PrecHiMn-4—A thermodynamic database for high-Mn steels

This paper concerns a Calphad database that was developed to describe precipitation of cubic carbides and nitrides (V, Nb and Ti) in high manganese steels and to describe phase equilibria in high manganese steels with high aluminium content. The database has also been shown to be useful for calculations on medium manganese steels and low-density steels with varying aluminium additions. Thus the database covers a significant fraction of the steels that are termed advanced high strength steels (AHSS) of the second and third generation. A number of systems were assessed (or reassessed) for the database, namely Fe–Mn–Al, Fe–Mn–C, Fe–Nb, Mn–Nb, Fe–Mn–Nb, Fe–Nb–V, Fe–Nb–C, Mn–Nb–C, Fe–Mn–Nb–C, Nb–N, Fe–Mn–Nb–N. The remaining systems were taken from published assessments. The database covers the elements Fe, Mn, Al, Si, V, Nb, Ti, C and N.     

Thermodynamic description of the Al−Fe−Nb system

The Al−Fe−Nb system was critically assessed by means of the CALPHAD technique. The solution phases (liquid, face-centered cubic and body-centered cubic) were modeled with the Redlich–Kister equation. The thermodynamic models of compounds Al₁₃Fe₄, Al₂Fe and Al₅Fe₂ in the Al–Fe system and Al₃Nb and AlNb₃ in the Al–Nb system kept consistent with ones in the corresponding binary systems. The Fe₂Nb and μ in the Fe–Nb system, Al₈Fe₅ in the Al–Fe system, and AlNb₂ in the Al–Nb system were treated as the formulae (Al,Fe,Nb)₂(Fe,Nb), (Al,Fe,Nb)₁Nb₄(Fe,Nb)₂(Al,Fe,Nb)₆, (Al,Fe,Nb)₈(Al,Fe,Nb)₅ and (Al,Nb)_0.533(Al,Fe,Nb)_0.333Nb_0.134, respectively. B2 phase was treated as the ordered phase of bcc phase with the thermodynamic models (Al,Fe,Nb)_0.5(Al,Fe,Nb)_0.5(Va)₃ and (Al,Fe,Nb)_0.25(Al,Fe,Nb)_0.25(Al,Fe,Nb)_0.25(Al,Fe,Nb)_0.25(Va)₃. On the basis of optimized thermodynamic parameters of Al–Fe, Al–Nb and Fe–Nb systems in literature, the Al–Fe–Nb system was optimized in the present work. One set of self-consistent thermodynamic parameters of the Al–Fe–Nb system was obtained corresponding to B2 ordered phase with two kinds of thermodynamic model. Five experimental isothermal sections at 1073, 1273, 1423, 1573 and 1723 K, and the liquidus surface projection were well reproduced in the present work.     

Thermodynamic optimization of the Mn–P and Fe–Mn–P systems

Thermodynamic modeling of the Mn–P and Fe–Mn–P systems in the full composition was carried out using the CALculation of PHAse Diagrams (CALPHAD) method based on the critical evaluation of all available phase equilibria and thermodynamic data. The liquid and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of the binary stoichiometric iron and manganese phosphides were determined based on reliable experimental data. The ternary (Fe,Mn)₃P, (Fe,Mn)₂P and (Fe,Mn)P phosphides were modeled as solid solutions with mutual substitution between Fe and Mn atoms. The Gibbs energy of the liquid solution was predicted using the Toop interpolation technique with P as an asymmetric component, without any ternary parameters. The thermodynamic properties of P in the entire composition region and the liquidus of the ternary system were well reproduced. Based on the thermodynamic models with optimized parameters, unexplored phase diagrams and thermodynamic properties of the Fe–Mn–P system were predicted.     

The carbonitride/austenite equilibrium in Fe(C + N)VNbMn system

The equilibrium compositions, at 1073 and 1123K, of the coexisting austenite (f.c.c.) and (Nb,V)(C,N) precipitate phases in steels containing 1.4 w/o Mn, 0.02 w/o N, up to 0.2 w/o C, 0.2 w/o V, 0.03 w/o Nb are computed using a Kohler, temperature dependent, subregular solution model for the component binary systems and an ideal solid solution model for (Nb,V)(C,N). It was found to be necessary to introduce certain simplifying approximations and these are set out in some detail. The computer method used involves reducing six equations with six unknowns to two nonlinear equations with two unknowns which are then solved using the Newton-Raphson iteration method. The calculated compositions of the precipitate phase are compared with the compositions measured earlier by quantitative X-ray microanalysis.     

Phase equilibria and thermodynamics of Mn–C,Mn–Si,Si–C binary systems and Mn–Si–C ternary system by critical evaluation,combined with experiment and thermodynamic modeling

Critical evaluation and thermodynamic optimization of Mn–C, Mn–Si, Si–C binary systems and Mn–Si–C ternary system were carried out over the whole composition range from room temperature to above the liquidus temperature. In order to provide critical experimental input for the thermodynamic modeling, some key experiments were carried out in the present study. The liquid solution was modeled using the Modified Quasichemical Model (MQM) in the pair approximation in order to take into account the Short-Range Ordering (SRO) exhibited in the solution. In particular, the SRO observed in the Mn–C binary liquid was reasonably accounted for by the present thermodynamic model, while the conventional random mixing model was not able to properly describe the SRO. All solid solutions were modeled using the Compound Energy Formalism (CEF). Model parameters were optimized to best reproduce the important thermodynamic properties and phase equilibrium data in three binary systems. By taking a reasonable interpolation method for Gibbs free energy of the liquid solution in the ternary Mn–Si–C system, it was shown that the present model successfully reproduced thermodynamic and phase equilibrium data in the ternary system without any adjustable ternary parameter. The present database can be used as a part of larger thermodynamic database for the ferromanganese alloy.     

Atomic mobilities, uphill diffusion and proeutectic ferrite growth in Fe–Mn–C alloys

Following the treatment in CALPHAD, experimental data on diffusivities in Fe–Mn and Fe–C binary systems are critically evaluated with the DICTRA software to derive atomic mobilities. The effect of magnetic ordering on diffusion in bcc phase is taken into account, and the obtained atomic mobilities are expressed as functions of temperature and compositions with the Redlick–Kister polynomials. Based on the mobility parameters obtained in this work for the end-members and the interaction terms, comprehensive comparisons between the calculated and experimentally measured quantities are made. Due to the lack of experimental diffusivities for the ternary system, extrapolation based on binary information is performed, the results of which are used to study uphill diffusion of C in fcc Fe–Mn–C alloys. Such C diffusion against its own concentration gradient is a common occurrence for ternary systems containing one interstitial element, provided that the initial alloy compositions of diffusion couples are well chosen. In addition, the operating tie line evolution for proeutectic ferrite growth is also investigated, where C diffusion-controlled fast and Mn diffusion-controlled slow growths are discussed.     

Thermodynamic modeling of Cr–Nb and Zr–Cr with extension to the ternary Zr–Nb–Cr system

The total energies of Laves phases in the Cr–Nb and Zr–Cr systems have been calculated by the pseudo-potential VASP code with a full relaxation of all structural parameters. The special quasirandom structures (SQSs) have been constructed and their total energies have been calculated by the VASP code to predict the enthalpies of mixing for bcc and hcp solid solution phases. The phonon calculations for the C14 and C15 Laves phases have been performed to analyze the phase stability at elevated temperatures. The experimental study on the Zr–Cr system has been carried out at different temperatures to determine the phase boundaries. Based on these results, thermodynamic models of Cr–Nb and Zr–Cr with extension to the ternary Zr–Nb–Cr systems have been developed in this work by using the CALPHAD approach.     

Experimental investigations and thermodynamic modelling of the Cr–Nb–Sn–Zr system

This work reports the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system. In a previous paper, the thermodynamic modelling of the Cr–Nb–Sn system was presented. Since no experimental data were available for the Cr–Sn–Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 °C. A ternary C14 phase has been identified on the Sn-poor side of the phase diagram. In addition to these experimental data, Density Functional Theory (DFT) calculations are carried out in order to determine formation enthalpies of the stable and metastable compounds. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A2 and A3 binary solid solutions. Finally, these experimental and calculated data in addition to those from the literature, are used as input data for the Calphad modelling of the Cr–Zr, Nb–Zr and Sn–Zr binary systems and the Cr–Nb–Zr, Cr–Sn–Zr and Nb–Sn–Zr ternary systems. A complete database for the Cr–Nb–Sn–Zr quaternary system is provided.     

Thermodynamic assessment of the Ga–Gd,Ga–Nb and Gd–Nb binary phase diagrams towards the Ga–Gd–Nb system

The present work gives a thermodynamic optimization of the Ga–Gd, Ga–Nb and Gd–Nb binary systems based on the CALPHAD method. Redlich-Kister polynomials are used to describe the excess Gibbs energy of the liquid phase and the solid solutions. The Ga₂Gd (ϵ) and GaNb₃ (A15) phases, which present a large homogeneity range, were described using a two-sublattice model with the formula (Ga)₂(Ga,Gd)₁ and (Nb)₃(Ga,Nb)₁ respectively. The remaining intermediate phases, ht_Ga₄Nb, Ga₃Nb, Ga₁₃Nb₅, Ga₅ Nb₄, Ga₄ Nb₅, Ga₃Nb₅, Ga₆Gd, GaGd, Ga₂Gd₃ and Ga₃Gd₅, were treated as stoichiometric compounds. The generated thermodynamic parameters relative to the involved phases were critically discussed and used to build the Ga-Gd-Nb ternary system.     

Thermodynamic modeling of Ti–Cr–Mn ternary system

The Ti–Cr–Mn ternary system is one of the most important systems in the development of low cost titanium alloys. However, there are few reports of assessment for this system. In this paper, the previous works for the Ti–Cr–Mn system and the related binary sub-systems are reviewed. The thermodynamic parameters of TiMn₃ and TiMn₄ in the Ti–Mn system are reassessed in order to better describe the phase equilibrium involving TiMn₃ or/and TiMn₄ in the ternary system. Based on the Ti–Cr and the Cr–Mn systems modeled in the literature and the Ti–Mn system reassessed in this work, the Ti–Cr–Mn ternary system is assessed by means of the Calphad method using the ternary experimental data in the literature. The 1173 K and 1273 K isothermal sections are calculated. It is shown that the present calculated results are in good agreement with most of the experimental results.     

Interaction of metals with AlAs and InAs: Estimation of ternary Al-As-M and In-As-M phase diagrams

A comprehensive survey of approximately calculated Al-As-M and In-As-M (M=Ag, Au, Co, Cr, Cu, Fe, Hf, Ir, Mn, Mo, Nb, Ni, Os, Pd, Pt, Re, Rh, Ru, Ta, Ti, V, W and Zr) ternary phase diagrams at room temperature is presented. Regions of greater uncertainty are indicated by alternative tie lines. The calculations are based on following approximations: Ternary phases and solid solubilities are disregarded and the Gibbs energy of formation of binary compounds is mostly estimated by the enthalpy of formation calculated from Miedema's model. Binary phase diagram data were critically reviewed and listed in two tables. A systematic behavior of the ternary systems according to the periodic table is shown to exist.