Stability, structure and electronic properties of γ-Fe23C6 from first-principles theory
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 (FenCm) from the pure solids of the elements (α-phase and graphite) can be described as:
To compare the relative stability of different iron carbides, we use the formation enthalpy per atom (ΔHf):
At a temperature of 0 K and a pressure of 0 Pa, the enthalpy difference is equal to the energy difference, that is ΔH(FenCm) = ΔE(FenCm), 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 . 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:
- 1.
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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