    
DOI: 10.1557/jmr.2011.275     Document Type: Article

References (59)

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).
2. J. Li: The mechanics and physics of defect nucleation. MRS Bull. 32, 151 (2007).
3. T. Zhu, J. Li, S. Ogata, and S. Yip: Mechanics of ultra-strength materials. MRS Bull. 34, 167 (2009).
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 andmicrometer 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 fromcrack 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).
16. R. Becker and W. Döring: The kinetic treatment of nuclear formation in supersaturated vapors. Ann. Phys. (Weinheim) 24, 719 (1935).
17. H. Eyring: The activated complex in chemical reactions. J. Chem. Phys. 3, 107 (1935).
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 QuantumDynamics in Condensed Phase Simulations; B.J. Berne, G. Ciccotti, and D.F. Coker, Eds.; World Scientific: New York; 1998; pp. 385-404.
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).
22. D. Chandler: Introduction to Modern Statistical Mechanics; Oxford University Press: Oxford, UK; 1987.
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: UnderstandingMolecular Simulation: From Algorithms to Applications, Academic Press: San Diego, CA; 2002.
27. U.F. Kocks, A.S. Argon, and M.F. Ashby: Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19, 1 (1975).
28. J.F. Nye: physical Properties of Crystals: Their Representation by Tensors and Matrices; Clarendon Press: New York; 1957.
29. H. Xiao, O.T. Bruhns, and A. Meyers: Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mech. 124, 89105 (1997).
30. R. Bechmann, A.D. Ballato, and T.J. Lukaszek: Higher-order temperature coefficients of the elastic stiffinesses and complinaces of alpha-quartz. In Proceedings of the Institute of Radio Engineers, Vol. 50; 1962; p. 1812.
31. E. Whalley: Use of volumes of activation for determining reaction mechanisms. In Advances in Physical Organic Chemistry; V. Gold, Ed.; Academic Press: London; 1964; pp. 93-162.
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 pointdefect entropy in metals. Philos. Mag. A 81, 2591 (2001).
37. D. Gupta, Ed.: Diffusion Processes in Advanced Technological Materials; Springer: New York; 2002; p.140.
38. C. Kittel: Introduction to Solid State Physics, 8th ed.; Wiley: New York; 2004.
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).
46. M. Khantha, D.P. Pope and V. Vitek: Dislocation screening and the brittle-to-ductile transition: A Kosterlitz-Thouless type instability. Phys. Rev. Lett. 74, 684 (1994).
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. 3Al. 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. 3Al. 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).