- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Materials

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Quantum statistical theory of dislocation mobility in discrete lattices

Beñat Gurrutxaga Lerma

PDF

Phys. Rev. Materials 9, 123605 – Published 26 December, 2025

DOI: https://doi.org/10.1103/zzct-418n

Abstract

We present a first-principles quantum statistical theory of dislocation motion based on discrete lattice dynamics and the Keldysh nonequilibrium formalism. By treating the dislocation as a moving source coupled to the phonon field through exact Kanzaki forces, we derive a universal memory kernel that captures all phononmediated dissipation mechanisms without adjustable parameters. The theory naturally produces the experimentally observed drag regimes: linear phonon wind at low velocities, quadratic radiation damping at intermediate speeds, and finite drag enhancement near the speed of sound. Crucially, we demonstrate that the elastodynamic prediction of an infinite sound barrier is an artefact of continuum approximations; the discrete lattice structure and anharmonic phonon interactions regularize all singularities, permitting transonic motion at finite stress. Through systematic reduction via conserving approximations, we obtain practical mobility laws suitable for crystal plasticity and dislocation dynamics simulations. These take the form of either steady state algebraic relations or minimal differential systems that capture memory effects while adding negligible computational cost. All parameters derive directly from harmonic and anharmonic force constants, enabling predictive modeling across ten orders of magnitude in strain rate. Application to fcc and bcc metals yields drag coefficients and relaxation times in good agreement with molecular dynamics and available experiments, validating the approach. This work establishes a microscopic foundation for dislocation mobility and provides a pathway from atomistic properties to continuum plasticity without empirical fitting.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (151)

  1. J. P. Hirth and J. Lothe, Theory of Dislocations, 2nd edition (John Wiley & Sons, New York, 1982).
  2. E. Orowan, Problems of plastic gliding, Proc. Phys. Soc. 52, 8 (1940).
  3. M. A. Meyers, Dynamic Behavior of Materials (John Wiley, Hoboken, NJ, 1994).
  4. E. Van der Giessen and A. Needleman, Discrete dislocation plasticity: A simple planar model, Modell. Simul. Mater. Sci. Eng. 3, 689 (1995).
  5. T. Zhang, D. M. Collins, F. P. E. Dunne, and D. A. Shollock, Crystal plasticity and high-resolution electron backscatter diffraction analysis of full-field polycrystal ni superalloy strains and rotations under thermal loading, Acta Mater. 80, 25 (2014).
  6. F. R. N. Nabarro, Theory of Crystal Dislocations (Oxford University Press, Oxford, UK, 1967).
  7. J. Lothe, Theory of dislocation mobility in pure slip, J. App. Phys. 33, 2116 (1962).
  8. V. I. Alshits, M. D. Miltionskij, and R. K. Kotowski, The phonon wind as a nonlinear mechanism of dislocation dragging, Archives of Mechanics 31, 91 (1979).
  9. H. Kojima and T. Suzuki, Electron drag and flow stress in niobium and lead at 4.2 k, Phys. Rev. Lett. 21, 896 (1968).
  10. V. I. Alshits, The Phonondislocation Interaction and Its Role in Dislocation Dragging and Thermal Resistivity (Elsevier, New York, 1992), Vol. 31, pp. 625–697.
  11. D. N. Blaschke, Properties of dislocation drag from phonon wind at ambient conditions, Materials 12, 948 (2019).
  12. X. Markenscoff and L. Ni, The transient motion of a dislocation with a ramp-like core, J. Mech. Phys. Solids 49, 1603 (2001).
  13. X. Markenscoff and L. Ni, “Driving forces” and radiated fields for expanding/shrinking half-space and strip inclusions with general eigenstrains, Q. Appl. Math. 69, 529 (2011).
  14. D. N. Blaschke, Velocity dependent dislocation drag from phonon wind and crystal geometry, J. Phys. Chem. Solids 124, 24 (2019).
  15. D. N. Blaschke, E. Mottola, and D. L. Preston, On the velocity dependence of the dislocation drag coefficient from phonon wind, Tech. Rep. LA-UR-16-24559 (Los Alamos National Laboratory, Los Alamos, 2018).
  16. B. Gurrutxaga-Lerma, J. Verschueren, A. P. Sutton, and D. Dini, The mechanics and physics of high-speed dislocations: A critical review, Int. Mater. Rev. 66, 215 (2021).
  17. J. D. Eshelby, Uniformly moving dislocations, Proc. Phys. Soc. A 62, 307 (1949).
  18. J. D. Eshelby, The equation of motion of a dislocation, Phys. Rev. 90, 248 (1953).
  19. J. D. Eshelby, Supersonic dislocations and dislocations in dispersive media, Proc. Phys. Soc. B 69, 1013 (1956).
  20. F. R. N. Nabarro, Dislocations in a simple cubic lattice, Proc. Phys. Soc. London 59, 256 (1947).
  21. G. Leibfried, Über den einfluß thermisch angeregter schallwellen auf die plastische deformation, Z. Phys. 127, 344 (1950).
  22. W. P. Mason, Phonon viscosity and its effect on acoustic wave attenuation and dislocation motion, J. Acoust. Soc. Am. 32, 458 (1960).
  23. M. Li, Y. Tsurimaki, Q. Meng, N. Andrejevic, Y. Zhu, G. D. Mahan, and G. Chen, Theory of electron–phonon–dislon interacting system—toward a quantized theory of dislocations, New J. Phys. 20, 023010 (2018).
  24. T. D. Swinburne, S. L. Dudarev, and A. P. Sutton, Classical mobility of highly mobile crystal defects, Phys. Rev. Lett. 113, 215501 (2014).
  25. T. D. Swinburne and S. L. Dudarev, Phonon drag force acting on a mobile crystal defect: Full treatment of discreteness and nonlinearity, Phys. Rev. B 92, 134302 (2015).
  26. S. P. Fitzgerald, Kink pair production and dislocation motion, Sci. Rep. 6, 39708 (2016).
  27. W. P. Mason, Dislocation relaxations at low temperatures and the determination of the limiting shearing stress of a metal, Phys. Rev. 98, 1136 (1955).
  28. W. P. Mason, Drag on dislocations due to thermal losses of the phononphonon interaction type, J. App. Phys. 35, 2779 (1964).
  29. F. C. Frank, On the equations of motion of crystal dislocations, Proc. Phys. Soc. A 62, 131 (1949).
  30. E. Nadgornyi, Dislocation dynamics and mechanical properties of crystals, Prog. Mater. Sci. 31, 1 (1988).
  31. R. J. Clifton and X. Markenscoff, Elastic precursor decay and radiation from nonuniformly moving dislocations, J. Mech. Phys. Solids 29, 227 (1981).
  32. J. D. Eshelby and P. L. Pratt, Note on the heating effect of moving dislocations, Acta Metall. 4, 560 (1956).
  33. J. H. Weiner, Thermoelastic dissipation due to high-speed dislocations, J. App. Phys. 29, 1305 (1958).
  34. G. Schoeck and A. Seeger, The flow stress of iron and its dependence on impurities, Acta Metall. 7, 469 (1959).
  35. J. O. Kessler, Internal friction and defect interaction in germanium: Theoretical, Phys. Rev. 106, 654 (1957).
  36. J. O. Kessler, Internal friction and defect interaction in germanium: Experimental, Phys. Rev. 106, 646 (1957).
  37. J. P. Hirth, H. M. Zbib, and J. Lothe, Forces on high velocity dislocations, Modell. Simul. Mater. Sci. Eng. 6, 165 (1998).
  38. Y.-P. Pellegrini, Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach, Phys. Rev. B 90, 054120 (2014).
  39. X. Markenscoff, Comment on “dynamic peierls-nabarro equations for elastically isotropic crystals”, Phys. Rev. B 83, 056101 (2011).
  40. X. Markenscoff and R. J. Clifton, The nonuniformly moving edge dislocation, J. Mech. Phys. Solids 29, 253 (1981).
  41. L. Pillon, C. Denoual, and Y.-P. Pellegrini, Equation of motion for dislocations with inertial effects, Phys. Rev. B 76, 224105 (2007).
  42. S. Kim, H. Kim, K. Kang, and S. Y. Kim, Relativistic effect inducing drag on fast-moving dislocation in discrete system, Int. J. Plast. 126, 102629 (2019).
  43. W. G. Johnston and J. J. Gilman, Dislocation velocities, dislocation densities, and plastic flow in Lithium fluoride crystals, J. Appl. Phys. 30, 129 (1959).
  44. Z. Q. Wang, I. J Beyerlein, and R. LeSar, Slip band formation and mobile dislocation density generation in high rate deformation of single fcc crystals, Philos. Mag. 88, 1321 (2008).
  45. R. J. Clifton, On the analysis of elastic/visco-plastic waves of finite uniaxial strain, Sagamore Army Materials Research Conference Proceedings, Vol. 17 (Syracuse University Press, Syracuse, NY, 1971), pp. 73–116.
  46. E. B. Zaretsky and G. I. Kanel, Response of copper to shock-wave loading at temperatures up to the melting point, J. Appl. Phys. 114, 083511 (2013).
  47. E. B. Zaretsky, Impact response of cobalt over the 300-1400 K temperature range, J. Appl. Phys. 108, 083525 (2010).
  48. G. I. Kanel, S. V. Razorenov, E. B. Zaretsky, B. Herrman, and L. Meyer, Thermal “softening” and “hardening” of titanium and its alloy at high strain rates of shock-wave deforming, Phys. Solid State 45, 656 (2003).
  49. E. B. Zaretsky and G. I. Kanel, Effect of temperature, strain, and strain rate on the flow stress of aluminum under shock-wave compression, J. Appl. Phys. 112, 073504 (2012).
  50. B. Gurrutxaga-Lerma, M. A. Shehadeh, D. S. Balint, D. Dini, L. Chen, and D. E. Eakins, The effect of temperature on the elastic precursor decay in shock loaded fcc aluminium and bcc iron, Int. J. Plast. 96, 135 (2017).
  51. P. El Ters and M. A Shehadeh, Modeling the temperature and high strain rate sensitivity in bcc iron: Atomistically informed multiscale dislocation dynamics simulations, Int. J. Plast. 112, 257 (2019).
  52. Y. I. Golovin, Magnetoplastic effects in solids, Phys. Solid State 46, 789 (2004).
  53. C. S. Kim, T. J. Garosshen, and J. M. Galligan, Instantaneous dislocation velocity measurements for slowly moving dislocations, Scr. Metall. 23, 1959 (1989).
  54. D. A. Didenko and V. V. Pustovalov, Singularities in the temperature dependence of flow stress down to 1.4 k in aluminum single crystals of various purities and orientations, J. Low Temp. Phys. 11, 65 (1973).
  55. J. J. Gilman, Micromechanics of Flow in Solids (McGraw-Hill, New York, 1969).
  56. W. D. Nix and R. A. Menezes, Physics of strengthening mechanics in crystalline solids, Annu. Rev. Mater. Sci. 1, 313 (1971).
  57. E. Bitzek and P. Gumbsch, Dynamic aspects of dislocation motion: Atomistic simulations, Mater. Sci. Eng., A 400-401, 40 (2005).
  58. G. Po, Y. Cui, D. Rivera, D. Cereceda, T. D. Swinburne, J. Marian, and N. Ghoniem, A phenomenological dislocation mobility law for bcc metals, Acta Mater. 119, 123 (2016).
  59. S. Queyreau, J. Marian, M. R. Gilbert, and B. D. Wirth, Edge dislocation mobilities in bcc fe obtained by molecular dynamics, Phys. Rev. B 84, 064106 (2011).
  60. D. L. Olmsted, L. G. Hector, Jr., W. A. Curtin, and R. J. Clifton, Atomistic simulations of dislocation mobility in al, ni and al/mg alloys, Modell. Simul. Mater. Sci. Eng. 13, 371 (2005).
  61. M. R. Gilbert, S. Queyreau, and J. Marian, Stress and temperature dependence of screw dislocation mobility in α -Fe by molecular dynamics, Phys. Rev. B 84, 174103 (2011).
  62. P. Gumbsch and H. Gao, Dislocations faster than the speed of sound, Science 283, 965 (1999).
  63. J. Verschueren, B. Gurrutxaga-Lerma, D. S. Balint, A. P. Sutton, and D. Dini, Instabilities of high speed dislocations, Phys. Rev. Lett. 121, 145502 (2018).
  64. H. Tsuzuki, P. S. Branicio, and J. P. Rino, Molecular dynamics simulation of fast dislocations in copper, Acta Mater. 57, 1843 (2009).
  65. E. Oren, E. Yahel, and G. Makov, Dislocation kinematics: A molecular dynamics study in Cu, Modell. Simul. Mater. Sci. Eng. 25, 025002 (2017).
  66. T. Duong and M. J. Demkowicz, Resonance with surface waves induces forbidden velocity bands in dislocation glide, J. Mech. Phys. Solids 180, 105422 (2023).
  67. T. Duong and M. J. Demkowicz, On the mobility of dislocations intersecting 112 free surfaces in Cu, Acta Mater. 295, 121170 (2025).
  68. J. A. Caro and N. Glass, A lattice-dynamics model of the interaction of a dislocation with point defects, J. Phys. France 45, 1337 (1984).
  69. S. Ishioka, Uniform motion of a screw dislocation in a lattice, J. Phys. Soc. Jpn. 30, 323 (1971).
  70. B. Gurrutxaga-Lerma, The role of the mobility law of dislocations in the plastic response of shock loaded pure metals, Modell. Simul. Mater. Sci. Eng. 24, 065006 (2016).
  71. P. P. Gillis and J. Kratochvil, Dislocation acceleration, Philosophical Magazine 21, 425 (1970).
  72. G. Stefanucci and R. Van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge University Press, 2013).
  73. B. Gurrutxaga Lerma and J. Verschueren, Elastic models of dislocations based on atomistic kanzaki forces, Phys. Rev. B 98, 134104 (2018).
  74. B. Gurrutxaga-Lerma and J. Verschueren, Generalized kanzaki force field of extended defects in crystals with applications to the modeling of edge dislocations, Phys. Rev. Mater. 3, 113801 (2019).
  75. M. Born and K. Huang, Dynamical Theory of Cristal Lattices (Oxford University Press, New York, 1998).
  76. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks/Cole, Belmont, MA, 1976).
  77. S. Ishioka, Stress field around a high speed screw dislocation, J. Phys. Chem. Solids 36, 427 (1975).
  78. S. Ishioka, Steady motion of a dislocation in a lattice, J. Phys. Soc. Jpn. 34, 462 (1973).
  79. J. H. Weiner and M. Pear, Breakdown in high-speed edge dislocation motion, Philos. Mag. 31, 679 (1975).
  80. A. A. Maradudin, E. W. Montroll, and G. H. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation, Vol. 3 of Solid State Physics (Academic Press, New York, 1963).
  81. J. S. Toll, Causality and the dispersion relation: Logical foundations, Phys. Rev. 104, 1760 (1956).
  82. J. K. Kevorkian and J. D. Cole, Multiple Scale and Singular Perturbation Methods, Vol. 114 (Springer Science & Business Media, New York, 2012).
  83. H. Kanzaki, Point defects in face-centred cubic lattice–i distortion around defects, J. Phys. Chem. Solids 2, 24 (1957).
  84. G. Leibfried and N. Breuer, Point Defects in Metals I–Introduction to the Theory, Vol. 81 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1978).
  85. P. H. Dederichs, K. Schroeder, and R. Zeller, Point Defects in Metals II–Dynamical Properties and Diffusion Controlled Properties, Vol. 87 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1980).
  86. B. Gurrutxaga-Lerma, Static and dynamic multipolar field expansions of dislocations and cracks in solids, Int. J. Eng. Sci. 128, 165 (2018).
  87. R. Burridge and L. Knopoff, Body force equivalents for seismic dislocations, Bull. Seismol. Soc. America 54, 1875 (1964).
  88. T. Mura, Micromechics of Defects in Solids, 2nd edition (Kluwer Academic Publishers, Amsterdam, 1982).
  89. E. W. Hart, A uniaxial strain model for a lüder's band, Acta Metall. 3, 146 (1955).
  90. J. Rammer and H. Smith, Quantum field-theoretical methods in transport theory of metals, Rev. Mod. Phys. 58, 323 (1986).
  91. G. D. Mahan, Many-Particle Physics (Springer Science & Business Media, 2013).
  92. A. Kamenev, Field Theory of Nonequilibrium Systems (Cambridge University Press, Cambridge, UK, 2023).
  93. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, New York, 2008).
  94. I. M. Gel'fand and G. E. Shilov, Generalized Functions. Volume 2: Spaces of Fundamental and Generalized Functions, Vol. 261 (American Mathematical Soc., London, 2016).
  95. D. N. Blaschke, How to determine limiting velocities of dislocations in anisotropic crystals, J. Phys.: Condens. Matter 33, 503005 (2021).
  96. D. N. Blaschke, J. Chen, S. Fensin, and B. A. Szajewski, Clarifying the definition of ‘transonic’ screw dislocations, Philos. Mag. 101, 997 (2021).
  97. D. N. Blaschke, A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry, J. Mech. Phys. Solids 152, 104448 (2021).
  98. K. Katagiri, T. Pikuz, L. Fang, B. Albertazzi, S. Egashira, Y. Inubushi, G. Kamimura, R. Kodama, M. Koenig, B. Kozioziemski, et al., Transonic dislocation propagation in diamond, Science 382, 69 (2023).
  99. V. A. Alshits and V. L. Indenbom, Dynamic dragging of dislocations, Sov. Phys. Usp. 18, 1 (1975).
  100. G. A. Baker, P. Graves Morris, and Padé Approximants, Encyclopedia of Mathematics and its Applications, 2nd edition (Cambridge University Press, 1996).
  101. I. D. Abrahams, The application of padé approximants to wienerhopf factorization, IMA J. Appl. Math. 65, 257 (2000).
  102. M. I. Mendelev, M. J. Kramer, Chandler A. Becker, and M. Asta, Analysis of semi-empirical interatomic potentials appropriate for simulation of crystalline and liquid al and cu, Philos. Mag. 88, 1723 (2008).
  103. J. A. Gorman, D. S. Wood, and T. Vreeland, Mobility of dislocations in Aluminum, J. Appl. Phys. 40, 833 (1969).
  104. A. Carreras, Phonolammps, Available from https://github.com/abelcarreras/phonolammps.
  105. D. Frenkel and B. Smit, Understanding Molecular Simulation : From Algorithms to Applications 2nd edition (Academic Press, New York, 2002).
  106. K. Ito and V. Vitek, Atomistic study of nonschmid effects in the plastic yielding of bcc metals, Philos. Mag. A 81, 1387 (2001).
  107. C. Woodward and S. I. Rao, Flexible ab initio boundary conditions: Simulating isolated dislocations in bcc Mo and Ta, Phys. Rev. Lett. 88, 216402 (2002).
  108. V. Vitek and V. Paidar, Non-planar dislocation cores: A ubiquitous phenomenon affecting mechanical properties of crystalline materials, in Dislocations in Solids Vol. 14 (Elsevier, New York, 2008), pp. 439–514.
  109. D. Rodney, L. Ventelon, E. Clouet, L. Pizzagalli, and F. Willaime, Ab initio modeling of dislocation core properties in metals and semiconductors, Acta Mater. 124, 633 (2017).
  110. J. M. Luttinger and J. C. Ward, Ground-state energy of a many-fermion system. II, Phys. Rev. 118, 1417 (1960).
  111. G. Baym and L. P. Kadanoff, Conservation laws and correlation functions, Phys. Rev. 124, 287 (1961).
  112. D. J. Hooton, A new treatment of anharmonicity in lattice thermodynamics, London, Edinburgh, Dublin Philos. Mag. J. Sci. 46, 422 (1955).
  113. Thomas R Koehler, Theory of the self-consistent harmonic approximation with application to solid neon, Phys. Rev. Lett. 17, 89 (1966).
  114. D. C Wallace, Thermodynamics of Crystals (Wiley, NY, 1972).
  115. N. R. Werthamer, Self-consistent phonon formulation of anharmonic lattice dynamics, Phys. Rev. B 1, 572 (1970).
  116. L. Dezerald, L. Proville, L. Ventelon, F. Willaime, and D. Rodney, 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, 094105 (2015).
  117. R. A. Cowley, Anharmonic crystals, Rep. Prog. Phys. 31, 123 (1968).
  118. A. A. Maradudin, A. E. Fein, and G. H. Vineyard, On the evaluation of phonon widths and shifts, Phys. Status Solidi (b) 2, 1479 (1962).
  119. B. Fultz, Vibrational thermodynamics of materials, Prog. Mater. Sci. 55, 247 (2010).
  120. G. Grimvall, Thermophysical Properties of Materials (Elsevier, 1999).
  121. D.-B. Zhang, T. Sun, and R. M. Wentzcovitch, Phonon quasiparticles and anharmonic free energy in complex systems, Phys. Rev. Lett. 112, 058501 (2014).
  122. A. Carreras, A. Togo, and I. Tanaka, DynaPhoPy: A code for extracting phonon quasiparticles from molecular dynamics simulations, Comput. Phys. Commun. 221, 221 (2017).
  123. J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford University Press, 2001).
  124. To assess whether supersonic dislocation motion (vd>cL) is physically attainable before lattice instability, we estimate the required stress. From the phase-space analysis at the Brillouin zone boundary, the maximum radiated power scales as: Pmax∼μB2cT2k03a3(2π)3ωD, (179)where we have included the Debye frequency ωD∼cTk0 as the characteristic emission frequency. With k0=π/a, this yields: Pmax∼μB2cT8a. (180) The stress required to sustain motion at vd=cL follows from the power balance τBcL=Pmax: τsupersonic∼μBcT8acL. (181) For typical metals where cL≈2cT and B=b≈a/2 (fcc), we obtain: τsupersonic∼μ162≈μ23. (182) Comparing to the ideal shear strength τideal≈μ/18, this suggests that supersonic motion requires stresses approaching 30%–80% of the ideal strength. Given that real crystals typically fail through nucleation of defects or cracks at ∼0.1τideal, sustained supersonic dislocation motion appears unlikely in practice. However, transient supersonic motion following high-velocity nucleation events or shock loading remains kinematically possible, as observed in molecular dynamics simulations [62, 64].
  125. S. Dyatlov and M. Zworski, Mathematical Theory of Scattering Resonances, Vol. 200 of Graduate Studies in Mathematics (AMS, Providence, RI, 2019).
  126. R. Thomson, C. Hsieh, and V. Rana, Lattice trapping of fracture cracks, J. App. Phys. 42, 3154 (1971).
  127. J. R. Kermode, T. Albaret, D. Sherman, N. Bernstein, P. Gumbsch, M. C. Payne, G. Csányi, and A. De Vita, Low-speed fracture instabilities in a brittle crystal, Nature (London) 455, 1224 (2008).
  128. M. J. Wootton and B. Gurrutxaga-Lerma, Lattice resonance-induced kinematic nucleation of twins in crystalline materials, Scr. Mater. 268, 116893 (2025).
  129. H. Tsuzuki, P. S. Branicio, and J. P. Rino, Accelerating dislocations to transonic and supersonic speeds in anisotropic metals, Appl. Phys. Lett. 92, 191909 (2008).
  130. X. Markenscoff and S. Huang, Analysis for a screw dislocation accelerating through the shear-wave speed barrier, J. Mech. Phys. Solids 56, 2225 (2008).
  131. X. Markenscoff and S. Huang, The energetics of dislocations accelerating and decelerating through the shear-wave speed barrier, Appl. Phys. Lett. 94, 021906 (2009).
  132. M. Lazar, The gauge theory of dislocations: A uniformly moving screw dislocation, Proc. R. Soc. A 465, 2505 (2009).
  133. V. Celli and N. Flytzanis, Motion of a screw dislocation in a crystal, J. Appl. Phys. 41, 4443 (1970).
  134. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Dover Books on Mathematics (Dover Publications, Mineola, NY, 2012).
  135. M.-C. Marinica, L. Ventelon, M. R. Gilbert, L. Proville, S. L. Dudarev, J. Marian, G. Bencteux, and F. Willaime, Interatomic potentials for radiation defects and dislocations in tungsten, J. Phys.: Condens. Matter 25, 395502 (2013).
  136. R. Ravelo, T. C. Germann, O. Guerrero, Q. An, and B. L. Holian, Shock-induced plasticity in tantalum single crystals: Interatomic potentials and large-scale molecular-dynamics simulations, Phys. Rev. B 88, 134101 (2013).
  137. X. W. Zhou, R. A. Johnson, and H. N. G. Wadley, Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers, Phys. Rev. B 69, 144113 (2004).
  138. M. I. Mendelev and Alexander H. King, The interactions of self-interstitials with twin boundaries, Philos. Mag. 93, 1268 (2013).
  139. R. W. Rohde and C. H. Pitt, Dislocation velocities in nickel single crystals, J. App. Phys. 38, 876 (1967).
  140. A. P. L. Turner and T. Vreeland, The effect of stress and temperature on the velocity of dislocations in pure iron monocrystals, acta metall, Acta Metall. 18, 1225 (1970).
  141. G. S. Baker and S. H. Carpenter, Dislocation mobility and motion under combined stresses, J. App. Phys. 38, 1586 (1967).
  142. M. Reiner, The Deborah number, Phys. Today 17(1), 62 (1964).
  143. V. V. Bulatov and W. Cai, Computer Simulations of Dislocation (Oxford University Press, Oxford, UK, 2006).
  144. F. P. Dunne and N. Petrinic, Introduction to Computational Plasticity (Oxford University Press, Oxford, 2005).
  145. https://github.com/benatgurrutxaga/Quantum-Statistics-of-Dislocation-Mobility.
  146. R. J. Marks, Introduction to Shannon Sampling and Interpolation Theory (Springer Science & Business Media, 2012).
  147. A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys.: Condens. Matter 35, 353001 (2023).
  148. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton, LAMMPS - A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
  149. P. Hirel, Atomsk: A tool for manipulating and converting atomic data files, Comput. Phys. Commun. 197, 212 (2015).
  150. C. Chicone, Ordinary Differential Equations with Applications, Texts in Applied Mathematics (Springer-Verlag, NY, 1999).
  151. W. H. Press, Numerical Recipes 3rd Edition: The Art of Scientific Computing (Cambridge University Press, 2007).

Outline

Information

Phys. Rev. Materials 9, 123605– Published 26 December, 2025
  • Received 29 July 2025
  • Accepted 8 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation