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

A. Leineweber, S. L. Shang, Z. K. Liu

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)374-384
Number of pages11
JournalActa Materialia
Volume86
DOIs
StatePublished - Mar 2015

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Lattice constants
Vacancies
Phase boundaries
Density functional theory
Ferrite
Temperature
Metastable phases
Gibbs free energy
Martensite
Austenite
Phase diagrams
Enthalpy
Etching
Quenching
Solid solutions
Anisotropy

All Science Journal Classification (ASJC) codes

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

Cite this

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title = "C-vacancy concentration in cementite, Fe3C1-z, in equilibrium with α-Fe[C] and γ-Fe[C]",
abstract = "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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C-vacancy concentration in cementite, Fe3C1-z, in equilibrium with α-Fe[C] and γ-Fe[C]. / Leineweber, A.; Shang, S. L.; Liu, Z. K.

In: Acta Materialia, Vol. 86, 03.2015, p. 374-384.

Research output: Contribution to journalArticle

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

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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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