Modeling the Thermally Activated Mobility of Dislocations at the Atomic Scale

  • Laurent Proville
  • David RodneyEmail author
Living reference work entry


We review in this chapter how to model the mobility of isolated dislocations at the atomic scale when glide requires to overcome energy barriers and is thermally activated, as is typically the case in body-centered cubic metals. We first recall the boundary and loading conditions used to model an isolated dislocation. We then detail a static approach based on the Transition State Theory parameterized on atomistic calculations to predict dislocation mobility. Finally, we address the low-temperature regime and explain how to include quantum corrections to the dislocation mobility law.



DR acknowledges support from LABEX iMUST (ANR-10-LABX-0064) of Université de Lyon (program “Investissements d’Avenir”, ANR-11-IDEX-0007).


  1. Alshits VI (1992) Elastic strain fields and dislocation mobility. North-Holland, AmsterdamGoogle Scholar
  2. Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammarling S, McKenney A, Sorensen D (1999) LAPACK users’ guide, 3rd edn. Society for Industrial and Applied Mathematics, PhiladelphiaCrossRefGoogle Scholar
  3. Ashcroft N, Mermin N (1976) Solid state physics. Saunders College Publishing, LondonzbMATHGoogle Scholar
  4. Bacon DJ, Osetsky YN, Rodney D (2008) In: Hirth J, Kubin L (eds) Dislocations in solids, Dislocation-Obstacle Interactions at the Atomic Level. Elsevier, AmsterdamGoogle Scholar
  5. Barvinschi B, Proville L, Rodney D (2014) Quantum Peierls stress of straight and kinked dislocations and effect of non-glide stresses. Model Simul Mater Sci Eng 22:025006ADSCrossRefGoogle Scholar
  6. Basinski ZS, Duesbery MS, Taylor R (1971) Influence of shear stress on screw dislocations in a model sodium lattice. Can J Phys 49:2160–2180ADSCrossRefGoogle Scholar
  7. Benderskii V, Makarov D, Wight C (1994) Chemical dynamics at low temperature. Wiley-Interscience, New YorkCrossRefGoogle Scholar
  8. Bhate N, Clifton R, Phillips R (2002) Atomistic simulations of the motion of an edge dislocation in aluminum using the embedded atom method. In: AIP conference proceedings, vol 620. American Institute of Physics, Atlanto, Georgia pp 339–342Google Scholar
  9. Brunner D, Diehl J (1992) Extension of measurements of the tensile flow stress of high-purity α-iron single crystals to very low temperatures. Atlanta, Georgia, Z Metalkd 83:828Google Scholar
  10. Bulatov VV, Cai W (2006) Computer simulations of dislocations. Oxford University Press, New-YorkzbMATHGoogle Scholar
  11. Cai W, Bulatov VV (2004) Mobility laws in dislocation dynamics simulations. Mater Sci Eng A 387:277–281CrossRefGoogle Scholar
  12. Caillard D (2010) Kinetics of dislocations in pure Fe. Part II. In situ straining experiments at low temperature. Acta Mater 58:3504–3515CrossRefGoogle Scholar
  13. Caillard D, Martin JL (2003) Thermally activated mechanisms in crystal plasticity. Pergamon, AmsterdamGoogle Scholar
  14. Cereceda D, Diehl M, Roters F, Raabe D, Perlado JM, Marian J (2016) Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations. Int J Plast 78:242–265CrossRefGoogle Scholar
  15. Chaussidon J, Fivel M, Rodney D (2006) The glide of screw dislocations in BCC Fe: atomistic static and dynamic simulations. Acta Mater 54:3407CrossRefGoogle Scholar
  16. Chen Z, Mrovec M, Gumbsch P (2013) Atomistic aspects of screw dislocation behavior in α-iron and the derivation of microscopic yield criterion. Model Simul Mater Sci Eng 21:055023ADSCrossRefGoogle Scholar
  17. Dezerald L, Proville L, Ventelon L, Willaime F, Rodney D (2015) First-principles prediction of kink-pair activation enthalpy on screw dislocations in BCC transition metals: V, Nb, Ta, Mo, W, and Fe. Phys Rev B 91:094105ADSCrossRefGoogle Scholar
  18. Dezerald L, Rodney D, Clouet E, Ventelon L, Willaime F (2016) Plastic anisotropy and dislocation trajectory in BCC metals. Nat Commun 7:11695ADSCrossRefGoogle Scholar
  19. Dorn JE, Rajnak S (1964) Nucleation of kink pairs and the Peierls’ mechanism of plastic deformation. Trans Metal Soc AIME 230:1052Google Scholar
  20. Gilbert MR, Queyreau S, Marian J (2011) Stress and temperature dependence of screw dislocation mobility in α-Fe by molecular dynamics. Phys Rev B 84:174103ADSCrossRefGoogle Scholar
  21. Gillan M (1987) Quantum-classical crossover of the transition rate in the damped double well. J Phys C 20:3621ADSCrossRefGoogle Scholar
  22. Gordon PA, Neeraj T, Li Y, Li J (2010) Screw dislocation mobility in BCC metals: the role of the compact core on double-kink nucleation. Model Simul Mater Sci Eng 18:085008ADSCrossRefGoogle Scholar
  23. Gordon PA, Neeraj T, Mendelev MI (2011) Screw dislocation mobility in BCC metals: a refined potential description for α-Fe. Philos Mag Lett 91:3931–3945ADSCrossRefGoogle Scholar
  24. Gröger R, Vitek V (2008) Multiscale modeling of plastic deformation of molybdenum and tungsten. III. Effects of temperature and plastic strain rate. Acta Mater 56:5426–5439CrossRefGoogle Scholar
  25. Gröger R, Vitek V (2015) Determination of positions and curved transition pathways of screw dislocations in BCC crystals from atomic displacements. Mater Sci Eng A 643:203CrossRefGoogle Scholar
  26. Gumbsch P, Gao H (1999) Dislocations faster than the speed of sound. Science 283:965–968ADSCrossRefGoogle Scholar
  27. Guyot P, Dorn JE (1967) A critical review of the Peierls mechanism. Can J Phys 45:983ADSCrossRefGoogle Scholar
  28. Henkelman G, Jóhannesson G, Jónsson H (2000) Methods for finding saddle points and minimum energy paths: theoretical methods in condensed phase chemistry, chap 10. In: Schwartz SD (ed) Progress in theoretical chemistry and physics, vol 5. Springer, Dordrecht, pp 269–302Google Scholar
  29. Hirth JP, Lothe J (1982) Theory of dislocations. Wiley, New YorkzbMATHGoogle Scholar
  30. Johnston WG, Gilman JJ (1959) Dislocation velocities, dislocation densities, and plastic flow in LiF crystals. J Appl Phys 30:129ADSCrossRefGoogle Scholar
  31. Koizumi H, Kirchner HOK, Suzuki T (2002) Lattice wave emission from a moving dislocation. Phys Rev B 65:214104ADSCrossRefGoogle Scholar
  32. Kubin L (2013) Dislocations, mesoscale simulations and plastic flow. Oxford University Press, OxfordCrossRefGoogle Scholar
  33. Kuramoto E, Aono Y, Kitajima K (1979) Thermally activated slip deformation between 0.7 and 77 K in high-purity iron single crystals. Philos Mag 39:717Google Scholar
  34. Landau L, Lifshitz E (1977) Quantum mechanics non-relativistic theory. Elsevier Science Ltd, OxfordzbMATHGoogle Scholar
  35. Landeiro Dos Reis M, Choudhury A, Proville L (2017) Ubiquity of quantum zero-point fluctuations in dislocation glide. Phys Rev B 95:094103ADSCrossRefGoogle Scholar
  36. Leibfried G (1950) Uber den einfluss thermisch angeregter schallwellen auf die plastische deformation. Z Phys 127:344ADSMathSciNetCrossRefGoogle Scholar
  37. Marian J, Cai W, Bulatov VV (2004) Dynamic transitions from smooth to rough to twinning in dislocation motion. Nat Mater 3:158ADSCrossRefGoogle Scholar
  38. Miller W (1975) Semiclassical limit of quantum mechanical transition state theory for nonseparable systems. J Chem Phys 62:1899ADSCrossRefGoogle Scholar
  39. Mills G, Jónsson H, Schenter GK (1995) Reversible work transition state theory: application to dissociative adsorption of hydrogen. Surf Sci 324:305ADSCrossRefGoogle Scholar
  40. Mordehai D, Ashkenazy Y, Kelson I, Makov G (2003) Dynamic properties of screw dislocations in Cu: a molecular dynamics study. Phys Rev B 67:24112ADSCrossRefGoogle Scholar
  41. Mrovec M, Nguyen-Manh D, Elsasser C, Gumbsch P (2011) Magnetic bond-order potential for iron. Phys Rev Lett 106:246402ADSCrossRefGoogle Scholar
  42. Nadgornyi E (1988) Dislocation dynamics and mechanical properties of crystals. In: Progress in materials science. Pergamon Press OxfordGoogle Scholar
  43. Nosenko V, Morfill G, Rosakis P (2011) Direct experimental measurement of the speed-stress relation for dislocations in a plasma crystal. Phys Rev Lett 106:155002ADSCrossRefGoogle Scholar
  44. Olmsted DL, Hector Jr LG, Curtin WA, Clifton RJ (2005) Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys. Model Simul Mater Sci Eng 13:371–388ADSCrossRefGoogle Scholar
  45. Oren E, Yahel E, Makov G (2017) Dislocation kinematics: a molecular dynamics study in Cu. Model Simul Mater Sci Eng 25:025002ADSCrossRefGoogle Scholar
  46. Osetsky YN, Bacon DJ (2003) An atomic-level model for studying the dynamics of edge dislocations in metals. Model Simul Mater Sci Eng 11:427ADSCrossRefGoogle Scholar
  47. Patinet S, Proville L (2008) Depinning transition for a screw dislocation in a model solid solution. Phys Rev B 78:104109ADSCrossRefGoogle Scholar
  48. Proville L, Patinet S (2010) Atomic-scale models for hardening in FCC solid solutions. Phys Rev B 82:054115ADSCrossRefGoogle Scholar
  49. Proville L, Rodney D, Marinica MC (2012) Quantum effect on thermally activated glide of dislocations. Nat Mater 11:845–849ADSCrossRefGoogle Scholar
  50. Rodney D (2004) Molecular dynamics simulation of screw dislocations interacting with interstitial frank loops in a model FCC crystal. Acta Mater 52:607–614CrossRefGoogle Scholar
  51. Rodney D, Martin G (2000) Dislocation pinning by glissile interstitial loops in a nickel crystal: a molecular-dynamics study. Phys Rev B 61:8714ADSCrossRefGoogle Scholar
  52. Rodney D, Proville L (2009) Stress-dependent Peierls potential: influence on kink-pair activation. Phys Rev B 79:094108ADSCrossRefGoogle Scholar
  53. Saroukhani S, Warner DH (2017) Investigating dislocation motion through a field of solutes with atomistic simulations and reaction rate theory. Acta Mater 128:77–86CrossRefGoogle Scholar
  54. Suzuki T, Takeuchi S, Yoshinaga H (1991) Dislocation dynamics and plasticity, vol 12. Springer, BerlinGoogle Scholar
  55. Ventelon L, Willaime F (2007) Core structure and Peierls potential of screw dislocations in α-fe from first principles: cluster versus dipole approaches. J Comput-Aided Mater Des 14:85–94ADSCrossRefGoogle Scholar
  56. Ventelon L, Willaime F, Clouet E, Rodney D (2013) Ab initio investigation of the Peierls potential of screw dislocations in BCC Fe and W. Acta Mater 61:3973CrossRefGoogle Scholar
  57. Vineyard GH (1957) Frequency factors and isotope effects in solid state rate processes. J Phys Chem Solids 3:121–127ADSCrossRefGoogle Scholar
  58. Weinberger C, Tucker G, Foiles S (2013) Peierls potential of screw dislocations in BCC transition metals: predictions from density functional theory. Phys Rev B 87:054114ADSCrossRefGoogle Scholar
  59. Wen M, Ngan AHW (2000) Atomistic simulation of kink-pairs of screw dislocations in body-centred cubic iron. Acta Mater 48:4255–4265CrossRefGoogle Scholar
  60. Woodward C, Rao SI (2002) Flexible ab initio boundary conditions: simulating isolated dislocations in BCC Mo and Ta. Phys Rev Lett 88:216402ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.DEN-Service de Recherche de Metallurgie Physique, CEA, Universite Paris-Saclay, F-91191Gif sur YvetteFrance
  2. 2.Institut Lumière MatièreUniversité Lyon 1Villeurbanne CEDEXFrance

Section editors and affiliations

  • Wei Cai
    • 1
  • Somnath Ghosh
    • 2
  1. 1.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.Departments of Civil Engineering, Mechanical Engineering, and Materials Science and EngineeringJohns Hopkins UniversityBaltimoreUSA

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