Stability, structure and electronic properties of γ-Fe23C6 from first-principles theory

doi:10.1016/j.actamat.2010.01.025

Acta Materialia

Volume 58, Issue 8, May 2010, Pages 2968-2977

https://doi.org/10.1016/j.actamat.2010.01.025 Get rights and content

Abstract

First-principles’ calculations of GGA and GGA + U type have been performed for γ-Fe₂₃C₆, a complex iron carbide with 116 atom in the unit cell. GGA results were found to be in better agreement with experimental data than GGA + U results. Various occupancies for Wyckoff positions and corresponding magnetic orderings have been explored. Our calculations reveal that the crystal structure is composed of a framework of strongly linked Fe atoms, and additional stabilizing Fe and C atoms positioned in cavities. The local electronic and magnetic properties vary strongly among the non-equivalent Fe sites in γ-Fe₂₃C₆. The lattice parameters of γ-Fe₂₃C₆ match those of austenite well. Surprisingly, pure γ-Fe₂₃C₆ is found to be more stable than commonly occurring θ-Fe₃C cementite. Moreover, the calculations show low vacancy energy (about 0.37 eV) for Fe at 4a sites in γ-Fe₂₃C₆. Conditions of formation and factors hampering the formation of γ-Fe₂₃C₆ in steel manufacturing processes are discussed.

Introduction

Recently Branagan and colleagues [1] prepared a nanocomposite iron alloy from a metallic glass. The alloy exhibits low-temperature superplasticity with an ultimate tensile strength of 1800 MPa and a tensile elongation of 230%. The prepared samples contain nanocomposite microstructures composed of α-Fe, Fe₂₃C₆ and Fe₃B. Fe₂₃C₆, or more generally M₂₃C₆ (M = Fe, Cr, Ni, etc.), phases have a faced-centered cubic structure (γ-). These phases have been found in different steels, e.g. stainless and tool steels [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], and have been observed as precipitates at the grain boundary of steels, as well [1], [2], [7]. Moreover, γ-M₂₃C₆ phases are present in iron meteorites with the mineral names haxonite (M = Fe, Ni) and isovite (M = Fe, Cr) [12], [13], [14].

Although γ-Fe₂₃C₆, or γ-M₂₃C₆ more generally, has been reported in different Fe-based alloys, steels and minerals, detailed experimental and theoretical knowledge about the chemical composition and crystal structure, as well as the electronic and magnetic properties, is still scarce. γ-M₂₃C₆ phases exist generally in multinary alloys. The existence and stability of a pure γ-Fe₂₃C₆ phase are not clear. The only theoretical papers are by Xie and colleagues [15], [16], [17], who performed atomistic simulations for several compounds of γ-M₂₃C₆, with M = Cr, Mn, Fe, W, etc. In the present paper we report results of first-principles calculations for γ-Fe₂₃C₆, as well as for θ-Fe₃C for comparison. The stability of both iron carbides is compared to the mixture of corresponding elemental solids (α-Fe and graphite). Different chemical compositions and structural configurations of γ-Fe₂₃C₆ were also taken into account. The local electronic and magnetic properties were investigated. The information obtained here is not only useful in understanding the formation, stability and structures of γ-Fe₂₃C₆-based phases in Fe-alloys, steels and Fe-minerals, but also in understanding the electronic and magnetic properties of γ-(Fe, M)₂₃C₆-type compounds and minerals [2], [12], [13], [14], [17], [18], [19].

Section snippets

Stability of iron carbides

The formation enthalpy (ΔH) of an iron carbide (Fe_nC_m) from the pure solids of the elements (α-phase and graphite) can be described as: $Δ H = H ({Fe}_{n} C_{m}) - (nH (Fe) + mH (C))$

To compare the relative stability of different iron carbides, we use the formation enthalpy per atom (ΔH_f): $Δ H_{f} = Δ H / (n + m)$

At a temperature of 0 K and a pressure of 0 Pa, the enthalpy difference is equal to the energy difference, that is ΔH(Fe_nC_m) = ΔE(Fe_nC_m), when we ignore the zero-point vibration contribution.

It is generally known that

Results of the calculations for γ-Fe₂₃₋_nC₆ (n = 0, ±1, 3)

We first performed total energy calculations for the elemental solids diamond and α-Fe. The GGA-calculated diamond lattice parameter is 3.5713 Å, which agrees with the experimental value (3.5668 Å at 300 K) [20] and other recent GGA calculations (3.5745 Å) [22]. The energy of graphite at 0 K and 0 Pa is obtained by substracting 17 meV atom^–1 [20] from the value for diamond, yielding −9.113 eV per C atom for graphite.

α-Fe has a bcc structure. Both GGA and two GGA + U results are listed in Table 1. The

Conclusions

We performed total energy calculations for the binary iron carbide γ-Fe₂₃C₆, which is cubic with the space group $F m \bar{3} m$ . The ground state of γ-Fe₂₃C₆ exhibits a ferromagnetic structure. The Fe 3d orbitals are almost fully occupied for the spin-up electrons. The structure of γ-Fe₂₃C₆ has been analyzed as consisting of two parts: a framework composed of Fe3 and Fe4 atoms, and stabilizers (Fe1, Fe2 and C atoms) in the framework cavities. γ-Fe₂₃C₆ is found to exhibit a number of unusual features:

Acknowledgements

Jouk Jansen (Nano-HREM, TU-Delft) is acknowledged for kind help with the software. Dr. Dave Hanlon and Dr. Steven Celotto (Corus RDT) are acknowledged for useful discussions. The authors acknowledge financial support from the Materials Innovation Institute (M2i, Project No. MC5.06280) and from the Stichting Technologie en Wetenschap (STW, Proj. No. 07532), The Netherlands.

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Citation Excerpt :
The problem can be solved by theoretical calculation. Using first principles calculations, the thermodynamic stability, chemical bonding, hardness and elastic properties of M23C6 compounds have been well studied [13–16]. However, the researches on the mechanical properties of M23C6 only focus on its elastic properties, while there is insufficient research on the mechanical properties of M23C6 under a larger strain.
To investigate the fatigue behavior of steel or Ni-based superalloy, it is necessary to identify the mechanism of crack initiation and non-uniform deformation by studying the mechanical properties of M₂₃C₆ carbides. The effects of temperature, vacancies, and void on the mechanical properties of M₂₃C₆ (M = Fe) carbides are investigated by the molecular dynamics method. Furthermore, in order to identify the slip system which is the most conductive to dislocation activity for M₂₃C₆ type carbides, based on the generalized stacking fault energy (GSFE) model of Fe₂₃C₆, the three-dimensional GSFE surface is calculated. The results show that Fe₂₃C₆ is more prone to cleavage fracture along the [110] direction than along the [100] and the [111] directions at the same temperature; the void size has a great effect on the tensile stress curve of Fe₂₃C₆ along the [100] direction but has little effect on the tensile stress curve along [110] and [111] directions. The slip of Fe₂₃C₆ on the (111) plane tends to follow the [11 $\overline{2}$ ] direction, and Fe₂₃C₆ is more likely to produce the dislocation structure on the (111) plane than on the (110) plane.

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Stability, structure and electronic properties of γ-Fe23C6 from first-principles theory

Abstract

Introduction

Section snippets

Stability of iron carbides

Results of the calculations for γ-Fe23−nC6 (n = 0, ±1, 3)

Conclusions

Acknowledgements

Scripta Metall

Geochim Cosmochim Acta

ICARUS

Acta Mater

Acta Mater

Acta Mater

J Magn Magn Mater

Comput Mater Sci

J Alloys Compd

J Phys Chem Solid

Physica B

Surf Sci

Prog Solid State Chem

Nanotechnology

The theory of transformation in metals and alloys

Nature

J Phys

Metall Trans

Metall Trans

ISIJ Int

Mater Sci Forum

Adv Eng Mater

Nature

Metall Trans

Stability, structure and electronic properties of γ-Fe₂₃C₆ from first-principles theory

Results of the calculations for γ-Fe₂₃₋_nC₆ (n = 0, ±1, 3)