### Abstract

We present an efficient methodology for computing solute-induced changes in lattice parameters and elastic stiffness coefficients C_{ij} of single crystals using density functional theory. We introduce a solute strain misfit tensor that quantifies how solutes change lattice parameters due to the stress they induce in the host crystal. Solutes modify the elastic stiffness coefficients through volumetric changes and by altering chemical bonds. We compute each of these contributions to the elastic stiffness coefficients separately, and verify that their sum agrees with changes in the elastic stiffness coefficients computed directly using fully optimized supercells containing solutes. Computing the two elastic stiffness contributions separately is more computationally efficient and provides more information on solute effects than the direct calculations. We compute the solute dependence of polycrystalline averaged shear and Young's moduli from the solute dependence of the single-crystal C_{ij}. We apply this methodology to substitutional Al, B, Cu, Mn, Si solutes and octahedral interstitial C and N solutes in bcc Fe. Comparison with experimental data indicates that our approach accurately predicts solute-induced changes in the lattice parameter and elastic coefficients. The computed data can be used to quantify solute-induced changes in mechanical properties such as strength and ductility, and can be incorporated into mesoscale models to improve their predictive capabilities.

Language | English (US) |
---|---|

Pages | 503-513 |

Number of pages | 11 |

Journal | Computational Materials Science |

Volume | 126 |

DOIs | |

State | Published - Jan 1 2017 |

### Fingerprint

### Keywords

- Ab initio
- Elastic constants
- Ferrite
- Iron
- Lattice parameters
- Solutes
- Steel

### ASJC Scopus subject areas

- Computer Science(all)
- Chemistry(all)
- Materials Science(all)
- Mechanics of Materials
- Physics and Astronomy(all)
- Computational Mathematics

### Cite this

*Computational Materials Science*,

*126*, 503-513. DOI: 10.1016/j.commatsci.2016.09.040

**Ab initio calculations of the lattice parameter and elastic stiffness coefficients of bcc Fe with solutes.** / Fellinger, Michael R.; Hector, Louis G.; Trinkle, Dallas R.

Research output: Research - peer-review › Article

*Computational Materials Science*, vol 126, pp. 503-513. DOI: 10.1016/j.commatsci.2016.09.040

}

TY - JOUR

T1 - Ab initio calculations of the lattice parameter and elastic stiffness coefficients of bcc Fe with solutes

AU - Fellinger,Michael R.

AU - Hector,Louis G.

AU - Trinkle,Dallas R.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We present an efficient methodology for computing solute-induced changes in lattice parameters and elastic stiffness coefficients Cij of single crystals using density functional theory. We introduce a solute strain misfit tensor that quantifies how solutes change lattice parameters due to the stress they induce in the host crystal. Solutes modify the elastic stiffness coefficients through volumetric changes and by altering chemical bonds. We compute each of these contributions to the elastic stiffness coefficients separately, and verify that their sum agrees with changes in the elastic stiffness coefficients computed directly using fully optimized supercells containing solutes. Computing the two elastic stiffness contributions separately is more computationally efficient and provides more information on solute effects than the direct calculations. We compute the solute dependence of polycrystalline averaged shear and Young's moduli from the solute dependence of the single-crystal Cij. We apply this methodology to substitutional Al, B, Cu, Mn, Si solutes and octahedral interstitial C and N solutes in bcc Fe. Comparison with experimental data indicates that our approach accurately predicts solute-induced changes in the lattice parameter and elastic coefficients. The computed data can be used to quantify solute-induced changes in mechanical properties such as strength and ductility, and can be incorporated into mesoscale models to improve their predictive capabilities.

AB - We present an efficient methodology for computing solute-induced changes in lattice parameters and elastic stiffness coefficients Cij of single crystals using density functional theory. We introduce a solute strain misfit tensor that quantifies how solutes change lattice parameters due to the stress they induce in the host crystal. Solutes modify the elastic stiffness coefficients through volumetric changes and by altering chemical bonds. We compute each of these contributions to the elastic stiffness coefficients separately, and verify that their sum agrees with changes in the elastic stiffness coefficients computed directly using fully optimized supercells containing solutes. Computing the two elastic stiffness contributions separately is more computationally efficient and provides more information on solute effects than the direct calculations. We compute the solute dependence of polycrystalline averaged shear and Young's moduli from the solute dependence of the single-crystal Cij. We apply this methodology to substitutional Al, B, Cu, Mn, Si solutes and octahedral interstitial C and N solutes in bcc Fe. Comparison with experimental data indicates that our approach accurately predicts solute-induced changes in the lattice parameter and elastic coefficients. The computed data can be used to quantify solute-induced changes in mechanical properties such as strength and ductility, and can be incorporated into mesoscale models to improve their predictive capabilities.

KW - Ab initio

KW - Elastic constants

KW - Ferrite

KW - Iron

KW - Lattice parameters

KW - Solutes

KW - Steel

UR - http://www.scopus.com/inward/record.url?scp=84994314312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994314312&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2016.09.040

DO - 10.1016/j.commatsci.2016.09.040

M3 - Article

VL - 126

SP - 503

EP - 513

JO - Computational Materials Science

T2 - Computational Materials Science

JF - Computational Materials Science

SN - 0927-0256

ER -