Dislocation drag from phonon wind in an isotropic crystal at large velocities
Abstract
The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force $vB$ $(ν, T, ρ)$ on the dislocation. In early studies the drag coefficient B was computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, $$c_T$$ . In this paper we derive analytic expressions for the velocity dependence of B up to $$c_T$$ in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to B in the range 1%–90% $$c_T$$ for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as $$ν → c_T$$ , whereas B is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1604033
- Report Number(s):
- LA-UR-19-25851
Journal ID: ISSN 1478-6435; TRN: US2104183
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Philosophical Magazine (2003, Print)
- Additional Journal Information:
- Journal Name: Philosophical Magazine (2003, Print); Journal Volume: 100; Journal Issue: 5; Journal ID: ISSN 1478-6435
- Publisher:
- Taylor & Francis
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Dislocations in crystals; drag coefficient; phonon wind
Citation Formats
Blaschke, Daniel N., Mottola, Emil, and Preston, Dean L. Dislocation drag from phonon wind in an isotropic crystal at large velocities. United States: N. p., 2019.
Web. doi:10.1080/14786435.2019.1696484.
Blaschke, Daniel N., Mottola, Emil, & Preston, Dean L. Dislocation drag from phonon wind in an isotropic crystal at large velocities. United States. https://doi.org/10.1080/14786435.2019.1696484
Blaschke, Daniel N., Mottola, Emil, and Preston, Dean L. Wed .
"Dislocation drag from phonon wind in an isotropic crystal at large velocities". United States. https://doi.org/10.1080/14786435.2019.1696484. https://www.osti.gov/servlets/purl/1604033.
@article{osti_1604033,
title = {Dislocation drag from phonon wind in an isotropic crystal at large velocities},
author = {Blaschke, Daniel N. and Mottola, Emil and Preston, Dean L.},
abstractNote = {The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force $vB$ $(ν, T, ρ)$ on the dislocation. In early studies the drag coefficient B was computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, $c_T$ . In this paper we derive analytic expressions for the velocity dependence of B up to $c_T$ in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to B in the range 1%–90% $c_T$ for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as $ν → c_T$ , whereas B is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.},
doi = {10.1080/14786435.2019.1696484},
journal = {Philosophical Magazine (2003, Print)},
number = 5,
volume = 100,
place = {United States},
year = {Wed Dec 25 00:00:00 EST 2019},
month = {Wed Dec 25 00:00:00 EST 2019}
}
Web of Science
Works referenced in this record:
Dislocation kinematics: a molecular dynamics study in Cu
journal, December 2016
- Oren, E.; Yahel, E.; Makov, G.
- Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 2
Analytic model of the remobilization of pinned glide dislocations from quasi-static to high strain rates
journal, July 2015
- Hunter, A.; Preston, D. L.
- International Journal of Plasticity, Vol. 70
Averaging of elastic constants for polycrystals
journal, October 2017
- Blaschke, Daniel N.
- Journal of Applied Physics, Vol. 122, Issue 14
Dislocation Mobility in Copper
journal, August 1967
- Greenman, W. Frank; Vreeland, Thad; Wood, David S.
- Journal of Applied Physics, Vol. 38, Issue 9
Dislocation Mobility in Pure Copper at 4.2 °K
journal, October 1973
- Jassby, K. M.; Vreeland, T.
- Physical Review B, Vol. 8, Issue 8
The energetics of dislocations accelerating and decelerating through the shear-wave speed barrier
journal, January 2009
- Markenscoff, Xanthippi; Huang, Surong
- Applied Physics Letters, Vol. 94, Issue 2
Dislocation Contributions to the Modulus and Damping in Copper at Megacycle Frequencies
journal, February 1961
- Alers, G. A.; Thompson, D. O.
- Journal of Applied Physics, Vol. 32, Issue 2
Overdamped resonance of dislocations in copper
journal, April 1962
- Stern, R. M.; Granato, A. V.
- Acta Metallurgica, Vol. 10, Issue 4
Die experimentelle Ermittlung der elastischen Konstanten höherer Ordnung
journal, December 1960
- Seeger, Alfred; Buck, Otto
- Zeitschrift für Naturforschung A, Vol. 15, Issue 12
Finite Deformations of an Elastic Solid
journal, April 1937
- Murnaghan, F. D.
- American Journal of Mathematics, Vol. 59, Issue 2
Second- and third-order elastic coefficients in polycrystalline aluminum alloy AMg6
journal, November 2015
- Volkov, A. D.; Kokshaiskii, A. I.; Korobov, A. I.
- Acoustical Physics, Vol. 61, Issue 6
Properties of Dislocation Drag from Phonon Wind at Ambient Conditions
journal, March 2019
- Blaschke, Daniel
- Materials, Vol. 12, Issue 6
Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic Effect
journal, February 1961
- Toupin, R. A.; Bernstein, B.
- The Journal of the Acoustical Society of America, Vol. 33, Issue 2
Theory of Dislocation Mobility in Pure Slip
journal, June 1962
- Lothe, Jens
- Journal of Applied Physics, Vol. 33, Issue 6
Supersonic Dislocation Kinetics from an Augmented Peierls Model
journal, January 2001
- Rosakis, Phoebus
- Physical Review Letters, Vol. 86, Issue 1
A multiscale strength model for extreme loading conditions
journal, April 2011
- Barton, N. R.; Bernier, J. V.; Becker, R.
- Journal of Applied Physics, Vol. 109, Issue 7
Velocity dependent dislocation drag from phonon wind and crystal geometry
journal, January 2019
- Blaschke, Daniel N.
- Journal of Physics and Chemistry of Solids, Vol. 124
Line tension of a dislocation moving through an anisotropic crystal
journal, June 2018
- Blaschke, Daniel N.; Szajewski, Benjamin A.
- Philosophical Magazine, Vol. 98, Issue 26
Anharmonicity Contributions to Dislocation Drag
journal, April 1972
- Brailsford, A. D.
- Journal of Applied Physics, Vol. 43, Issue 4
Probing the character of ultra-fast dislocations
journal, November 2015
- Ruestes, C. J.; Bringa, E. M.; Rudd, R. E.
- Scientific Reports, Vol. 5, Issue 1
Dislocation mobility in potassium and iron single crystals
journal, March 1975
- Urabe, N.; Weertman, J.
- Materials Science and Engineering, Vol. 18, Issue 1
Moving dislocations in disordered alloys: Connecting continuum and discrete models with atomistic simulations
journal, July 2006
- Marian, J.; Caro, A.
- Physical Review B, Vol. 74, Issue 2
Dislocation Mobility in Aluminum
journal, July 1972
- Parameswaran, V. R.; Urabe, N.; Weertman, J.
- Journal of Applied Physics, Vol. 43, Issue 7
Finite deformations of an elastic solid
journal, May 1952
- Wahl, A. M.
- Journal of the Franklin Institute, Vol. 253, Issue 5
Is Intersonic Dislocation Motion Possible? Singularity Analysis for an Edge Dislocation Accelerating through the Shear Wave Speed Barrier
journal, March 2008
- Huang, S.; Markenscoff, X.
- Experimental Mechanics, Vol. 49, Issue 2
Mobility of Dislocations in Aluminum
journal, February 1969
- Gorman, J. A.; Wood, D. S.; Vreeland, T.
- Journal of Applied Physics, Vol. 40, Issue 2
Thermodynamics of Crystals
journal, November 1972
- Wallace, Duane C.; Callen, Herbert
- American Journal of Physics, Vol. 40, Issue 11
Dynamic Peierls-Nabarro equations for elastically isotropic crystals
journal, January 2010
- Pellegrini, Yves-Patrick
- Physical Review B, Vol. 81, Issue 2
Acoustic attenuation studies of the frictional force on a fast moving dislocation
journal, November 1964
- Suzuki, T.; Ikushima, A.; Aoki, M.
- Acta Metallurgica, Vol. 12, Issue 11
Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions
journal, January 2016
- Luscher, D. J.; Mayeur, J. R.; Mourad, H. M.
- International Journal of Plasticity, Vol. 76
Analysis for a screw dislocation accelerating through the shear-wave speed barrier
journal, June 2008
- Markenscoff, Xanthippi; Huang, Surong
- Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 6
Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys
journal, March 2005
- Olmsted, David L.; HectorJr, Louis G.; Curtin, W. A.
- Modelling and Simulation in Materials Science and Engineering, Vol. 13, Issue 3
New estimates of the third-order elastic constants for isotropic aggregates of cubic crystals
journal, April 1997
- Lubarda, V. A.
- Journal of the Mechanics and Physics of Solids, Vol. 45, Issue 4
Third-Order Constants of a Cubic Quasi-Isotropic Solid
journal, June 1990
- Wasserbäch, W.
- physica status solidi (b), Vol. 159, Issue 2
Uniformly Moving Dislocations
journal, May 1949
- Eshelby, J. D.
- Proceedings of the Physical Society. Section A, Vol. 62, Issue 5
Dislocation dynamics and mechanical properties of crystals
journal, January 1988
- Nadgornyi, E.
- Progress in Materials Science, Vol. 31
High dislocation velocities and the structures of slip bands in shock loaded high purity lithium fluoride
journal, January 1964
- Cotner, J.; Weertman, J.
- Discussions of the Faraday Society, Vol. 38
Stress and temperature dependence of screw dislocation mobility in -Fe by molecular dynamics
journal, November 2011
- Gilbert, M. R.; Queyreau, S.; Marian, J.
- Physical Review B, Vol. 84, Issue 17
Elastic precursor wave decay in shock-compressed aluminum over a wide range of temperature
journal, January 2018
- Austin, Ryan A.
- Journal of Applied Physics, Vol. 123, Issue 3
Plastic deformation under high-rate loading: The multiscale approach
journal, July 2010
- Krasnikov, V. S.; Kuksin, A. Yu.; Mayer, A. E.
- Physics of the Solid State, Vol. 52, Issue 7
Aspects of the Theories of Dislocation Mobility and Internal Friction
journal, February 1960
- Lothe, Jens
- Physical Review, Vol. 117, Issue 3
Third‐Order Elastic Constants of Single‐Crystal and Polycrystalline Columbium
journal, June 1968
- Graham, L. J.; Nadler, H.; Chang, Roger
- Journal of Applied Physics, Vol. 39, Issue 7
Response of copper to shock-wave loading at temperatures up to the melting point
journal, August 2013
- Zaretsky, E. B.; Kanel, G. I.
- Journal of Applied Physics, Vol. 114, Issue 8
Dynamic Peierls-Nabarro equations for elastically isotropic crystals
text, January 2009
- Pellegrini, Yves-Patrick
- arXiv
Line tension of a dislocation moving through an anisotropic crystal
text, January 2017
- Blaschke, Daniel N.; Szajewski, Benjamin A.
- arXiv
Properties of dislocation drag from phonon wind at ambient conditions
text, January 2019
- Blaschke, Daniel N.
- arXiv
Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys
text, January 2004
- Olmsted, David L.; Hector, Louis G.; Curtin, W. A.
- arXiv
Third-Order Constants of a Cubic Quasi-Isotropic Solid
journal, June 1990
- Wasserbäch, W.
- physica status solidi (b), Vol. 159, Issue 2
Dislocation mobility in potassium and iron single crystals
journal, March 1975
- Urabe, N.; Weertman, J.
- Materials Science and Engineering, Vol. 18, Issue 1
High dislocation velocities and the structures of slip bands in shock loaded high purity lithium fluoride
journal, January 1964
- Cotner, J.; Weertman, J.
- Discussions of the Faraday Society, Vol. 38
Mobility of Dislocations in Aluminum
journal, February 1969
- Gorman, J. A.; Wood, D. S.; Vreeland, T.
- Journal of Applied Physics, Vol. 40, Issue 2
Response of copper to shock-wave loading at temperatures up to the melting point
journal, August 2013
- Zaretsky, E. B.; Kanel, G. I.
- Journal of Applied Physics, Vol. 114, Issue 8
Supersonic Dislocations Observed in a Plasma Crystal
journal, July 2007
- Nosenko, V.; Zhdanov, S.; Morfill, G.
- Physical Review Letters, Vol. 99, Issue 2
Works referencing / citing this record:
Analytic model of the remobilization of pinned glide dislocations: Including dislocation drag from phonon wind
journal, August 2020
- Blaschke, Daniel N.; Hunter, Abigail; Preston, Dean L.
- International Journal of Plasticity, Vol. 131