Thermodynamic assessment of the Mn–C system

doi:10.1016/j.calphad.2010.05.002

Calphad

Volume 34, Issue 3, September 2010, Pages 279-285

https://doi.org/10.1016/j.calphad.2010.05.002 Get rights and content

Abstract

The manganese–carbon system has been assessed by means of the CALPHAD method. There is a previous description of this system [W. Huang, Scand. J. Metall., 19 (1990) 26–32], but since then a number of high quality experimental investigations have been published. In addition ab initio calculations of the enthalpies of formation of the manganese carbides have been performed to support the thermodynamic evaluation. The liquid, $α$ -Mn, $β$ -Mn, $γ$ -Mn, $δ$ -Mn and $ε$ -Mn phases are described as solution phases and the carbides Mn₂₃C₆, Mn₃C, Mn₅C₂ and Mn₇C₃ are described as stoichiometric compounds. A good description of most experimental data, in particular the more recent data, has been achieved. The uncertainties in the thermodynamic properties of the stoichiometric carbides and the liquid are quite small, but fairly large uncertainties remain for the phase equilibria and thermodynamic properties of the solid solution phases.

Introduction

The high manganese TRIP (“transformation induced plasticity”) and TWIP (“twinning induced plasticity”) steels provide great potential in applications for structural components in the automotive industry, owing to their excellent tensile strength-ductility property combination [1]. The development of these materials requires a full understanding of thermodynamic stability of the phases that constitute the ternary Fe–Mn–C system. The study, presented in this paper, is part of a project whose aim is to provide a precise and reliable thermodynamic description for the Fe–Mn–C system. The present work is focused on the assessment of the binary Mn–C system using the CALPHAD approach. This system has been described previously by Huang [2] while liquid of the system has also been assessed by Lee [3], [4]. Since then new high quality experimental data on the liquidus [5], [6], [7], [8], [9] and the partial Gibbs energy of manganese in various solid state phase equilibria [10] have been published. Data on enthalpy of formation of manganese carbides obtained by ab initio calculation in the present work have also been taken into account. The calculated phase diagram of the Mn–C system is shown in Fig. 1.

Section snippets

Survey of literature information

Experimental thermodynamic and phase equilibrium data of the Mn–C system, available up to 1989, have already been reviewed in detail in a previous evaluation [2]. In the present work, a brief review of these data will be presented. The current understanding of the Mn–C system has evolved gradually and there are still a number of unresolved issues. The first systematic investigation of the Mn–C system was made by Vogel and Döring [11], but there are many discrepancies between their data and

Ab initio calculations

In order to obtain the enthalpies of formation $Δ H_{f}$ of the already known (Mn₃C, Mn₅C₂, Mn₇C₃, and Mn₂₃C₆) and, additionally, two hypothetical manganese carbides (MnC and Mn₂C) at 0 K, we performed calculations based on density-functional theory (DFT). Structure optimisations of the binary bulk phases from first principles were achieved with the Vienna ab initio simulation package (VASP) [31], [32] using projector-augmented waves (PAW) [33], [34] with a kinetic energy cutoff of 500 eV; the

Thermodynamic models and optimisation of parameters

In the CALPHAD method all available thermodynamic and phase equilibrium data for the system are evaluated simultaneously to obtain one set of model equations for the Gibbs energies of all phases as functions of temperature and composition. Some of these expressions contain adjustable coefficients that are often referred to as model parameters. The optimal values for the model parameters providing the best match between available experimental values and the calculated quantities are usually

Ab initio calculations

The structures of the already known carbides Mn₇C₃, Mn₅C₂, Mn₃C, and Mn₂₃C₆ were constructed using their experimental structure data [13], [43]. The structural relaxations of the four carbides led to only small changes of the lattice parameters and tiny changes of the atomic positions. This confirmed the basic stability (or, at least, metastability) of the structures because an unstable structure would distort upon optimisation. The optimised lattice parameters, as shown in Table 3 together

Conclusions

A consistent thermodynamic description of the entire Mn–C system was obtained by considering the ab initio calculation values and critically assessed literature data. In comparison to the previous modeling, an improvement has been achieved. However, it should be noted that substantial uncertainties remain concerning the solid state phase equilibria of the solid solution phases.

Acknowledgements

The authors gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center (SFB) 761 “Stahl—ab initio: Quantenmechanisch geführtes Design neuer Eisenbasis-Werkstoffe”. We like to thank the supercomputing center of Research Center Jülich for letting us use their computational resources.

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Thermodynamic assessment of the Mn–C system

Abstract

Introduction

Section snippets

Survey of literature information

Ab initio calculations

Thermodynamic models and optimisation of parameters

Ab initio calculations

Conclusions

Acknowledgements

J. Iron Steel Res. Int.

J. Alloys Compd.

Comput. Mater. Sci.

Phys. Rev. B

CALPHAD

ISIJ Int.

Scand. J. Metall.

Metall. Trans. B

ISIJ Int.

Int. J. Mater. Res. (formerly Z. Metallkd.)

Steel Res.

Dokl. Akad. Nauk

ISIJ Int.

Dokl. Phys. Chem.

Arch. Eisenhüttenwes.

Sci. Rep. Res. Inst. Tokohu Univ. Ser. A

J. Iron Steel Inst.

Metall. Trans.

Metall. Trans. B

Giessereiforschung

Trans. JIM

Arch. Eisenhüttenwes.

J. Iron Steel Inst.

Metrologia