### Abstract

New data are presented on the ambient-temperature values of the orthorhombic lattice parameters of cementite (θ, Fe_{3}C_{1-z}). The cementite was obtained by electrolytically etching away the ferrite or martensite from quenched dual-phase Fe-C alloys equilibrated at 823 K ≤ T ≤ 1323 K, i.e. in the α (ferrite) + θ or γ (austenite) + θ two-phase fields, followed by quenching. In qualitative agreement with earlier data (Petch, 1944), the decrease in the lattice parameters a and c and the simultaneous increase in b with increasing equilibration temperature T can be attributed to an increase in the fraction of C vacancies, z, in Fe_{3}C_{1-}_{z} in equilibrium with the corresponding Fe[C] terminal solid-solution phase (α or γ). The experimental data are compared with results on C-vacancy-induced lattice-parameter changes obtained by first-principles calculations performed within the framework of density-functional theory (DFT). The anisotropy of the changes in the lattice parameters a, b and c predicted by DFT agrees qualitatively with the experimentally observed changes occurring with increasing equilibration temperature. Eventually, the equilibration-temperature dependence of the unit-cell volume of the cementite, V = abc, was used to calculate T-dependent values of the vacancy fraction z, thereby yielding data for the α + θ/θ and γ + θ/θ phase boundaries in the metastable phase diagram of Fe-Fe_{3}C. In particular, the α + θ/θ phase boundary determined could be interpreted in terms of Gibbs energy of C-vacancy formation in cementite, whereby its enthalpy contribution agrees well with the results of the first-principles calculations.

Original language | English (US) |
---|---|

Pages (from-to) | 374-384 |

Number of pages | 11 |

Journal | Acta Materialia |

Volume | 86 |

DOIs | |

State | Published - Mar 2015 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Ceramics and Composites
- Polymers and Plastics
- Metals and Alloys

### Cite this

}

_{3}C

_{1-}

_{z}, in equilibrium with α-Fe[C] and γ-Fe[C]',

*Acta Materialia*, vol. 86, pp. 374-384. https://doi.org/10.1016/j.actamat.2014.11.046

**C-vacancy concentration in cementite, Fe _{3}C_{1-}_{z}, in equilibrium with α-Fe[C] and γ-Fe[C].** / Leineweber, A.; Shang, S. L.; Liu, Z. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - C-vacancy concentration in cementite, Fe3C1-z, in equilibrium with α-Fe[C] and γ-Fe[C]

AU - Leineweber, A.

AU - Shang, S. L.

AU - Liu, Z. K.

PY - 2015/3

Y1 - 2015/3

N2 - New data are presented on the ambient-temperature values of the orthorhombic lattice parameters of cementite (θ, Fe3C1-z). The cementite was obtained by electrolytically etching away the ferrite or martensite from quenched dual-phase Fe-C alloys equilibrated at 823 K ≤ T ≤ 1323 K, i.e. in the α (ferrite) + θ or γ (austenite) + θ two-phase fields, followed by quenching. In qualitative agreement with earlier data (Petch, 1944), the decrease in the lattice parameters a and c and the simultaneous increase in b with increasing equilibration temperature T can be attributed to an increase in the fraction of C vacancies, z, in Fe3C1-z in equilibrium with the corresponding Fe[C] terminal solid-solution phase (α or γ). The experimental data are compared with results on C-vacancy-induced lattice-parameter changes obtained by first-principles calculations performed within the framework of density-functional theory (DFT). The anisotropy of the changes in the lattice parameters a, b and c predicted by DFT agrees qualitatively with the experimentally observed changes occurring with increasing equilibration temperature. Eventually, the equilibration-temperature dependence of the unit-cell volume of the cementite, V = abc, was used to calculate T-dependent values of the vacancy fraction z, thereby yielding data for the α + θ/θ and γ + θ/θ phase boundaries in the metastable phase diagram of Fe-Fe3C. In particular, the α + θ/θ phase boundary determined could be interpreted in terms of Gibbs energy of C-vacancy formation in cementite, whereby its enthalpy contribution agrees well with the results of the first-principles calculations.

AB - New data are presented on the ambient-temperature values of the orthorhombic lattice parameters of cementite (θ, Fe3C1-z). The cementite was obtained by electrolytically etching away the ferrite or martensite from quenched dual-phase Fe-C alloys equilibrated at 823 K ≤ T ≤ 1323 K, i.e. in the α (ferrite) + θ or γ (austenite) + θ two-phase fields, followed by quenching. In qualitative agreement with earlier data (Petch, 1944), the decrease in the lattice parameters a and c and the simultaneous increase in b with increasing equilibration temperature T can be attributed to an increase in the fraction of C vacancies, z, in Fe3C1-z in equilibrium with the corresponding Fe[C] terminal solid-solution phase (α or γ). The experimental data are compared with results on C-vacancy-induced lattice-parameter changes obtained by first-principles calculations performed within the framework of density-functional theory (DFT). The anisotropy of the changes in the lattice parameters a, b and c predicted by DFT agrees qualitatively with the experimentally observed changes occurring with increasing equilibration temperature. Eventually, the equilibration-temperature dependence of the unit-cell volume of the cementite, V = abc, was used to calculate T-dependent values of the vacancy fraction z, thereby yielding data for the α + θ/θ and γ + θ/θ phase boundaries in the metastable phase diagram of Fe-Fe3C. In particular, the α + θ/θ phase boundary determined could be interpreted in terms of Gibbs energy of C-vacancy formation in cementite, whereby its enthalpy contribution agrees well with the results of the first-principles calculations.

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U2 - 10.1016/j.actamat.2014.11.046

DO - 10.1016/j.actamat.2014.11.046

M3 - Article

AN - SCOPUS:84921486232

VL - 86

SP - 374

EP - 384

JO - Acta Materialia

JF - Acta Materialia

SN - 1359-6454

ER -