Introduction

The current work continues an earlier started project[1,2] for the development of a thermodynamic database of phosphorus containing Fe-X systems. In such a way a simple and compatible thermodynamic database for three-component steels is to be designed. It would provide important and practical input data for thermodynamic-kinetic models simulating their solidification.[3] The first two contributions concern the systems Fe-Cr-P[1] and Fe-Cu-P.[2]

The goal of the current work is to attain, for the first time, thermodynamic optimizations for the Fe-Mn-P and the Mn-P systems. The latter is based on the earlier Mn-P optimization of Miettinen.[4] The adjustable thermodynamic parameters used for the description of the Fe-Mn and the Fe-P phase diagrams are taken from Huang[5] and from Shim et al.,[6] respectively.

Phases, Modeling and Data

Detailed descriptions for the substitutional solution and sublattice models and their parameters are available from Ref 7 and in this journal by Ref 1. Thus, abbreviated descriptions of the phases and models are presented only (Table 1). The solution phases (liquid, bcc_A2, fcc_A1, cbcc_A12, cub_A13) are described with the substitutional solution model. Some phosphides are described with the sublattice model (Fe3P, Fe2P, Mn3P) and other phases are treated as stoichiometric (FeP, Mn3P2, MnP, white_P).

Table 1 Phases and their modeling in the present Fe-Mn-P description
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Complete mutual solubility was assumed between Fe2P and Mn2P, in agreement with the experimental data of Ref 8,9, though according to other authors,[10-12] an ordering reaction (at an undetermined temperature) yielding to an orthorhombic structure for compositions 0.31 < x < 0.62 of (Fe1−x ,Mn x )2P[13] was observed.

The experimental studies on the Fe-Mn-P system up to 1988 have been reviewed by Raghavan.[13] Table 2 shows the experimental information[9,14-22] selected in the current optimization for the Mn-P and Fe-Mn-P systems.

Table 2 Experimental data applied in the current optimization of the Mn-P and Fe-Mn-P systems
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Results

The thermodynamic description of the Fe-Mn-P system is presented in Table 3. The parameters marked with a reference code were adopted from earlier assessments and those marked with O* or E* were, respectively, optimized or estimated in the current study. By O*, the parameter was optimized using literature experimental data (Table 2) and by E*, the parameter was estimated arbitrarily.

Table 3 Thermodynamic description of the Fe-Mn-P system
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As previously reported,[1] the Gibbs energy expressions of Fe3P, Fe2P and FeP have been simplified by changing the reference states of Fe and P from HSER (used by Shim et al.[6]) to bcc-Fe and white P, respectively. In a similar way, the reference states for the Gibbs energy expression for Mn3P has been changed from cub-Mn and P2-gas (used by Zaitsev et al.[19]) to bcc-Fe and white P (Table 3). This change has no perceptible influence on the function values.

Further, calculated phase equilibria and thermodynamic quantities have been compared to original experimental data to in order to verify the results. All calculations were carried out with the ThermoCalc software.[24]

Figures 1 and 2 show the Fe-Mn and Fe-P phase diagrams calculated with the parameters of Huang[5] and of Miettinen and Vassilev,[1] respectively. Figure 3 shows the Mn-P phase diagram optimized in the current study. The agreement with the experimental data is good, as shown by Huang[5] for Fe-Mn, by[1,6] for Fe-P, and in Fig. 3 for Mn-P.

Fig. 1
figure 1

Calculated with the parameters of Huang[5] Fe-Mn phase diagram

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Fig. 2
figure 2

Calculated with the parameters of Miettinen and Vassilev[1] Fe-P phase diagram. The diagram is identical to that of Shim et al.,[6] excluding minor deviations in the bcc and fcc regions

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Fig. 3
figure 3

Mn-P phase diagram, calculated with the parameters optimized in this work, together with experimental data points of Berak and Heumann[14]

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Calculated Mn and P activities in liquid alloys at 1320 °C are shown in Fig. 4 and 5, while calculated Gibbs energies of formation of Mn3P and Mn2P are plotted in Fig. 6. The agreement with the experimental data of Ref 15-19 is reasonable.

Fig. 4
figure 4

Calculated activity of Mn in liquid Mn-P alloys at 1320 °C, together with experimental—Batalin et al.[16] and calculated—Zaitsev et al.[19] data points. The reference state used is liquid Mn

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Fig. 5
figure 5

Calculated in this work P-activity in liquid Mn-P alloys at 1320 °C (solid curve), together with experimental[15,16] and calculated[19] data points. The reference state is P2-gas

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Fig. 6
figure 6

Calculated in this work Gibbs energies of formation of Mn3P and Mn2P, together with experimental data points.[17-19] The reference states used are cub-Mn and P2-gas

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The calculated liquidus projection of the Fe-Mn-P system, together with experimental data points of Vogel and Berak[9] is shown in Fig. 7. It is of worth noting that the manganese content in point U4 (see also Table 4) is inconsistent. This inconsistency was accepted since a stronger stabilization for the cub-phase would have lead to a too extensive primary surface for this phase (see the rounded form of the calculated cub-phase region in Fig. 7), whereas Vogel and Berak[9] presented it as a triangle starting from the binary Mn-P side and approaching point U4 as a very narrow region. The latter authors[9] suggested one more invariant point, U5, due to splitting of the fcc phase into Fe-rich and Mn-rich fcc phases. This point was ignored in the current work as such splitting has not been observed in the Fe-Mn system.[13]

Fig. 7
figure 7

Calculated liquidus projection of the Fe-Mn-P system, together with experimental data points of Vogel and Berak.[9] Shown also are the calculated liquidus isotherms between 1000 and 1500 °C (dotted lines)

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Table 4 Calculated in this study (calc) and experimental (exp) invariant points in the Fe-Mn-P system
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Calculated vertical and isothermal sections are presented in Figs. 8, 9, 10, 11, 12, 13, 14, and 15, correspondingly. Good agreement of the current calculations with the experimental data of Vogel and Berak[9,20] is observed.

Fig. 8
figure 8

Calculated vertical section of the Fe-Mn-P system at mass ratio w Fe:w Mn = 19, together with experimental data points of Vogel and Berak[9] (Liquidus—liquidus points, 2. Arrest—thermal arrest data)

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Fig. 9
figure 9

Calculated vertical section of the Fe-Mn-P system at mass ratio w Fe:w Mn = 9:1, together with experimental data points of Vogel and Berak[9] (Liquidus—liquidus points, 2. Arrest—thermal arrest data)

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Fig. 10
figure 10

Calculated vertical section of the Fe-Mn-P system at mass ratio w Fe:w Mn = 5:5, together with experimental data points of Vogel and Berak[9] (Liquidus—liquidus points, 2. Arrest—thermal arrest data)

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Fig. 11
figure 11

Calculated vertical section of the Fe-Mn-P system at mass ratio w Fe:w Mn = 1:9, together with experimental data points of Vogel and Berak[9] (Liquidus—liquidus points, 2. Arrest—thermal arrest data)

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Fig. 12
figure 12

Calculated vertical section of the Fe-Mn-P system at 6 wt.% P, together with experimental data points of Vogel and Berak[9] (Liquidus—liquidus points, 2. Arrest—thermal arrest data)

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Fig. 13
figure 13

Calculated vertical section of the Fe-Mn-P system at 12 wt.% P, together with experimental data points of Vogel and Berak[9] (Liquidus—liquidus points, 2. Arrest—thermal arrest data)

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Fig. 14
figure 14

Calculated isotherm of the Fe-Mn-P system at 1000 °C, together with experimental data points of Kaneko et al.[20]

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Fig. 15
figure 15

Calculated isotherm of the Fe-Mn-P system at 800 °C, together with experimental data points of Kaneko et al.[20]

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In Fig. 16 the conformity between the calculated and experimental[21,22] P-activity coefficient (γ MnP ) data in liquid phase has been verified. The agreement is good, however, the temperature dependence of the calculated γ MnP values is slightly different from the experimental.

Fig. 16
figure 16

Calculated P-activity coefficient, γ MnP , in liquid Fe-Mn-P alloys at 1400 and 1550 °C, together with experimental data points of Schenck et al.[21] and Ban et al.,[22] respectively

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Finally, it is of worth noting that the formation of a liquid phase miscibility gap in the phosphorus-rich corner of the ternary system, at about 600 K, has been predicted. No experimental data is available to confirm the appearance of that gap but this was accepted in the present evaluation, in order to keep the liquid state ternary interaction parameters (Table 3) reasonably simple for the practical calculations at lower phosphorus contents. From theoretical view point[25] such a miscibility gap should be expected, because of the large difference between the atomic radii of the iron and manganese atoms, from one side, and that one of the phosphorus atoms, from other side. Moreover, there is a significant dissimilarity between the chemical character (e.g. the electronegativity) of the phosphorous and the metallic elements (Fe and Mn, in this case).

Summary

A thermodynamic description has been obtained for the ternary Fe-Mn-P system and its binary sub-system, Mn-P, making use of literature experimental thermodynamic and phase equilibrium data. In the current ternary phase diagram description, twelve phases, i.e., liquid, bcc, fcc, cbcc, cub, Fe3P (dissolving Mn), Fe2P (extending to Mn2P), Mn3P (dissolving Fe), FeP, Mn3P2, MnP and white-P, have been considered. Good or reasonable correlations between the calculated and the experimental thermodynamic and phase equilibrium data have been obtained.

The new Fe-Mn-P description is added as the next member of the thermodynamic database of Fe-X-P systems. No earlier thermodynamic optimization has been found in the open literature for this ternary system.