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Title: Geometries of edge and mixed dislocations in bcc Fe from first principles calculations

Abstract

We use density functional theory (DFT) to compute the core structures of $$a_0[100](010)$$ edge, $$a_0[100](011)$$ edge, $$a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$$ edge, and $$a_0/2[111](1\bar{1}0)$$ $$71^{\circ}$$ mixed dislocations in body-centered cubic (bcc) Fe. The calculations are performed using flexible boundary conditions (FBC), which effectively allow the dislocations to relax as isolated defects by coupling the DFT core to an infinite harmonic lattice through the lattice Green function (LGF). We use the LGFs of the dislocated geometries in contrast to most previous FBC-based dislocation calculations that use the LGF of the bulk crystal. The dislocation LGFs account for changes in the topology of the crystal in the core as well as local strain throughout the crystal lattice. A simple bulk-like approximation for the force constants in a dislocated geometry leads to dislocation LGFs that optimize the core structures of the $$a_0[100](010)$$ edge, $$a_0[100](011)$$ edge, and $$a_0/2[111](1\bar{1}0)$$ $$71^{\circ}$$ mixed dislocations. This approximation fails for the $$a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$$ dislocation however, so in this case we derive the LGF from more accurate force constants computed using a Gaussian approximation potential. The standard deviations of the dislocation Nye tensor distributions quantify the widths of the dislocation cores. The relaxed cores are compact, and the local magnetic moments on the Fe atoms closely follow the volumetric strain distributions in the cores. We also compute the core structures of these dislocations using eight different classical interatomic potentials, and quantify symmetry differences between the cores using the Fourier coefficients of their Nye tensor distributions. Most of the core structures computed using the classical potentials agree well with the DFT results. Furthermore the DFT core geometries provide benchmarking for classical potential studies of work-hardening, as well as substitutional and interstitial sites for computing solute-dislocation interactions that serve as inputs for mesoscale models of solute strengthening and solute diffusion near dislocations.

Authors:
 [1];  [2];  [3];  [1]
  1. Univ. of Illinois, Urbana, IL (United States). Dept. of Materials Science and Engineering
  2. Univ. of Illinois, Urbana, IL (United States). Dept. of Materials Science and Engineering; Univ. of Florida, Gainesville, FL (United States). Dept. of Materials Science and Engineering
  3. General Motors Global R&D Center, Warren, MI (United States)
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States); General Motors Global R&D Center, Warren, MI (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE); National Science Foundation (NSF)
OSTI Identifier:
1481001
Alternate Identifier(s):
OSTI ID: 1492141
Grant/Contract Number:  
EE0005976; 1410596
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Materials
Additional Journal Information:
Journal Volume: 2; Journal Issue: 11; Journal ID: ISSN 2475-9953
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; dislocation; edge, mixed; bcc Fe; iron; first principles; DFT

Citation Formats

Fellinger, Michael R., Tan, Anne Marie Z., Hector, Louis G., and Trinkle, Dallas R. Geometries of edge and mixed dislocations in bcc Fe from first principles calculations. United States: N. p., 2018. Web. doi:10.1103/PhysRevMaterials.2.113605.
Fellinger, Michael R., Tan, Anne Marie Z., Hector, Louis G., & Trinkle, Dallas R. Geometries of edge and mixed dislocations in bcc Fe from first principles calculations. United States. doi:10.1103/PhysRevMaterials.2.113605.
Fellinger, Michael R., Tan, Anne Marie Z., Hector, Louis G., and Trinkle, Dallas R. Mon . "Geometries of edge and mixed dislocations in bcc Fe from first principles calculations". United States. doi:10.1103/PhysRevMaterials.2.113605. https://www.osti.gov/servlets/purl/1481001.
@article{osti_1481001,
title = {Geometries of edge and mixed dislocations in bcc Fe from first principles calculations},
author = {Fellinger, Michael R. and Tan, Anne Marie Z. and Hector, Louis G. and Trinkle, Dallas R.},
abstractNote = {We use density functional theory (DFT) to compute the core structures of $a_0[100](010)$ edge, $a_0[100](011)$ edge, $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations in body-centered cubic (bcc) Fe. The calculations are performed using flexible boundary conditions (FBC), which effectively allow the dislocations to relax as isolated defects by coupling the DFT core to an infinite harmonic lattice through the lattice Green function (LGF). We use the LGFs of the dislocated geometries in contrast to most previous FBC-based dislocation calculations that use the LGF of the bulk crystal. The dislocation LGFs account for changes in the topology of the crystal in the core as well as local strain throughout the crystal lattice. A simple bulk-like approximation for the force constants in a dislocated geometry leads to dislocation LGFs that optimize the core structures of the $a_0[100](010)$ edge, $a_0[100](011)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations. This approximation fails for the $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ dislocation however, so in this case we derive the LGF from more accurate force constants computed using a Gaussian approximation potential. The standard deviations of the dislocation Nye tensor distributions quantify the widths of the dislocation cores. The relaxed cores are compact, and the local magnetic moments on the Fe atoms closely follow the volumetric strain distributions in the cores. We also compute the core structures of these dislocations using eight different classical interatomic potentials, and quantify symmetry differences between the cores using the Fourier coefficients of their Nye tensor distributions. Most of the core structures computed using the classical potentials agree well with the DFT results. Furthermore the DFT core geometries provide benchmarking for classical potential studies of work-hardening, as well as substitutional and interstitial sites for computing solute-dislocation interactions that serve as inputs for mesoscale models of solute strengthening and solute diffusion near dislocations.},
doi = {10.1103/PhysRevMaterials.2.113605},
journal = {Physical Review Materials},
number = 11,
volume = 2,
place = {United States},
year = {2018},
month = {11}
}

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Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Characterization and visualization of the lattice misfit associated with dislocation cores
journal, March 2005


Dislocation multi-junctions and strain hardening
journal, April 2006

  • Bulatov, Vasily V.; Hsiung, Luke L.; Tang, Meijie
  • Nature, Vol. 440, Issue 7088
  • DOI: 10.1038/nature04658

Theory and simulation of the diffusion of kinks on dislocations in bcc metals
journal, February 2013


Ab initio calculations of the lattice parameter and elastic stiffness coefficients of bcc Fe with solutes
journal, January 2017


Projector augmented-wave method
journal, December 1994


Edge dislocation mobilities in bcc Fe obtained by molecular dynamics
journal, August 2011


The core structure of ½(111) screw dislocations in b.c.c. crystals
journal, May 1970


Dislocation interaction with C in α-Fe: A comparison between atomic simulations and elasticity theory
journal, August 2008


Structure and mobility of the 12<111>{112} edge dislocation in BCC iron studied by molecular dynamics
journal, March 2009


Ab initio modeling of quasielastic neutron scattering of hydrogen pipe diffusion in palladium
journal, August 2016


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Magnetostriction of iron
journal, February 1983

  • du Tremolet de Lacheisserie, E.; Mendia Monterroso, R.
  • Journal of Magnetism and Magnetic Materials, Vol. 31-34
  • DOI: 10.1016/0304-8853(83)90704-7

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995


Hydrogen-induced change in core structures of {110}[111] edge and {110}[111] screw dislocations in iron
journal, September 2013

  • Wang, Shuai; Hashimoto, Naoyuki; Ohnuki, Somei
  • Scientific Reports, Vol. 3, Issue 1
  • DOI: 10.1038/srep02760

Quantitative modeling of the equilibration of two-phase solid-liquid Fe by atomistic simulations on diffusive time scales
journal, January 2015


Microstructure and mechanical properties of super-strong nanocrystalline tungsten processed by high-pressure torsion
journal, September 2006


Effect of orientation of prismatic dislocation loops on interaction with free surfaces in BCC iron
journal, December 2017


PHON: A program to calculate phonons using the small displacement method
journal, December 2009


Atomic-scale investigation of point defects and hydrogen-solute atmospheres on the edge dislocation mobility in alpha iron
journal, August 2014

  • Bhatia, M. A.; Groh, S.; Solanki, K. N.
  • Journal of Applied Physics, Vol. 116, Issue 6
  • DOI: 10.1063/1.4892630

Atomistic simulation of the a0 〈100〉 binary junction formation and its unzipping in body-centered cubic iron
journal, February 2014


Quantum effect on thermally activated glide of dislocations
journal, August 2012

  • Proville, Laurent; Rodney, David; Marinica, Mihai-Cosmin
  • Nature Materials, Vol. 11, Issue 10
  • DOI: 10.1038/nmat3401

Reactions between glide dislocations and forest dislocations in anisotropie B.C.C. metals
journal, July 1985


Deviations and polarity of [100] dislocations in bcc metals
journal, June 2010


Green's function boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations
journal, January 1998


Edge dislocations as sinks for sub-nanometric radiation induced defects in α-iron
journal, January 2018


High-precision sampling for Brillouin-zone integration in metals
journal, August 1989


Computation of the lattice Green function for a dislocation
journal, August 2016


Thermally-activated deformation of BCC metals and alloys
journal, January 1992


First-principles simulations of dislocation cores
journal, July 2005


Electronic effect of kink in the edge dislocation in bcc iron: A first-principles study
journal, July 2006

  • Chen, Li-qun; Wang, Chong-yu; Yu, Tao
  • Journal of Applied Physics, Vol. 100, Issue 2
  • DOI: 10.1063/1.2217984

Ab-initio simulation of isolated screw dislocations in bcc Mo and Ta
journal, May 2001


Second-order junctions and strain hardening in bcc and fcc crystals
journal, May 2008


Achieving DFT accuracy with a machine-learning interatomic potential: Thermomechanics and defects in bcc ferromagnetic iron
journal, January 2018


Representation of dislocation cores using Nye tensor distributions
journal, July 2005


Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling
journal, July 1978

  • Sinclair, J. E.; Gehlen, P. C.; Hoagland, R. G.
  • Journal of Applied Physics, Vol. 49, Issue 7
  • DOI: 10.1063/1.325395

Electronic states and doping effect of carbon in the edge-dislocation core of bcc iron
journal, June 2004


Ab initio investigation of the Peierls potential of screw dislocations in bcc Fe and W
journal, June 2013


Computer simulation of point defect properties in dilute Fe—Cu alloy using a many-body interatomic potential
journal, March 1997


Interaction of an edge dislocation with Cu–Ni-vacancy clusters in bcc iron
journal, December 2011


Development of new interatomic potentials appropriate for crystalline and liquid iron
journal, December 2003


Thermodynamics of hexagonal-close-packed iron under Earth’s core conditions
journal, July 2001


Ab Initio Study of Screw Dislocations in Mo and Ta: A New Picture of Plasticity in bcc Transition Metals
journal, February 2000


Special points for Brillouin-zone integrations
journal, June 1976

  • Monkhorst, Hendrik J.; Pack, James D.
  • Physical Review B, Vol. 13, Issue 12, p. 5188-5192
  • DOI: 10.1103/PhysRevB.13.5188

The glide of screw dislocations in bcc Fe: Atomistic static and dynamic simulations☆
journal, August 2006


Ab initio modeling of the two-dimensional energy landscape of screw dislocations in bcc transition metals
journal, January 2014


Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


Influence of the dislocation core on the glide of the ½〈111〉{110} edge dislocation in bcc-iron: An embedded atom method study
journal, May 2014


“Conjugate Channeling” Effect in Dislocation Core Diffusion: Carbon Transport in Dislocated BCC Iron
journal, April 2013


Embedded-atom potential for Fe and its application to self-diffusion on Fe(100)
journal, May 2006


Density functional theory studies of screw dislocation core structures in bcc metals
journal, January 2003


Direct calculation of the lattice Green function with arbitrary interactions for general crystals
journal, June 2012


First-principles data for solid-solution strengthening of magnesium: From geometry and chemistry to properties
journal, October 2010


Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
journal, April 2010


Comparison of empirical interatomic potentials for iron applied to radiation damage studies
journal, November 2010


Some surprising features of the plastic deformation of body-centered cubic metals and alloys
journal, July 1983


Interatomic potentials for hydrogen in α –iron based on density functional theory
journal, May 2009

  • Ramasubramaniam, Ashwin; Itakura, Mitsuhiro; Carter, Emily A.
  • Physical Review B, Vol. 79, Issue 17
  • DOI: 10.1103/PhysRevB.79.174101

Irradiation-Induced Formation of Nanocrystallites with C 15 Laves Phase Structure in bcc Iron
journal, January 2012


Anisotropic continuum theory of lattice defects
journal, January 1980


Ab initio Force Constant Approach to Phonon Dispersion Relations of Diamond and Graphite
journal, December 1995


Improved tetrahedron method for Brillouin-zone integrations
journal, June 1994


Screw dislocation mobility in BCC metals: the role of the compact core on double-kink nucleation
journal, November 2010

  • Gordon, P. A.; Neeraj, T.; Li, Y.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 18, Issue 8
  • DOI: 10.1088/0965-0393/18/8/085008

Flexible Ab Initio Boundary Conditions: Simulating Isolated Dislocations in bcc Mo and Ta
journal, May 2002


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    De novo exploration and self-guided learning of potential-energy surfaces
    journal, October 2019

    • Bernstein, Noam; Csányi, Gábor; Deringer, Volker L.
    • npj Computational Materials, Vol. 5, Issue 1
    • DOI: 10.1038/s41524-019-0236-6

    Influence of hydrogen core force shielding on dislocation junctions in iron
    journal, March 2020


    De novo exploration and self-guided learning of potential-energy surfaces
    text, January 2019

    • Bernstein, N.; Csányi, G.; Deringer, Volker
    • Apollo - University of Cambridge Repository
    • DOI: 10.17863/cam.43816