JYRKI MIETTINEN & VILLE-VALTTERI VISURI & TIMO FABRITIUS THERMODYNAMIC DESCRIPTION OF THE FE AL MN SI C SYSTEM FOR MODELLING SOLIDIFICATION OF STEELS

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1 OULU 2019 C 704 ACTA UNIVERSITATIS OULUENSIS C Jyrki Miettinen & Ville-Valtteri Visuri & Timo Fabritius THERMODYNAMIC DESCRIPTION OF THE FE AL MN SI C SYSTEM FOR MODELLING SOLIDIFICATION OF STEELS TECHNICA UNIVERSITY OF OULU, FACULTY OF TECHNOLOGY, PROCESS METALLURGY RESEARCH UNIT

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3 ACTA UNIVERSITATIS OULUENSIS C Technica 704 JYRKI MIETTINEN & VILLE-VALTTERI VISURI & TIMO FABRITIUS THERMODYNAMIC DESCRIPTION OF THE FE AL MN SI C SYSTEM FOR MODELLING SOLIDIFICATION OF STEELS UNIVERSITY OF OULU, OULU 2019

4 Copyright 2019 Acta Univ. Oul. C 704, 2019 Reviewed by Professor Klaus Hack Professor Pertti Koukkari ISBN (Paperback) ISBN (PDF) ISSN (Printed) ISSN (Online) Cover Design Raimo Ahonen JUVENES PRINT TAMPERE 2019

5 Miettinen, Jyrki & Visuri, Ville-Valtteri & Fabritius, Timo, Thermodynamic description of the Fe Al Mn Si C system for modelling solidification of steels. University of Oulu, Faculty of Technology, Process Metallurgy Research Unit Acta Univ. Oul. C 704, 2019 University of Oulu, P.O. Box 8000, FI University of Oulu, Finland Abstract Advanced high-strength (AHS) steels containing aluminium, manganese, silicon, and carbon have widely been studied for automotive applications. It is particularly important to know their solidification behaviour and final structure after the austenite decomposition process. A thermodynamic database named the Iron Alloy Database (IAD) has been developed to provide consistent thermodynamic data for the purpose of simulating the solidification of steels. This work presents a thermodynamic assessment of the Fe Al Mn Si C system and 19 subsystems. The results suggest a good agreement between thermodynamic descriptions and the measured data. Keywords: Fe Al Mn Si C system, solidification, steels, thermodynamics

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7 Miettinen, Jyrki & Visuri, Ville-Valtteri & Fabritius, Timo, Fe Al Mn Si C systeemin termodynaaminen kuvaus teräksien jähmettymisen mallintamiseen. Oulun yliopisto, Teknillinen tiedekunta, Prosessimetallurgian tutkimusyksikkö Acta Univ. Oul. C 704, 2019 Oulun yliopisto, PL 8000, Oulun yliopisto Tiivistelmä Alumiinia, mangaania, piitä ja hiiltä sisältäviä kehittyneitä suurlujuusteräksiä on tutkittu runsaasti autoteollisuuden sovelluskohteiden näkökulmasta. Erityisen mielenkiinnon kohteena on niiden jähmettyminen ja lopullinen rakenne austeniitin hajoamisprosessin jälkeen. Termodynaaminen Iron Alloys Database (IAD) tietokanta on kehitetty tuottamaan konsistenttia termodynaamista dataa terästen jähmettymisen simulointiin. Tämä työ esittelee Fe Al Mn Si C systeemin ja 19 alisysteemin termodynaamisen arvioinnin. Tulokset osoittavat, että termodynaamiset kuvaukset vastaavat mitattua aineistoa. Asiasanat: Fe Al Mn Si C systeemi, jähmettyminen, termodynamiikka, teräs

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9 In memory of Jukka Laine

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11 Acknowledgements This study represents a continuation of long-term research into modelling solidification of steels, which started with the development of the interdendritic solidification (IDS) model at the former Helsinki University of Technology (the present-day Aalto University) in The research work has continued until present day, and at the University of Oulu since The creation of this book was executed within the framework of the Genome of Steel profiling project. The authors would like to acknowledge the Academy of Finland (project ) and the Finnish Cultural Foundation for funding this work. June 6, 2019 J. Miettinen, V.-V. Visuri & T. Fabritius 9

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13 List of abbreviations Abbreviations AHS IAD RK RKM SER SGTE Advanced high-strength Iron Alloy Database Redlich Kister excess model Redlich Kister Muggianu excess model Standard element reference: K (25 C) and 1 bar Scientific Group Thermodata Europe Symbols a i A cm Ac 1 Ac 3 Ae 1 Ae 3 E f i G H L P R T U w i x i y i γ i Activity of component i Temperature at which transformation of cementite (Fe 3 C) to austenite is completed during heating [K] Temperature at which austenite begins to form during heating [K] Temperature at which transformation of ferrite to austenite is completed during heating [K] Temperature of ferrite+cementite/graphite formation under equilibrium conditions [K] Temperature of ferrite formatiom under equilibrium conditions [K] Ternary eutectic reaction Activity coefficient of component i related to the 1 wt-% standard state Gibbs free energy [J/mol] Enthalpy [J/mol] Interaction parameter [J/mol] Ternary peritectic reaction Gas constant [J/(mol K)] Temperature [K] Ternary quasi-peritectic reaction Weight fraction of component i Mole fraction of component i Site fraction of component i (atoms) in a sublattice of a phase Activity coefficient of component i related to the Raoultian standard state 11

14 Subscripts bcc cub dia E fcc gra hcp L mo ϕ Body-centred cubic crystal structure (ferrite) Cubic crystal structure Diamond Excess Face-centred cubic crystal structure (austenite) Graphite Hexagonal close-packed crystal structure Liquid Magnetic ordering Phase 12

15 Contents Abstract Tiivistelmä Acknowledgements 9 List of abbreviations 11 Contents 13 1 Introduction Overview of studied systems Simplifications Thermodynamic models 21 3 Binary subsystems Fe Al system Phases, modelling, and data Results Fe Mn system Phases, modelling, and data Results Fe Si system Phases, modelling, and data Results Fe C system Phases, modelling, and data Results Al Mn system Phases, modelling, and data Results Al Si system Phases, modelling, and data Results Al C system Phases, modelling, and data Results

16 3.8 Mn Si system Phases, modelling, and data Results Mn C system Phases, modelling, and data Results Si C system Phases, modelling, and data Results Ternary subsystems Fe Al Mn system Phases, modelling, and data Results Fe Al Si system Phases, modelling, and data Results Fe Al C system Phases, modelling, and data Results Fe Mn Si system Phases, modelling, and data Results Fe Mn C system Phases, modelling, and data Results Fe Si C system Phases, modelling, and data Results Mn Si C system Phases, modelling, and data Results Quaternary subsystems Fe Al Mn C system Phase, modelling, and data Results

17 5.2 Fe Mn Si C system Phases, modelling, and data Results Fe Al Mn Si C Phases, modelling, and data Results Conclusions 217 References

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19 1 Introduction Lately, advanced high-strength (AHS) steels containing Al, Mn, Si, and C have been widely studied for automotive applications. It is particularly important to know how they solidify and what is their final structure after the austenite decomposition process. A systematic way to study these fields is to apply thermodynamic kinetic software, like the interdendritic solification (IDS) model [1, 2]. Since 2000, the thermodynamic Iron Alloy Database (IAD) [3] has been developed to get simple and consistent thermodynamic data for the IDS model. For AHS steels, the most essential thermodynamic description is that of the quinary Fe Al Mn Si C system, which is presented in this study. 1.1 Overview of studied systems Most of the sub-systems of the Fe Al Mn Si C system have already been assessed in the literature (see Table 1), but of these assessments, only the Fe Mn description of Huang [4] has been directly adapted to IAD. This is due to the decision to simplify certain phase descriptions of the literature, so that they are easier to use in the calculations of the IDS model. Descriptions of Al Mn Si and Al Mn C ternary systems (assessed by Du et al. [5] and Zheng et al. [6]) were not included in IAD. The reason is in their complex nature and the fact that their compounds take no part in the phase equilibria of the iron-rich corner. Thermodynamic data is also missing from the ternary Al Si C system, which has not been assessed in the open literature. For these reasons, we apply the quaternary Fe X Y Z system interaction parameters for the solution phases (liquid, bcc, and fcc) to optimize their energetic state in the iron-rich corner of the Fe Al Mn Si C system. This is a practical choice, as non-ferrous ternary systems are beyond the focus of this study. The following sections introduce the applied thermodynamic models, and the subdescriptions of the Fe Al Mn Si C system assessed for IAD. Also shown is their validation, with the available experimental data, and a comparison with some earlier calculation, if available. All calculations were performed with ThermoCalc software [7], using IAD as its user database. The unary thermodynamic data of the pure components 17

20 are identical to those of the Scientific Group Thermodata Europe (SGTE) [8], except for carbon in the bcc and fcc phases. Table 1. Thermodynamic descriptions of the Fe Al Mn Si C system. System Literature assessment IAD This work Binary subsystems Chapter 3 Fe Al [9 12] X Section 3.1 Fe Mn [4, 13, 14] [4] Section 3.2 Fe Si [15 17] X Section 3.3 Fe C [18] X Section 3.4 Al Mn [19 23] X Section 3.5 Al Si [24 26] X Section 3.6 Al C [27] X Section 3.7 Mn Si [28, 29] X Section 3.8 Mn C [30, 31] X Section 3.9 Si C [32] X Section 3.10 Ternary subsystems Chapter 4 Fe Al Mn [23, 33 35] X Section 4.1 Fe Al Si [36 39] X Section 4.2 Fe Al C [12, 27, 40 43] X Section 4.3 Fe Mn Si [44, 45] X Section 4.4 Fe Mn C [46, 47] X Section 4.5 Fe Si C [15, 16] X Section 4.6 Al Mn Si [5] Al Mn C [6] Mn Si C [48, 49] X Section 4.7 Quaternary subsystems Chapter 5 Fe Al Mn C [50 52] X Section 5.1 Fe Mn Si C [53] X Section 5.2 Fe Al Mn Si C NA X Chapter 6 Notes: NA = no direct evidence of the assessment status. 1.2 Simplifications Concerning the present Fe Al Mn Si C description, the most essential simplification in IAD is that carbon in the bcc and fcc phases (structures) is treated as a substitutional component. In reality, carbon atoms occupy their own sublattice in these two structures, which should therefore be modelled by a two-sublattice model [54]. This also concerns the magnetic ordering part of the bcc structure. However, applying the substitutional solution model for any component of the alloy makes the IDS simulations faster. This 18

21 is a clear advantage, as IDS is also used in real-time online processes of continuous casting, where we have numerous strand locations needing simulation. Besides, as IDS simulates non-equilibrium solidification (taking kinetics into account), the calculation times are longer than in conventional thermodynamic software simulating equilibrium solidification. This is due to the step-wise calculations of IDS (i.e. the result of any step always depends on the result of the earlier step), whereas to determine a fully equilibrium state, only a single calculation is needed. These factors highlight the requirement for high computational efficiency. The second simplification in IAD is to make the complex compound description as simple as possible, whenever this is possible. Again, the purpose is to simplify the IDS calculation and shorten the computation time. In the present Fe Al Mn Si C description, the only simplified compound description is that of the Kappa phase (κ). That phase has been modelled with quite different and complex sublattice formulations, far from being usable in the IDS model. The third simplification is that IAD ignores the B2 ordering of the bcc phase in alloys, where the Al and Si contents are high. Consequently, it clearly simplifies the calculations of the IDS model. In fact, we do not operate with such high Al and Si contents in typical steels, but in spite of that, the energetic contribution due to the ordering effect was added to the disordered part of the bcc phase. By this treatment, we were able to fit the calculated bcc containing phase equilibria from IAD with the measurements of the literature. Once more, one is reminded that the simplifications in IAD discussed above are due to their application in the IDS solidification model. By this treatment, the structure of that model could be kept reasonably simple, to accelerate the calculations, but also to allow a simultaneous solution of the thermodynamic and diffusion equations of the model. The latter gives, no doubt, more accurate results in the Euler-type, progressive step-wise calculations than a method making the diffusion and thermodynamic calculations separately, e.g. by using some conventional thermodynamic software as a sub-module. Of course, the applied simplifications will also result in some uncertainty in the IDS-results, but in typical steels, this mainly concerns the mutual component occupation in the simplified compounds, whereas the compound fractions, with respect to those of the solution phase, are still accurately calculated. 19

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23 2 Thermodynamic models The molar Gibbs energy of a substitutional solution phase, liquid (L), bcc (ferrite), or fcc (austenite), is expressed as G ϕ = n i=1 x ϕ i G,ϕ i + RT n i=1 x ϕ i lnx ϕ i + G E,ϕ, (1) where x ϕ i is the mole fraction of component i in phase ϕ, G,ϕ i is the Gibbs energy of a pure component i in phase ϕ expressed relative to its enthalpy in the standard element reference (SER) state of K (25 C) and 1 bar [8], R is the gas constant, and T is the temperature. The first and the second summations represent the mechanical mixture of pure components and the contribution of mixing entropy. The third term (G E,ϕ ) is the excess Gibbs free energy, which can be expressed as follows: G E,ϕ n 1 = i=1 n j=i+1 x ϕ i xϕ j Lϕ i j + n 2 i=1 n 1 j=i+1 n k= j+1 x ϕ i xϕ j xϕ k Lϕ i jk n 3 n 2 n 1 n + i=1 j=i+1 k= j+1 l=k+1 x ϕ i xϕ j xϕ k xϕ l Lϕ i jkl, (2) where parameters L ϕ describe the interactions between the components indicated by the proper subscripts. Binary parameters L ϕ i j and ternary parameters Lϕ i jk can have the following composition dependencies [55, 56]: L ϕ m max ( ) i j = L ϕ i j x ϕ m i xϕ j, (3) m=0 L ϕ i jk = νϕ i Lϕ ii jk + νϕ j Lϕ i j jk + νϕ k Lϕ i jkk, (4) where m is the degree of the binary parameter (m max = maximum degree), while the ν i are composition variables defined as ν i = x i + (1 x i x j x k )/3. The quaternary parameters L i jkl are treated either as constants or as function of temperature only. Note that for the bcc and fcc phases of iron alloys, a contribution due to magnetic ordering must be added to Eq. 1. This contribution is expressed as G mo,ϕ m = RT ln ( β ϕ + 1 ) f (τ), (5) 21

24 where β ϕ is a composition-dependent parameter related to the total magnetic entropy and τ is defined as τ = T /Tc ϕ, where Tc ϕ is the critical temperature of magnetic ordering. Function f (τ) in Eq. 5 takes the polynomial form proposed by Hillert and Jarl [57]. Most compounds appearing in the Fe Al Mn Si C system have quite a simple formulation, being stoichiometric or semi-stoichiometric. For the binary and ternary stoichiometric compounds, A a B b and A a B b C c, the Gibbs energy is expressed as G,θ G,θ A a B b = αg,ϕ1 A + bg,ϕ2 B + A + BT +CT lnt + DT 2, (6) A a B b C c = αg,ϕ1 A + bg,ϕ2 B + cg,ϕ3 C + A + BT +CT lnt + DT 2, (7) where G,ϕ i is the Gibbs energy of pure component i in its stable phase (ϕ) at K (25 C) [8], while terms A to D are optimized coefficients. For the ternary semistoichiometric compounds, (A,B) a C c, the Gibbs energy is expressed as ) Gm θ = ya θ G,θ A:C + yθ BG,θ B:C (y + αrt A θ lnyθ A + yθ B lnyb θ + ya θ yθ BLA,B:C θ, (8) where G,θ A:C and G,θ B:C are the Gibbs energies of pure A ac c and B a C c, ya θ and yθ B are the site fraction of A and B atoms occupying the first sublattice, and LA,B:C θ is a parameter describing the interaction between A and B atoms in that sublattice. As an example, Eq. 8 holds well for the Fe Mn C system carbides, (Fe,Mn) 3 C (cementite), (Fe,Mn) 5 C 2, and (Fe,Mn) 5 C 2. Eq. 8 is also applied for the Fe Al C system Kappa phase (κ), but by Mn alloying, its formulation extends to (Fe,Al,Mn) 7 C. 22

25 3 Binary subsystems 3.1 Fe Al system The Fe Al binary system has been assessed in [10 12]. The assessments of Jacobs and Schmid-Fetzer [11], and Phan et al. [12] are the most successful, but they are somewhat complex. The simpler assessment of Seierstein [10] was later modified by IAD optimizing new parameter expressions for the liquid, bcc, fcc, Al 5 Fe 4, and Al 13 Fe 4 phases. In addition, the bcc phase description of Seierstein [10] was simplified by ignoring the B2 ordering, but including its effect in the disordered bcc phase. The purpose was to simplify the binary Fe Al description and the following Fe Al X descriptions for practical calculations of solidification modelling of steels. The present work reviews the Fe Al description from IAD and shows its experimental verification Phases, modelling, and data Table 2 shows the phases and their modelling. Table 3 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 4. Table 2. Phases and their modelling in the Fe-Al description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) hcp_a3 ( hcp, metastable) cbcc_a12 ( cbcc, metastable) cub_a13 ( cub, metastable) Al 5 Fe 4 Al 2 Fe Al 5 Fe 2 Al 13 Fe 4 Modelling (Al,Fe), substitutional, RK (Al,Fe), substitutional, RK (Al,Fe), substitutional, RK (Al,Fe), substitutional, RK (Al,Fe), substitutional, RK (Al,Fe), substitutional, RK (Al,Fe), substitutional, RK (Al) 2 (Fe), stoichiometric (Al) 5 (Fe) 2, stoichiometric (Al) 13 (Fe) 4, stoichiometric 23

26 Table 3. Data applied in the assessment verification for Fe Al from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [58 63] bcc+fcc region of the Fe-rich side [64] fcc region of the Al-rich side [65 67] Enthalpy of mixing of liquid alloys at 1600 C [68] Activity of Al in liquid alloys at 1600 C [69 75] Chemical potentials in liquid alloys at 1600 C [74] Enthalpy of mixing of bcc alloys at 756 to 1327 C [76 79] Activity of Al in bcc alloys at 900 to 1300 C [79 82] Chemical potentials in solid at 900 to 627 C [74, 83] Enthalpy of formation of solid alloys at 25 C [84] Curie temperature in bcc alloys [63, 85, 86] Table 4. Thermodynamic description of the Fe Al system by IAD. Equation liquid (1 sublattice, sites: 1, constituents: Al,Fe) L L Al,Fe = ( T ) + ( T )(x Al x Fe ) + ( T )(x Al x Fe ) 2 Reference bcc (1 sublattice, sites: 1, constituents: Al,Fe) LAl,Fe bcc Al x Fe ) IAD Tc bcc = 1043x Fe + x Al x Fe ( 1100(x Al x Fe )) IAD β bcc = 2.22x Fe [8] fcc (1 sublattice, sites: 1, constituents: Al,Fe) LAl,Fe fcc Al x Fe ) + (+10000)(x Al x Fe ) 2 IAD Tc fcc = 201x Fe [8] β fcc = 2.1x Fe [8] hcp (m) (1 sublattice, sites: 1, constituents: Al,Fe) L hcp Al,Fe = ( T ) (estimated) [10] cub (m) (1 sublattice, sites: 1, constituents: Al,Fe) LAl,Fe cub = ( T ) (estimated) IAD cbcc (m) (1 sublattice, sites: 1, constituents: Al,Fe) LAl,Fe cbcc = ( T ) (estimated) [10] Al 5 Fe 4 (1 sublattice, sites: 1, constituents: Al,Fe) G,Al 5Fe 4 Al = G,fcc Al + ( T ) [10] G,Al 5Fe 4 Fe = G,bcc Fe + (+5009) [10] L Al 5Fe 4 Al,Fe = ( T ) + ( 16000)(x Al x Fe ) IAD Al 2 Fe (2 sublattices, sites: 2:1, constituents: Al:Fe) G,Al 2Fe Al:Fe = 2G,fcc Al + G,bcc Fe + ( T ) [10] Notes: (m) = metastable phase. Thermodynamic data of pure components are given by [8] unless not shown in the table. IAD 24

27 Table 4 (continued) Equation Reference Al 5 Fe 2 (2 sublattices, sites: 5:2, constituents: Al:Fe) G,Al 5Fe 2 Al:Fe = 5G,fcc Al + 2G,bcc Fe + ( T ) [10] Al 13 Fe 4 (2 sublattices, sites: 0.752:0.248, constituents: Al:Fe) G,Al 13Fe 4 Al:Fe = 0.752G,fcc Al G,bcc Fe + ( T ) IAD Notes: (m) = metastable phase. Thermodynamic data of pure components are given by [8] unless not shown in the table Results The results of calculations from IAD and Seierstein [10] together with the experimental data (Table 3) are presented in Figures The agreement is reasonably good in both calculations. In Figure 1, note the simplified treatment for the bcc phase by IAD ignoring the B2 ordering of Seierstein [10] but including its effect energetically, and the simplified (stoichiometric) description of the Al 13 Fe 4 phase from IAD. Note also the improved agreement from IAD for the bcc+fcc loop at high temperatures (but not at low temperatures) (Figure 2), for the molar and partial mixing enthalpies in liquid (Figure 3), and for the Curie temperature of the bcc phase (Figure 14). Fig. 1. Calculated phase diagram of the Fe Al system together with assessed experimental data points (08Gwy [58], 27Gwy [59], 60Lee [60], 80Sch [61], 90Ind [62], and 07Ste [63]). The solid lines are calculations from IAD, and the dotted lines are those from [10]. Note the disorder order transition line of bcc [10] not existing in IAD. 25

28 Fig. 2. Calculated fcc+bcc region of the Fe Al system together with experimental data points (67Roc [64]). Solid lines are calculations from IAD, and the dotted lines are those from [10]. Fig. 3. Calculated fcc region in the Al-rich corner of the Fe Al system together with experimental data points (48Edg [65], 49Cru [66], and 88Osc [67]). Solid lines are calculations from IAD, and the dotted lines are those from [10]. 26

29 Fig. 4. Calculated molar and partial mixing enthalpies in liquid Fe Al alloys at 1600 C together with experimental data points [68]. Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure liquid Fe and Al. Fig. 5. Calculated activity of Al in liquid Fe Al alloys at 1600 C together with experimental data points (73Hul [74] and 81Sch [68]). The data from [68] are based on [69 73, 75]. Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference state used is pure liquid Al. 27

30 Fig. 6. Calculated chemical potentials of Fe and Al in liquid Fe Al alloys at 1600 C together with experimental data points [74]. Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure liquid Fe and Al. Fig. 7. Calculated mixing enthalpy of bcc Fe Al alloys at 756 C and 1327 C together with experimental data points (00Rzy [76], 01Bre [77], 03Ben [78], and 03Raj [79]). Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure fcc Fe and pure liquid Al. 28

31 Fig. 8. Calculated activity of Al in bcc Fe Al alloys from 900 C to 1300 C together with experimental data points (93Jac [82], 03Raj [79], 61Rad [80], and 64Eld [81]). Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference state used is pure liquid Al. Fig. 9. Calculated chemical potentials of Fe and Al in solid Fe Al alloys at 900 C together with experimental data points [74]. Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure bcc Fe and pure liquid Al. 29

32 Fig. 10. Calculated chemical potentials of Fe and Al in solid Fe Al alloys at 827 C together with experimental data points [83]. Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure bcc Fe and pure liquid Al. Fig. 11. Calculated chemical potentials of Fe and Al in solid Fe Al alloys at 727 C together with experimental data points [83]. Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure bcc Fe and pure liquid Al. 30

33 Fig. 12. Calculated chemical potentials of Fe and Al in solid Fe Al alloys at 627 C together with experimental data points [83]. Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure bcc Fe and pure fcc Al. Fig. 13. Calculated enthalpy of formation of solid Fe Al alloys at 25 C together with experimental data points (37Kor [84]). Solid lines are calculations from IAD, and the dotted lines are those from [10]. The reference states used are pure bcc Fe and pure fcc Al. 31

34 Fig. 14. Calculated Curie temperature of the bcc phase together with experimental data points (67Sin [85], 80Kos [86], and 07Ste [63]). Solid lines are calculations from IAD, and the dotted lines are those from [10]. 3.2 Fe Mn system The Fe Mn system has been assessed by Huang [4], Lee and Lee [13], and Witusiewicz et al. [14]. The assessment of Huang [4] was adapted to IAD due to its use in many higher-order SGTE assessments. Note that Witusiewicz et al. [14] gives slightly better agreement with the experimental data, but apply quite a complex temperature function for the interaction parameter of the fcc phase. The present work reviews the Fe Mn description of Huang [4] and shows its experimental verification Phases, modelling, and data Table 5 shows the phases and their modelling. Table 6 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 7. 32

35 Table 5. Phases and their modelling in the Fe Mn description of [4]. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) cbcc_a12 ( cbcc) cub_a13 ( cub) hcp_a3 ( hcp, metastable) Modelling (Fe,Mn), substitutional, RK (Fe,Mn), substitutional, RK (Fe,Mn), substitutional, RK (Fe,Mn), substitutional, RK (Fe,Mn), substitutional, RK (Fe,Mn), substitutional, RK Table 6. Data applied in the assessment verification for Fe Mn [4]. Experimental data Reference(s) Phase equilibria of the phase diagram [87 89] Enthalpy of mixing in liquid alloys at 1600 C [90] Enthalpy of mixing in fcc alloys at 1170 C [91] Chemical potential of Mn in solid alloys at 800 and 1077 C [91, 92] Neel temperature of fcc alloys [93 96] Table 7. Thermodynamic description of the Fe Mn system [4]. Equation liquid (1 sublattice, sites: 1, constituents: Fe,Mn) Reference L L Fe,Mn = ( T ) + (1145)(x Fe x Mn ) [4] bcc (1 sublattice, sites: 1, constituents: Fe,Mn) LFe,Mn bcc = ( T ) [4] Tc bcc = 1043x Fe 580x Mn + x Fe x Mn (123) [4] β bcc = 2.22x Fe 0.27x Mn [4] fcc (1 sublattice, sites: 1, constituents: Fe,Mn) LFe,Mn fcc Fe x Mn ) [4] Tc fcc = 201x Fe 1620x Mn + x Fe x Mn ( (x Fe x Mn )) [4] β fcc = 2.1x Fe 1.86x Mn [4] cbcc (1 sublattice, sites: 1, constituents: Fe,Mn) LFe,Mn cbcc = ( 10184) [4] cub (1 sublattice, sites: 1, constituents: Fe,Mn) LFe,Mn cub = ( T ) [4] hcp (m) (1 sublattices, sites: 1, constituents: Fe,Mn) L hcp Fe,Mn = ( T ) + (273)(x Fe x Mn ) [47] Tc hcp = 1620x Mn [4] β hcp = 1.86x Mn [4] Notes: (m) = metastable phase; Gibbs energy data of pure components are given by [8]. 33

36 3.2.2 Results The results of calculations by Huang [4] together with the experimental data (Table 6) are presented in Figures The agreement is reasonably good. Good agreement was also obtained between the calculated and experimental [87, 93] metastable fcc+hcp equilibria, not reviewed here. Fig. 15. Calculated [4] Fe Mn phase diagram together with experimental data points (43Tro [87], 57Hel [88], and 82Sri [89]). 34

37 Fig. 16. Calculated [4] enthalpy of mixing of liquid Fe Mn alloys at 1600 C together with experimental data points (74Bat [90]). The reference states used are pure liquid Fe and pure liquid Mn. Fig. 17. Calculated [4] enthalpy of mixing of fcc Fe Mn alloys at 1170 C together with experimental data points (87Kub [91] corrected by [4]). The reference states used are pure fcc Fe and pure fcc Mn. 35

38 Fig. 18. Calculated [4] chemical potentials of Mn in solid Fe Mn alloys at 800 C and 1077 C together with experimental data points (87Kub [91] and 74Ben [92]). The reference used is pure cub Mn. Fig. 19. Calculated Neel temperature of fcc Fe Mn alloys together with experimental data points [93 96] (reprinted by permission from [4] c 1989 Elsevier Ltd). 36

39 3.3 Fe Si system The Fe Si binary system has been assessed by Lacaze and Sundman [15], and Cui and Jung [17]. The former assessment was later modified by Miettinen [16] optimizing a new description for the liquid phase. It resulted in better agreement with the experimental bcc+l region. More recently, the bcc phase description of Miettinen [16] was simplified by IAD, ignoring the B2 ordering, but including its effect in the disordered bcc phase. The purpose was to simplify the binary Fe Si description and the following Fe Si X descriptions for practical calculations of solidification modelling of steels. The present work reviews the Fe Si description from IAD and shows its experimental verification. A more accurate and critical description of the Fe Si system has later been given by Cui and Jung [17]. In that description, however, more complex solution models were applied for the liquid phase, in regard to the simple substitutional solution model in IAD Phases, modelling, and data Table 8 shows the phases and their modelling, while Table 9 shows the experimental data selected for the assessment verification. The thermodynamic description of the system is presented in Table 10. Table 8. Phases and their modelling in the Fe Si description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) Fe 2 Si Fe 5 Si 3 FeSi FeSi 2 -H FeSi 2 -L dia_a4 ( dia) Modelling (Fe,Si), substitutional, RK (Fe,Si), substitutional, RK (Fe,Si), substitutional, RK (Fe) 2 (Si), stoichiometric (Fe) 5 (Si) 3, stoichiometric (Fe)(Si), stoichiometric (Fe) 3 (Si) 7, stoichiometric (Fe)(Si) 2, stoichiometric pure Si 37

40 Table 9. Data applied in the assessment verification for Fe Si from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [97 104] Enthalpy of mixing of liquid alloys, at 1600 C [ ] Partial enthalpies of mixing in liquid alloys at 1600 C [71, ] Activity coefficient of Si in liquid alloys at 1600 C and 1500 C [109, 112, 113] Activity coefficient of Si in bcc alloys at 1350 to 1100 C [114] Enthalpy of formation of solid alloys at 25 C [84, 115] Table 10. Thermodynamic description of the Fe Si system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Fe,Si) L L Fe,Si = ( T ) + ( T )(x Fe x Si ) Reference +( T )(x Fe x Si ) 2 + ( T )(x Fe x Si ) 3 [16] bcc (1 sublattice, sites: 1, constituents: Fe,Si) LFe,Si bcc = ( T ) + ( T )(x Fe x Si ) +( T )(x Fe x Si ) 2 Tc bcc = 1043x Fe + x Fe x Si (+504(x Fe x Si )) [15] β bcc = 2.22x Fe [8] fcc (1 sublattice, sites: 1, constituents: Fe,Si) LFe,Si fcc Fe x Si ) + (89907)(x Fe x Si ) 2 [15] Tc fcc = 201x Fe [8] β fcc = 2.1x Fe [8] Fe 2 Si (2 sublattices, sites: 2:1, constituents: Fe:Si) G,Fe 2Si Fe:Si = 2G,bcc Fe + G,dia Si + ( T ) [15] Fe 5 Si 3 (2 sublattices, sites: 5:3, constituents: Fe:Si) G,Fe 5Si 3 Fe:Si = 5G,bcc Fe + 3G,dia Si + ( T ) [15] FeSi (2 sublattices, sites: 1:1, constituents: Fe:Si) G,FeSi Fe:Si FeSi 2 -H (2 sublattices, sites: 3:7, constituents: Fe:Si) = G,bcc Fe + G,dia Si + ( T ) [15] G,FeSi 2-H Fe:Si = 3G,bcc Fe + 7G,dia Si + ( T ) [15] FeSi 2 -L (2 sublattices, sites: 1:2, constituents: Fe:Si) G,FeSi 2-L Fe:Si = G,bcc Fe + 2G,dia Si + ( T ) [15] Notes: Thermodynamic data of pure components are given by [8]. IAD 38

41 3.3.2 Results The results of calculations from IAD and Lacaze and Sundman [15] together with the experimental data (Table 9) are presented in Figures The agreement is reasonably good by both calculations. In Figure 20, note the simplified treatment for the bcc phase by IAD ignoring the B2 ordering of [15] but including its effect energetically, and the improved agreement for the bcc+liq equilibrium from IAD. Fig. 20. Calculated Fe Si phase diagram together with experimental data points (30Hau [97], 40Osa [98], 66Fis [99], 67Ube [100], 68Kos [101], 68Pit [102], 75Sch [103], and 80Sch [104]). The solid lines are calculations from IAD, and the dotted lines are from [15]. Note the disorder order transition line of bcc [15] not existing in the description from IAD. 39

42 Fig. 21. Calculated fcc+bcc region of the Fe Si system together with experimental data points (66Fis [99]). The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig. 22. Calculated enthalpy of mixing of liquid Fe Si alloys at 1600 C together with experimental data points (62Ger [105], 66ElK [106], 73Fil [107], and 75Igu [108]). The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference states used are pure liquid Fe and Si. 40

43 Fig. 23. Calculated partial enthalpies of mixing in liquid Fe Si alloys at 1600 C together with experimental data points for Fe [109,111] and Si [71, ].The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference states used are pure liquid Fe and Si. Fig. 24. Calculated activity coefficient of Si in liquid Fe Si alloys at 1600 C together with experimental data points (81Cha [113]). The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state for Si is pure liquid Si. 41

44 Fig. 25. Calculated activity coefficient of Si in liquid Fe Si alloys at 1500 C together with experimental data points (61Hsu [112] and 63Tur [109]). The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state for Si is pure liquid Si. Fig. 26. Calculated activity coefficient of Si in bcc Fe Si alloys together with experimental data points (75Sak [114]). The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state for Si is pure diamond Si. 42

45 Fig. 27. Calculated enthalpy of formation of solid Fe Si alloys at 25 C together with experimental data points (36Kör [115] and 37Kör [84]). The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference states used are pure bcc Fe and pure diamond Si. 3.4 Fe C system The Fe C system has been assessed by Gustafson [18] applying interstitial filling of carbon atoms in the solid solution phases. This description was later modified by IAD assuming substitutional filling of carbon atoms in the bcc and fcc phases. In that work, the original interstitial solution data from Gustafson [18] was accurately fitted to substitutional solution data. In addition, a simpler temperature function was introduced for the Gibbs energy of formation of Fe 3 C. The purpose was to simplify the Fe C description and the following Fe X C descriptions for practical calculations of solidification modelling of steels. The present work reviews the Fe C description from IAD and shows its experimental verification Phases, modelling, and data Table 11 shows the phases and their modelling. Table 12 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table

46 Table 11. Phases and their modelling in the Fe C description of IAD. Phase Liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) hcp_a3 ( hcp, metastable) Fe 3 C ( M 3 C, cementite) graphite ( gra) Modelling (C,Fe), substitutional, RK (C,Fe), substitutional, RK (C,Fe), substitutional, RK (Fe)(C,Va) 0.5, sublattice (Fe) 3 (C), stoichiometric pure C Table 12. Data applied in the assessment verification for Fe C from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [ ] Activity of C in liquid alloys at 1760 and 1550 C [ ] Activity of C in fcc alloys from 1400 to 800 C [ ] Activity of C in bcc alloys from 825 to 575 C [134, 135] Activity of C at low temperatures [136] Heat content of FeC [137, 138] Table 13. Thermodynamic description of the Fe C system by IAD. Equation liquid (1 sublattice, sites: 1, constituents: C, Fe) Reference L L C,Fe = ( T ) + (+19300)(x C x Fe ) + ( T )(x C x Fe ) 2 [18] bcc (1 sublattice, sites: 1, constituents: C, Fe) G,bcc C = G,gra C + ( T ) IAD LC,Fe bcc C x Fe ) + ( 7.858T )(x C x Fe ) 2 IAD Tc bcc = 1043(x Fe + x C ) 200x Fe x C IAD β bcc = 2.22(x Fe + x C ) IAD fcc (1 sublattice, sites: 1, constituents: C, Fe) G,fcc C = G,gra C + ( T ) IAD LC,Fe fcc = ( T ) + ( T )(x C x Fe ) IAD +( T )(x C x Fe ) 2 Tc fcc = 201(x Fe + x C ) IAD β fcc = 2.1(x Fe + x C ) IAD hcp (m) (2 sublattices, sites: 1:0.5, constituents: Fe:C,Va) G,hcp Fe:C = G,bcc Fe G,hcp Fe:Va = G,hcp Fe + 0.5G,gra C + ( T ) [18] L hcp Fe:C,Va Fe 3 C (M 3 C) (2 sublattices, sites: 3:1, constituents: Fe:C) = ( 22126) [139] G,Fe 3C Fe:C = 3G,bcc Fe + G,gra C + ( T T lnt T 2 ) [18] #) Notes: (m) = metastable phase, #) = simplified function. The reference states of Fe and C changed from H SER. Using the original function of Gustafson [18] has no detectable effect on the results. [8] 44

47 3.4.2 Results The results of calculations from IAD and Gustafson [18] together with the experimental data (Table 12) are presented in Figures The agreement is reasonably good by both calculations. Note that in Figures and 31 33, within the given scaling, the solid lines overlap the dotted lines indicating that the substitutional solution bcc and fcc descriptions from IAD agree very well with the interstitial solution bcc and fcc descriptions of Gustafson [18]. The only exception is the slight deviation in the bcc/bcc+fcc boundary of Figure 29, which is due to logarithmic scaling. Fig. 28. Calculated high-temperature portion of the Fe C phase diagram together with experimental data points (52Chi [119], 60Buc [122], 61Ben [123], 62Neu [124], 71Wad [125], and 83Chi [126]). The solid lines are calculations from IAD, and the dotted lines are from [18]. 45

48 Fig. 29. Calculated low-temperature portion of the Fe C phase diagram together with experimental data points (37Meh [116], 49Sta [117], 50Wer [118], 55Lin [120], 59Smi [121], and 85Has [127]). The solid lines are calculations from IAD, and the dotted lines are from [18]. Fig. 30. Calculated (IAD) activity of C liquid Fe C alloys at temperatures ranging from 1550 C to 1760 C together with experimental data points (53Ric [128], 53San [129], and 59Cze [130]). The calculations are virtually identical to those from [18]. The reference state of C is pure graphite. 46

49 Fig. 31. Calculated (IAD) activity of C in fcc Fe C alloys at temperatures ranging from 800 C to 1400 C together with experimental data points (46Smi [131], 69Ban [132], 70Ban [133], and 76Lob [134]). The calculations are virtually identical to those from [18]. The reference state of C is pure graphite. Fig. 32. Calculated activity of C in bcc Fe C alloys at temperatures ranging from 575 C to 848 C together with experimental data points [134, 135]. The solid lines are calculations from IAD, and the dotted lines are from [18]. The reference state of C is pure graphite. 47

50 Fig. 33. Calculated (IAD) C activity phase diagram of the Fe C system at low temperatures together with experimental data points (50Bro [136]). The calculations are virtually identical to those from [18]. The reference state of C is pure graphite. Fig. 34. Calculated heat content of FeC (cementite) together with experimental data points (34Nae [137] and 35Umi [138]). The solid line shows the calculations from IAD, and the dotted line is from [18]. 48

51 3.5 Al Mn system The Al Mn system has been assessed in [19 22]. The assessment of Liu et al. [22] was later modified by Umino et al. [23] and IAD optimizing new descriptions for the bcc and fcc phases [23], and for compounds Al 11 Mn 4 and Al 8 Mn 5 (IAD). In the latter case, a tiny region of B2 ordering assessed by Liu et al. [22] in the middle of the diagram was ignored. The purpose was to simplify the binary description and the following Fe Al Mn description for practical calculations of solidification modelling of steels. The present work reviews the Al Mn description from IAD and shows its experimental verification Phases, modelling, and data Table 14 shows the phases and their modelling. Table 15 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 16. Table 14. Phases and their modelling in the Al Mn description from IAD. Phase Liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) hcp_a3 ( hcp) cbcc_a12 ( cbcc) cub_a13 ( cub) Al 8 Mn 5 _D8 10 ( Al 8 Mn 5 ) Al 11 Mn 4 Al 4 Mn Al 6 Mn Al 12 Mn Modelling (Al,Mn), substitutional, RK (Al,Mn), substitutional, RK (Al,Mn), substitutional, RK (Al,Mn), substitutional, RK (Al,Mn), substitutional, RK (Al,Mn), substitutional, RK (Al) 12 (Mn) 4 (Al,Mn) 10, sublattice, RK (Al) 11 (Mn) 4, stoichiometric (Al) 4 (Mn), stoichiometric (Al) 6 (Mn), stoichiometric (Al) 12 (Mn), stoichiometric Table 15. Data applied in the assessment verification for Al Mn from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [20, ] Enthalpy of mixing of liquid alloys at 1353 C [150] Activity of Al in liquid alloys at 1297 C [151] Enthalpy of formation of solid alloys at 25 C [152] 49

52 Table 16. Thermodynamic description of the Al-Mn system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Al,Mn) Reference L L Al,Mn = ( T ) + ( T )(x Al x Mn ) + ( 2639)(x Al x Mn ) 2 [22] bcc (1 sublattice, sites: 1, constituents: Al,Mn) LAl,Mn bcc Al x Mn ) [23] Tc bcc = 580x Mn [8] β bcc = 0.27x Mn [8] fcc (1 sublattice, sites: 1, constituents: Al,Mn) LAl,Mn fcc Al x Mn ) [23] Tc fcc = 1620x Mn [8] β fcc = 1.86x Mn [8] hcp (1 sublattice, sites: 1, constituents: Al,Mn) L hcp Al,Mn = ( T ) + ( T )(x Al x Mn ) [22] +( T )(x Al x Mn ) 2 Tc hcp = 1620x Mn [8] β hcp = 1.86x Mn [8] cbcc (1 sublattice, sites: 1, constituents: Al,Mn) LAl,Mn cbcc = ( T ) [22] Tc cbcc = 285x Mn [8] β cbcc = 0.66x Mn [8] cub (1 sublattice, sites: 1, constituents: Al,Mn) LAl,Mn cub Al x Mn ) [22] Al 8 Mn 5 (3 sublattices, sites: 12:4:10, constituents: Al:Mn:Al,Mn) G,Al 8Mn 5 Al:Mn:Al = 22G,fcc Al + 4G,cbcc Mn + ( T ) [22] G,Al 8Mn 5 Al:Mn:Mn = 12G,fcc Al + 14G,cbcc Mn + ( T ) [22] L Al 8Mn 5 Al:Mn:Al,Mn = ( T ) + ( T )(y Al y Mn ) IAD Al 11 Mn 4 (2 sublattices, sites: 11:4, constituents: Al:Mn) G Al 11Mn 4 Al:Mn = 11G,fcc Al + 4G,cbcc Mn + ( T ) IAD Al 4 Mn (2 sublattices, sites: 4:1, constituents: Al:Mn) G,Al 4Mn Al:Mn Al 6 Mn (2 sublattices, sites: 6:1, constituents: Al:Mn) = 4G,fcc Al + G,cbcc Mn + ( T ) [22] G,Al 6Mn Al:Mn = 6G,fcc Al + G,cbcc + Mn + ( T ) [22] Al 12 Mn (2 sublattices, sites: 12:1, constituents: Al:Mn) G,Al 12Mn Al:Mn = 12G,fcc Al + G,cbcc Mn + ( T ) [22] Notes: Gibbs energy data of pure components are given by [8]. 50

53 3.5.2 Results The results of calculations from IAD and Umino et al. [23] together with the experimental data (Table 15) are presented in Figures The agreement is reasonably good by both calculations. Additional experimental phase equilibrium data are available from Müller et al. [153], but these data are not presented in Figure 35, as they strongly overlap the other data. Fig. 35. Calculated Al Mn phase diagram together with experimental data points (33Dix [140], 58Kon [145], 60Kos [147], 71God [148], 87Mur [20], and 96Liu [149]). The solid lines are calculations from IAD, and the dotted lines are from [23]. 51

54 Fig. 36. Calculated (IAD) Al-rich portion of the Al Mn phase diagram together with experimental data points (33Dix [140], 40Fah [141], 43Phi [142], 45But [143], 53Obi [144], and 58Liv [146]). The calculations are identical to those of [23]. Fig. 37. Calculated (IAD) enthalpy of mixing of liquid Al Mn alloys at 1353 C together with experimental data points (73Esi [150]). The calculations are identical to those of [23]. The reference states used are pure liquid Al and Mn. 52

55 Fig. 38. Calculated (IAD) activity of Al in liquid Al Mn alloys at 1297 C together with experimental data points (72Bat [151]). The calculations are identical to those of [23]. The reference state used is pure liquid Al. Fig. 39. Calculated enthalpy of formation of solid Al Mn alloys at 25 C together with experimental data points (60Kub [152]). The solid line shows the calculations from IAD, and the dotted line is from [23]. The reference states used are pure fcc Al and pure cbcc Mn. 53

56 3.6 Al Si system The Al Si system has been assessed by Dörner et al. [24], Murray and McAlister [25], and Gröbner et al. [26]. The assessment of Gröbner et al. [26] was later modified by IAD introducing a new description for the dia phase of the system. The present work reviews the Al Si description from IAD and shows its experimental verification Phases, modelling, and data Table 17 shows the phases and their modelling. Table 18 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 19. Table 17. Phases and their modelling in the Al Si description from IAD. Phase liquid ( L) bcc_a2 ( bcc, metastable) fcc_a1 ( fcc) hcp_a3 ( hcp, metastable) dia_a4 ( dia) Modelling (Al,Si), substitutional, RK (Al,Si), substitutional, RK (Al,Si), substitutional, RK (Al,Si), substitutional, RK (Al,Si), substitutional, RK Table 18. Data applied in the assessment verification for Al Si from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [ ] Enthalpy of mixing of liquid alloys at 1400 C [84, 174, 175] Partial enthalpy of solid Si in liquid alloys at 700 C [176] Activity of Al in liquid alloys at 1200 C [177, 178] Chemical potential of Al in liquid alloys [171, 179] 54

57 Table 19. Thermodynamic description of the Al Si system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Al,Si) Reference L L Al,Si = ( T ) + ( T )(x Al x Si ) + (2265)(x Al x Si ) 2 [26] bcc (m) (1 sublattice, sites: 1, constituents: Al,Si) LAl,Si bcc = Lfcc Al,Si IAD fcc (1 sublattice, sites: 1, constituents: Al,Si) LAl,Si fcc = ( T ) [26] hcp (m) (1 sublattice, sites: 1, constituents: Al,Si) L hcp Al,Si = Lfcc Al,Si [26] dia (1 sublattice, sites: 1, constituents: Al,Si) G,dia Al = G,fcc Al + (+30T ) [26] LAl,Si dia = ( T ) IAD Notes: (m) = metastable phase; Gibbs energy data of pure components are given by [8] unless not shown in the table Results The results of calculations from IAD together with the experimental data (Table 18) are presented in Figures The agreement is reasonably good. In Figure 42, note the improved agreement for the experimental dia phase region by IAD, in regard to the calculations from Gröbner et al. [26]. In other figures, there are no differences in the calculations from IAD and [26]. Additional experimental data for the Al activity in liquid alloys at 887 C is available in [180]. These data agree well with the calculations. 55

58 Fig. 40. Calculated (IAD) Al Si phase diagram together with experimental data points (08Fra [154], 14Rob [155], 34Mat [160], 47Sin [163], 55Cra [164], 69Ber [171], and 76Kob [172]). The calculations are practically identical to those from [26]. Fig. 41. Calculated (IAD) Al-rich portion of the Al Si phase diagram together with experimental data points (26Ota [156], 27Gwy [157], 28Dix [158], 29Ana [159], 40Dur [161], 42Bor [162], 47Sin [163], 61Gla [167], 66Kov [168], and 68Dri [169]). The calculations are virtually identical to those from [26]. 56

59 Fig. 42. Calculated Si-rich portion of the Al Si phase diagram together with experimental data points (56Mil [165], 57Nav [166], 68Loz [170], and 03Yos [173]). The solid lines are calculations from IAD, and the dashed lines are from [26]. Fig. 43. Calculated (IAD) enthalpy of mixing of liquid Al Si alloys at 1400 C together with experimental data points (37Kor [84], 81Bat [174], and 81Bro [175]). The calculations are identical to those from [26]. The reference states used are pure liquid Al and Si. 57

60 Fig. 44. Calculated (IAD) partial enthalpy of solid Si in liquid Al Si alloys at 700 C together with experimental data points (67Mat [176]). The calculations are identical to those from [26]. The reference state used is diamond Si. Fig. 45. Calculated (IAD) activity of Al in liquid Al Si alloys at 1200 C together with experimental data points (67Mit [177] and 75Cha [178]). The calculations are identical to those from [26]. The reference state used is pure liquid Al. 58

61 Fig. 46. Calculated (IAD) chemical potential of Al in liquid Al Si alloys at 827 C together with experimental data points (69Ber [171] and 79Sch [179]). The calculations are identical to those from [26]. The reference state for Al is pure liquid Al. Fig. 47. Calculated (IAD) chemical potential of Al in liquid Al Si alloys above 660 C together with experimental data points [171]. The calculations are identical to those from [26]. The reference state used is pure liquid Al. 59

62 Fig. 48. Calculated (IAD) chemical potential of Al in liquid Al Si alloys below 660 C together with experimental data points [171]. The calculations are identical to those from [26]. The reference state used is pure fcc Al. 3.7 Al C system The Al C system has been assessed by Kumar and Raghavan [27] applying interstitial filling of C atoms in the solid solution phases. This description was later modified by IAD assuming substitutional filling of C atoms in the bcc and fcc phases. The purpose was to simplify the Al C description and the following Fe Al C description for practical calculations of solidification modelling of steels. The present work reviews the Al C description from IAD and shows its experimental verification Phases, modelling, and data Table 20 shows the phases and their modelling. Table 21 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 22. Note the metastable bcc phase description from IAD. 60

63 Table 20. Phases and their modelling in the Al C description from IAD. Phase liquid ( L) bcc_a2 ( bcc, metastable) fcc_a1 ( fcc) Al 4 C 3 graphite ( gra) Modelling (Al,C), substitutional, RK (Al,C), substitutional, RK (Al,C), substitutional, RK (Al) 4 (C) 3, stoichiometric pure C Table 21. Data applied in the assessment verification for Al C from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [181, 182] Gibbs energy of formation of Al 4 C 3 at 1600 C [183] Table 22. Thermodynamic description of the Al C system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Al,C) Reference L L Al,C = ( T ) + ( T )(x Al x C ) [27] bcc (m) (1 sublattice, sites: 1, constituents: Al,C) G,bcc C = G,gra C + ( T ) IAD LAl,C bcc = 0 IAD fcc (1 sublattice, sites: 1, constituents: Al,C) G,fcc C = G,gra C + ( T ) IAD LAl,C fcc = 0 IAD Al 4 C 3 (2 sublattices, sites: 4:3, constituents: Al:C) G,Al 4C 3 Al:C = 4G,fcc Al + 3G,gra C + ( T ) [27] Notes: (m) = metastable phase; Gibbs energy data of pure components are given by [8] unless not shown in the table Results The results of calculations from IAD together with the experimental data (Table 21) are presented in Figure 49. The calculations agree well with the experimental data and they are practically identical to those from [27]. Choudary and Belton [183] measured the Gibbs energy of formation of Al 4 C 3 at 1600 C, yielding a value of 88.8 kj/mol. This agrees well with the calculated value of 88 kj/mol. A good agreement with the calculated and measured [184] enthalpy of formation of Al 4 C 3 at 25 C was also reported in [27]. 61

64 Fig. 49. Calculated (IAD) Al-rich portion of the Al C phase diagram together with experimental data points (79Mot [181] and 87Ode [182]). 3.8 Mn Si system The Mn Si system has been assessed by Chevalier et al. [28] and Tibballs [29]. The description of Tibballs [29] was later modified by IAD introducing simpler temperature functions for the Gibbs energies of formation of all silicides. In addition, the stability of Mn 6 Si was slightly decreased from that of Tibballs [29] to get better agreement with the experimental data, as shown by Chevalier et al. [28]. The purpose was to simplify the Mn Si description and the subsequent Fe Mn Si description for practical calculations of solidification modelling of steels. The present work reviews the Mn Si description from IAD and shows its experimental verification Phases, modelling, and data Tables show the phases and their modelling, the data applied for the assessment verification, and the thermodynamic description of the system, respectively. 62

65 Table 23. Phases and their modelling in the Mn Si description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) cbcc_a12 ( cbcc) cub_a13 ( cub) Mn 6 Si Mn 9 Si 2 Mn 3 Si Mn 5 Si 3 (member of Fe 5 Si 3 ) MnSi (member of FeSi) Mn 11 Si 19 dia_a4 ( dia) Modelling (Mn,Si), substitutional, RK (Mn,Si), substitutional, RK (Mn,Si), substitutional, RK (Mn,Si), substitutional, RK (Mn,Si), substitutional, RK (Mn) 6 (Si), stoichiometric (Mn) 9 (Si) 2, stoichiometric (Mn) 3 (Si), stoichiometric (Mn) 5 (Si) 3, stoichiometric (Mn)(Si), stoichiometric (Mn) 11 (Si) 19, stoichiometric pure Si Table 24. Data applied in the assessment verification for Mn Si from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [ ] Enthalpy of mixing in liquid alloys at 1500 and 1427 C [190, 191] Chemical potentials in liquid alloys at 1427, 1407, and 1350 C [ ] Gibbs energy of formation of solid alloys at 1007 and 25 C [196, 197] Table 25. Thermodynamic description of the Mn Si system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Mn,Si) Reference L L Mn,Si = ( T ) + ( T )(x Mn x Si ) [29] +( T )(x Mn x Si ) 2 + (16168)(x Mn x Si ) 3 bcc (1 sublattice, sites: 1, constituents: Mn,Si) LMn,Si bcc Mn x Si ) [29] Tc bcc = 580x Mn [29] β bcc = 0.27x Mn [29] fcc (1 sublattice, sites: 1, constituents: Mn,Si) LMn,Si fcc Mn x Si) [29] Tc fcc = 1620x Mn [29] β fcc = 1.86x Mn [29] cbcc (1 sublattice, sites: 1, constituents: Mn,Si) LMn,Si cbcc Mn x Si ) [29] cub (1 sublattice, sites: 1, constituents: Mn,Si) LMn,Si cub Mn x Si ) [29] Notes: #) = simplified function. The reference states of Mn and Si changed from H SER of [29]. 63

66 Table 25 (continued) Equation Reference Mn 6 Si (2 sublattices, sites: 17:3, constituents: Mn:Si) G,Mn 6Si Mn:Si = 17G,cbcc Mn + 3G,dia Si + ( T 39.22T lnt ) IAD Mn 9 Si 2 (2 sublattices, sites: 33:7, constituents: Mn:Si) G,Mn 9Si 2 Mn:Si = 33G,cbcc Mn + 7G,dia Si [29] #) +( T T lnt T 2 ) Mn 3 Si (2 sublattices, sites: 3:1, constituents: Mn:Si) G,Mn 3Si Mn:Si = 3G,cbcc Mn + G,dia Si + ( T T lnt T 2 ) [29] #) Mn 5 Si 3 (2 sublattices, sites: 5:3, constituents: Mn:Si) G,Mn 5Si 3 Mn:Si = 5G,cbcc Mn +3G,dia Si +( T T lnt T 2 ) [29] #) MnSi (2 sublattices, sites: 1:1, constituents: Mn:Si) G,MnSi Mn:Si Mn 11 Si 19 (2 sublattices, sites: 11:19, constituents: Mn:Si) G,Mn 11Si 19 Mn:Si = G,cbcc Mn + G,dia Si + ( T T lnt T 2 ) [29] #) = 11G,cbcc Mn + 19G,dia Si [29] #) +( T T lnt T 2 ) Notes: #) = simplified function. The reference states of Mn and Si changed from H SER of [29] Results The results of calculations by IAD and Tibballs [29] together with the experimental data (Table 24) are presented in Figures The agreement is reasonably good in both calculations. In Figure 50, note the lower stability of Mn 6 Si from IAD in regard to that of Tibballs [29]. 64

67 Fig. 50. Calculated Mn Si phase diagram together with experimental data points (06Doe [185], 33Vog [186], 61Dud [187], 70Mag [189], and 64Wie [188]). The solid lines are calculations from IAD, and the dotted lines are from [29]. Fig. 51. Calculated (IAD) mixing enthalpy of liquid Mn Si alloys at 1500 C together with experimental data points (74Gor [190] and 89Zai1 [191]). The calculations are identical to those from [29]. The reference states used are pure liquid Mn and pure liquid Si. 65

68 Fig. 52. Calculated (IAD) chemical potentials of Mn and Si in liquid Mn Si alloys at 1427 C together with experimental data points [191, 195]. The calculations are identical to those from [29]. The reference states used are pure liquid Mn and pure liquid Si. Fig. 53. Calculated (IAD) chemical potential of Mn and Si in liquid Mn Si alloys at 1407 C together with experimental data points [193]. The calculations are identical to those of [29]. The reference states used are pure liquid Mn and pure dia Si. 66

69 Fig. 54. Calculated (IAD) chemical potential of Mn and Si in liquid Mn Si alloys at 1350 C together with experimental data points [192, 194]. The calculations are identical to those from [29]. The reference states used are pure liquid Mn and pure dia Si. Fig. 55. Calculated (IAD) Gibbs energy of formation of solid Mn Si alloys at 1007 C together with experimental data points (89Zai2 [197]). The calculations are practically identical to those from [29]. The reference states used are pure cub Mn and pure dia Si 67

70 Fig. 56. Calculated (IAD) Gibbs energy of formation of solid Mn Si alloys at 25 C together with experimental data points (73Cha [196]). The calculations are practically identical to those from [29]. The reference states used are pure cbcc Mn and pure dia Si. Fig. 57. Calculated Gibbs energies of formation of Mn 6 Si, Mn 9 Si 2, Mn 3 Si, Mn 5 Si 3, MnSi, and Mn 11 Si 19. The solid lines are calculations from IAD, and the dotted lines are from 98Tib [29]. The reference states used are pure cbcc Mn and pure diamond Si. 68

71 3.9 Mn C system The Mn C system has been assessed in [30, 31] applying interstitial filling of carbon atoms in the solid solution phases. The latter description was later modified by IAD assuming substitutional filling of carbon atoms in the bcc and fcc phases. The purpose was to simplify the Mn C description and the subsequent Fe Mn C description for practical calculations of solidification modelling of steels. However, for the hcp, cbcc, and cub phases, seldom present in the phase equilibria of steels, the interstitial filling of carbon atoms was still applied. The present work reviews the Mn C description from IAD and shows its experimental verification Phases, modelling, and data Table 26 shows the phases and their modelling. Table 27 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 28. Table 26. Phases and their modelling in the Mn C description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) cbcc_a12 ( cbcc) cub_a13 ( cub) hcp_a3 ( hcp) Mn 23 C 6 ( M 23 C 6 ) Mn 7 C 3 ( M 7 C 3 ) Mn 5 C 2 ( M 5 C 2 ) Mn 3 C ( M 3 C cementite) graphite ( gra) Modelling (C,Mn), substitutional, RK (C,Mn), substitutional, RK (C,Mn), substitutional, RK (Mn)(C,Va), sublattice, RK (Mn)(C,Va), sublattice, RK (Mn)(C,Va) 0.5, sublattice, RK (Mn) 23 (C) 6, stoichiometric (Mn) 7 (C) 3, stoichiometric (Mn) 5 (C) 2, stoichiometric (Mn) 3 (C), stoichiometric pure C Table 27. Data applied in the assessment verification for Mn C from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [ ] Activity coefficient of Mn and C in liquid alloys from 1355 to 1500 C [9, 205, 206] Enthalpy of formation of solid Mn C alloys at 25 C [ ] Chemical potential diagram for Mn [202, 210, 211] 69

72 Table 28. Thermodynamic description of the Mn C system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: C,Mn) Reference L L C,Mn = ( T ) + (+6313)(x C x Mn ) + (+23281)(x C x Mn ) 2 [31] bcc (1 sublattice, sites: 1, constituents: C,Mn) G,bcc C = G,gra C + ( T ) IAD LC,Mn bcc IAD Tc bcc = 580x Mn x C IAD β bcc = 0.27x Mn x C IAD fcc (1 sublattice, sites: 1, constituents: C,Mn) G,fcc C = G,gra C + ( T ) IAD LC,Mn fcc C x Mn ) 2 IAD Tc fcc = 1620x Mn 201x C IAD β fcc = 1.86x Mn 2.1x C IAD cbcc (2 sublattices, sites: 1:1, constituents: Mn:C,Va) G,cbcc Mn:C = G,cbcc Mn G,cbcc Mn:Va = G,cbcc Mn + G,gra C + ( T ) [31] LMn:C,Va cbcc = ( 52204) [31] cub (2 sublattices, sites: 1:1, constituents: Mn:C,Va) G,cub Mn:C = G,cbcc Mn G,cub Mn:Va = G,cub Mn + G,gra C + (+2607) [31] LMn:C,Va cub = ( 10175) [31] hcp (2 sublattices, sites: 1:0.5, constituents: Mn:C,Va) G,hcp Mn:C = G,cbcc Mn G,hcp Mn:Va = G,hcp Mn G,Mn 23C 6 Mn:Mn:C = 23G,cbcc Mn + 0.5G,gra C + ( T ) [31] [8] L hcp Mn:C,Va = ( 5006) [31] Tc hcp = 1620x Mn [30] β hcp = 1.86x Mn [30] Mn 23 C 6 (M 23 C 6 ) (3 sublattices, sites: 20:3:6, constituents: Mn:Mn:C) + 6G,gra C + ( T ) [31] Mn 5 C 2 (M 5 C 2 ) (2 sublattices, sites: 5:2, constituents: Mn:C) G,Mn 5C 2 Mn:C = 5G,cbcc Mn + 2G,gra C + ( T ) [31] Mn 7 C 3 (M 7 C 3 ) (2 sublattices, sites: 7:3, constituents: Mn:C) G,Mn 7C 3 Mn:C = 7G,cbcc Mn + 3G,gra C + ( T ) [31] Mn 3 C (M 3 C cem) (2 sublattices, sites: 3:1, constituents: Mn:C) G,Mn 3C Mn:C = 3G,cbcc Mn + G,gra C + ( T ) [31] Notes: Thermodynamic data of pure components are given by [8] unless not shown in the table. [8] [8] 70

73 3.9.2 Results The results of calculations from IAD, Huang [30], and Hallstedt et al. [31] together with the experimental data (Table 27) are presented in Figures The agreement is reasonably good in each calculation. Note, however, the narrower fcc region in Figure 58 by the measurements of Benz et al. [200]. Additional experimental phase equilibrium data are available from Isobe [212] and Ma et al. [213]. These agree well with the calculated liquidus temperatures. The measurements from Isobe [212], however, do not correlate with the calculated solid state phase equilibria. Concerning Figure 58, note that [92, 214] presented somewhat different results from those of [202, 210, 211]. Consequently, they do not agree so well with the calculations. Fig. 58. Calculated Mn C phase diagram together with experimental data points (56Tur [198], 58Tur [199], 89Sic [202], 95Das [203], 07Fen [204], 73Ben [200], and 77Sch [201]). The solid line shows the calculations from IAD, and the dotted lines are from [31]. 71

74 Fig. 59. Calculated activity coefficient of Mn in liquid Mn C alloys at 1355 C to 1500 C together with experimental data points (79Tan [205], 93Kat [9], and 03Kim [206]). The solid lines are the calculations from IAD and [31], and the dotted lines are from [30]. The reference state used is pure liquid Mn. Fig. 60. Calculated activity coefficient of C in liquid Mn-C alloys at 1355 C to 1500 C together with experimental data points (79Tan [205], 93Kat [9], and 03Kim [206]). The solid lines are the calculations from IAD and [31], and the dotted lines are from [30]. The reference state used is pure graphite C. 72

75 Fig. 61. Calculated (IAD) enthalpy of formation of solid Mn C alloys at 25 C together with experimental data points (80Daw [207], 88Sic [208], 97Mes [209], and 04Zai [210]). The reference states used are pure cbcc Mn and pure graphite C. Solid lines are the calculations from IAD and [31], and the dotted lines are from [30]. The reference states used are pure cbcc Mn and pure graphite C. Fig. 62. Calculated Mn chemical potential diagram of the Fe Mn C system together with experimental data points (69Ere [211], 89Sic [202], and 04Zai [210]). Solid lines are the calculations from IAD, which are very close to those from [31], and the dotted lines are calculations from [30]. The reference state used is pure cub Mn. 73

76 3.10 Si C system The Si C system has been assessed by Gröbner et al. [32], applying interstitial filling of carbon atoms in the solid solution phases. This description was later modified by IAD assuming substitutional filling of carbon atoms in the bcc and fcc phases. The purpose was to simplify the Si C description and the following Fe Si C description for practical calculations of solidification modelling of steels. The present work reviews the Si C description from IAD and its experimental verification Phases, modelling, and data Table 29 shows the phases and their modelling, while Table 30 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 31. Note the metastable bcc and fcc phase description from IAD. Table 29. Phases and their modelling in the Si C description from IAD. Phase liquid ( L) bcc_a2 ( bcc, metastable) fcc_a1 ( fcc, metastable) dia_a4 ( dia) SiC graphite ( gra) Modelling (C,Si), substitutional, RK (C,Si), substitutional, RK (C,Si), substitutional, RK (C,Si), substitutional, RK (Si)(C), stoichiometric pure C Table 30. Data applied in the assessment verification for Si C from IAD. Experimental data Reference(s) Phase equilibria of the phase diagram [182, ] Heat content of SiC [ ] Gibbs energy of formation of SiC [223] Heat capacity of SiC [224] 74

77 Table 31. Thermodynamic description of the Si C system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: C,Si) Reference LC,Si L = ( T ) IAD bcc (m) (1 sublattice, sites: 1, constituents: C,Si) G,bcc C = G,gra C + ( T ) IAD LC,Si bcc = 0 IAD fcc (m) (1 sublattice, sites: 1, constituents: C,Si) G,fcc C = G,gra C + ( T ) IAD LC,Si fcc = 0 IAD dia (1 sublattice, sites: 1, constituents: C,Si) G,dia C = G,gra C + ( T T lnt ) [225] #) LC,Si dia = (+93387) [32] SiC (2 sublattices, sites: 1:1, constituents: Si:C) G,SiC Si:C = G,dia Si + G,gra C + ( T T lnt T 2 ) [225] #) Notes: (m) = metastable phase; #) = simplified function. Thermodynamic data of pure components are given by [8] unless not shown in the table. The reference state of C changed from H SER Results The results of calculations from IAD and Gröbner et al. [32] together with the experimental data (Table 30) are presented in Figures The agreement is reasonably good in both calculations. In Figures 65 and 66, note the better agreement for the Gibbs energy of formation of SiC and the slightly worse agreement for the heat capacity of SiC from IAD. The latter is mainly due to the simple temperature function applied by IAD for the Gibbs energy of formation of SiC. 75

78 Fig. 63. Calculated Si-rich portion of the Si C phase diagram together with experimental data points (58Hal [215], 59Sca [216], 60Dol [217], 87Ode [182], 93Kle [218], and 93Ott [226]). The solid lines are calculations from IAD, and the dotted line is from [32]. Fig. 64. Calculated heat content of SiC together with experimental data points (23Mag [219], 52Hum [220], 64Kir [221], 66Gus [222], and 71Che [227]). The solid line shows the calculations from IAD, and the dotted line is from [32]. 76

79 Fig. 65. Calculated Gibbs energy of formation of SiC together with experimental data points (89Bar [223]). The solid line shows the calculations from IAD, and the dotted line is from [32]. The reference states used are pure diamond for Si and pure graphite for C. Fig. 66. Calculated heat capacity of SiC together with experimental data points (77Stu [224]). The solid line shows the calculations from IAD, and the dotted line is from [32]. The reference states used are pure diamond for Si and pure graphite for C. 77

80 78

81 4 Ternary subsystems 4.1 Fe Al Mn system Experimental studies on the Fe Al Mn system have been reviewed by [228, 229], and a thermodynamic assessment has been given by [23, 33 35]. The Fe-Mn side of the system was later reassessed by IAD to get a simple Fe Al Mn description for practical calculations of solidification modelling of steels. This was a reasonable choice also due to the differences in the binary Al Fe and Al Mn between IAD and [23, 33 35]. The present work reviews the Fe Al Mn description from IAD and shows its experimental verification. For accurate thermodynamic calculations of the whole Fe Al Mn system, the assessment of Zheng et al. [35] is highly recommended Phases, modelling, and data Table 32 shows the phases and their modelling. Table 33 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 34. It should be noted that the ternary extensions of the Al-rich compounds of the system are not assessed by IAD. This is due the complex phase equilibria of these phases and the fact that bcc phase acts as a barrier isolating these phases from the Fe Mn rich phases. Consequently, only six solution phases remained to be assessed. To calculate the phase equilibria in the Al-rich-corner, one should use the description in [35]. Table 32. Phases and their modelling in the Fe Mn side Fe Al Mn description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) cbcc_a12 ( cbcc) cub_a13 ( cub) hcp_a3 ( hcp) Modeling (Al,Fe,Mn), substitutional, RKM (Al,Fe,Mn), substitutional, RKM (Al,Fe,Mn), substitutional, RKM (Al,Fe,Mn), substitutional, RKM (Al,Fe,Mn), substitutional, RKM (Al,Fe,Mn), substitutional, RKM 79

82 Table 33. Data applied in the assessment verification for Fe Al Mn from IAD. Experimental data Reference(s) Liquidus projection [230] 7 isothermal sections: at 1200, 1100, 1000, 900, 850, 800, and 760 C [23, 33, ] 3 vertical sections: at 10 and 30 wt-% Al and at 20 wt-% Mn [230] Enthalpy of mixing in liquid alloys at 1597 C and along [236] sections of constant x Fe :x Mn, x Fe :x Al, and x Mn :x Al ratios Activity coefficient γmn Al in liquid alloys at 1600 C [237, 238] *) Notes: *) theoretical. Table 34. Thermodynamic description of the Fe Al Mn system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Al,Fe,Mn) L L Al,Fe = ( T ) + ( T )(x Al x Fe ) + ( T )(x Al x Fe ) 2 Reference L L Al,Mn = ( T ) + ( T )(x Al x Mn ) + ( 2639)(x Al x Mn ) 2 [22] L L Fe,Mn = ( T ) + (1145)(x Fe x Mn ) [4] LAl,Fe,Mn L = ( 20000)x Al + (+0)x Fe + (+20000)x Mn IAD bcc (1 sublattice, sites: 1, constituents: Al,Fe,Mn) LAl,Mn bcc Al x Mn ) [23] LAl,Fe bcc Al x Fe ) IAD LFe,Mn bcc = ( T ) [4] LAl,Fe,Mn bcc Al + ( T )x Fe + (+13000)x Mn IAD Tc bcc = 1043x Fe 580x Mn + x Al x Fe ( 1100(x Al x Fe )) + x Fe x Mn (123) IAD β bcc = 2.22x Fe 0.27x Mn [4] fcc (1 sublattice, sites: 1, constituents: Al,Fe,Mn) LAl,Mn fcc Al x Mn ) [23] LAl,Fe fcc Al x Fe ) + (+10000)(x Al x Fe ) 2 IAD LFe,Mn fcc Fe x Mn ) [4] LAl,Fe,Mn fcc Al + ( T )x Fe + ( 15000)x Mn IAD Tc fcc = 201x Fe 1620x Mn + x Fe x Mn ( (x Fe x Mn )) [4] β fcc = 2.1x Fe 1.86x Mn [4] hcp (1 sublattice, sites: 1, constituents: Al,Mn) L hcp Al,Fe = T [10] L hcp Al,Mn = ( T ) + ( T )(x Al x Mn ) [22] +( T )(x Al x Mn ) 2 L hcp Fe,Mn = ( T ) + (273)(x Fe x Mn ) [4] Tc hcp = 1740x Mn [4] β hcp = 1.86x Mn [4] Notes: thermodynamic data of pure components are given by [8] unless not shown in the table. IAD 80

83 Table 34 (continued) Equation Reference cbcc (1 sublattice, sites: 1, constituents: Al,Mn) LAl,Fe cbcc = ( T ) [10] LAl,Mn cbcc = ( T ) [22] LFe,Mn cbcc = ( 10184) [4] cub (1 sublattice, sites: 1, constituents: Al,Mn) L cub Al,Mn = ( T ) + ( 6289)(x Al x Mn ) [22] LFe,Mn cub = ( T ) [4] L cub Al,Fe = ( T ) IAD LAl,Fe,Mn cub = ( T )x Al + ( T )x Fe + ( 6000)x Mn IAD Notes: thermodynamic data of pure components are given by [8] unless not shown in the table Results The results of calculations from IAD together with the experimental data (Table 33) are presented in Figures The agreement is reasonably good. In Figures 67 and 74, note the stronger stability for the fcc phase by [230, 231], and in Figure 72, note the wider bcc+fcc region reported by Shvedov and Goretskij [232]. These disagreements could not be diminished by calculations without making the agreement with the measurements of [23, 235] much worse. In Figure 80, note the scattered theoretical estimations for the activity coefficient γmn Al, and the reasonable average value by the calculations. These theoretical estimations are based on data interpolation using periodic tables of pure elements [237] and the pseudopotential formalism coupled with the free energy of the hard sphere system [238]. 81

84 Fig. 67. Calculated (IAD) liquidus projection in the Fe Al Mn system. Shown also are the calculated liquidus isotherms between 1500 C and 1200 C (dotted lines) together with experimental data points [230]. The broken line shows the bcc+fcc+l monovariant line estimated by [230]. Fig. 68. Calculated (IAD) isotherm of 1200 C in the Fe Al Mn system together with experimental data points (06Umi [23], 96Liu [235], and 92Xu [234]). 82

85 Fig. 69. Calculated (IAD) isotherm of 1100 C in the Fe Al Mn system together with experimental data points (06Umi [23], 92Liu [233], and 92Xu [234]). Fig. 70. Calculated (IAD) isotherm of 1000 C in the Fe Al Mn system together with experimental data points (06Umi [23], 93Liu [33], and 92Xu [234]). 83

86 Fig. 71. Calculated (IAD) isotherm of 900 C in the Fe Al Mn system together with experimental data points (06Umi [23] and 96Liu [235]). The experimental three-phase triangle of [23] is shown in grey. Fig. 72. Calculated (IAD) isotherm of 850 C in the Fe Al Mn system together with experimental data points [232]. 84

87 Fig. 73. Calculated (IAD) isotherm of 800 C in the Fe Al Mn system together with experimental data points (06Umi [23] and 96Liu [235]). The experimental three-phase triangle of [23] is shown in grey. Fig. 74. Calculated (IAD) Fe-rich isotherm of 760 C in the Fe Al Mn system together with experimental data points [231]. 85

88 Fig. 75. Calculated (IAD) vertical section of 10 wt-% Al and 30 wt-% Al in the Fe Al Mn system together with experimental data points (33Kos [230]). Fig. 76. Calculated (IAD) vertical section of 20 wt-% Mn in the Fe Al Mn system together with experimental data points [230]. 86

89 Fig. 77. Calculated (IAD) enthalpy of mixing in liquid Fe Al Mn alloys at 1597 C and along sections of constant x Fe :x Mn ratios together with experimental data points [236]. The reference states used are pure liquid components. Fig. 78. Calculated (IAD) enthalpy of mixing in liquid Fe Al Mn alloys at 1597 C and along sections of constant x Fe :x Al ratios together with experimental data points [236]. The reference states used are pure liquid components. 87

90 Fig. 79. Calculated (IAD) enthalpy of mixing in liquid Fe-Al-Mn alloys at 1597 C and along sections of constant x Mn :x Al ratios together with experimental data points [236]. The reference states used are pure liquid components. Fig. 80. Calculated (IAD) activity coefficient γ Al Mn in liquid Fe Al Mn alloys at 1600 C together with theoretically determined data points (72Bod [237] and 98Uen [238]). 88

91 4.2 Fe Al Si system Experimental studies on the Fe Al Si system have been reviewed by [ ], and a thermodynamic assessment has been given by [36 39]. Due to the numerous ternary compounds, the phase equilibria of the system are relatively complex. Du et al. [39] succeeded in assessing the solid-state equilibria of the system quite well, including ten ternary compounds in their description. The liquid containing phase equilibria, however, were not described so well. That was shown by the more recent measurements of Marker et al. [244], who constructed two new isotherms and four new isopleths for the systems. In addition, they detected a new high-temperature ternary compound of τ 12 not observed in the earlier studies. Due to these reasons, the system was reassessed by IAD. Note, however, that the B2 ordering of the bcc phase was not considered by IAD, but its energetic effect was included in the disordered bcc phase, to simplify the Fe Al Si description for practical calculations of solidification modelling of steels. The present work reviews the Fe Al Si description from IAD and shows its experimental verification Phases, modelling, and data Table 35 shows the phases and their modelling. The phase formulations for the ternary compounds of τ n (n = 1...8,10,11) and τ 12 are identical to those in [39] and [244], respectively. Table 36 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table

92 Table 35. Phases and their modelling in the Fe Al Si description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) dia_a4 ( dia) Al 5 Fe 4 ( α 1 ) Al 2 Fe ( α 2 ) (dissolving Si) Al 5 Fe 2 ( α 3 ) (dissolving Si) Al 13 Fe 4 ( α 4 ) (dissolving Si) Fe 2 Si Fe 5 Si 3 FeSi (dissolving Al) FeSi 2 -H ( β H ) (dissolving Al) FeSi 2 -L ( β L ) (dissolving Al) τ 1 -AlFeSi ( τ 1 ) τ 2 -AlFeSi ( τ 2 ) τ 3 -AlFeSi ( τ 3 ) τ 4 -AlFeSi ( τ 4 ) τ 5 -AlFeSi ( τ 5 ) τ 6 -AlFeSi ( τ 6 ) τ 7 -AlFeSi ( τ 7 ) τ 8 -AlFeSi ( τ 8 ) τ 10 -AlFeSi ( τ 10 ) τ 11 -AlFeSi ( τ 11 ) τ 12 -AlFeSi ( τ 12 ) Modelling (Al,Fe,Si), substitutional, RKM (Al,Fe,Si), substitutional, RKM (Al,Fe,Si), substitutional, RKM (Al,Fe,Si), substitutional, RKM (Al,Fe), substitutional, RKM (Al,Si) 2 (Fe), sublattice, RKM (Al,Si) 5 (Fe) 2, sublattice, RKM (Al,Si) 13 (Fe) 4, sublattice, RKM (Fe) 2 (Si), stoichiometric (Fe) 5 (Si) 3, stoichiometric (Fe)(Al,Si), sublattice, RKM (Fe) 3 (Al,Si) 7, sublattice, RKM (Fe)(Al,Si) 2, sublattice, RKM (Al,Si) 5 (Fe) 3, sublattice, RKM (Al,Si) 7 (Fe) 2, sublattice, RKM (Al) 11 (Fe) 5 (Si) 4, stoichiometric (Al,Si) 5 (Fe), sublattice, RKM (Al) 71 (Fe) 19 (Si) 10, stoichiometric (Al) 9 (Fe) 2 (Si) 2, stoichiometric (Al,Si) 3 (Fe), sublattice, RKM (Al,Si) 2 (Fe), sublattice, RKM (Al) 12 (Fe) 5 (Si) 3, stoichiometric (Al) 17 (Fe) 6 (Si) 3, stoichiometric (Al) 12 (Fe) 9 (Si) 4, stoichiometric 90

93 Table 36. Data applied in the assessment verification for Fe Al Si from IAD. Experimental data Reference(s) Liquidus projection [245] 6 isothermal sections: at 1100, 1020, 900, 800, 727, and 550 C [244, ] 8 vertical sections: at 60, 50, 40, 35, and 27 at-% Fe [244] Liquidus temperatures along 80, 70, 60, 55, 50, and 45 wt-% Fe [245] Liquidus temperatures along 33, 30, 25, 22, 17, and 14 at-% Fe [39, 248] 4 Vertical sections: at 20, 15, 10, and 5 wt-% Fe [39, 245, 249] 3 Vertical sections: at 5 at-% Al, and at 10 and 20 wt-% Al [244, 245] 3 Vertical sections: at 2, 10, and 13.5 wt-% Si [39, 245, ] Enthalpy of mixing of liquid alloys at 1477 C [254] Activity of Al in liquid alloys at 1627 C [255] Activity of Al in liquid alloys between 1108 and 790 C [256] Activity of Al in liquid alloys at 900 C [180, 257] Activity coefficient γal Si in liquid alloys at 1600 C [258] Heat content of τ 5 phase [39] Enthalpy of formation of solid alloys at 25 C [259, 260] Table 37. Thermodynamic description of the Fe Al Si system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Al,Fe,Si) L L Al,Fe = ( T ) + ( T )(x Al x Fe ) + ( T )(x Al x Fe ) 2 Reference L L Al,Si = ( T ) + ( T )(x Al x Si ) + (2265)(x Al x Si ) 2 [26] L L Fe,Si = ( T ) + ( T )(x Fe x Si ) [16] +( T )(x Fe x Si ) 2 + ( T )(x Fe x Si ) 3 LAl,Fe,Si L = ( T )x Al + ( T )x Fe + (+80000)x Si bcc (1 sublattice, sites: 1, constituents: Al,Fe,Si) LAl,Fe bcc = ( T ) + ( T )(x Al x Fe ) LAl,Si bcc = Lfcc Al,Si LFe,Si bcc = ( T ) + ( T )(x Fe x Si ) +( T )(x Fe x Si ) 2 LAl,Fe,Si bcc Al + ( )x Fe + ( 95000)x Si IAD Tc bcc = 1043x Fe + x Al x Fe ( 1100(x Al x Fe )) + x Fe x Si (504(x Fe x Si )) IAD β bcc = 2.22x Fe [8] Notes: thermodynamic data of pure components are given by [8] unless not shown in the table. IAD IAD IAD IAD IAD 91

94 Table 37 (continued) Equation Reference fcc (1 sublattice, sites: 1, constituents: Al,Fe,Si) LAl,Fe fcc Al x Fe ) + (+10000)(x Al x Fe ) 2 IAD LAl,Si fcc = ( T ) [26] LFe,Si fcc Fe x Si ) + (+89907)(x Fe x Si ) 2 [15] LAl,Fe,Si fcc IAD Tc fcc = 201x Fe [8] β fcc = 2.1x Fe [8] dia (1 sublattice, sites: 1, constituents: Al,Si) G,dia Al = G,fcc Al + (+30T ) [26] LAl,Si dia = ( T ) [26] Al 5 Fe 4 (α 1 ) (1 sublattice, sites: 1, constituents: Al,Fe) G,Al 5Fe 4 Al = G,fcc Al + ( T ) [10] G,Al 5Fe 4 Fe = G,bcc Fe + (+5009) [10] L Al 5Fe 4 Al,Fe = ( T ) + ( 16000)(x Al x Fe ) IAD Al 2 Fe (α 2 ) (2 sublattices, sites: 2:1, constituents: Al:Fe) G,Al 2Fe Al:Fe G,Al 2 = 2G,fcc Al + G,bcc Fe + ( T ) [10] FeSi:Fe = 2G,dia Si + G,bcc Fe Al 5 Fe 2 (α 3 ) (2 sublattices, sites: 5:2, constituents: Al,Si:Fe) G,Al 5Fe 2 Al:Fe G,Al 5Fe 2 Si:Fe L Al 5Fe 2 = 5G,fcc Al + 2G,bcc = 5G,dia Si Al,Si:Fe = ( ) + 2G,bcc Fe IAD Fe + ( T ) [10] Al 13 Fe 4 (α 4 ) (2 sublattices, sites: 0.752:0.248, constituents: Al,Si:Fe) G,Al 13Fe 4 Al:Fe = 0.752G,fcc Al G,bcc Fe + ( T ) IAD G,Al 13Fe 4 Si:Fe L Al 13Fe 4 Al,Si:Fe = 0.752G,dia Si = ( T ) IAD G,bcc Fe Fe 2 Si (2 sublattices, sites: 2:1, constituents: Fe:Si) G,Fe 2Si Fe:Si Fe 5 Si 3 (2 sublattices, sites: 5:3, constituents: Fe:Si) G,Fe 5Si 3 Fe:Si = 2G,bcc Fe + G,dia Si + ( T ) [15] = 5G,bcc Fe + 3G,dia Si + ( T ) [15] Fe 5 Si 3 (2 sublattices, sites: 5:3, constituents: Fe:Si) G,FeSi Fe:Al = G,bcc Fe + G,fcc Al + (+60000) IAD G,FeSi Fe:Si = G,bcc Fe + G,dia Si + ( T ) [15] LFe:Al,Si FeSi = ( T ) IAD FeSi 2 -H (β H ) (2 sublattices, sites: 3:7, constituents: Fe,Al:Si) G,FeSi 2-H Fe:Al = 3G,bcc Fe + 7G,fcc Al + ( T ) IAD G,FeSi 2-H Fe:Si = 3G,bcc Fe + 7G,dia Si + ( T ) [15] = ( T ) IAD L FeSi 2-H Fe:Al,Si Notes: thermodynamic data of pure components are given by [8] unless not shown in the table. IAD IAD IAD 92

95 Table 37 (continued) Equation FeSi 2 -L (β L ) (2 sublattices, sites: 1:2, constituents: Fe,Al:Si) G,FeSi 2-L Fe:Al = G,bcc Fe + 2G,fcc G,τ 1 Al:Fe = 5G,fcc Al G,τ 1 Si:Fe = 5G,dia Si L τ 1 Reference Al + ( 40000) IAD + 2G,dia Si + ( T ) [15] G,FeSi 2-L Fe:Si = G,bcc Fe τ 1 -AlFeSi (τ 1 ) (2 sublattices, sites: 5:3, constituents: Al,Si:Fe) + 3G,bcc Fe + ( T ) IAD + 3G,bcc Fe + ( T ) IAD Al,Si:Fe = ( T ) + ( )(y Al y Si ) IAD τ 2 -AlFeSi (τ 2 ) (2 sublattices, sites: 7:2, constituents: Al,Si:Fe) G,τ 2 Al:Fe = 7G,fcc Al + 2G,bcc Fe + ( ) IAD G,τ 2 Si:Fe = 7G,dia Si + 2G,bcc Fe + ( ) IAD L τ 2 Al,Si:Fe = ( T ) IAD τ 3 -AlFeSi (τ 3 ) (3 sublattices, sites: 11:5:4, constituents: Al:Fe:Si) G,τ 3 Al:Fe:Si = 11G,fcc Al + 5G,bcc Fe + 4G,dia Si + ( T ) IAD τ 4 -AlFeSi (τ 4 ) (2 sublattices, sites: 5:1, constituents: Al,Si:Fe) G,τ 4 Al:Fe = 5G,fcc Al + G,bcc Fe + ( 55000) IAD G,τ 4 Si:Fe = 5G,dia Si + G,bcc Fe + (+50000) IAD L τ 4 Al,Si:Fe = ( T ) IAD τ 5 -AlFeSi (τ 5 ) (3 sublattices, sites: 71:19:10, constituents: Al:Fe:Si) G,τ 5 Al:Fe:Si = 71G,fcc Al + 19G,bcc Fe + 10G,dia Si + ( T ) IAD τ 6 -AlFeSi (τ 6 ) (3 sublattices, sites: 9:2:2, constituents: Al:Fe:Si) G,τ 6 Al:Fe:Si = 9G,fcc Al + 2G,bcc Fe + 2G,dia Si + ( T ) IAD τ 7 -AlFeSi (τ 7 ) (2 sublattices, sites: 3:1, constituents: Al,Si:Fe) G,τ 7 Al:Fe = 3G,fcc Al + G,bcc Fe + ( 85000) IAD G,τ 7 Si:Fe = 3G,dia Si + G,bcc Fe + ( 35000) IAD L τ 7 Al,Si:Fe = ( T ) IAD τ 8 -AlFeSi (τ 8 ) (2 sublattices, sites: 2:1, constituents: Al,Si:Fe) G,τ 8 Al:Fe = 2G,fcc Al + G,bcc Fe IAD G,τ 8 Si:Fe = 2G,dia Si + G,bcc Fe + ( 40000) IAD L τ 8 Al,Si:Fe = ( T ) IAD τ 10 -AlFeSi (τ 10 ) (3 sublattices, sites: 12:5:3, constituents: Al:Fe:Si) G,τ 10 Al:Fe:Si = 12G,fcc Al + 5G,bcc Fe + 3G,dia Si + ( T ) IAD τ 11 -AlFeSi (τ 11 ) (3 sublattices, sites: 17:6:3, constituents: Al:Fe:Si) G,τ 11 Al:Fe:Si = 17G,fcc Al + 6G,bcc Fe + 3G,dia Si + ( ) IAD τ 12 -AlFeSi (τ 12 ) (3 sublattices, sites: 12:9:4, constituents: Al:Fe:Si) G,τ 12 Al:Fe:Si = 12G,fcc Al + 9G,bcc Fe + 4G,dia Si + ( T ) IAD Notes: thermodynamic data of pure components are given by [8] unless not shown in the table. 93

96 4.2.2 Results The results of calculations from IAD and Du et al. [39] together with the experimental data (Table 36) are presented in Figures and Tables The agreement is reasonable in both calculations for the solid-state phase equilibria. For the phase equilibria involving liquid, however, the agreement from IAD is clearly better than from Du et al. [39]. This is due to the decision of IAD to rely on the numerous DTA and TA measurements from [244, 245] on the phase equilibria phase equilibria that include liquids, and the Al activity measurements made by [255, 258] for Fe-rich liquid alloys. Du et al. [39], instead, applied (in their optimization) the relatively few invariant temperatures determined by Krendelsberger et al. [248] from ternary alloys, which were mostly poor in Fe. The previously mentioned measurements from [245, 255, 258] were not used, and those from Marker et al. [244] were not available in 2008 for Du et al. [39]. As a result, their liquid phase became too stable to satisfy the phase equilibria and the liquid-state Al activity data in the Fe-rich part of the system. Figure 81 shows the calculated (IAD) liquidus projection of the system. With 19 primary surfaces, that projection is quite complex. The same 19 primary surfaces are also present in the liquidus projections determined by Krendelsberger et al. [248] and calculated by Du et al. [39] (Figure 82), though their shapes are sometimes quite different. In the early study by Takeda and Mutuzaki [245], instead, shows primary surfaces for only 16 phases, as only six of the present nine ternary τ compounds had been detected in those days. 94

97 Fig. 81. Calculated (IAD) liquidus projection in the Fe Al Si system. The calculated liquidus isotherms between 1500 C and 800 C are shown with dotted lines. Fig. 82. Experimental [248] and calculated [39] liquidus projection in the Fe Al Si system. (Left figure reprinted by permission from [248] c 2007 Springer Nature; right figure reprinted by permission from [39] c 2008 Elsevier Ltd). 95

98 The calculated temperatures and the liquid compositions of the invariant reactions (given by E, U, and P type codes in Figure 81) are tabulated in Table 38. No comparison is given with the invariant reaction data calculated by [38,39], or determined by [245, 248]. This is due to the high diversity of those data based on the different ternary compound determinations by [245, 248] and their different treatment in the calculations from [38, 39]. Table 38. Calculated (IAD) invariant points of the Fe Al Si system. Equilibrium Code Temperature ( C) Al in liq (at-%) Si in liq (at-%) L = bcc + Fe 2 Si + FeSi E L = fcc + dia +τ 6 E L + bcc + FeSi = τ 1 P L + τ 1 + τ 11 = τ 3 P L + FeSi 2 -H + τ 1 = τ 8 P L + τ 3 + τ 11 = τ 2 P L + τ 1 + τ 3 = τ 7 P L + dia + τ 7 = τ 4 P L + Al 13 Fe 4 + τ 11 = τ 5 P L + τ 4 + τ 5 = τ 6 P L + Al 5 Fe 4 = bcc + Al 2 Fe U L + Al 2 Fe = bcc + Al 5 Fe 2 U L + Al 5 Fe 2 = bcc + Al 13 Fe 4 U L + FeSi = FeSi 2 -H + τ 1 U L + Al 13 Fe 4 = bcc + τ 11 U L + bcc = τ 1 + τ 11 U L + FeSi 2 -H = dia + τ 8 U L + τ 1 = τ 7 + τ 8 U L + τ 3 = τ 2 + τ 7 U L + τ 8 = dia + τ 7 U L + τ 7 = τ 2 + τ 4 U L + τ 11 = τ 2 + τ 5 U L + τ 2 = τ 4 + τ 5 U L + Al 13 Fe 4 = fcc + τ 5 U L + τ 5 = fcc + τ 6 U L + τ 4 = dia + τ 6 U On the whole, as the invariant points are only indirect determinations made by interpolating or extrapolating the original measurements, and they always depend on the way the researcher views their data compilation, they were not used as primary data by IAD. Instead, the original direct measurements were preferred. This caused some deviation in the location of certain primary surfaces, when compared with those from [39, 248]. 96

99 As can be seen in Figure 82, the monovariant lines determined by [39,248] connect surface τ 1 to surfaces Al 5 Fe 2 and Al 13 Fe 4, whereas according to IAD, there is no contact between the τ 1 and Al 5 Fe 2 or Al 13 Fe 4 surfaces. This is because of the high stability of the bcc phase in IAD. Another interesting difference between the calculation from IAD and the determination of Takeda and Mutuzaki [245] is the temperature and liquid composition value of reaction L + bcc + FeSi = τ 1 (invariant P 1 ). According to IAD, that reaction occurs at 1064 C at a liquid composition of 36.5 at-% Al and 28.6 at-% Si (see Table 38), whereas the corresponding values in the determination of [245] are 1050 C, 42.2 at-% Al, and 24.9 at-% Si, respectively. According to calculations from Du et al. [39], the reaction is eutectic as L = bcc + FeSi + τ 1 and the temperature and composition values are 1054 C, 29.2 at-% Al, and 26.6 at-% Si. So, the peritectic temperature and the Si composition from IAD are slightly higher than those from [39,245], though the Al composition from IAD is between those of [39, 245]. Even in that case it should be noted that IAD also takes into account the most recent phase equilibrium measurements by Marker et al. [244], well covering the region of the considered invariant reaction of P 1. Unfortunately, however, Marker et al. [244] gave no estimation for the temperature and composition of reaction L + bcc + FeSi = τ 1. Figures show six calculated isothermal sections of the system at 1100 C, 1020 C, 900 C, 800 C, 727 C, and 550 C as well as two experimental isotherms at 727 C and 550 C. In Figures 83 and 84, note the bcc and liquid phase regions suggested by [246] after modifying the experimentally determined phase equilibria of Takeda and Mutuzaki [245]. At both temperatures (1100 C and 1020 C), the experimental bcc phase region, in the vicinity of the Fe Al compounds, is less stable than obtained by the calculations from IAD. These calculated results, however, are supported by the recently assessed Fe Al phase diagram [11] showing that the bcc phase region can extend up to about 50 at-% Al. 97

100 Fig. 83. Calculated (IAD) isotherm of 1100 C in the Fe Al Si system together with the bcc and liquid phase regions suggested by 03Gup [246] after modifying the experimentally determined phase equilibria of [245] (dotted lines). Fig. 84. Calculated (IAD) isotherm of 1020 C in the Fe Al Si system together with the bcc and liquid phase regions suggested by 03Gup [246] after modifying the experimentally determined phase equilibria of [245] (dotted lines). 98

101 Figures and 89 show the complex phase equilibria calculated at 900 C, 800 C, 727 C, and 550 C, respectively. This complexity is due to the numerous ternary compounds involved. The agreement with the experimental measurements is mostly good and similar to that of Du et al. [39], though there are also some exceptions. As an example, note absence of the experimentally determined FeSi 2 -H + dia + L triangle at 900 C, and the absence of the experimentally determined bcc + Al 5 Fe 2 + τ 1 triangle and two phase region of FeSi + τ 8 at 550 C. See also the experimental isotherms of 727 C and 550 C in Figures 88 and 90, to make a more detailed comparison with the calculated isotherms of Figures 87 and 89. In the isotherms of 900 C and 800 C (Figures 85 and 86), note the presence of compound τ 12, detected recently by Marker et al. [244]. According to them, that compound is stable between 1005 C and 720 C, whereas according to calculations from IAD, the corresponding temperature range is 1000 C to 730 C. Note that the lower limit of 720 C by Marker et al. [244] was raised to 730 C by IAD, as τ 12 was not detected at 727 C by Bosselet et al. [247] (see Figure 87). Its decomposition at 730 C occurs via the reaction τ 12 = bcc + Al 5 Fe 2 + τ 1, as reported also by [244], but its formation at 1000 C occurs via the reaction bcc + Al 5 Fe 2 + Al 13 Fe 4 = τ 12, whilst [244] suggested that it was bcc + Al 5 Fe 2 + τ 1 = τ 12. Fig. 85. Calculated (IAD) isotherm of 900 C in the Fe Al Si system together with the experimental data points of [244] for one-phase regions. The experimental three-phase triangles are shown in grey. The numbers denote index n of phase τ n. 99

102 Fig. 86. Calculated (IAD) isotherm of 800 C in the Fe Al Si system together with the experimental data points of [244] for one-phase regions and [39] for three-phase alloys (white stars). The experimental three-phase triangles of [244] are shown in grey. The numbers denote index n of phase τ n. Fig. 87. Calculated (IAD) isotherm of 727 C in the Fe Al Si system together with the onephase data points picked from the experimental isotherm from [247] (see Figure 88). The numbers denote index n of phase τ n. 100

103 Fig. 88. Experimental (04Bos [247]) isotherm of 727 C in the Fe Al Si system (modified from [247]). Fig. 89. Calculated (IAD) isotherm of 550 C in the Fe Al Si system together with the onephase data points picked from the experimental isotherm from [248] (see Figure 90). The numbers denote index n of phase τ n. 101

104 Fig. 90. Experimental (07Kre [248]) isotherm of 550 C in the Fe Al Si system (modified from [248]). Figures show 17 calculated vertical sections of the system at various, fixed Fe, Al, and Si contents. In Figures 96 and 97, however, only the liquidus temperatures of the vertical sections, calculated with numerous Fe contents, are presented. All the figures also use dotted lines to show the vertical sections or the liquidus of those sections calculated by Du et al. [39]. In most cases, the agreement is much worse than obtained by calculations from IAD. This is mainly due to the fact that the most recent measurements of [244] were not available for Du et al. [39]. 102

105 Fig. 91. Calculated vertical section of 60 at-% Fe in the Fe Al Si system together with experimental data points [244]. The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. Fig. 92. Calculated vertical section of 50 at-% Fe in the Fe Al Si system together with experimental data points [244]. The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. The broken line shows the approximate solidus of FeSi, which could not be plotted with ThermoCalc. 103

106 Fig. 93. Calculated vertical section of 40 at-% Fe in the Fe Al Si system together with experimental data points from [244] and [248] (07Kre). The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. Fig. 94. Calculated vertical section of 35 at-% Fe in the Fe Al Si system together with experimental data points [244]. The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. 104

107 Fig. 95. Calculated vertical section of 27 at-% Fe in the Fe Al Si system together with experimental data points [244]. The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. Fig. 96. Calculated (IAD) liquidus temperatures along vertical sections of 80, 70, 60, 55, 50, and 45 wt-% Fe in the Fe Al Si system together with experimental data points (04Tak [245]). 105

108 Fig. 97. Calculated (IAD) liquidus temperatures along vertical sections of 33, 30, 25, 22, 17, and 14 at-% Fe in the Fe Al Si system together with experimental data points (07Kre [248] and 08Du [39]). Fig. 98. Calculated vertical section of 20 wt-% Fe in the Fe Al Si system together with experimental data points [245]. The solid lines are calculations from IAD, and the dotted line shows the liquidus and L+dia region calculated in [39]. 106

109 Fig. 99. Calculated vertical section of 15 wt-% Fe in the Fe Al Si system together with experimental data points (32Nis [249], 40Tak [245], and 08Du [39]). The solid lines are calculations from IAD, and the dotted line shows the liquidus and L+dia region calculated in [39]. Fig Calculated vertical section of 10 wt-% Fe in the Fe Al Si system together with experimental data points (32Nis [249] and 40Tak [245]). The solid lines are calculations from IAD, and the dotted line shows the liquidus and L+dia region calculated in [39]. 107

110 Fig Calculated vertical section of 5 wt-% Fe in the Fe Al Si system together with experimental data points [245]. The solid lines are calculations from IAD, and the dotted line shows the liquidus and L+dia region calculated in [39]. Fig Calculated vertical section of 5 at-% Al in the Fe Al Si system together with experimental data points [244]. The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. 108

111 Fig Calculated vertical section of 10 wt-% Al in the Fe Al Si system together with experimental data points [245]. The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. Fig Calculated vertical section of 20 wt-% Al in the Fe Al Si system together with experimental data points [245]. The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. 109

112 Fig Calculated vertical section of 2 wt-% Si in the Fe Al Si system together with experimental data points (32Nis [249] and 40Tak [245]). The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. Fig Calculated vertical section of 10 wt-% Si in the Fe Al Si system together with experimental data points (51Now [250], 88Zak [251], and 08Du [39]). The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. 110

113 Fig Calculated vertical section of 13.5 wt-% Si in the Fe Al Si system together with experimental data points (88Zak [251], 96Gil [252], and 04Pon [253]). The solid lines are calculations from IAD, and the dotted line shows the liquidus calculated in [39]. Figures show calculated results from IAD and Du et al. [39] for the mixing enthalpies of liquid (Figure 108), Al activities in liquid (Figures ) and heat content of the τ 5 phase (Figure 114). In Figure 108, note the slightly better agreement with the experimental data from IAD, but also the increasing deviation in both calculations when approaching the binary Fe Si alloys. Figure 109 shows a relatively moderate agreement by both calculations for the Al activities in liquid, though the agreement from IAD is still better. The agreement between the calculated and measured Al activities in Figures is reasonably good in both calculations, and even a bit better in [39], but in Figure 113, the calculations from [39] totally fail to agree with the measurements and the calculations from IAD, agreeing well with each other. Figure 114, instead, shows excellent agreement for the measured heat content of τ 5 phase, in both calculations. 111

114 Fig Calculated enthalpy of mixing of liquid Fe Al Si alloys at 1477 C together with experimental data points [254]. The solid lines are calculations from IAD, and the dotted lines are from [39]. The reference states used are pure liquid components. Fig Calculated activity of Al in liquid Fe Al Si alloys at 1627 C together with experimental data points [255]. The solid lines are calculations from IAD, and the dotted lines are from [39]. The reference state used is pure liquid Al. 112

115 Fig Calculated activity of Al in liquid Fe Al Si alloys at w Fe :w Si = together with experimental data points [256]. The solid lines are calculations from IAD, and the dotted lines are from [39]. The reference state used is pure liquid Al. Fig Calculated activity of Al in liquid Fe Al Si alloys at five w Fe :w Si ratios together with experimental data points [256]. The solid lines are calculations from IAD, and the dotted lines are from [39]. The reference state used is pure liquid Al. 113

116 Fig Calculated activity of Al in liquid Fe Al Si alloys at two w Fe :w Si ratios together with experimental data points (73Per [257] and 89Bon [180]). The solid lines are calculations from IAD, and the dotted lines are from [39]. The reference state used is pure liquid Al. Fig Calculated activity coefficient γ Si Al in liquid Fe Al Si alloys at 1600 C together with experimental data points (60 Wil [258]). The solid line shows the calculations from IAD, and the dotted line shows those from [39]. 114

117 Fig Calculated (IAD) heat content of τ 5 phase together with experimental data points (08Du [39]). The calculations are practically identical to those from [39]. Table 39 shows calculated IAD and measured enthalpies of formation of solid Fe Al Si alloys at 25 C. The agreement is reasonable, but all the calculated values are lower than the measured ones. It should be noted that the alloy compositions of Table 39 represent ternary compound compositions, which sometimes differ from those assessed by [39, 244] and accepted in IAD. Hence, the calculations from IAD are affected also by the presence of some other phases. Table 39. Calculated (IAD) and experimental [259, 260] enthalpies of formation of solid Fe Al Si alloys at 25 C (composition in at-%). Alloy Calculated H (kj/mol) Experimental H (kj/mol) Reference Al 36 Fe 36 Si [259] Al 38 Fe 32 Si [260] Al 40 Fe 40 Si [259] Al 4 2Fe 39 Si [259] Al 48 Fe 15 Si [260] Al 50 Fe 25 Si [260] Al 53.8 Fe 15.4 Si [260] Al 58 Fe 22 Si [260] Al 60 Fe 20 Si [260] Al 60 Fe 25 Si [259] Al 70 Fe 15 Si [260] Al 72 Fe 18 Si [259] 115

118 Finally, Table 40 shows calculated and measured liquid compositions of some Al-rich Fe Al Si alloys. The agreement is reasonable in all calculations. Table 40. Calculated and experimental liquid compositions of some Al-rich Fe Al Si alloys. Composition (wt-%) Temp. Nominal Calc. [22] Calc. [39] Calc. IAD Exp. [251] ( C) Fe Si Fe Si Fe Si Fe Si Fe Si Fe Al C system Experimental studies on the Fe Al C system have been reviewed by [ ] and a thermodynamic assessment has been given by [12, 27, 40 43], applying interstitial filling of carbon atoms in the bcc and fcc phases. The Kappa phase (κ) of the system has been modelled with quite different and complex sublattice formulations, reviewed by [12, 43]. The system was later reassessed by IAD assuming substitutional filling of C atoms in these phases and a constant carbon composition for the ternary Kappa phase (κ) of the system. The purpose was to get a simple Fe Al C description for practical calculations of solidification modelling of steels. The present work reviews the Fe Al C description from IAD and shows its experimental verification Phases, modelling, and data Table 41 shows the phases and their modelling. Table 42 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table

119 Table 41. Phases and their modelling in the Fe Al C description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) Al 5 Fe 4 Al 2 Fe Al 5 Fe 2 Al 13 Fe 4 Al 4 C 3 Fe 3 C ( M 3 C = cementite) Kappa ( κ) graphite ( gra) Modelling (Al,C,Fe), substitutional, RKM (Al,C,Fe), substitutional, RKM (Al,C,Fe), substitutional, RKM (Al,Fe), substitutional, RKM (Al) 2 (Fe), stoichiometric (Al) 5 (Fe) 2, stoichiometric (Al) 13 (Fe) 4, stoichiometric (Al) 4 (C) 3, stoichiometric (Fe) 3 (C), stoichiometric (Al,Fe) 7 (C), sublattice pure C Table 42. Data applied in the assessment verification for Fe Al C from IAD. Experimental data Reference(s) Liquidus projection [263, 265, 266] Liquidus isotherms between 2000 and 1700 C [267] Graphite solubility in liquid alloys at x Fe :x Al = 7 and 3 [267] Liquidus isotherms between 1450 and 1300 C [268, 269] 6 isothermal sections between 1400 and 800 C [12, 263, 268, 270] 5 vertical sections: at 1.5, 7, and 15 wt-% Al, [42, 263, 268, ] and at 0.2 and 0.7 wt-% C Activity of Al in C saturated liquid alloys at 1600 C [69] Iso-activities of C in fcc alloys from 1200 to 950 C [273] 117

120 Table 43. Thermodynamic description of the Fe Al C system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Al,C,Fe) Reference LAl,C L = ( T ) + ( T )(x Al x C ) [27] LAl,Fe L = ( T ) + ( T )(x Al x Fe ) + ( T )(x Al x Fe ) 2 IAD L L C,Fe = ( T ) + (+19300)(x C x Fe ) + ( T )(x C x Fe ) 2 [18] IAD LAl,C,Fe L = (+20000)x Al + ( 60000)x C + ( T )x Fe IAD bcc (1 sublattice, sites: 1, constituents: Al,C,Fe) G,bcc C = G,gra C + ( T ) IAD LAl,Fe bcc Al x Fe ) IAD LC,Fe bcc C x Fe ) + ( 7.858T )(x C x Fe ) 2 IAD LAl,C,Fe bcc = ( T ) Tc bcc = 1043(x Fe + x C ) + x Al x Fe ( 1100(x Al x Fe )) 200x Fe x C IAD β bcc = 2.22(x Fe + x C ) IAD fcc (1 sublattice, sites: 1, constituents: Al,C,Fe) G,fcc C = G,gra C + ( T ) IAD LAl,Fe fcc = ( T ) + (+22000)(x Al x Fe ) + (+10000)(x Al x Fe ) 2 IAD LC,Fe fcc = ( T ) + ( T )(x C x Fe ) IAD +( T )(x C x Fe ) 2 IAD LAl,C,Fe fcc = ( T ) Tc fcc = 201(x Fe + x C ) IAD β fcc = 2.1(x Fe + x C ) IAD Al 5 Fe 4 (1 sublattice, sites: 1, constituents: Al,Fe) G,Al 5Fe 4 Al = G,fcc Al + ( T ) [10] G,Al 5Fe 4 Fe = G,bcc Fe + (+5009) [10] L Al 5Fe 4 Al,Fe = ( T ) + ( 16000)(x Al x Fe ) IAD Al 2 Fe (2 sublattices, sites: 2:1, constituents: Al:Fe) G,Al 2Fe Al:Fe = 2G,fcc Al + G,bcc Fe + ( T ) [10] Al 5 Fe 2 (2 sublattices, sites: 5:2, constituents: Al:Fe) G,Al 5Fe 2 Al:Fe = 5G,fcc Al + 2G,bcc Fe + ( T ) [10] Al 13 Fe 4 (2 sublattices, sites: 0.752:0.248, constituents: Al:Fe) G,Al 13Fe 4 Al:Fe = 0.752G,fcc Al G,bcc Fe + ( T ) IAD Al 4 C 3 (2 sublattices, sites: 4:3, constituents: Al:C) G,Al 4C 3 Al:C = 4G,fcc Al + 3G,gra C + ( T ) [27] Fe 3 C (M 3 C) (2 sublattices, sites: 3:1, constituents: Fe:C) G,M 3C Fe:C = 3G,bcc Fe + G,gra C + ( T T lnt T 2 ) IAD Kappa (κ) (2 sublattices, sites: 7:1, constituents: Al,Fe,Mn:C) G,κ Al:C = 7G,fcc Al + G,gra C + ( T ) IAD G,κ Fe:C = 7G,bcc Fe + G,gra C + ( T ) IAD LAl,Fe:C κ = ( T ) IAD Notes: Thermodynamic data of pure components are given by [8] unless not shown in the table. 118

121 4.3.2 Results Results of calculations from IAD together with the experimental data (Table 42) are presented in Figures and Table 44. The agreement is reasonable. Some disagreement, however, is seen in Figures This is mainly due to the semistoichiometric treatment of the κ phase, having a constant carbon composition (in mole fraction), whereas the experimental data shows a wider composition range for that phase. Note also the stronger extension of the fcc region with increasing Al content in Figure 119, in regard to the measurements from Phan et al. [12]. On the other hand, the two fcc points of Palm and Inden [263] located in the bcc primary phase region in Figure 115 indicate that the stability of the fcc phase could be even stronger. Additional experimental data, for the Al activity coefficient in liquid, is available from [69]. These data show slightly higher activity coefficients than those presented in Figure 129. Fig Calculated (IAD) liquidus projection of the Fe Al C system together with experimental data points: 95Pal [263] for the primary surfaces and 69Loh [265] (via Table 44), 86Sch [266] (via Table 44), 95Pal [263], and 14Pha [12] for the four-phase equilibria. The dotted lines show the calculated liquidus isotherms between 1500 C and 1250 C. 119

122 Table 44. Four-phase equilibria of the Fe Al C system. Equilibrium Code Temperature ( C) Al (wt-%) C (wt-%) Type Ref. L + bcc = fcc + κ U Calc. IAD Calc. [27] Calc. [40] Calc. [41] Calc. [12, 43] Exp. [265] Exp. [266] Exp. [263] L + κ = bcc + gra U Calc. IAD Calc. [27] Calc. [40] Calc. [41] Calc. [12, 43] Exp. [265] Exp. [266] Exp. [263] L + κ = fcc + gra U Calc. IAD Calc. [27] Calc. [40] Calc. [41] Calc. [12, 43] Exp. [265] Exp. [266] Exp. [263] L = bcc + gra + Al 4 C 3 E Calc. IAD Calc. [27] Calc. [40] Calc. [41] Calc. [12, 43] 120

123 Fig Calculated (IAD) liquidus isotherms of 2000 C, 1850 C, and 1700 C in the Fe Al C system together with experimental data points (89Ode [267]). Fig Calculated (IAD) graphite solubility in liquid Fe Al C alloys together with experimental data points (89Ode [267]). 121

124 Fig Calculated (IAD) liquidus isotherms of 1450 C, 1440 C, 1400 C, 1350 C, and 1300 C in the iron-rich corner of the Fe Al C system together with experimental data points (38Loh [268] and 86Sch [266]). Fig Calculated (IAD) isotherm of 1400 C in the iron-rich corner of the Fe Al C system together with experimental data points (38Loh [268] and 14Pha [12]). 122

125 Fig Calculated (IAD) isotherm of 1250 C in the iron-rich corner of the Fe Al C system together with experimental data points [270]. Fig Calculated (IAD) isotherm of 1200 C in the iron-rich corner of the Fe Al C system together with experimental data points [12, 12, 263, 270]. The tie-line points are from [12]. 123

126 Fig Calculated (IAD) isotherm of 1100 C in the iron-rich corner of the Fe Al C system together with experimental data points [12, 270]. The tie-line points are from [12]. Fig Calculated (IAD) isotherm of 1000 C in the iron-rich corner of the Fe Al C system together with experimental data points [12, 263, 270]. The tie-line points are from [12]. 124

127 Fig Calculated (IAD) isotherm of 800 C in the iron-rich corner of the Fe Al C system together with experimental data points [263]. Fig Calculated (IAD) vertical section of 1.5 wt-% Al in the Fe Al C system together with experimental data points [271]. The dotted lines show the calculated metastable equilibria with cementite. 125

128 Fig Calculated (IAD) vertical section of 7 wt-% Al in the Fe Al C system together with experimental data points [263, 268, 270]. Fig Calculated (IAD) vertical section of 15 wt-% Al in the Fe Al C system together with experimental data points [268]. 126

129 Fig Calculated (IAD) vertical section of 0.2 wt-% C in the Fe Al C system together with experimental data points (09Li [42] for arrests and 13Pre [272] for peritectic and solidus). Fig Calculated (IAD) vertical section of 0.7 wt-% C in the Fe Al C system together with experimental data points [268]. 127

130 Fig Calculated Al activity in binary Fe Al melts and C-saturated Fe Al C melts at 1600 C together with experimental data points (81Sch [68], 73Hul [74], and 55Chi [69]). Fig Calculated (IAD) iso-activity lines of C in fcc Fe Al C alloys at 1200 C together with experimental data points [273]. The reference state used is pure graphite C. 128

131 Fig Calculated (IAD) iso-activity lines of C in fcc Fe Al C alloys at 1100 C together with experimental data points [273]. The reference state used is pure graphite C. Fig Calculated (IAD) iso-activity lines of C in fcc Fe Al C alloys at 1000 C together with experimental data points [273]. The reference state used is pure graphite C. 129

132 Fig Calculated (IAD) iso-activity lines of C in fcc Fe Al C alloys at 1050 C and 950 C together with experimental data points [273]. The reference state used is pure graphite C. 4.4 Fe Mn Si system Experimental studies on the Fe Mn Si system have been reviewed by Raynor and Rivlin [274], and Raghavan [262]. Furthermore, a thermodynamic assessment has been given by Forsberg and Ågren [44], and Zheng et al. [45]. The system was later reassessed by IAD get a simple Fe Mn Si description for practical calculations of solidification modelling of steels. That assessment has a slight emphasis on the iron-rich measurements, in regard to those in [44, 45]. The present work reviews the Fe Mn Si description from IAD and shows its experimental verification Phases, modelling, and data Table 45 shows the phases and their modeling. Table 46 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 47. Note that complete mutual solubility was assumed between Fe 5 Si 3 and Mn 5 Si 3, and between FeSi and MnSi, based on the studies reported in [274]. 130

133 Table 45. Phases and their modelling in the Fe Mn Si description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) cbcc_a12 ( cbcc) cub_a13 ( cub) Fe 5 Si 3 (extending to Mn 5 Si 3 ) FeSi (extending to MnSi) Mn 3 Si (dissolving Fe) Fe 2 Si FeSi 2 -H FeSi 2 -L Mn 6 Si Mn 9 Si 2 Mn 11 Si 19 dia_a4 ( dia) Modelling (Fe,Mn,Si), substitutional, RKM (Fe,Mn,Si), substitutional, RKM (Fe,Mn,Si), substitutional, RKM (Fe,Mn,Si), substitutional, RKM (Fe,Mn,Si), substitutional, RKM (Fe,Mn) 5 (Si) 3, sublattice, RKM (Fe,Mn)(Si), sublattice, RKM (Fe,Mn) 3 (Si), sublattice, RKM (Fe) 2 (Si), stoichiometric (Fe) 3 (Si) 7, stoichiometric (Fe)(Si) 2, stoichiometric (Mn) 6 (Si), stoichiometric (Mn) 9 (Si) 2, stoichiometric (Mn) 11 (Si) 19, stoichiometric pure Si Table 46. Data applied in the assessment verification for Fe Mn Si from IAD. Experimental data Reference(s) Liquidus projection [274, 275] Liquidus isotherms at 1400, 1300, 1200, and 1100 C [276] 5 isothermal sections: at 1058, 1000, 900, 800, and 700 C [ ] 9 vertical sections: at w Mn :w Fe = 0.087, 0.176, 0.429, 0.818, [276, 279] 2.077, and 7.621, and at x Si = 0.28, x Si = 0.35 and x Si = 0.5 Activity of Mn in liquid alloys [280, 281] Enthalpy of mixing in liquid alloys at 1687 C [282] Table 47. Thermodynamic description of the Fe Mn Si system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: Fe,Mn,Si) Reference L L Fe,Mn = ( T ) + (1145)(x Fe x Mn ) [4] L L Fe,Si = ( T ) + ( T )(x Fe x Si ) [16] +( T )(x Fe x Si ) 2 + ( T )(x Fe x Si ) 3 L L Mn,Si = ( T ) + ( T )(x Mn x Si ) [29] +( T )(x Mn x Si ) 2 + (16168)(x Mn x Si ) 3 LFe,Mn,Si L = ( T )x Fe + ( T )x Mn + ( T )x Si Notes: Gibbs energy data of pure components are given by [8]. IAD 131

134 Table 47 (continued) Equation Reference bcc (1 sublattice, sites: 1, constituents: Fe,Mn,Si) LFe,Mn bcc = ( T ) [4] LFe,Si bcc = ( T ) + ( T )(x Fe x Si ) IAD +( T )(x Fe x Si ) 2 LMn,Si bcc Mn x Si ) [29] LFe,Mn,Si bcc Fe + (+10000)x Mn + (+20000)x Si IAD Tc bcc = 1043x Fe 580x Mn + x Fe x Mn (123) + x Fe x Si (504(x Fe x Si )) [15] β bcc = 2.22x Fe 0.27x Mn [4] Tc fcc = 201x Fe 1620x Mn + x Fe x Mn ( (x Fe x Mn )) [4] β fcc = 2.1x Fe 1.86x Mn [8] IAD fcc (1 sublattice, sites: 1, constituents: Fe,Mn,Si) LFe,Mn fcc Fe x Mn ) [4] LFe,Si fcc Fe x Si ) + (89907)(x Fe x Si ) 2 [15] LMn,Si fcc Mn x Si ) [29] LFe,Mn,Si fcc = ( T ) Tc fcc = 201x Fe 1620x Mn + x Fe x Mn ( (x Fe x Mn )) [4] β fcc = 2.1x Fe 1.86x Mn [8] cbcc (1 sublattice, sites: 1, constituents: Fe,Mn,Si) LFe,Mn cbcc [4] LFe,Si cbcc Fe x Si ) + (62240)(x Fe x Si ) 2 [44] LMn,Si cbcc Mn x Si ) [29] LFe,Mn,Si cbcc = ( 91507) [44] cub (1 sublattice, sites: 1, constituents: Fe,Mn,Si) LFe,Mn cub = ( T ) [4] LFe,Si cub Fe,Si [44] LMn,Si cub Mn x Si ) [29] LFe,Mn,Si cub Fe,Mn,Si [44] Fe 5 Si 3 (Mn 5 Si 3 ) (2 sublattices, sites: 5:3, constituents: Fe,Mn:Si) G,Fe 5Si 3 Fe:Si G,Fe 5Si 3 Mn:Si = 5G,bcc Fe + 3G,dia Si + ( T ) [15] = 5G,cbcc Mn + 3G,dia Si + ( T T lnt T 2 ) IAD L Fe 5Si 3 Fe,Mn:Si = (+24568) [44] FeSi (MnSi) (2 sublattices, sites: 1:1, constituents: Fe,Mn:Si) G,FeSi Fe:Si = G,bcc Fe + G,dia Si + ( T ) [15] G,FeSi Mn:Si = G,cbcc Mn + G,dia Si + ( T T lnt T 2 ) IAD LFe,Mn:Si FeSi = ( T ) IAD Notes: Gibbs energy data of pure components are given by [8]. 132

135 Table 47 (continued) Equation Mn 3 Si (2 sublattices, sites: 3:1, constituents: Fe,Mn:Si) G,Mn 3Si Fe:Si = 3G,bcc Fe + G,dia G,Mn 3Si Mn:Si = 3G,cbcc Mn L Mn 3Si Fe,Mn:Si = ( 13500) Reference Si + ( T ) IAD + G,dia Si + ( T T lnt T 2 ) IAD Fe 2 Si (2 sublattices, sites: 2:1, constituents: Fe:Si) G,Fe 2Si Fe:Si FeSi 2 -H (2 sublattices, sites: 3:7, constituents: Fe:Si) = 2G,bcc Fe + G,dia Si + ( T ) [15] G,FeSi 2-H Fe:Si = 3G,bcc Fe + 7G,dia Si + ( T ) [15] FeSi 2 -L (2 sublattices, sites: 1:2, constituents: Fe:Si) G,FeSi 2-L Fe:Si = G,bcc Fe + 2G,dia Si + ( T ) [15] Mn 6 Si (2 sublattices, sites: 17:3, constituents: Mn:Si) G,Mn 6Si Mn:Si = 17G,cbcc Mn + 3G,dia Si + ( T 39.22T lnt ) IAD Mn 9 Si 2 (2 sublattices, sites: 33:7, constituents: Mn:Si) G,Mn 9Si 2 Mn:Si = 33G,cbcc Mn + 7G,dia Si +( T T lnt T 2 ) Mn 11 Si 19 (2 sublattices, sites: 11:19, constituents: Mn:Si) G,Mn 11Si 19 Mn:Si = 11G,cbcc Mn + 19G,dia Si +( T T lnt T 2 ) Notes: Gibbs energy data of pure components are given by [8]. IAD IAD IAD Results The results of calculations from IAD, and Forsberg and Ågren [44] together with the experimental data (Table 46) are presented in Figures and Table 48. The agreement is reasonably good in both calculations, but slightly better in IAD for the different phase equilibria. The agreement in IAD is of the same level than the calculations of Zheng et al. [45]. Table 48. Calculated (IAD) invariant points of the Fe Mn Si system. Reaction Code Temperature ( C) Mn in liq (wt-%) Si in liq (wt-%) L + fcc = bcc + cub U L + Fe 2 Si + FeSi = Fe 5 Si 3 P L + Fe 2 Si = bcc + Fe 5 Si 3 U L + fcc = Fe 5 Si 3 + Mn 3 Si U L + bcc = fcc + Mn 3 Si U L + Mn 9 Si 2 = Mn 3 Si + cub U L + fcc = Mn 3 Si + cub U

136 In the liquidus projection in Figure 135, note the straight experimental monovariant lines, which are probably due to the limited amount of experimental data. According to Forsberg and Ågren [44], the fcc and Mn 3 Si regions extend to lower Mn contents than from IAD. In Figures , note the wide bcc phase region from [44] extending to Si contents above x Si = This anomaly is due to the non-activated B2 ordering of bcc from [44], whereas in IAD, the effect of B2-ordering was included energetically in the description of the disordered bcc phase. Additional experimental data, for the liquid Fe Mn Si alloys, are available from [ ]. These studies were not included in the optimization of IAD and [44], as there was little information, or it was inconsistent with the selected experimental information. Fig Calculated (IAD) liquidus projection of the Fe Mn Si system together with the suggested experimental region (dotted line) [275] reviewed by [274]. 134

137 Fig Calculated liquidus isotherms of 1400 C, 1300 C, 1200 C, and 1100 C of the Fe Mn Si system together with experimental data points interpolated from the work of 37Vog [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated isotherm of 1058 C in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. 135

138 Fig Calculated isotherm of 1000 C in the Fe Mn Si system together with experimental data points [277, 278]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated isotherm of 900 C in the Fe Mn Si system together with experimental data points [278]. The solid lines are calculations from IAD, and the dotted lines are from [44]. 136

139 Fig Calculated isotherm of 800 C in the Fe Mn Si system together with experimental data points [278, 279]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated isotherm of 700 C in the Fe Mn Si system together with experimental data points [278]. The solid lines are calculations from IAD, and the dotted lines are from [44]. 137

140 Fig Calculated vertical section of w Mn :w Fe = in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated vertical section of w Mn :w Fe = in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. 138

141 Fig Calculated vertical section of w Mn :w Fe = in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated vertical section of w Mn :w Fe = in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. 139

142 Fig Calculated vertical section of w Mn :w Fe = in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated vertical section of w Mn :w Fe = in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. 140

143 Fig Calculated liquidus at x Si = 0.28 in the Fe Mn Si system together with experimental data points [279]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated liquidus at x Si = 0.35 in the Fe Mn Si system together with experimental data points [279]. The solid lines are calculations from IAD, and the dotted lines are from [44]. 141

144 Fig Calculated liquidus at x Si = 0.5 in the Fe Mn Si system together with experimental data points [276]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated activity of Mn in liquid Fe Mn Si alloys (Set 1) together with experimental data points (78Gee [280]). The solid lines are calculations from IAD, and the dotted lines are from [44]. The reference state used is pure liquid Mn. 142

145 Fig Calculated activity of Mn in liquid Fe Mn Si alloys (Set 2) together with experimental data points (78Gee [280]). The solid lines are calculations from IAD, and the dotted lines are from [44]. The reference state used is pure liquid Mn. Fig Calculated activity of Mn in liquid Fe Mn Si alloys (Set 3) together with experimental data points (78Gee [280]). The solid lines are calculations from IAD, and the dotted lines are from [44]. The reference state used is pure liquid Mn. 143

146 Fig Calculated activity of Mn in liquid Fe Mn Si alloys (Set 4) together with experimental data points (78Gee [280]). The solid lines are calculations from IAD, and the dotted lines are from [44]. The reference state used is pure liquid Mn. Fig Calculated activity of Mn in liquid Fe Mn Si alloys at 1427 C and at x Mn = 0.5 together with experimental data points [280]. The solid lines are calculations from IAD, and the dotted lines are from [44]. The reference state used is pure liquid Mn. 144

147 Fig Calculated activity ratio a Mn :a Fe in liquid Fe Mn Si alloys at 1560 C and at x Si = 0.10 together with experimental data points [281]. The solid lines are calculations from IAD, and the dotted lines are from [44]. Fig Calculated enthalpy of mixing in liquid Fe Mn Si alloys at 1687 C together with experimental data points [282]. The solid lines are calculations from IAD, and the dotted lines are from [44]. The reference states used are pure liquid components. 145

148 4.5 Fe Mn C system Experimental studies on the Fe Mn C system have been reviewed by [ ], and a thermodynamic assessment has been given by [46, 47], applying interstitial filling of C atoms in the solid solution phases. The description of Djurovic et al. [47] was preferred due to its improved treatment of metastable iron carbides and it was later modified by IAD assuming substitutional filling of C atoms in the bcc and fcc phases. The purpose was to simplify the Fe Mn C description for practical calculations of solidification modelling of steels. The present work reviews the Fe Mn C description from IAD and shows its experimental verification Phases, modelling, and data Table 49 shows the phases and their modelling. Table 50 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table 51. Table 49. Phases and their modelling in the Fe Mn C description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) cbcc_a12 ( cbcc) cub_a13 ( cub) hcp_a3 ( hcp) M 23 C 6 M 7 C 3 M 5 C 2 M 3 C ( cementite) graphite ( gra) Modelling (C,Fe,Mn), substitutional, RKM (C,Fe,Mn), substitutional, RKM (C,Fe,Mn), substitutional, RKM (Fe,Mn)(C,Va), sublattice, RKM (Fe,Mn)(C,Va), sublattice, RKM (Fe,Mn)(C,Va)0.5, sublattice, RKM (Fe,Mn) 20 (Fe,Mn) 3 (C) 6, sublattice, RKM (Fe,Mn) 7 (C) 3, sublattice, RKM (Fe,Mn) 5 (C) 2, sublattice, RKM (Fe,Mn) 3 (C), sublattice, RKM pure C 146

149 Table 50. Data applied in the assessment verification for Fe Mn C from IAD. Experimental data Reference(s) 2 liquidus projections, on the Mn/C and Mn/T planes [201] Graphite solubility in liquid alloys between 1690 and 1290 C [119, 198, 206, 289, 290] 6 vertical sections: at 1.5, 20, 40, 50, 60, and 80 wt-% Mn [201, 291] Partition of C and Mn between fcc and liquid phases [292, 293] 1 isothermal section at 1000 C [294] Mn iso-activities in liquid alloys at 1550, 1500, 1463, and 1400 C [205, 295] Enthalpy of mixing of liquid alloys with x Mn = 0.2 [296] and x Mn = 0.4 at 1627 C Activity coefficient f C Mn in liquid alloys at 1600 to 1500 C [ ] Carbon iso-activities in fcc alloys at 1147 and 1000 C [301, 302] Activity of C in fcc alloys at 900 C [303] Partition of Mn between fcc and M 3 C [304] Partition of Mn between fcc and M 3 C at 1100, 1000, and 800 C [294, 302, 305] Partition of Mn between bcc and M 3 C between 700 and 580 C [305, 306] Eutectoid fcc/(bcc + M 3 C) lines on the Mn/T and Mn/C planes [ ] Gibbs energy of formation of M 3 C [294] 147

150 Table 51. Thermodynamic description of the Fe Mn C system by IAD. Equation liquid (1 sublattice, sites: 1, constituents: C,Fe,Mn) Reference L L C,Fe = ( T ) + (+19300)(x C x Fe ) + ( T )(x C x Fe ) 2 [18] L L C,Mn = ( T ) + (+6313)(x C x Mn ) + (+23281)(x C x Mn ) 2 [31] L L Fe,Mn = ( T ) + (1145)(x Fe x Mn ) [4] LC,Fe,Mn L = ( 90000)x C + ( T )x Fe + (+30000)x Mn IAD bcc (1 sublattice, sites: 1, constituents: C,Fe,Mn) G,bcc C = G,gra C + ( T ) IAD LC,Fe bcc C x Fe ) + ( 7.858T )(x C x Fe ) 2 IAD LC,Mn bcc IAD LFe,Mn bcc = ( T ) [4] LC,Fe,Mn bcc IAD Tc bcc = 1043(x Fe + x C ) 580x Mn 200x Fe x C + x Fe x Mn (123) IAD β bcc = 2.22(x Fe + x C ) 0.27x Mn IAD fcc (1 sublattice, sites: 1, constituents: C,Fe,Mn) G,fcc C = G,gra C + ( T ) IAD LC,Fe fcc C x Fe ) IAD +( T )(x C x Fe ) 2 LC,Mn fcc C x Mn ) 2 IAD LFe,Mn fcc Fe x Mn ) [4] LC,Fe,Mn fcc C + ( )x Fe + ( )x Mn IAD Tc fcc = 201(x Fe + x C ) 1620x Mn + x Fe x Mn ( (x Fe x Mn )) IAD β fcc = 2.1(x Fe + x C ) 1.86x Mn IAD cbcc (2 sublattices, sites: 1:1, constituents: Fe,Mn:C,Va) G,cbcc Fe:C = G,bcc Fe + G,gra G,cbcc Fe:Va = G,cbcc Fe G,cbcc Mn:C = G,cbcc Mn G,cbcc Mn:Va = G,cbcc Mn C + (+80000) [46] [8] + G,gra C + ( T ) [31] LFe:C,Va cbcc = ( 34671) [46] LFe,Mn:Va cbcc = ( 10184) [4] LMn:C,Va cbcc = ( 52204) [31] LFe,Mn:C cbcc = ( 36732) [47] cub (2 sublattices, sites: 1:1, constituents: Fe,Mn:C,Va) G,cub Fe:C = G,bcc Fe G,cub Fe:Va = G,cub Fe G,cub Mn:C = G,cbcc Mn G,cub Mn:Va = G,cub Mn + G,gra C + (+90000) [46] [8] + G,gra C + (+2607) [31] LFe:C,Va cub = ( 34671) [46] LFe,Mn:Va cub = ( T ) [4] LMn:C,Va cub = ( 10175) [31] LFe,Mn:C cub = ( 36732) [47] Notes: Thermodynamic data of pure components are given by [8] unless not shown in the table. [8] [8] 148

151 Table 51 (continued) Equation hcp (2 sublattices, sites: 1:0.5, constituents: Fe,Mn:C,Va) G,hcp Fe:C = G,bcc Fe G,hcp Fe:Va = G,hcp Fe G,hcp Mn:C = G,cbcc Mn G,hcp Mn:Va = G,hcp Mn L hcp Fe:C,Va Reference + 0.5G,gra C + ( T ) [18] [8] + 0.5G,gra C + ( T ) [31] = ( 22126) [18] L hcp Mn:C,Va = ( 5006) [31] L hcp Fe,Mn:Va = ( T ) + (273)(y Fe y Mn ) [47] L hcp Fe,Mn:C = ( T ) + ( 28300)(y Fe y Mn ) IAD Tc hcp = 1620x Mn β hcp = 1.86x Mn M 23 C 6 (3 sublattices, sites: 20:3:6, constituents: Fe,Mn:Fe,Mn:C) = 23/3G,M 3C Fe:C + (6 23/3)G,gra G,M 23C 6 Fe:Fe:C C + (+15000) [47] G,M 23C 6 Mn:Mn:C = 23G,cbcc Mn + 6G,gra C + ( T ) [31] G,M 23C 6 Fe:Mn:C = 20G,bcc Fe + 3G,cbcc Mn + 6G,gra C + (20/23)G,M 23C 6 Fe:Fe:C + (3/23)G,M 23C 6 Mn:Mn:C [47] G,M 23C 6 Mn:Fe:C = 20G,cbcc Mn + 3G,bcc Fe + 6G,gra C + (20/23)G,M 23C 6 Mn:Mn:C + (3/23)G,M 23C 6 Fe:Fe:C [47] L M 23C 6 Fe,Mn:Fe,Mn:C = ( 95000) [47] M 5 C 2 (2 sublattices, sites: 5:2, constituents: Fe,Mn:C) G,M 5C 2 Fe:C = (5/3)G,M 3C Fe:C + (1/3)G,gra C + (+6200) [47] G,M 5C 2 Mn:C = 5G,cbcc Mn + 2G,gra C + ( T ) [31] = ( T ) [47] L M 5C 3 Fe,Mn:C M 7 C 3 (2 sublattices, sites: 7:3, constituents: Fe,Mn:C) G,M 7C 3 Fe:C = (7/3)G,M 3C Fe:C + (2/3)G,gra C + (+13200) [47] G,M 7C 3 Mn:C = 7G,cbcc Mn + 3G,gra C + ( T ) [31] = ( T ) [47] L M 7C 3 Fe,Mn:C M 3 C (2 sublattices, sites: 3:1, constituents: Fe,Mn:C) G,M 3C Fe:C = 3G,bcc Fe + G,gra G,M 3C Mn:C C + ( T T lnt T 2 ) IAD = 3G,cbcc Mn + G,gra C + ( T ) [31] = ( T ) [47] L M 3C Fe,Mn:C Notes: Thermodynamic data of pure components are given by [8] unless not shown in the table. [8] [46] [46] 149

152 4.5.2 Results The results of calculations from IAD and Djurovic et al. [47] together with the experimental data (Table 50) are presented in Figures and Table 52. The agreement is reasonably good in both calculations. Additional experimental phase equilibrium data are available from Ni et al. [310], and Che and Wang [311] for graphite solubility in liquid alloys, and from Sil man [312] for the Mn partition between fcc and M 3 C. The agreement of the former data with calculations from IAD and [47] is between reasonable and moderate, whereas that of [312] is very poor. Note also the disagreeing experimental data of Benz et al. [294] at low temperatures and Mn contents criticized by Djurovic et al. [47]. Table 52. Calculated and experimental invariant points in the Fe Mn C system. wt-% in liq Reaction Code Temperature ( C) Mn C Type Ref. L + gra + M 7 C 3 = M 5 C 2 P Calc. IAD Calc. [47] Exp. [201] L + M 7 C 3 = M 5 C 2 + hcp U Calc. IAD Calc. [47] Exp. [201] L + M 5 C 2 + gra = M 3 C P Calc. IAD Calc. [47] Exp. [201] L + M 5 C 2 + hcp = M 3 C P Calc. IAD Calc. [47] Exp. [201] L + gra = fcc + M 3 C U Calc. IAD Calc. [47] Exp. [201] L + hcp = M 3 C + fcc U Calc. IAD Calc. [47] Exp. [201] 150

153 Fig Calculated (IAD) liquidus projection on the Mn/C plane of the Fe Mn C system together with experimental invariant data points (77Sch [201]). The dotted lines also show the calculated liquidus isotherms between 1450 C and 1150 C. Fig Calculated graphite solubility in liquid Fe Mn C alloys together with experimental data points (52Chi [119], 63Sch [289], 03Kim [206], and 56Tur [198]). The solid lines are calculations from IAD, and the dotted lines are from [47]. Data from [198] include points from [119]. 151

154 Fig Calculated graphite solubility in liquid Fe Mn C alloys together with experimental data points (69Sch [290]). The solid lines are calculations from IAD, and the dotted lines are from [47]. Fig Calculated liquidus projection on the Mn/T plane of the Fe Mn C system together with experimental data points (77Sch [201]). The solid line shows the calculations from IAD, and the dotted lines are from [47]. 152

155 Fig Calculated vertical section of the Fe Mn C system at 1.5 wt-% Mn together with experimental data points (99Jac [291]). The solid lines are calculations from IAD, and the dotted lines are from [47]. Fig Calculated vertical section of the Fe Mn C system at 20 wt-% Mn together with experimental data points (77Sch [201]). The solid lines are calculations from IAD, and the dotted lines are from [47]. 153

156 Fig Calculated vertical section of the Fe Mn C system at 40 wt-% Mn together with experimental data points (77Sch [201]). The solid lines are calculations from IAD, and the dotted lines are from [47]. Fig Calculated vertical section of the Fe Mn C system at 50 wt-% Mn together with experimental data points (77Sch [201]). The solid lines are calculations from IAD, and the dotted lines are from [47]. 154

157 Fig Calculated vertical section of the Fe Mn C system at 60 wt-% Mn together with experimental data points (77Sch [201]). The solid lines are calculations from IAD, and the dotted lines are from [47]. Fig Calculated vertical section of the Fe Mn C system at 80 wt-% Mn together with experimental data points (77Sch [201]). The solid lines are calculations from IAD, and the dotted lines are from [47]. 155

158 Fig Calculated partition of C and Mn between fcc and liquid phases in Fe 3 wt-% Si C alloys together with experimental data points (80Ume [292] and 85Kag [293]). The solid lines are calculations from IAD, and the dotted lines are from [47]. Fig Calculated isotherm of the Fe Mn C system at 1000 C together with experimental data points [294]. The solid lines are calculations from IAD, and the dotted lines are from [47]. 156

159 Fig Calculated Mn iso-activities in liquid Fe Mn C alloys at 1550 C together with experimental data points [295]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure liquid Mn. Fig Calculated Mn iso-activities in liquid Fe Mn C alloys at 1500 C together with experimental data points [295]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure liquid Mn. 157

160 Fig Calculated Mn iso-activities in liquid Fe Mn C alloys at 1463 C together with experimental data points [295]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure liquid Mn. Fig Calculated Mn iso-activities in liquid Fe Mn C alloys at 1400 C together with experimental data points [205]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure liquid Mn. 158

161 Fig Calculated enthalpy of mixing of liquid Fe Mn C alloys at 1627 C together with experimental data points [296]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure liquid Fe, Mn and C. Fig Calculated activity coefficient f C Mn in liquid Fe Mn C alloys at 1550 C together with smoothed experimental data points (57Oht [297], 58Sch [298], 66Sch [299], and 74Muk [300]). The solid line shows the calculations from IAD, and the dotted line shows those from [47]. 159

162 Fig Calculated C iso-activities in fcc Fe Mn C alloys at 1147 C together with experimental data points [301]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure graphite C. Fig Calculated C iso-activities in fcc Fe Mn C alloys at 1000 C together with experimental data points [301,302]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure graphite C. 160

163 Fig Calculated activity of C in fcc Fe Mn C alloys at 900 C together with experimental data points [303]. The solid lines are calculations from IAD, and the dotted lines are from [47]. The reference state used is pure graphite C. Fig Calculated partition of Mn between fcc and M 3 C in fcc Fe Mn C alloys (90Hua [46], 11Dju [47], and IAD) together with experimental data points (67Hil [304]). 161

164 Fig Calculated partition of Mn between fcc and M 3 C in the Fe Mn C system together with experimental data points (73Ben [294], 77Nis [302], and 64Koc [305]). The solid lines are calculations from IAD, and the dotted lines are from calculations of [47]. Fig Calculated partition of Mn between bcc and M 3 C in the Fe Mn C system together with experimental data points (64Koc [305] and 61Gur [306]) The solid lines are calculations from IAD, and the dotted lines are from [47]. 162

165 Fig Calculated eutectoid fcc/(bcc + M 3 C) line on the Mn/T plane of the Fe Mn C system together with experimental data points (32Bai [307], 36Wal [308], and 72Hil [309]). The solid lines are calculations from IAD, and the dotted lines are from [47]. Fig Calculated eutectoid fcc/(bcc + M 3 C) line on the Mn/C plane of the Fe Mn C system together with experimental data points (32Bai [307] and 36Wal [308]). The solid lines are calculations from IAD, and the dotted lines are from [47]. 163

166 Fig Calculated (IAD) Gibbs energy of formation of M 3 C together with experimental data points (73Ben [294]). The calculations are identical to those of [47]. The reference states used are pure cbcc Mn and pure graphite C. 4.6 Fe Si C system Experimental studies on the Fe Si C system have been reviewed by Raghavan [313]. A thermodynamic assessment has been given by [15, 16], applying interstitial filling of carbon atoms in the solid solution phases. The description of Miettinen [16] was later modified by IAD assuming substitutional filling of C atoms in the bcc and fcc phases. The purpose was to simplify the Fe Si C description for practical calculations of solidification modelling of steels. The present work reviews the Fe Si C description from IAD and shows its experimental verification. Table 53 shows the phases and their modelling Phases, modelling, and data Table 54 shows the experimental information selected for the assessment verification. The thermodynamic description of the system is presented in Table

167 Table 53. Phases and their modelling in the Fe Si C description from IAD. Phase liquid ( L) bcc_a2 ( bcc) fcc_a1 ( fcc) dia_a4 ( dia) Fe 3 C ( M 3 C cem) Fe 2 Si Fe 5 Si 3 FeSi FeSi 2 -H FeSi 2 -L SiC Fe 6 SiC ( K) graphite ( gra) Modelling (C,Fe,Si), substitutional, RKM (C,Fe,Si), substitutional, RKM (C,Fe,Si), substitutional, RKM (C,Si), substitutional, RKM (Fe)3(C), stoichiometric (Fe) 2 (Si), stoichiometric (Fe) 5 (Si) 3, stoichiometric (Fe)(Si), stoichiometric (Fe) 3 (Si) 7, stoichiometric (Fe)(Si) 2, stoichiometric (Si)(C), stoichiometric (Fe) 6 (Si)(C), stoichiometric pure C Table 54. Data applied in the assessment verification for Fe Si C from IAD. Experimental data Reference(s) Liquidus projection [ ] Graphite solubility in liquid alloys at 1550 and 1350 C [290] 5 isothermal sections: at 1350, 1250, 1150, 1000, and 900 C [99, 314, 315, 317, 318] Partition of C and Si between fcc and liquid phases [292, 293] 9 vertical sections, at 0.99 wt-% Si (high and low temperature [272, 314, 315, 319] sections) and at 2.08, 2.3, 3.5, 4.2, 4.3, 5.3, 6.12, and 7.9 wt-% Si Temperature along monovariants L + gra + fcc (stable), [15, , ] L + gra + bcc (stable), L + cem + fcc (metastable), and L + Fe 6 SiC + fcc (metastable) Si content in the bcc and fcc phase of bcc + fcc + gra equilibrium [324] Carbon iso-activities in liquid alloys at 1600 and 1550 C [269, 325] Silicon iso-activities in liquid alloys at 1500 and 1420 C [326, 327] Enthalpy of mixing of liquid alloys at x C = and 1627 C [296] Activity coefficient γsi C in liquid alloys with 5 to 26 at-% C at 1530 C [328] Activity coefficient of C in fcc alloys at 1147 and 1000 C [301, 317, 318] Activity of C in fcc alloys at 900 C [303] Activity of C in bcc alloys at 1000, 900, and 800 C [273, 317, 329] Metastable liquidus projection (graphite and diamond suspended) [330] 4 metastable isothermal sections: at 1000, 900, 820, and 740 C [330, 331] (graphite and diamond suspended) 165

168 Table 55. Thermodynamic description of the Fe Si C system from IAD. Equation liquid (1 sublattice, sites: 1, constituents: C,Fe,Si) Reference L L C,Fe = ( T ) + (+19300)(x C x Fe ) + ( T )(x C x Fe ) 2 [18] LC,Si L = ( T ) IAD LFe,Si L = ( T ) + ( T )(x Fe x Si ) [16] +( T )(x Fe x Si ) 2 + ( T )(x Fe x Si ) 3 IAD LC,Fe,Si L = ( T )x C + ( T )x Fe + ( T )x Si IAD bcc (1 sublattice, sites: 1, constituents: C,Fe,Si) G,bcc C = G,gra C T IAD LC,Fe bcc C x Fe ) + ( 7.858T )(x C x Fe ) 2 IAD LC,Si bcc = 0 (bcc not stable in binary Si C) LFe,Si bcc Fe x Si ) IAD +( T )(x Fe x Si ) 2 IAD LC,Fe,Si bcc C + ( T )x Fe + ( )x Si IAD Tc bcc = 1043(x Fe + x C ) 200x Fe x C + x Fe x Si (504(x Fe x Si )) IAD β bcc = 2.22(x Fe + x C ) IAD fcc (1 sublattice, sites: 1, constituents: C,Fe,Si) G,fcc C = G,gra C T IAD LC,Fe fcc = ( T ) + ( T )(x C x Fe ) IAD +( T )(x C x Fe ) 2 IAD LC,Si fcc = 0 (fcc not stable in binary Si C) LFe,Si fcc Fe x Si ) + (89907)(x Fe x Si ) 2 [15] LC,Fe,Si fcc C + ( T )x Fe + ( T )x Si IAD Tc fcc = 201(x Fe + x C ) IAD β fcc = 2.1(x Fe + x C ) IAD dia (1 sublattice, sites: 1, constituents: C,Si) G,dia C = G,gra C T T lnt IAD LC,Si dia = (+93387) [32] Fe 3 C (M 3 C cem) (2 sublattices, sites: 3:1, constituents: Fe:C) G,Fe 3C Fe:C = 3G,bcc Fe + G,gra C + ( T T lnt T 2 ) IAD Fe 2 Si (2 sublattices, sites: 2:1, constituents: Fe:Si) G,Fe 2Si Fe:Si = 2G,bcc Fe + G,dia Si + ( T ) [15] Fe 5 Si 3 (2 sublattices, sites: 5:3, constituents: Fe:Si) G,Fe 5Si 3 Fe:Si = 5G,bcc Fe + 3G,dia Si + ( T ) [15] FeSi (2 sublattices, sites: 1:1, constituents: Fe:Si) G,FeSi Fe:Si FeSi 2 -H (2 sublattices, sites: 3:7, constituents: Fe:Si) = G,bcc Fe + G,dia Si + ( T ) [15] G,FeSi 2-H Fe:Si = 3G,bcc Fe + 7G,dia Si + ( T ) [15] Notes: Gibbs energy data of pure components are given by [8] unless not shown in the table. 166

169 Table 55 (continued) Equation Reference FeSi 2 -L (2 sublattices, sites: 1:2, constituents: Fe:Si) G,FeSi 2-L Fe:Si = G,bcc Fe + 2G,dia Si + ( T ) [15] SiC (2 sublattices, sites: 1:1, constituents: Si:C) G,SiC Si:C = G,dia Si + G,gra C + ( T T lnt T 2 ) IAD Fe 6 SiC ( K) (3 sublattices, sites: 6:1:1, constituents: Fe:Si:C) G,K Fe:Si:C = 6G,bcc Fe + G,dia Si + G,gra C + ( T ) IAD Notes: Gibbs energy data of pure components are given by [8] unless not shown in the table Results The results of calculations from IAD, and Lacaze and Sundman [15] together with the experimental data (Table 54) are presented in Figures and Table 56. The agreement is reasonably good in both calculations but slightly better in IAD. Additional experimental data, for the graphite solubility and Si activity coefficient in liquid are available from [109,332], respectively. The first set of data agrees well with the calculations and the experimental data of Schürmann and Kramer [290], while the latter set of data agrees only moderately with the calculations and the experimental data from Chipman and Baschwitz [328]. Table 56. Calculated and experimental invariant points in the Fe Si C system for which experimental data are available. wt-% in liq Reaction Code Temperature ( C) Si C Type Ref. L = bcc + fcc + gra E Calc. IAD Calc. [15] Exp. [314] L = fcc + cem + Fe 6 SiC E M Calc. IAD L = fcc + cem + Fe 8 Si 2 C Calc. [15] L = fcc + cem + Fe 45 Si 9 C Exp. [330] bcc + L = fcc + Fe 6 SiC U M Calc. IAD bcc + L = fcc + Fe 8 Si 2 C Calc. [15] bcc + L = fcc + Fe 45 Si 9 C Exp. [330] Notes: superscript M denotes metastable equilibrium. 167

170 Fig Calculated (IAD) liquidus projection of the Fe Si C system together with experimental data points (85Sch [316], 52Hil [314], and 68Pat [315]). Shown also are the calculated liquidus isotherms between 1600 C and 1200 C (dotted lines). "IP" denotes the invariant point (see Table 56). Fig Calculated graphite solubility in liquid Fe Si C alloys together with experimental data points (69Sch [290]). The solid lines are calculations from IAD, and dotted lines are from [15]. 168

171 Fig Calculated isotherm of the Fe Si C system at 1350 C together with experimental data points (52Hil [314], 66Fis [99], and 68Pat [315]). The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig Calculated isotherm of the Fe Si C system at 1250 C together with experimental data points (66Fis [99] and 68Pat [315]). The solid lines are calculations from IAD, and the dotted lines are from [15]. 169

172 Fig Calculated isotherm of the Fe Si C system at 1150 C together with experimental data points (66Fis [99] and 67Sch [318]). The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig Calculated (IAD) isotherm and carbon iso-activities (dotted lines) of the Fe Si C system at 1000 C together with experimental data points of [317] for carbon iso-activities and [318] for graphite solubility. 170

173 Fig Calculated (IAD) isotherm and carbon iso-activities (dotted lines) of the Fe Si C system at 900 C together with experimental data points of [318]. Fig Calculated partition of C and Si between fcc and liquid phases in Fe 3 wt-% Si C alloys together with experimental data points (80Ume [292] and 85Kag [293]). The solid lines are calculations from IAD, and the dotted lines are from [15]. 171

174 Fig Calculated high-temperature vertical section of the Fe Si C system at 0.99 wt-% Si together with experimental data points [272]. The solid lines are calculations from IAD, and the dotted lines are from calculations of [15]. Fig Calculated low-temperature vertical section of the Fe Si C system at 0.99 wt-% Si together with experimental data points [272]. The solid lines are calculations from IAD, and the dotted lines are from [15]. 172

175 Fig Calculated vertical section of the Fe Si C system at 2.08 wt-% Si together with experimental data points [315]. The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig Calculated vertical section of the Fe Si C system at 2.30 wt-% Si together with experimental data points [314]. The solid lines are calculations from IAD, and the dotted lines are from [15]. 173

176 Fig Calculated vertical section of the Fe Si C system at 3.50 wt-% Si together with experimental data points [314]. The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig Calculated vertical section of the Fe Si C system at 4.20 wt-% Si together with experimental data points [315]. The solid lines are calculations from IAD, and the dotted lines are from [15]. 174

177 Fig Calculated vertical section of the Fe Si C system at 4.30 wt-% Si together with experimental data points [319]. The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig Calculated vertical section of the Fe Si C system at 5.20 wt-% Si together with experimental data points [314]. The solid lines are calculations from IAD, and the dotted lines are from [15]. 175

178 Fig Calculated vertical section of the Fe Si C system at 6.12 wt-% Si together with experimental data points [315]. The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig Calculated vertical section of the Fe Si C system at 7.9 wt-% Si together with experimental data points [314]. The solid lines are calculations from IAD, and the dotted lines are from [15]. 176

179 Fig Calculated temperature evolution along monovariants L+gra+fcc (stable), L+gra+bcc (stable), L+cem+fcc (metastable), L+Fe 6 SiC+fcc (metastable) in the Fe Si C system together with experimental data points (11Con [320], 36Han [321], 68Pat [315], 85Sch [316], 91Lac [15], 62Old [322], and 72Moo [323]). The solid lines are calculations from IAD, and the dotted lines are from [15]. Fig Calculated silicon contents in the bcc and the fcc phase of the bcc fcc graphite equilibrium in the Fe Si C system together with experimental data points (71Fri [324]). The solid lines are calculations from IAD, and the dotted lines are from [15]. 177

180 Fig Calculated iso-activity lines of C in liquid Fe Si C alloys at 1600 C together with experimental data points [269]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure graphite C. Fig Calculated iso-activity lines of C in liquid Fe Si C alloys at 1550 C together with experimental data points [325]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure graphite C. 178

181 Fig Calculated iso-activity lines of Si in liquid Fe Si C alloys at 1500 C together with experimental data points [327]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure diamond Si. Fig Calculated iso-activity lines of Si in liquid Fe Si C alloys at 1420 C together with experimental data points [326]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure diamond Si. 179

182 Fig Calculated enthalpy of mixing of liquid Fe Si C alloys at 1627 C together with experimental data points [296]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference states used are pure liquid Fe, Si, and C. Fig Calculated activity coefficient γ C Si in liquid Fe Si C alloys at 1530 C containing at-% C together with experimental data points (63Chi [328]) containing 5 26 at-% C. The solid lines are calculations from IAD, and the dotted lines are from [15]. 180

183 Fig Calculated activity coefficient lines of C at various silicon contents y Si = x Si /(x Fe + x Si ) in fcc Fe Si C alloys at 1147 C together with experimental data points [301]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure graphite C. Fig Calculated activity coefficient lines of C at various silicon contents y Si = x Si /(x Fe + x Si ) in fcc Fe Si C alloys at 1000 C together with experimental data points [317, 318]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure graphite C. 181

184 Fig Calculated activity of C in fcc Fe Si C alloys at 900 C together with experimental data points [303]. The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure graphite C. Fig Calculated activity of C in bcc Fe Si C alloys at 1000 C together with experimental data points (71Chr [329] and 48Smi [317]). The solid lines are calculations from IAD, and the dotted lines are from [15]. The reference state used is pure graphite C. 182