# 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:

- Univ. of Illinois, Urbana, IL (United States). Dept. of Materials Science and Engineering
- 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
- 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

- Grant/Contract Number:
- EE0005976; 1410596

- Resource Type:
- Journal Article: 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.
```

```
@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 = {Mon Nov 26 00:00:00 EST 2018},

month = {Mon Nov 26 00:00:00 EST 2018}

}

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

##
Projector augmented-wave method

journal, December 1994

- Bl�chl, P. E.
- Physical Review B, Vol. 50, Issue 24, p. 17953-17979

##
From ultrasoft pseudopotentials to the projector augmented-wave method

journal, January 1999

- Kresse, G.; Joubert, D.
- Physical Review B, Vol. 59, Issue 3, p. 1758-1775

##
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

##
Efficient iterative schemes for *ab initio* total-energy calculations using a plane-wave basis set

journal, October 1996

- Kresse, G.; Furthm�ller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186