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Critical thermodynamic evaluation and optimization of the MnO–“ TiO2 ”–“ Ti2O3 ” system
Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 235–247 www.elsevier.com/locate/calphad
Critical thermodynamic evaluation and optimization of the MnO–“TiO2”–“Ti2O3” system Youn-Bae Kang a,∗ , In-Ho Jung b , Hae-Geon Lee c a Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 790-784, Republic of Korea b Research Institute of Industrial Science and Technology (RIST), Pohang, 790-600, Republic of Korea c Graduate Institute of Ferrous Technology (GIFT), Pohang University of Science and Technology (POSTECH), Pohang, 790-784, Republic of Korea
Received 5 February 2006; received in revised form 19 April 2006; accepted 8 May 2006 Available online 13 June 2006
Abstract A complete review, critical evaluation, and thermodynamic optimization of the phase equilibrium and thermodynamic properties of the MnO–“TiO2 ”–“Ti2 O3 ” systems at 1 bar pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model. The Gibbs energy of spinel, pyrophanite and pseudobrookite solid solutions were modeled using the Compound Energy Formalism, and rutile solid solution was treated as a simple Henrian solution. Manganosite solid solution was assumed to dissolve both Ti4+ and Ti3+ . A set of optimized model parameters for all phases was obtained which reproduces all available reliable thermodynamic and phase equilibrium data within experimental error limits from 25 ◦ C to above the liquidus temperatures over the entire composition ranges and in the range of pO2 from 10−20 to 10−7 bar. Complex phase relationships in these systems have been elucidated, and discrepancies among the data have been resolved. The database of model parameters can be used along with software for Gibbs energy minimization in order to calculate any phase diagram section or thermodynamic properties. c 2006 Elsevier Ltd. All rights reserved.
Keywords: MnO–TiO2 –Ti2 O3 ; Solution thermodynamics; Non-metallic inclusion; Phase diagram
1. Introduction Generally, non-metallic inclusions in steel products have been known to be harmful to the quality of final products. In order to overcome this, many investigations have been conducted about the removal of inclusions from molten steel during the refining process. Recently, an innovative concept has arisen in which non-metallic inclusions can be utilized to enhance the properties of steel products [1]. By controlling the chemistry, size and distribution of nonmetallic inclusions, those inclusions can be utilized as nuclei for transformation from austenite to α-ferrite. The size of the transformed α-ferrite is fine enough to enhance the steel strength. Among the non-metallic inclusions which can act as the nucleus, MnO–SiO2 –TiOx –MnS type inclusions ∗ Corresponding address: Centre de Recherche en Calcul Thermochimique ´ (CRCT), Ecole Polytechnique, Montreal, Quebec, Canada H3C 3A7. Tel.: +1 514 340 4711x4303; fax: +1 514 340 5840. E-mail address: [email protected] (Y.-B. Kang).
c 2006 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter doi:10.1016/j.calphad.2006.05.001
have been recognized as one of the most effective for grain refinement. Several investigations have been conducted to characterize the role of those inclusions on grain refinement [2–5]. However, unfortunately, even the phase relations for this inclusion system are not exactly known. To date, research has been performed on the liquidus and thermodynamic properties of MnO–SiO2 –TiOx –MnS system by several investigators [6–10]. However, in most of those studies, the oxygen potential, which plays an important role in the phase equilibria and thermodynamics of the system, was not controlled quantitatively and possible solid solutions were overlooked. Thus, in the present study, we attempt to investigate the phase equilibria and thermodynamics for the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system by experiment and thermodynamic modeling by considering the above-mentioned facts. Experimentally determined phase relations were reported in two previous articles [11,12]. In this article, thermodynamic modeling on the MnO–“TiO2 ”–“Ti2 O3 ” system will be reported based on the reported experimental data including
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Table 1 Optimized model parameters of the solutions in the MnO–“TiO2 ”–“Ti2 O3 ” system (G, H , ∆, L: J/mol, S, C p: J/mol K)a,b Manganosite s.s.: MnO–TiO2 –TiO1.5 G ◦ (TiO2 in manganosite s.s.) = G ◦ (TiO2 , rutile) + 22175.2 G ◦ (TiO1.5 in manganosite s.s.) = 0.5G ◦ (Ti2 O3 ) + 30024.4 Spinel s.s.: (Mn2+ )T [Mn2+ , Ti4+ , Ti3+ ]O 2 O4 G ◦ (Mn2 TiO4 , cubic) H◦298 K = −1744 003.42, S◦298 K = 170.41 C p = 168.15 + 0.0174T − 2556 424T −2 G MG = G ◦ (MnTi2 O4 ) H◦298 K = −1920 102.79, S◦298 K = 140.65 C p = 213.79 + 0.0093T − 2789 257.99T −2 − 750.22T −0.5 − 1968 461 709T −3 G ◦ (Mn2 TiO4 , cubic) =1/2(G MM + G MT ) + 2RT ln(1/2) G MT = G MG Pyrophanite s.s.: (Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B O3 G MT = G ◦ (MnTiO3 , pyrophanite) H◦298 K = −1363 254.23, S◦298 K = 104.04 C p = 121.67 + 0.0093T − 2188 232T −2 G GG = G ◦ (Ti2 O3 ) G GT = G GG ∆IL = G MG + G GT − G MT − G GG = 106 630.70 − 57.22T L Mn2+ ,Ti3+ :Ti4+ = L Mn2+ ,Ti3+ :Ti3+ = 8368 Pseudobrookite s.s.: (Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B 2 O5 G MT = G ◦ (“MnTi2 O5 ”) H◦298 K = −2286 501.78, S◦298 K = 163.66 C p = 247.15 − 4501 984T −2 − 1026.15T −0.5 + 455 637 600T −3 G ◦ (Ti3 O5 ) =1/2(G GT + G GG ) + 2RT ln(1/2) G GT = G GG ∆PB = G MG + G GT − G MT − G GG = −64 955.40 + 44.62T Rutile s.s.: TiO2 –TiO1.5 G ◦ (TiO1.5 in rutile s.s.) = 0.5G ◦ (Ti2 O3 ) + 22 592.93 + 2.59T Liquid oxide: MnO–TiO2 –TiO1.5 c For “TiO2 ”–“Ti2 O3 ” system 01 ◦ ∆gTiO ,TiO = 10 545, qTiO 1.5
2
1.5 ,TiO2
02 = −112 366, qTiO
1.5 ,TiO2
03 = 209 542.80, qTiO
1.5 ,TiO2
= −98 420
For MnO–“TiO2 ” system 01 02 ◦ ∆gMnO,TiO = −19 246.4, qMnO,TiO = −37483.83, qMnO,TiO = 10 460 2 2 2 For MnO–“Ti2 O3 ” and MnO–“TiO2 ”–“Ti2 O3 ” systems (Toop-like asymmetric with MnO singled out) No parameter was used. a The Gibbs energies of end-members of the solid and liquid solutions and of the other stoichiometric compounds in the MnO–TiO –Ti O system are taken from 2 2 3
Refs. [18]. b M, T and G denote Mn2+ , Ti4+ and Ti3+ , respectively. c Binary parameters of the Modified Quasichemical Model are defined in Ref. [16,17].
phase diagram and thermodynamic properties. All solid solutions, which correspond to typical inclusions in steels, are modeled as well as liquid oxide. The optimization of the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system will be presented in the next article in the present series [13]. 2. Thermodynamic models Thermodynamic models for the solution phases in the present system are summarized below, and all optimized model parameters are listed in Table 1.
2.1. Molten oxide For the molten oxide phase, the Modified Quasichemical Model [14,15] was used. This model has recently been further developed and summarized [16,17]. Short-range ordering is taken into account by considering second-nearestneighbor pair exchange reactions. For example, for the MnO–“TiO2 ”–“Ti2 O3 ” molten oxide, these reactions are: (A–A) + (B–B) = 2(A–B)
∆gAB
(1)
where A and B are Mn, Ti4+ and Ti3+ , and (i– j) represents a second-nearest-neighbor i– j pair. The parameters of the
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model are the Gibbs energies of these reactions, which may be expanded as empirical functions of composition. Although manganese can exist in the trivalent state in the slag at high oxygen partial pressures, in the present study only divalent manganese is considered, while trivalent and tetravalent titanium are considered to exist in the molten oxide. The MnO–“TiO2 ” and “TiO2 ”–“Ti2 O3 ” binary liquid oxides were already optimized using the Modified Quasichemical Model by Eriksson and Pelton [18] along with the secondnearest-neighbor “coordination numbers” of Mn, Ti4+ and Ti3+ , used in the Modified Quasichemical Model. However, in the present study, the binary model parameters for these molten oxides were re-optimized (1) to reproduce recent experimental data in the MnO–“TiO2 ” system [11] and (2) to give better results on higher order systems from the “TiO2 ”–“Ti2 O3 ” system. For the ternary MnO–“TiO2 ”–“Ti2 O3 ” system, a Toop-like “asymmetric approximation” [19,20] was used with MnO as the “asymmetric component” in order to estimate the Gibbs energy of the ternary liquid from the binary parameters. The MnO–“Ti2 O3 ” binary liquid oxide was treated as an ideal solution. No ternary parameters were used for the MnO–“Ti2 O3 ”–“TiO2 ” system. The optimized model parameters are listed in Table 1.
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Ti3+ , respectively. Thus, end-members MM, MT and MG are 2+ Mn3 O2− 4 , MnTi2 O4 and MnTi2 O4 . Hence, this solution was actually treated as an ideal solution among these end-members. The schematic figure for the spinel solid solution is shown in Fig. 1. Mn2 TiO4 , which is a real neutral compound, is assumed as an equimolar ideal mixture between MT (MnTi2 O2+ 4 ) and 2− MM (Mn3 O4 ). That is: 1 1 G ◦ (Mn2 TiO4 ) = (G MM + G MT ) + 2RT ln . (4) 2 2 G ◦ (Mn2 TiO4 ) was taken from Eriksson and Pelton [18] but its H◦298 was adjusted during optimization. The optimized value of H◦298 K (−1744 kJ/mol) in the present study may be compared with the recommended value in Barin’s compilation (−1750 kJ/mol) [26]. S◦298 K was kept to be the same as that in Barin’s compilation (170.41 J/mol K). No Gibbs energy data for MnTi2 O4 has been known. Thus, G MG was first estimated by assuming that the Gibbs energy of formation of MnTi2 O4 from MnO and Ti2 O3 is equal to the Gibbs energy of formation of Mn2 TiO4 from 2MnO and TiO2 [27]. And the H◦298 K of MnTi2 O4 was then slightly varied during optimization. G MT was assumed to be the same as G ◦ (MnTi2 O4 ). No excess Gibbs energy parameter was required during the optimization.
2.2. Manganosite 2.4. Pyrophanite
From the EPMA analysis [11], it was observed that Ti (Ti4+ + Ti3+ ) can dissolve into pure MnO up to ∼3 mass pct and that the solubility changes with temperature and oxygen partial pressure. Therefore, the manganosite solid solution was modeled such that both Ti4+ and Ti3+ dissolve into pure MnO by assuming association of vacancy with Ti cations and random mixing in the cationic site in a rock salt structure.
Pyrophanite has an ilmenite structure (hexagonal, R3) with two cationic sublattices [28]. In the MnTiO3 –Ti2 O3 solid solution, Mn2+ and Ti3+ ions are assumed to mix randomly on one sublattice, while Ti3+ and Ti4+ mix randomly on the other sublattice as [24]:
2.3. Spinel
(Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B O3
Mn2 TiO4 and MnTi2 O4 form an extensive spinel solid solution [21]. MnTi2 O4 is a typical 2–3 type spinel while Mn2 TiO4 is a 2–4 type spinel. Spinel has an FCC structure, in which cations occupy octahedral and tetrahedral interstices. From X-ray diffraction studies, Mn2 TiO4 is almost an inverse spinel while MnTi2 O4 is a normal spinel [22,23]. Thus, the following model structure was considered as suggested by Pelton et al. [24]:
The Gibbs energy equation of the pyrophanite solid solution per formula unit is as follows:
(Mn2+ )T [Mn2+ , Ti4+ , Ti3+ ]O 2 O4
(2)
where the first and second brackets represent the tetrahedral site and octahedral site, respectively. The spinel solid solution was modeled in the framework of the Compound Energy Formalism (CEF) with two sublattices [25]. The Gibbs energy equation of the spinel solid solution per formula unit is as follows: G = yM G MM + yT G MT + yG G MG + 2RT(yM ln yM + yT ln yT + yG ln yG )
(3)
where yi and G ji represent the site fraction of cation i in the octahedral sublattice and standard Gibbs energy of endmember ji. The notation M, T and G means Mn2+ , Ti4+ and
(5)
A B A B G = yM yT G MT + yM yG G MG + yGA yTB G GT + yGA yGB G GG A A + RT(yM ln yM + yGA ln yGA )
+ RT(yTB ln yTB + yGB ln yGB ) + G E x
(6)
where all notations M, T and G are identical to those in spinel. Thus, end-members MT, MG, GT and GG are MnTiO3 , 1+ E x is an excess Gibbs energy MnTiO1− 3 , Ti2 O3 and Ti2 O3 . G between cations in a sublattice as: X X j j j G Ex = yki yli ym L kl:m + yki yl ym L k:lm (7) m
k
The schematic figure for the pyrophanite solid solution is shown in Fig. 1. G MT and G GG are the Gibbs energy of pure MnTiO3 and Ti2 O3 compounds, respectively, and are taken from Eriksson and Pelton [18]. H◦298 K and S◦298 K of MnTiO3 were slightly changed from those of Eriksson and Pelton during optimization. The optimized values of H◦298 K (−1363 kJ/mol) and S◦298 K (104.04 J/mol K) may be compared with the recommended values in Barin’s compilation (−1359 kJ/mol
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Fig. 1. Schematic figures of model structures (Compound Energy Formalism) for solid solutions in the Mn–Ti–O system. (a) Spinel solid solution. (b) Pyrophanite solid solution. (c) Pseudobrookite solid solution.
and 104.935 J/mol K) [26]. The following reciprocal reaction was considered: 1+ MnTiO3 + Ti2 O3 = MnTiO1− 3 + Ti2 O3
∆IL = G MG + G GT − G MT − G GG
(8)
where ∆IL is a model parameter which means a tendency to form a Mn2+ (A)–Ti3+ (B) and a Ti4+ (A)–Ti3+ (B) pair bond prior to a Mn2+ (A)–Ti4+ (B) and a Ti3+ (A)–Ti3+ (B) pair bond in the ilmenite structure. Either one of G MG or G GT may be assigned an arbitrary value while the other is then given by the reciprocal reaction parameter. In the present study, G GT was set to be the same as G GG . 2.5. Pseudobrookite Pseudobrookite is orthorhombic, Bbmm space group, with 4AB2 O5 formula unit in the unit cell. All the cations are in octahedral coordination. There are two kinds of octahedral site, with fourfold (A sites) and eightfold (B sites) multiplicity [29]. In the “MnTi2 O5 ”–Ti3 O5 solid solution, in which “MnTi2 O5 ” is actually unstable relative to dissociation into pyrophanite and rutile [11], Mn2+ and Ti3+ ions are assumed to mix randomly on one sublattice, while Ti3+ and Ti4+ mix randomly on the other sublattice as [24]: (Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B2 O5
(9)
The Gibbs energy equation of the pyrophanite solid solution per formula unit is as follows:
A B A B G = yM yT G MT + yM yG G MG + yGA yTB G GT + yGA yGB G GG A A + RT(yM ln yM + yGA ln yGA )
+ 2RT(yTB ln yTB + yGB ln yGB )
(10)
where all notations M, T and G are same as those in spinel. Thus, end-members MT, MG, GT and GG are MnTi2 O5 , 1+ MnTi2 O2− and Ti3 O1− 5 , Ti3 O5 5 . Hence, this solution was actually treated as an ideal solution among these end-members. The schematic figure for the pseudobrookite solid solution is shown in Fig. 1. Ti3 O5 , which is a real neutral compound, is assumed to be an equimolar ideal mixture between GT 1− (Ti3 O1+ 5 ) and GG (Ti3 O5 ), similar to what was done for Mn2 TiO4 in spinel. That is: 1 1 ◦ G (Ti3 O5 ) = (G GT + G GG ) + 2RT ln (11) 2 2 G ◦ (Ti3 O5 ) was taken from Eriksson and Pelton [18]. The Gibbs energy of the hypothetical “MnTi2 O5 ” was taken from Pelton et al. [24] and its H◦298 K and S◦298 K were slightly adjusted during optimization. The following reciprocal reaction was considered: 2− 1+ MnTi2 O5 + Ti3 O1− 5 = MnTi2 O5 + Ti3 O5
∆PB = G MG + G GT − G MT − G GG
(12)
where ∆PB is a model parameter which has a similar meaning to ∆IL in the pseudobrookite structure. Either G MG or G GT may be assigned an arbitrary value while the other is then given by the reciprocal reaction parameter. In the present study, G GT
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was set to be identical to G GG . No excess Gibbs energy was required. The solution models for spinel, pyrophanite (ilmenite structure) and pseudobrookite solid solutions are essentially identical to models developed by Pelton et al. [24] and successfully applied in the Fe–Ti–O [30] and Mg–Ti–O systems [24]. 2.6. Rutile TiO2 in the form of rutile has non-stoichiometry toward the Ti2 O3 direction and is usually expressed as TiO2−δ . Defect mechanisms in rutile have not yet been fully confirmed. Eriksson and Pelton [18] modeled the rutile solid solution using a simple Henrian solution model while Waldner and Eriksson [31] used the CEF with (Ti4+ )(O2− , Va2− )2 structure. Since the defect mechanism is not clear, we prefer to use the rather simple model. Therefore, in the present study, the same model of Eriksson and Pelton [18] was used but temperature dependence was assigned to the Henrian activity coefficient of TiO1.5 in order to reproduce all experimental data over the wide range of temperature. Several Magn´eli phases (Tin O2n−1 , n ≥ 4) were considered as stoichiometric compounds. All model parameters optimized in the present study are listed in Table 1. All thermodynamic calculations and optimization were carried out using the FactSage thermochemical computing system [32].
Fig. 2. Equilibrium oxygen partial pressure of rutile s.s. in equilibrium with the highest Magn´eli phase (“Ti20 O39 ”). Experimental data are taken from several sources [33–42]. The line is calculated from the model in the present study.
3. Critical evaluation and optimization for the MnO– “TiO2 ”–“Ti2 O3 ” system The MnO–“TiO2 ” system and the “TiO2 ”–“Ti2 O3 ” system were optimized by Eriksson and Pelton [18]. Gibbs energies of all Magn´eli phases were also evaluated and they were used in the present study. In the present study, the MnO–“TiO2 ” system was re-optimized and extended to the MnO–“TiO2 ”–“Ti2 O3 ” system by considering phase equilibria at low pO2 . The rutile solid solution and molten oxide in the “TiO2 ”–“Ti2 O3 ” system was revised to give better results. Spinel, pyrophanite and pseudobrookite in the MnO–“TiO2 ”–“Ti2 O3 ” system were once modeled by Pelton et al. [24]. However, they were reoptimized in the present study by considering new experimental data [11]. 3.1. Revision of the “TiO2”–“Ti2 O3” system Several studies have been conducted to measure the nonstoichiometry of rutile and oxygen partial pressure at the lower boundary of rutile (two-phase equilibrium with rutile and the highest Magn´eli phase, i.e., “Ti20 O39 ” [18]). Figs. 2 and 3 show calculated oxygen partial pressure and non-stoichiometry as functions of reciprocal temperature along with experimental data from several investigators [33–42]. These data were used to optimize the model parameters for the rutile solid solution. In order to reproduce the non-stoichiometry of rutile at all temperature ranges, a temperature dependent Henrian activity coefficient was necessary.
Fig. 3. Non-stoichiometry of rutile s.s. (TiO2−δ ) in equilibrium with the highest Magn´eli phase (“Ti20 O39 ”) as a function of temperature. Experimental data are taken from several sources [33–39]. The line is calculated from the model in the present study.
During optimization in the MnO–“TiO2 ”–“Ti2 O3 ” system, an unexpected liquid (metastable) immiscibility was calculated near the Ti2 O3 rich region. This resulted from the model parameters in the “TiO2 ”–“Ti2 O3 ” system optimized by Eriksson and Pelton [18]. Therefore, in the present study, the model parameters for the “TiO2 ”–“Ti2 O3 ” liquid oxide were slightly modified so as not to induce the abovementioned immiscibility. The calculated phase diagram of the “TiO2 ”–“Ti2 O3 ” system using the revised model parameters is shown in Fig. 4 along with experimental data [33–38,43,44]. The calculated phase diagram does not change significantly from the phase diagram in Eriksson and Pelton [18] but a better result is obtained in the higher order system. 3.2. Phase equilibria in the MnO–“TiO2”–“Ti2 O3” system Fig. 5 shows a calculated isothermal section of the MnO–“TiO2 ”–“Ti2 O3 ” system at 1400 ◦ C. At this temperature, all phases in this system appear except for molten oxide. Thin lines are calculated sections of the phase equilibria at several
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Fig. 4. Calculated phase diagram of the “Ti2 O3 ”–“TiO2 ” system. Liquid and rutile solutions were optimized in the present study and Gibbs energies of solid compounds were taken from Eriksson and Pelton [18]. Experimental data are taken from several sources [33–39,43,44].
Fig. 5. Calculated isothermal section in the MnO–“TiO2 ”–“Ti2 O3 ” system at 1400 ◦ C. Thin lines represent sections of phase equilibria under specified oxygen partial pressures (log pO2 (bar)). Dashed lines denote sections of phase equilibria under pCO/pCO2 = 1, 9 and C/CO equilibrium, respectively.
oxygen partial pressures. Moreover, the three dashed lines represent sections of the phase at pCO/pCO2 = 1, 9 and C/CO equilibrium conditions. Since manganese is only in its divalent state under the oxygen partial pressure considered in the present study, all these sections start from MnO. However, depending on the oxygen partial pressure, each section ends at a different point on the “TiO2 ”–“Ti2 O3 ” binary edge. For the condition of pCO/pCO2 = 1 (log pO2 = −8.62), the limiting point on the “TiO2 ”–“Ti2 O3 ” binary is very close to pure “TiO2 ”. Thus, the ternary system under this condition (pCO/pCO2 = 1) can be reasonably considered as the MnO–“TiO2 ” binary system. Only the spinel s.s., which is close to stoichiometric Mn2 TiO4 , and the pyrophanite s.s., which is close to stoichiometric MnTiO3 , are intermediate solid phases. The pseudobrookite s.s. is not stable under this condition. However, at pCO/pCO2 = 9 (log pO2 = −10.53), the section shifts slightly to the Ti2 O3 direction due to decreasing oxygen partial pressure (about two orders of magnitude). Thus, in this section, the pseudobrookite phase, whose composition lies
between hypothetical “MnTi2 O5 ” and Ti3 O5 , becomes stable although the limiting point on the “TiO2 ”–“Ti2 O3 ” binary is still in the rutile phase region. On the other hand, under the C/CO equilibrium condition, the oxygen partial pressure decreases drastically (log pO2 = −16.13) so that the limiting point locates at Ti3 O5 . Thus, the section shifts more to the direction of the MnO–“Ti2 O3 ” side and the stable regions of spinel and pyrophanite s.s. are wider than under previous conditions when this ternary system is projected onto the MnO–“TiO2 ” side from the oxygen corner. In Fig. 6(a)–(c), these three sections (pCO/pCO2 = 1, 9 and C/CO equilibrium) are drawn as typical phase diagrams (composition versus temperature) using the thermodynamic models with the optimized model parameters. Experimentally determined phase boundary data of the present authors [11] are also plotted. Equilibrium oxygen partial pressures at several temperatures were calculated using the F*A*C*T database [32] and are specified in the figures. The model parameters were optimized by the following steps. First, the model parameters for MnO–“TiO2 ” in the molten oxide were optimized to reproduce the MnO activity, which will be shown later, with simultaneous consideration of the liquidus of both manganosite and rutile. Then, the model parameters of manganosite, H◦298 K of Mn2 TiO4 in the spinel and H◦298 K of MnTiO3 in the pyrophanite were changed to reproduce the melting temperature and solid solubilities in each solid solution at pCO/pCO2 = 1. Experimental data at low oxygen partial pressure (pCO/pCO2 = 9 and C/CO equilibrium) were then used to optimize other model parameters of the spinel, pyrophanite and pseudobrookite solid solutions. For the optimization of phase equilibria among solid solutions at low temperature and low oxygen partial pressure, phase diagram data by Grey et al. [45] and the valency distribution in spinel by Amitani et al. [6] were also considered. From thermodynamic optimization, which can reproduce the above-mentioned phase diagram data, activities and so on (discussed in the next section), it has been predicted that Mn2 TiO4 melts congruently at 1463 ◦ C under pCO/pCO2 = 1. This is in agreement with what was reported by Grieve and White (congruent melting at 1460 ◦ C) [46], while Leusmann reported congruent melting at 1420 ± 10 ◦ C [47]. On the other hand, from the thermodynamic calculation, MnTiO3 melts at 1453 ◦ C (pCO/pCO2 = 1) congruently. This result is in conflict with those of Grieve and White (incongruent melting at 1360 ◦ C) and Leusmann (congruent melting at 1410 ± 10 ◦ C). However, in the previous study of the present authors [11], MnTiO3 never melted at 1400 ◦ C under pCO/pCO2 = 1 and 9. As discussed in a previous article [11], “MnTi2 O5 ” is unstable in the MnO–“TiO2 ” system, so the pseudobrookite phase does not appear in Fig. 6(a). However, as the oxygen partial pressure decreases, the pseudobrookite phase appears in between pyrophanite and rutile. From the experimental data, it can be inferred that pseudobrookite melts incongruently between 1450 ◦ C and 1500 ◦ C at pCO/pCO2 = 9 [11]. This melting behavior was well reproduced by thermodynamic optimization (incongruent melting at 1498 ◦ C).
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Fig. 6. Optimized phase diagram sections in the MnO–“TiO2 ”–“Ti2 O3 ” system under various gas conditions. Experimental data are taken from Kang and Lee [11]. The thick dashed line indicates the boundaries above which all oxides are no longer stable, and are hence reduced to metallic liquid (Zero Phase Fraction (ZPF) line [49] of metallic liquid). The dotted lines above the ZPF line are, therefore, metastable phase boundaries calculated without considering metallic liquid. (a) pCO/pCO2 = 1. (b) pCO/pCO2 = 9. (c) C/CO equilibrium.
As shown in Fig. 6(b), dissolution of Mn in the Ti-rich region (n Ti /(n Mn + n Ti ) > 0.95) in the temperature range 1400 ◦ C to 1550 ◦ C was observed in the previous study [11]. Grey et al. [45] reported that Mn dissolves in several Magn´eli phases at 1200 ◦ C accompanied by stabilizing the Magn´eli phases at a slightly higher oxygen partial pressure. Therefore, although the oxygen partial pressure is slightly higher than for the Magn´eli phases to be stable, it is thought that the Mn dissolves in the Magn´eli phases, stabilizing them even slightly higher oxygen partial pressure. However, this was not considered in the present study since the solubilities are rather small and the phase equilibria are still unclear. The phase diagram under C/CO equilibrium conditions in Fig. 6(c) shows that the oxide phases are reduced to metallic liquid due to the oxygen partial pressure being too low. In the calculation, thermodynamic data of the metallic phases were taken from Saunders [48]. The dashed line represents the ZPF (Zero Phase Fraction) line [49] of metallic liquid, so the oxide phases are reduced above this line. Experimental data are available for only the sub solidus region, thus the binary model parameter for the MnO–“Ti2 O3 ” in the molten oxide could not be evaluated. However, in the
optimization for the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system, it was found that setting zero for the binary model parameter was enough to reproduce experimental data under C/CO equilibrium conditions, which will be shown in the forthcoming article [13] on the thermodynamic optimization for the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system. Fig. 7(a)–(d) show the thermodynamically calculated phase diagram of the MnO–TiOx system under different fixed oxygen partial pressures from 10−5 to 10−20 bar. It was assumed that Mn3+ in the molten oxide and the solid oxides was negligible even at pO2 = 10−5 bar. These figures show how subsolidus phase equilibria vary with oxygen partial pressure and temperature. Generally, the n Ti /(n Mn +n Ti ) cationic molar ratio increases in the spinel, pyrophanite and pseudobrookite phases as the oxygen partial pressure decreases. This can be interpreted as Ti3+ stabilization in the solid solutions at low oxygen partial pressure. More clearly, this can be seen in Fig. 8(a)–(h), in which the phase equilibria of the Mn–Ti–O system are presented as n Ti /(n Mn +n Ti ) cationic molar ratio versus oxygen partial pressure at several temperatures. All lines are calculated from the thermodynamic models and the optimized parameters. Available experimental data reported by several researchers as
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Fig. 7. Predicted phase diagrams of the Mn–Ti–O system under various oxygen partial pressures. (a) pO2 = 10−5 bar. (b) pO2 = 10−10 bar. (c) pO2 = 10−15 bar. (d) pO2 = 10−20 bar.
well as the present authors are also compared, although the measured liquidus data by Amitani et al. [6], Kim et al. [9], Ohta and Morita [50] were not used in the optimization as discussed in a previous article [11]. Original experimental data by Amitani et al. [6] at 1300 ◦ C, deduced from their valency analysis, were plotted as open circles. However, their data were adjusted and re-plotted as half-filled circles. The reason will be discussed in Section 3.3. In Fig. 9, predicted oxygen partial pressures in a number of three-phase equilibria are shown until the equilibria are terminated by the molten oxide. 3.3. Activities and other thermodynamic properties in the MnO–“TiO2”–“Ti2 O3” system A number of investigations have been performed to measure the activity of MnO in the MnO–TiOx system [9,50–53]. Detailed experimental conditions for each experiment are summarized in Table 2. Fig. 10 shows the measured activity of MnO in the MnO–TiOx system. All these investigations employed chemical equilibration among gas/metal/oxide at high temperature. Usually Pt was used as reference metal but Cu or Ag was adopted in some investigations. During the evaluation for these investigations, it was found that the results of Martin and
Bell [52], K¨arsrud [53] and Kim et al. [9] had to be corrected because of the activity coefficient of Mn in the reference alloy they used. Martin and Bell [52] obtained the activity of MnO using γMn(Pt) of an earlier study by Smith and Davies [54]. However, the measured γMn(Pt) of Smith and Davies seems considerably lower than that of other investigations (see Appendix A). Thus, in the present study, the activity data of MnO from the investigation of Martin and Bell were not used directly but rather were corrected using newly evaluated activity–composition relations in the Pt–Mn alloy, which can reproduce a majority of the measured activity coefficient data within experimental error limits (see Appendix A). The result of K¨arsrud [53] was also re-interpreted. This is because they used γMn(Pt) measured by Abraham et al. [55]. However, they misused it. Abraham et al. [55] reported γMn(Pt) at 1500 ◦ C, in which the standard state of Mn was pure solid. However, K¨arsrud used the same relation as if its standard state was pure liquid Mn, for their calculation of the activity of Mn. Therefore, both previously reported activity data were corrected using the newly obtained γMn(Pt) expression (see Appendix A). On the other hand, Kim et al. [9] did an experiment using gas (pCO/pCO2 = 99, which corresponds to pO2 = 7.3 × 10−13 bar)/silver/oxide equilibration at 1450 ◦ C to measure the activity of MnO in molten oxide. However, as is seen in Fig. 8(e), the oxide composed of MnO and TiOx
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Y.-B. Kang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 235–247 Table 2 Detailed experimental conditions for activity measurements in the MnO–TiOx system Author Rao and Gaskell Rao and Gaskell Martin and Bell K¨arsrud Ohta and Morita Kim et al.
T (◦ C)
pO2 (bar)
Reference metal
Source of γMn
1500 1550 1500 1500 1600 1450
10−7 –10−6
Pt Pt Pt Pt Cu Aga
Rao and Gaskell [61] Rao and Gaskell [61] Smith and Davies [54] Abraham et al. [55] Ohta and Morita [50] Ito et al. [7]
7.0 × 10−7 1.1–1.6 × 10−6 1.3 × 10−7 1.9 × 10−10 7.3 × 10−13
a γ ◦ at 1450 ◦ C in their study was extrapolated from the γ ◦ at 1400 ◦ C by Ito et al. [7] assuming regular solution behavior of the Ag–Mn alloy. Mn Mn
Fig. 8. Calculated phase diagrams of the Mn–Ti–O system with oxygen partial pressure as an axis at several temperatures. Experimental data are taken from several sources [6,9,11,45,50]. All symbols mean experimentally measured phase boundary except for those in Fig. 8(a). (a) At 1200 ◦ C. (b) At 1300 ◦ C. (c) At 1350 ◦ C. (d) At 1400 ◦ C. (e) At 1450 ◦ C. (f) At 1500 ◦ C. (g) At 1550 ◦ C. (h) At 1600 ◦ C.
does not melt at this condition. It can be inferred from Fig. 8(e) that there should be two phase equilibria (monoxide + spinel, spinel + pyrophanite etc.) under this condition and the experimental data of Kim et al. also do not vary smoothly. Moreover, ◦ in their activity calculation, γMn(Ag) reported by Ito et al. [7] at ◦ 1400 C was extrapolated by assuming regular solution behavior between Ag and Mn. However, Jung [56] did measure the ◦ activity coefficient of Mn in Ag at 1450 ◦ C and reported γMn(Ag) ◦ at 1450 C is 0.596 (liquid Mn standard state). This value is quite different from the extrapolated value (0.395). Therefore,
◦ the measured γMn(Ag) value by Jung was used to re-calculate the activity of MnO reported by Kim et al. [9] The maximum difference of the activities after these corrections was ∼0.2. The calculated activity of MnO in the MnO–TiOx system is shown in Fig. 10 along with the reported experimental data. Data of Martin and Bell [52], K¨arsrud [53] and Kim et al. [9] were corrected values, as mentioned above. It is thought that the activity data of Kim et al. [9] are not for molten oxide but for several solid solutions. It seems that the temperature dependence of the activities is not conspicuous.
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Fig. 8. (continued)
Fig. 9. Predicted equilibrium oxygen partial pressures in several monovariant equilibria in the Mn–Ti–O system until the equilibria are terminated by the molten oxide.
Amitani et al. [6] measured the distribution of Ti valences in the spinel s.s. in equilibrium with manganosite by employing chemical equilibration of Cu–Mn alloy/manganosite/spinel at 1300 ◦ C followed by wet chemical analysis. Oxygen partial pressures in the systems were then estimated from the equilibrium reaction Mn(in Cu) + 1/2O2 (g) = MnO(s), for
Fig. 10. Activity of MnO (with respect to the pure solid MnO) in the MnO–TiOx system. Experimental data are taken from several sources [9,50– 53]. Lines are calculated from the model in the present study under the same oxygen partial pressures employed in the experiments.
which the Mn contents in the alloys were analyzed. They reasonably assumed that the activity of MnO(s) is unity. Thus, in order to estimate the oxygen partial pressure, the activity coefficient of Mn should be known. In their estimation, they used the activity coefficient of Mn in Cu–Mn alloy which
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FactSage thermochemical computing system. All reliable experimental data are reproduced within experimental error limits by a few model parameters. The phase diagrams of the MnO–“TiO2 ”–“Ti2 O3 ” system under different oxygen partial pressures have been proposed based on recently measured experimental data and thermodynamic modeling. Moreover, measured activities and valences of Ti in oxide systems could be reproduced well. With the present optimized database, it is now possible to calculate any phase diagram section of the MnO–“TiO2 ”–“Ti2 O3 ” system under various oxygen partial pressure at all compositions and temperatures. By coupling the presently developed database with other evaluated F*A*C*T databases for metallic solutions, gases, etc., complex slag/metal/solid/gas equilibria can be computed. Fig. 11. Distribution of Ti valences in the spinel s.s. in equilibrium with the manganosite s.s. at 1300 ◦ C. Experimental data are taken from Amitani et al. [6] (open symbols) and they are adjusted (half-filled symbols). The line is calculated from the model in the present study. See Section 3.3 for details of the adjustment.
was derived from the activity measurement by Spencer and ◦ Pratt [57] for the concentrated region of Mn, while γMn in Cu suggested by Oishi and Ono [58] was applied in the dilute region of Mn. Fig. 11 shows their evaluated Ti4+ /Ti3+ in the spinel as a function of oxygen partial pressure at 1300 ◦ C, as open symbols. Generally, increasing oxygen partial pressure results in increasing Ti4+ /Ti3+ ratio in spinel s.s. However, the open symbols do not show continuous behavior although there is no phase transformation. This is because they used an inconsistent set of γMn(Cu) over Mn concentration in Cu. As is shown in Fig. 11, agreement between open symbols and thermodynamic calculation in the present study is only good in low oxygen partial pressure (the concentrated region of Mn in Cu). Therefore, in order to calculate the oxygen partial pressure in their study more exactly, it is necessary to use a consistent set of γMn(Cu) during the calculation. In the present study, the Cu–Mn thermodynamic optimization, which was recently reported by Liu et al. [59], was used to evaluate γMn(Cu) . Using this new γMn(Cu) , oxygen partial pressures in the study of Amitani et al. [6] were re-calculated and the results plotted in Fig. 11 as half-filled symbols. It is clearly shown that Ti4+ /Ti3+ increases continuously and the re-evaluated results are in good agreement with the calculation. Also, from the redox reaction of Ti in spinel, it is expected that the slope of the line in Fig. 11 should be 1/4 if activity coefficients of Ti3+ and Ti4+ are reasonably assumed to be unity. The present thermodynamic calculation shows the slope close to 1/4 as seen in Fig. 11. TiO2 (Ti4+ ) = TiO1.5 (Ti3+ ) + 1/4O2 .
(13)
4. Conclusions A complete critical evaluation of all available phase diagram and thermodynamic data for the MnO–“TiO2 ”–“Ti2 O3 ” system was carried out, and a database of optimized model parameters was prepared at 1 bar total pressure using the
Acknowledgements ´ The authors wish to thank Prof. Arthur D. Pelton (Ecole Polytechnique de Montr´eal, Canada) for valuable discussions during the present study. Appendix A. Activity–composition relationship in the Pt– Mn alloy Much research has been conducted to measure the activity of MnO in oxide solution, which are either liquid phases or solid phases, by employing chemical equilibration among gas/slag(oxide)/reference metals. Usually, Pt or Cu has been used as the reference metal since those metals are noble enough not to dissolve into the oxide phase. A number of researches have used Pt as a reference metal to measure the activity of MnO in oxide solutions. In order to calculate the activity of MnO in oxide, the following reaction can be considered. Mn(s, in Pt–Mn alloy) + 1/2O2 (gas) ◦ = MnO(s, in oxide) ∆gA.1 ◦ ∆gA.1 aMnO . K A−1 = = exp − RT aMn ( pO2 )1/2
(A.1) (A.2)
◦ can be found in literature or thermodynamic databases ∆gA.1 and pO2 is usually controlled during experiments. Therefore, the activity of Mn in the Pt–Mn alloy must be known as a function of composition and temperature. Several researchers have investigated the activity–composition relation in Pt–Mn alloy at various temperatures [54,55,60–65]. However, some results of those researches are sometimes inconsistent with each other, and temperatures at which the activity–composition relation can be applied are discrete at 1300 ◦ C, 1400 ◦ C, 1500 ◦ C, 1550 ◦ C, 1600 ◦ C and 1650 ◦ C. Therefore this study attempted to compare all available experimental data and to express the activity–composition relation as a function of composition and temperature. The Gibbs free energy of Pt–Mn solid solution in the Pt-rich region can be expressed as follows, assuming that it behaves as a regular solution: ◦ ◦ ◦ G = n Pt gPt + n Mn (gMn + RT ln γMn(s) ) + RT(n Pt ln X Pt + n Mn ln X Mn ) + αn Pt n Mn /(n Pt + n Mn )
(A.3)
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Fig. A.1. Activity coefficients of Mn(relative to pure solid Mn) in Pt–Mn alloys at several temperatures. Experimental data are taken from several sources. The lines are calculated in the present study [54,55,60–65]. ◦ where γMn(s) is a Henrian activity coefficient of Mn in the Ptrich solution relative to pure solid Mn and α is a regular solution parameter. The purpose of this appendix is an evaluation of ◦ the Henrian activity coefficient, γMn(s) , and the regular solution parameter α in a wide range of temperatures to express the activity coefficient of Mn in Pt–Mn alloy by fitting the available and reliable experimental data. The partial Gibbs free energy of Mn can be derived from Eq. (A.3) as follows: ◦ ◦ gMn = gMn + RT ln X Mn + α(1 − X Mn )2 + RT ln γMn(s) .
(A.4) The last two terms in the above equation correspond to the excess partial free energy of Mn, i.e., RT ln γMn(s) . Thus, RT ln γMn(s) is linearly proportional to (1− X Mn )2 if we assume ◦ α and RT ln γMn(s) are composition independent. In this work, it was further assumed that α is a temperature independent pa◦ rameter and RT ln γMn(s) is expressed as a form of A + BT . All available experimental data (ln γMn(s) ) at several temperatures ◦ are shown in Fig. A.1. In order to determine α and RT ln γMn(s) , all experimental data which have been reported in the literature were examined but it was subsequently found that the data of Smith and Davies [54] were inconsistent with others at 1500 ◦ C and 1600 ◦ C, as seen in Fig. A.1. Therefore, the data of Smith et al. [54] were not considered for further evaluation. The effect of non-stoichiometry of pure MnO on the activity of MnO was considered from the result of Davies and Richardson [66] and the Gibbs free energy of the reaction (A.1) was taken from the FactSage thermochemical computing system [32]. After the optimization, it was found that the following parameters gave the best fit to the experimental data (J/mol): α = −151 463,
◦ RT ln γMn(s) = −(18 476.5 + 1.33716T ). (A.5)
Fig. A.2 summarizes the agreement between experimental and calculated activity coefficients for approximately 85
Fig. A.2. Agreement between experimental and calculated activity coefficients of Mn in the Pt–Mn alloys. The solid line represents the 1:1 corresponding line and dashed lines are ±25 pct error range.
experimental points. Model results in the majority of the data are in good agreement with experimental values over activity coefficients spanning six orders of magnitude and temperature in the range from 1300 to 1650 ◦ C, except for those of Smith and Davies [54]. References [1] S. Mizoguchi, J. Takamura, Proc. 6th Int. Iron and Steel Cong., ISIJ, Tokyo, 1990, p. 598. [2] H.S. Kim, H.G. Lee, W.G. Jung, ISIJ Int. 40 (2000) S82–S86. [3] H.S. Kim, H.G. Lee, K.S. Oh, Met. Mater.-Int. 6 (2000) 305–310. [4] H.S. Kim, H.G. Lee, K.S. Oh, Metall. Mater. Trans. A 32A (2001) 1519–1525. [5] H.S. Kim, H.G. Lee, K.S. Oh, ISIJ Int. 42 (2002) 1404–1411. [6] H. Amitani, K. Morita, N. Sano, ISIJ Int. 36 (1996) S26–S29. [7] M. Ito, K. Morita, N. Sano, ISIJ Int. 37 (1997) 839–843. [8] H. Tabaian, K. Morita, N. Sano, ISIJ Int. 36 (1996) 1313–1315. [9] T.G. Kim, W.K. Lee, J.H. Park, D.J. Min, H.S. Song, ISIJ Int. 41 (2001) 1460–1464. [10] A. Hasegawa, K. Morita, N. Sano, Tetsu-to-Hagan´e 81 (1995) 1109–1113. [11] Y.B. Kang, H.G. Lee, ISIJ Int. 45 (2005) 1543–1551. [12] Y.B. Kang, H.G. Lee, ISIJ Int. 45 (2005) 1552–1560. [13] Y.B. Kang, I.H. Jung, H.G. Lee, Critical thermodynamic evaluation and optimization of the MnO–SiO2 –TiO2 –“Ti2 O3 ” systems (in press). [14] A.D. Pelton, M. Blander, in: H.A. Fine, D.R. Gaskell (Eds.), Proc. 2nd Int. Conf. on Metall. Slags and Fluxes, AIME, Warrendale, PA, 1984, pp. 281–294. [15] A.D. Pelton, M. Blander, Metall. Trans. B 17B (1986) 805–815. [16] A.D. Pelton, S.A. Degterov, G. Eriksson, C. Robelin, Y. Dessureault, Metall. Mater. Trans. B 31B (2000) 651–659. [17] A.D. Pelton, P. Chartrand, Metall. Mater. Trans. A 32A (2001) 1355–1360. [18] G. Eriksson, A.D. Pelton, Metall. Trans. B 24B (1993) 795–805. [19] P. Chartrand, A.D. Pelton, J. Phase Equilib. 21 (2000) 141–147. [20] A.D. Pelton, CALPHAD 25 (2001) 319–328. [21] A. Lecerf, M. Rault, G. Villers, C. R. Acad. Sci. Paris 261 (1965) 749–752. [22] A. Lecerf, A. hardy, C. R. Acad. Sci. Paris 252 (1961) 131–133. [23] A. Hardy, A. Lecerf, M. Rault, G. Villers, C. R. Acad. Sci. Paris 259 (1964) 3462–3465.
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Critical thermodynamic evaluation and optimization of the MnO–“TiO2”–“Ti2O3” system Youn-Bae Kang a,∗ , In-Ho Jung b , Hae-Geon Lee c a Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 790-784, Republic of Korea b Research Institute of Industrial Science and Technology (RIST), Pohang, 790-600, Republic of Korea c Graduate Institute of Ferrous Technology (GIFT), Pohang University of Science and Technology (POSTECH), Pohang, 790-784, Republic of Korea
Received 5 February 2006; received in revised form 19 April 2006; accepted 8 May 2006 Available online 13 June 2006
Abstract A complete review, critical evaluation, and thermodynamic optimization of the phase equilibrium and thermodynamic properties of the MnO–“TiO2 ”–“Ti2 O3 ” systems at 1 bar pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model. The Gibbs energy of spinel, pyrophanite and pseudobrookite solid solutions were modeled using the Compound Energy Formalism, and rutile solid solution was treated as a simple Henrian solution. Manganosite solid solution was assumed to dissolve both Ti4+ and Ti3+ . A set of optimized model parameters for all phases was obtained which reproduces all available reliable thermodynamic and phase equilibrium data within experimental error limits from 25 ◦ C to above the liquidus temperatures over the entire composition ranges and in the range of pO2 from 10−20 to 10−7 bar. Complex phase relationships in these systems have been elucidated, and discrepancies among the data have been resolved. The database of model parameters can be used along with software for Gibbs energy minimization in order to calculate any phase diagram section or thermodynamic properties. c 2006 Elsevier Ltd. All rights reserved.
Keywords: MnO–TiO2 –Ti2 O3 ; Solution thermodynamics; Non-metallic inclusion; Phase diagram
1. Introduction Generally, non-metallic inclusions in steel products have been known to be harmful to the quality of final products. In order to overcome this, many investigations have been conducted about the removal of inclusions from molten steel during the refining process. Recently, an innovative concept has arisen in which non-metallic inclusions can be utilized to enhance the properties of steel products [1]. By controlling the chemistry, size and distribution of nonmetallic inclusions, those inclusions can be utilized as nuclei for transformation from austenite to α-ferrite. The size of the transformed α-ferrite is fine enough to enhance the steel strength. Among the non-metallic inclusions which can act as the nucleus, MnO–SiO2 –TiOx –MnS type inclusions ∗ Corresponding address: Centre de Recherche en Calcul Thermochimique ´ (CRCT), Ecole Polytechnique, Montreal, Quebec, Canada H3C 3A7. Tel.: +1 514 340 4711x4303; fax: +1 514 340 5840. E-mail address: [email protected] (Y.-B. Kang).
c 2006 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter doi:10.1016/j.calphad.2006.05.001
have been recognized as one of the most effective for grain refinement. Several investigations have been conducted to characterize the role of those inclusions on grain refinement [2–5]. However, unfortunately, even the phase relations for this inclusion system are not exactly known. To date, research has been performed on the liquidus and thermodynamic properties of MnO–SiO2 –TiOx –MnS system by several investigators [6–10]. However, in most of those studies, the oxygen potential, which plays an important role in the phase equilibria and thermodynamics of the system, was not controlled quantitatively and possible solid solutions were overlooked. Thus, in the present study, we attempt to investigate the phase equilibria and thermodynamics for the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system by experiment and thermodynamic modeling by considering the above-mentioned facts. Experimentally determined phase relations were reported in two previous articles [11,12]. In this article, thermodynamic modeling on the MnO–“TiO2 ”–“Ti2 O3 ” system will be reported based on the reported experimental data including
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Table 1 Optimized model parameters of the solutions in the MnO–“TiO2 ”–“Ti2 O3 ” system (G, H , ∆, L: J/mol, S, C p: J/mol K)a,b Manganosite s.s.: MnO–TiO2 –TiO1.5 G ◦ (TiO2 in manganosite s.s.) = G ◦ (TiO2 , rutile) + 22175.2 G ◦ (TiO1.5 in manganosite s.s.) = 0.5G ◦ (Ti2 O3 ) + 30024.4 Spinel s.s.: (Mn2+ )T [Mn2+ , Ti4+ , Ti3+ ]O 2 O4 G ◦ (Mn2 TiO4 , cubic) H◦298 K = −1744 003.42, S◦298 K = 170.41 C p = 168.15 + 0.0174T − 2556 424T −2 G MG = G ◦ (MnTi2 O4 ) H◦298 K = −1920 102.79, S◦298 K = 140.65 C p = 213.79 + 0.0093T − 2789 257.99T −2 − 750.22T −0.5 − 1968 461 709T −3 G ◦ (Mn2 TiO4 , cubic) =1/2(G MM + G MT ) + 2RT ln(1/2) G MT = G MG Pyrophanite s.s.: (Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B O3 G MT = G ◦ (MnTiO3 , pyrophanite) H◦298 K = −1363 254.23, S◦298 K = 104.04 C p = 121.67 + 0.0093T − 2188 232T −2 G GG = G ◦ (Ti2 O3 ) G GT = G GG ∆IL = G MG + G GT − G MT − G GG = 106 630.70 − 57.22T L Mn2+ ,Ti3+ :Ti4+ = L Mn2+ ,Ti3+ :Ti3+ = 8368 Pseudobrookite s.s.: (Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B 2 O5 G MT = G ◦ (“MnTi2 O5 ”) H◦298 K = −2286 501.78, S◦298 K = 163.66 C p = 247.15 − 4501 984T −2 − 1026.15T −0.5 + 455 637 600T −3 G ◦ (Ti3 O5 ) =1/2(G GT + G GG ) + 2RT ln(1/2) G GT = G GG ∆PB = G MG + G GT − G MT − G GG = −64 955.40 + 44.62T Rutile s.s.: TiO2 –TiO1.5 G ◦ (TiO1.5 in rutile s.s.) = 0.5G ◦ (Ti2 O3 ) + 22 592.93 + 2.59T Liquid oxide: MnO–TiO2 –TiO1.5 c For “TiO2 ”–“Ti2 O3 ” system 01 ◦ ∆gTiO ,TiO = 10 545, qTiO 1.5
2
1.5 ,TiO2
02 = −112 366, qTiO
1.5 ,TiO2
03 = 209 542.80, qTiO
1.5 ,TiO2
= −98 420
For MnO–“TiO2 ” system 01 02 ◦ ∆gMnO,TiO = −19 246.4, qMnO,TiO = −37483.83, qMnO,TiO = 10 460 2 2 2 For MnO–“Ti2 O3 ” and MnO–“TiO2 ”–“Ti2 O3 ” systems (Toop-like asymmetric with MnO singled out) No parameter was used. a The Gibbs energies of end-members of the solid and liquid solutions and of the other stoichiometric compounds in the MnO–TiO –Ti O system are taken from 2 2 3
Refs. [18]. b M, T and G denote Mn2+ , Ti4+ and Ti3+ , respectively. c Binary parameters of the Modified Quasichemical Model are defined in Ref. [16,17].
phase diagram and thermodynamic properties. All solid solutions, which correspond to typical inclusions in steels, are modeled as well as liquid oxide. The optimization of the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system will be presented in the next article in the present series [13]. 2. Thermodynamic models Thermodynamic models for the solution phases in the present system are summarized below, and all optimized model parameters are listed in Table 1.
2.1. Molten oxide For the molten oxide phase, the Modified Quasichemical Model [14,15] was used. This model has recently been further developed and summarized [16,17]. Short-range ordering is taken into account by considering second-nearestneighbor pair exchange reactions. For example, for the MnO–“TiO2 ”–“Ti2 O3 ” molten oxide, these reactions are: (A–A) + (B–B) = 2(A–B)
∆gAB
(1)
where A and B are Mn, Ti4+ and Ti3+ , and (i– j) represents a second-nearest-neighbor i– j pair. The parameters of the
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model are the Gibbs energies of these reactions, which may be expanded as empirical functions of composition. Although manganese can exist in the trivalent state in the slag at high oxygen partial pressures, in the present study only divalent manganese is considered, while trivalent and tetravalent titanium are considered to exist in the molten oxide. The MnO–“TiO2 ” and “TiO2 ”–“Ti2 O3 ” binary liquid oxides were already optimized using the Modified Quasichemical Model by Eriksson and Pelton [18] along with the secondnearest-neighbor “coordination numbers” of Mn, Ti4+ and Ti3+ , used in the Modified Quasichemical Model. However, in the present study, the binary model parameters for these molten oxides were re-optimized (1) to reproduce recent experimental data in the MnO–“TiO2 ” system [11] and (2) to give better results on higher order systems from the “TiO2 ”–“Ti2 O3 ” system. For the ternary MnO–“TiO2 ”–“Ti2 O3 ” system, a Toop-like “asymmetric approximation” [19,20] was used with MnO as the “asymmetric component” in order to estimate the Gibbs energy of the ternary liquid from the binary parameters. The MnO–“Ti2 O3 ” binary liquid oxide was treated as an ideal solution. No ternary parameters were used for the MnO–“Ti2 O3 ”–“TiO2 ” system. The optimized model parameters are listed in Table 1.
237
Ti3+ , respectively. Thus, end-members MM, MT and MG are 2+ Mn3 O2− 4 , MnTi2 O4 and MnTi2 O4 . Hence, this solution was actually treated as an ideal solution among these end-members. The schematic figure for the spinel solid solution is shown in Fig. 1. Mn2 TiO4 , which is a real neutral compound, is assumed as an equimolar ideal mixture between MT (MnTi2 O2+ 4 ) and 2− MM (Mn3 O4 ). That is: 1 1 G ◦ (Mn2 TiO4 ) = (G MM + G MT ) + 2RT ln . (4) 2 2 G ◦ (Mn2 TiO4 ) was taken from Eriksson and Pelton [18] but its H◦298 was adjusted during optimization. The optimized value of H◦298 K (−1744 kJ/mol) in the present study may be compared with the recommended value in Barin’s compilation (−1750 kJ/mol) [26]. S◦298 K was kept to be the same as that in Barin’s compilation (170.41 J/mol K). No Gibbs energy data for MnTi2 O4 has been known. Thus, G MG was first estimated by assuming that the Gibbs energy of formation of MnTi2 O4 from MnO and Ti2 O3 is equal to the Gibbs energy of formation of Mn2 TiO4 from 2MnO and TiO2 [27]. And the H◦298 K of MnTi2 O4 was then slightly varied during optimization. G MT was assumed to be the same as G ◦ (MnTi2 O4 ). No excess Gibbs energy parameter was required during the optimization.
2.2. Manganosite 2.4. Pyrophanite
From the EPMA analysis [11], it was observed that Ti (Ti4+ + Ti3+ ) can dissolve into pure MnO up to ∼3 mass pct and that the solubility changes with temperature and oxygen partial pressure. Therefore, the manganosite solid solution was modeled such that both Ti4+ and Ti3+ dissolve into pure MnO by assuming association of vacancy with Ti cations and random mixing in the cationic site in a rock salt structure.
Pyrophanite has an ilmenite structure (hexagonal, R3) with two cationic sublattices [28]. In the MnTiO3 –Ti2 O3 solid solution, Mn2+ and Ti3+ ions are assumed to mix randomly on one sublattice, while Ti3+ and Ti4+ mix randomly on the other sublattice as [24]:
2.3. Spinel
(Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B O3
Mn2 TiO4 and MnTi2 O4 form an extensive spinel solid solution [21]. MnTi2 O4 is a typical 2–3 type spinel while Mn2 TiO4 is a 2–4 type spinel. Spinel has an FCC structure, in which cations occupy octahedral and tetrahedral interstices. From X-ray diffraction studies, Mn2 TiO4 is almost an inverse spinel while MnTi2 O4 is a normal spinel [22,23]. Thus, the following model structure was considered as suggested by Pelton et al. [24]:
The Gibbs energy equation of the pyrophanite solid solution per formula unit is as follows:
(Mn2+ )T [Mn2+ , Ti4+ , Ti3+ ]O 2 O4
(2)
where the first and second brackets represent the tetrahedral site and octahedral site, respectively. The spinel solid solution was modeled in the framework of the Compound Energy Formalism (CEF) with two sublattices [25]. The Gibbs energy equation of the spinel solid solution per formula unit is as follows: G = yM G MM + yT G MT + yG G MG + 2RT(yM ln yM + yT ln yT + yG ln yG )
(3)
where yi and G ji represent the site fraction of cation i in the octahedral sublattice and standard Gibbs energy of endmember ji. The notation M, T and G means Mn2+ , Ti4+ and
(5)
A B A B G = yM yT G MT + yM yG G MG + yGA yTB G GT + yGA yGB G GG A A + RT(yM ln yM + yGA ln yGA )
+ RT(yTB ln yTB + yGB ln yGB ) + G E x
(6)
where all notations M, T and G are identical to those in spinel. Thus, end-members MT, MG, GT and GG are MnTiO3 , 1+ E x is an excess Gibbs energy MnTiO1− 3 , Ti2 O3 and Ti2 O3 . G between cations in a sublattice as: X X j j j G Ex = yki yli ym L kl:m + yki yl ym L k:lm (7) m
k
The schematic figure for the pyrophanite solid solution is shown in Fig. 1. G MT and G GG are the Gibbs energy of pure MnTiO3 and Ti2 O3 compounds, respectively, and are taken from Eriksson and Pelton [18]. H◦298 K and S◦298 K of MnTiO3 were slightly changed from those of Eriksson and Pelton during optimization. The optimized values of H◦298 K (−1363 kJ/mol) and S◦298 K (104.04 J/mol K) may be compared with the recommended values in Barin’s compilation (−1359 kJ/mol
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Fig. 1. Schematic figures of model structures (Compound Energy Formalism) for solid solutions in the Mn–Ti–O system. (a) Spinel solid solution. (b) Pyrophanite solid solution. (c) Pseudobrookite solid solution.
and 104.935 J/mol K) [26]. The following reciprocal reaction was considered: 1+ MnTiO3 + Ti2 O3 = MnTiO1− 3 + Ti2 O3
∆IL = G MG + G GT − G MT − G GG
(8)
where ∆IL is a model parameter which means a tendency to form a Mn2+ (A)–Ti3+ (B) and a Ti4+ (A)–Ti3+ (B) pair bond prior to a Mn2+ (A)–Ti4+ (B) and a Ti3+ (A)–Ti3+ (B) pair bond in the ilmenite structure. Either one of G MG or G GT may be assigned an arbitrary value while the other is then given by the reciprocal reaction parameter. In the present study, G GT was set to be the same as G GG . 2.5. Pseudobrookite Pseudobrookite is orthorhombic, Bbmm space group, with 4AB2 O5 formula unit in the unit cell. All the cations are in octahedral coordination. There are two kinds of octahedral site, with fourfold (A sites) and eightfold (B sites) multiplicity [29]. In the “MnTi2 O5 ”–Ti3 O5 solid solution, in which “MnTi2 O5 ” is actually unstable relative to dissociation into pyrophanite and rutile [11], Mn2+ and Ti3+ ions are assumed to mix randomly on one sublattice, while Ti3+ and Ti4+ mix randomly on the other sublattice as [24]: (Mn2+ , Ti3+ )A [Ti4+ , Ti3+ ]B2 O5
(9)
The Gibbs energy equation of the pyrophanite solid solution per formula unit is as follows:
A B A B G = yM yT G MT + yM yG G MG + yGA yTB G GT + yGA yGB G GG A A + RT(yM ln yM + yGA ln yGA )
+ 2RT(yTB ln yTB + yGB ln yGB )
(10)
where all notations M, T and G are same as those in spinel. Thus, end-members MT, MG, GT and GG are MnTi2 O5 , 1+ MnTi2 O2− and Ti3 O1− 5 , Ti3 O5 5 . Hence, this solution was actually treated as an ideal solution among these end-members. The schematic figure for the pseudobrookite solid solution is shown in Fig. 1. Ti3 O5 , which is a real neutral compound, is assumed to be an equimolar ideal mixture between GT 1− (Ti3 O1+ 5 ) and GG (Ti3 O5 ), similar to what was done for Mn2 TiO4 in spinel. That is: 1 1 ◦ G (Ti3 O5 ) = (G GT + G GG ) + 2RT ln (11) 2 2 G ◦ (Ti3 O5 ) was taken from Eriksson and Pelton [18]. The Gibbs energy of the hypothetical “MnTi2 O5 ” was taken from Pelton et al. [24] and its H◦298 K and S◦298 K were slightly adjusted during optimization. The following reciprocal reaction was considered: 2− 1+ MnTi2 O5 + Ti3 O1− 5 = MnTi2 O5 + Ti3 O5
∆PB = G MG + G GT − G MT − G GG
(12)
where ∆PB is a model parameter which has a similar meaning to ∆IL in the pseudobrookite structure. Either G MG or G GT may be assigned an arbitrary value while the other is then given by the reciprocal reaction parameter. In the present study, G GT
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was set to be identical to G GG . No excess Gibbs energy was required. The solution models for spinel, pyrophanite (ilmenite structure) and pseudobrookite solid solutions are essentially identical to models developed by Pelton et al. [24] and successfully applied in the Fe–Ti–O [30] and Mg–Ti–O systems [24]. 2.6. Rutile TiO2 in the form of rutile has non-stoichiometry toward the Ti2 O3 direction and is usually expressed as TiO2−δ . Defect mechanisms in rutile have not yet been fully confirmed. Eriksson and Pelton [18] modeled the rutile solid solution using a simple Henrian solution model while Waldner and Eriksson [31] used the CEF with (Ti4+ )(O2− , Va2− )2 structure. Since the defect mechanism is not clear, we prefer to use the rather simple model. Therefore, in the present study, the same model of Eriksson and Pelton [18] was used but temperature dependence was assigned to the Henrian activity coefficient of TiO1.5 in order to reproduce all experimental data over the wide range of temperature. Several Magn´eli phases (Tin O2n−1 , n ≥ 4) were considered as stoichiometric compounds. All model parameters optimized in the present study are listed in Table 1. All thermodynamic calculations and optimization were carried out using the FactSage thermochemical computing system [32].
Fig. 2. Equilibrium oxygen partial pressure of rutile s.s. in equilibrium with the highest Magn´eli phase (“Ti20 O39 ”). Experimental data are taken from several sources [33–42]. The line is calculated from the model in the present study.
3. Critical evaluation and optimization for the MnO– “TiO2 ”–“Ti2 O3 ” system The MnO–“TiO2 ” system and the “TiO2 ”–“Ti2 O3 ” system were optimized by Eriksson and Pelton [18]. Gibbs energies of all Magn´eli phases were also evaluated and they were used in the present study. In the present study, the MnO–“TiO2 ” system was re-optimized and extended to the MnO–“TiO2 ”–“Ti2 O3 ” system by considering phase equilibria at low pO2 . The rutile solid solution and molten oxide in the “TiO2 ”–“Ti2 O3 ” system was revised to give better results. Spinel, pyrophanite and pseudobrookite in the MnO–“TiO2 ”–“Ti2 O3 ” system were once modeled by Pelton et al. [24]. However, they were reoptimized in the present study by considering new experimental data [11]. 3.1. Revision of the “TiO2”–“Ti2 O3” system Several studies have been conducted to measure the nonstoichiometry of rutile and oxygen partial pressure at the lower boundary of rutile (two-phase equilibrium with rutile and the highest Magn´eli phase, i.e., “Ti20 O39 ” [18]). Figs. 2 and 3 show calculated oxygen partial pressure and non-stoichiometry as functions of reciprocal temperature along with experimental data from several investigators [33–42]. These data were used to optimize the model parameters for the rutile solid solution. In order to reproduce the non-stoichiometry of rutile at all temperature ranges, a temperature dependent Henrian activity coefficient was necessary.
Fig. 3. Non-stoichiometry of rutile s.s. (TiO2−δ ) in equilibrium with the highest Magn´eli phase (“Ti20 O39 ”) as a function of temperature. Experimental data are taken from several sources [33–39]. The line is calculated from the model in the present study.
During optimization in the MnO–“TiO2 ”–“Ti2 O3 ” system, an unexpected liquid (metastable) immiscibility was calculated near the Ti2 O3 rich region. This resulted from the model parameters in the “TiO2 ”–“Ti2 O3 ” system optimized by Eriksson and Pelton [18]. Therefore, in the present study, the model parameters for the “TiO2 ”–“Ti2 O3 ” liquid oxide were slightly modified so as not to induce the abovementioned immiscibility. The calculated phase diagram of the “TiO2 ”–“Ti2 O3 ” system using the revised model parameters is shown in Fig. 4 along with experimental data [33–38,43,44]. The calculated phase diagram does not change significantly from the phase diagram in Eriksson and Pelton [18] but a better result is obtained in the higher order system. 3.2. Phase equilibria in the MnO–“TiO2”–“Ti2 O3” system Fig. 5 shows a calculated isothermal section of the MnO–“TiO2 ”–“Ti2 O3 ” system at 1400 ◦ C. At this temperature, all phases in this system appear except for molten oxide. Thin lines are calculated sections of the phase equilibria at several
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Fig. 4. Calculated phase diagram of the “Ti2 O3 ”–“TiO2 ” system. Liquid and rutile solutions were optimized in the present study and Gibbs energies of solid compounds were taken from Eriksson and Pelton [18]. Experimental data are taken from several sources [33–39,43,44].
Fig. 5. Calculated isothermal section in the MnO–“TiO2 ”–“Ti2 O3 ” system at 1400 ◦ C. Thin lines represent sections of phase equilibria under specified oxygen partial pressures (log pO2 (bar)). Dashed lines denote sections of phase equilibria under pCO/pCO2 = 1, 9 and C/CO equilibrium, respectively.
oxygen partial pressures. Moreover, the three dashed lines represent sections of the phase at pCO/pCO2 = 1, 9 and C/CO equilibrium conditions. Since manganese is only in its divalent state under the oxygen partial pressure considered in the present study, all these sections start from MnO. However, depending on the oxygen partial pressure, each section ends at a different point on the “TiO2 ”–“Ti2 O3 ” binary edge. For the condition of pCO/pCO2 = 1 (log pO2 = −8.62), the limiting point on the “TiO2 ”–“Ti2 O3 ” binary is very close to pure “TiO2 ”. Thus, the ternary system under this condition (pCO/pCO2 = 1) can be reasonably considered as the MnO–“TiO2 ” binary system. Only the spinel s.s., which is close to stoichiometric Mn2 TiO4 , and the pyrophanite s.s., which is close to stoichiometric MnTiO3 , are intermediate solid phases. The pseudobrookite s.s. is not stable under this condition. However, at pCO/pCO2 = 9 (log pO2 = −10.53), the section shifts slightly to the Ti2 O3 direction due to decreasing oxygen partial pressure (about two orders of magnitude). Thus, in this section, the pseudobrookite phase, whose composition lies
between hypothetical “MnTi2 O5 ” and Ti3 O5 , becomes stable although the limiting point on the “TiO2 ”–“Ti2 O3 ” binary is still in the rutile phase region. On the other hand, under the C/CO equilibrium condition, the oxygen partial pressure decreases drastically (log pO2 = −16.13) so that the limiting point locates at Ti3 O5 . Thus, the section shifts more to the direction of the MnO–“Ti2 O3 ” side and the stable regions of spinel and pyrophanite s.s. are wider than under previous conditions when this ternary system is projected onto the MnO–“TiO2 ” side from the oxygen corner. In Fig. 6(a)–(c), these three sections (pCO/pCO2 = 1, 9 and C/CO equilibrium) are drawn as typical phase diagrams (composition versus temperature) using the thermodynamic models with the optimized model parameters. Experimentally determined phase boundary data of the present authors [11] are also plotted. Equilibrium oxygen partial pressures at several temperatures were calculated using the F*A*C*T database [32] and are specified in the figures. The model parameters were optimized by the following steps. First, the model parameters for MnO–“TiO2 ” in the molten oxide were optimized to reproduce the MnO activity, which will be shown later, with simultaneous consideration of the liquidus of both manganosite and rutile. Then, the model parameters of manganosite, H◦298 K of Mn2 TiO4 in the spinel and H◦298 K of MnTiO3 in the pyrophanite were changed to reproduce the melting temperature and solid solubilities in each solid solution at pCO/pCO2 = 1. Experimental data at low oxygen partial pressure (pCO/pCO2 = 9 and C/CO equilibrium) were then used to optimize other model parameters of the spinel, pyrophanite and pseudobrookite solid solutions. For the optimization of phase equilibria among solid solutions at low temperature and low oxygen partial pressure, phase diagram data by Grey et al. [45] and the valency distribution in spinel by Amitani et al. [6] were also considered. From thermodynamic optimization, which can reproduce the above-mentioned phase diagram data, activities and so on (discussed in the next section), it has been predicted that Mn2 TiO4 melts congruently at 1463 ◦ C under pCO/pCO2 = 1. This is in agreement with what was reported by Grieve and White (congruent melting at 1460 ◦ C) [46], while Leusmann reported congruent melting at 1420 ± 10 ◦ C [47]. On the other hand, from the thermodynamic calculation, MnTiO3 melts at 1453 ◦ C (pCO/pCO2 = 1) congruently. This result is in conflict with those of Grieve and White (incongruent melting at 1360 ◦ C) and Leusmann (congruent melting at 1410 ± 10 ◦ C). However, in the previous study of the present authors [11], MnTiO3 never melted at 1400 ◦ C under pCO/pCO2 = 1 and 9. As discussed in a previous article [11], “MnTi2 O5 ” is unstable in the MnO–“TiO2 ” system, so the pseudobrookite phase does not appear in Fig. 6(a). However, as the oxygen partial pressure decreases, the pseudobrookite phase appears in between pyrophanite and rutile. From the experimental data, it can be inferred that pseudobrookite melts incongruently between 1450 ◦ C and 1500 ◦ C at pCO/pCO2 = 9 [11]. This melting behavior was well reproduced by thermodynamic optimization (incongruent melting at 1498 ◦ C).
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Fig. 6. Optimized phase diagram sections in the MnO–“TiO2 ”–“Ti2 O3 ” system under various gas conditions. Experimental data are taken from Kang and Lee [11]. The thick dashed line indicates the boundaries above which all oxides are no longer stable, and are hence reduced to metallic liquid (Zero Phase Fraction (ZPF) line [49] of metallic liquid). The dotted lines above the ZPF line are, therefore, metastable phase boundaries calculated without considering metallic liquid. (a) pCO/pCO2 = 1. (b) pCO/pCO2 = 9. (c) C/CO equilibrium.
As shown in Fig. 6(b), dissolution of Mn in the Ti-rich region (n Ti /(n Mn + n Ti ) > 0.95) in the temperature range 1400 ◦ C to 1550 ◦ C was observed in the previous study [11]. Grey et al. [45] reported that Mn dissolves in several Magn´eli phases at 1200 ◦ C accompanied by stabilizing the Magn´eli phases at a slightly higher oxygen partial pressure. Therefore, although the oxygen partial pressure is slightly higher than for the Magn´eli phases to be stable, it is thought that the Mn dissolves in the Magn´eli phases, stabilizing them even slightly higher oxygen partial pressure. However, this was not considered in the present study since the solubilities are rather small and the phase equilibria are still unclear. The phase diagram under C/CO equilibrium conditions in Fig. 6(c) shows that the oxide phases are reduced to metallic liquid due to the oxygen partial pressure being too low. In the calculation, thermodynamic data of the metallic phases were taken from Saunders [48]. The dashed line represents the ZPF (Zero Phase Fraction) line [49] of metallic liquid, so the oxide phases are reduced above this line. Experimental data are available for only the sub solidus region, thus the binary model parameter for the MnO–“Ti2 O3 ” in the molten oxide could not be evaluated. However, in the
optimization for the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system, it was found that setting zero for the binary model parameter was enough to reproduce experimental data under C/CO equilibrium conditions, which will be shown in the forthcoming article [13] on the thermodynamic optimization for the MnO–SiO2 –“TiO2 ”–“Ti2 O3 ” system. Fig. 7(a)–(d) show the thermodynamically calculated phase diagram of the MnO–TiOx system under different fixed oxygen partial pressures from 10−5 to 10−20 bar. It was assumed that Mn3+ in the molten oxide and the solid oxides was negligible even at pO2 = 10−5 bar. These figures show how subsolidus phase equilibria vary with oxygen partial pressure and temperature. Generally, the n Ti /(n Mn +n Ti ) cationic molar ratio increases in the spinel, pyrophanite and pseudobrookite phases as the oxygen partial pressure decreases. This can be interpreted as Ti3+ stabilization in the solid solutions at low oxygen partial pressure. More clearly, this can be seen in Fig. 8(a)–(h), in which the phase equilibria of the Mn–Ti–O system are presented as n Ti /(n Mn +n Ti ) cationic molar ratio versus oxygen partial pressure at several temperatures. All lines are calculated from the thermodynamic models and the optimized parameters. Available experimental data reported by several researchers as
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Fig. 7. Predicted phase diagrams of the Mn–Ti–O system under various oxygen partial pressures. (a) pO2 = 10−5 bar. (b) pO2 = 10−10 bar. (c) pO2 = 10−15 bar. (d) pO2 = 10−20 bar.
well as the present authors are also compared, although the measured liquidus data by Amitani et al. [6], Kim et al. [9], Ohta and Morita [50] were not used in the optimization as discussed in a previous article [11]. Original experimental data by Amitani et al. [6] at 1300 ◦ C, deduced from their valency analysis, were plotted as open circles. However, their data were adjusted and re-plotted as half-filled circles. The reason will be discussed in Section 3.3. In Fig. 9, predicted oxygen partial pressures in a number of three-phase equilibria are shown until the equilibria are terminated by the molten oxide. 3.3. Activities and other thermodynamic properties in the MnO–“TiO2”–“Ti2 O3” system A number of investigations have been performed to measure the activity of MnO in the MnO–TiOx system [9,50–53]. Detailed experimental conditions for each experiment are summarized in Table 2. Fig. 10 shows the measured activity of MnO in the MnO–TiOx system. All these investigations employed chemical equilibration among gas/metal/oxide at high temperature. Usually Pt was used as reference metal but Cu or Ag was adopted in some investigations. During the evaluation for these investigations, it was found that the results of Martin and
Bell [52], K¨arsrud [53] and Kim et al. [9] had to be corrected because of the activity coefficient of Mn in the reference alloy they used. Martin and Bell [52] obtained the activity of MnO using γMn(Pt) of an earlier study by Smith and Davies [54]. However, the measured γMn(Pt) of Smith and Davies seems considerably lower than that of other investigations (see Appendix A). Thus, in the present study, the activity data of MnO from the investigation of Martin and Bell were not used directly but rather were corrected using newly evaluated activity–composition relations in the Pt–Mn alloy, which can reproduce a majority of the measured activity coefficient data within experimental error limits (see Appendix A). The result of K¨arsrud [53] was also re-interpreted. This is because they used γMn(Pt) measured by Abraham et al. [55]. However, they misused it. Abraham et al. [55] reported γMn(Pt) at 1500 ◦ C, in which the standard state of Mn was pure solid. However, K¨arsrud used the same relation as if its standard state was pure liquid Mn, for their calculation of the activity of Mn. Therefore, both previously reported activity data were corrected using the newly obtained γMn(Pt) expression (see Appendix A). On the other hand, Kim et al. [9] did an experiment using gas (pCO/pCO2 = 99, which corresponds to pO2 = 7.3 × 10−13 bar)/silver/oxide equilibration at 1450 ◦ C to measure the activity of MnO in molten oxide. However, as is seen in Fig. 8(e), the oxide composed of MnO and TiOx
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Y.-B. Kang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 235–247 Table 2 Detailed experimental conditions for activity measurements in the MnO–TiOx system Author Rao and Gaskell Rao and Gaskell Martin and Bell K¨arsrud Ohta and Morita Kim et al.
T (◦ C)
pO2 (bar)
Reference metal
Source of γMn
1500 1550 1500 1500 1600 1450
10−7 –10−6
Pt Pt Pt Pt Cu Aga
Rao and Gaskell [61] Rao and Gaskell [61] Smith and Davies [54] Abraham et al. [55] Ohta and Morita [50] Ito et al. [7]
7.0 × 10−7 1.1–1.6 × 10−6 1.3 × 10−7 1.9 × 10−10 7.3 × 10−13
a γ ◦ at 1450 ◦ C in their study was extrapolated from the γ ◦ at 1400 ◦ C by Ito et al. [7] assuming regular solution behavior of the Ag–Mn alloy. Mn Mn
Fig. 8. Calculated phase diagrams of the Mn–Ti–O system with oxygen partial pressure as an axis at several temperatures. Experimental data are taken from several sources [6,9,11,45,50]. All symbols mean experimentally measured phase boundary except for those in Fig. 8(a). (a) At 1200 ◦ C. (b) At 1300 ◦ C. (c) At 1350 ◦ C. (d) At 1400 ◦ C. (e) At 1450 ◦ C. (f) At 1500 ◦ C. (g) At 1550 ◦ C. (h) At 1600 ◦ C.
does not melt at this condition. It can be inferred from Fig. 8(e) that there should be two phase equilibria (monoxide + spinel, spinel + pyrophanite etc.) under this condition and the experimental data of Kim et al. also do not vary smoothly. Moreover, ◦ in their activity calculation, γMn(Ag) reported by Ito et al. [7] at ◦ 1400 C was extrapolated by assuming regular solution behavior between Ag and Mn. However, Jung [56] did measure the ◦ activity coefficient of Mn in Ag at 1450 ◦ C and reported γMn(Ag) ◦ at 1450 C is 0.596 (liquid Mn standard state). This value is quite different from the extrapolated value (0.395). Therefore,
◦ the measured γMn(Ag) value by Jung was used to re-calculate the activity of MnO reported by Kim et al. [9] The maximum difference of the activities after these corrections was ∼0.2. The calculated activity of MnO in the MnO–TiOx system is shown in Fig. 10 along with the reported experimental data. Data of Martin and Bell [52], K¨arsrud [53] and Kim et al. [9] were corrected values, as mentioned above. It is thought that the activity data of Kim et al. [9] are not for molten oxide but for several solid solutions. It seems that the temperature dependence of the activities is not conspicuous.
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Fig. 8. (continued)
Fig. 9. Predicted equilibrium oxygen partial pressures in several monovariant equilibria in the Mn–Ti–O system until the equilibria are terminated by the molten oxide.
Amitani et al. [6] measured the distribution of Ti valences in the spinel s.s. in equilibrium with manganosite by employing chemical equilibration of Cu–Mn alloy/manganosite/spinel at 1300 ◦ C followed by wet chemical analysis. Oxygen partial pressures in the systems were then estimated from the equilibrium reaction Mn(in Cu) + 1/2O2 (g) = MnO(s), for
Fig. 10. Activity of MnO (with respect to the pure solid MnO) in the MnO–TiOx system. Experimental data are taken from several sources [9,50– 53]. Lines are calculated from the model in the present study under the same oxygen partial pressures employed in the experiments.
which the Mn contents in the alloys were analyzed. They reasonably assumed that the activity of MnO(s) is unity. Thus, in order to estimate the oxygen partial pressure, the activity coefficient of Mn should be known. In their estimation, they used the activity coefficient of Mn in Cu–Mn alloy which
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FactSage thermochemical computing system. All reliable experimental data are reproduced within experimental error limits by a few model parameters. The phase diagrams of the MnO–“TiO2 ”–“Ti2 O3 ” system under different oxygen partial pressures have been proposed based on recently measured experimental data and thermodynamic modeling. Moreover, measured activities and valences of Ti in oxide systems could be reproduced well. With the present optimized database, it is now possible to calculate any phase diagram section of the MnO–“TiO2 ”–“Ti2 O3 ” system under various oxygen partial pressure at all compositions and temperatures. By coupling the presently developed database with other evaluated F*A*C*T databases for metallic solutions, gases, etc., complex slag/metal/solid/gas equilibria can be computed. Fig. 11. Distribution of Ti valences in the spinel s.s. in equilibrium with the manganosite s.s. at 1300 ◦ C. Experimental data are taken from Amitani et al. [6] (open symbols) and they are adjusted (half-filled symbols). The line is calculated from the model in the present study. See Section 3.3 for details of the adjustment.
was derived from the activity measurement by Spencer and ◦ Pratt [57] for the concentrated region of Mn, while γMn in Cu suggested by Oishi and Ono [58] was applied in the dilute region of Mn. Fig. 11 shows their evaluated Ti4+ /Ti3+ in the spinel as a function of oxygen partial pressure at 1300 ◦ C, as open symbols. Generally, increasing oxygen partial pressure results in increasing Ti4+ /Ti3+ ratio in spinel s.s. However, the open symbols do not show continuous behavior although there is no phase transformation. This is because they used an inconsistent set of γMn(Cu) over Mn concentration in Cu. As is shown in Fig. 11, agreement between open symbols and thermodynamic calculation in the present study is only good in low oxygen partial pressure (the concentrated region of Mn in Cu). Therefore, in order to calculate the oxygen partial pressure in their study more exactly, it is necessary to use a consistent set of γMn(Cu) during the calculation. In the present study, the Cu–Mn thermodynamic optimization, which was recently reported by Liu et al. [59], was used to evaluate γMn(Cu) . Using this new γMn(Cu) , oxygen partial pressures in the study of Amitani et al. [6] were re-calculated and the results plotted in Fig. 11 as half-filled symbols. It is clearly shown that Ti4+ /Ti3+ increases continuously and the re-evaluated results are in good agreement with the calculation. Also, from the redox reaction of Ti in spinel, it is expected that the slope of the line in Fig. 11 should be 1/4 if activity coefficients of Ti3+ and Ti4+ are reasonably assumed to be unity. The present thermodynamic calculation shows the slope close to 1/4 as seen in Fig. 11. TiO2 (Ti4+ ) = TiO1.5 (Ti3+ ) + 1/4O2 .
(13)
4. Conclusions A complete critical evaluation of all available phase diagram and thermodynamic data for the MnO–“TiO2 ”–“Ti2 O3 ” system was carried out, and a database of optimized model parameters was prepared at 1 bar total pressure using the
Acknowledgements ´ The authors wish to thank Prof. Arthur D. Pelton (Ecole Polytechnique de Montr´eal, Canada) for valuable discussions during the present study. Appendix A. Activity–composition relationship in the Pt– Mn alloy Much research has been conducted to measure the activity of MnO in oxide solution, which are either liquid phases or solid phases, by employing chemical equilibration among gas/slag(oxide)/reference metals. Usually, Pt or Cu has been used as the reference metal since those metals are noble enough not to dissolve into the oxide phase. A number of researches have used Pt as a reference metal to measure the activity of MnO in oxide solutions. In order to calculate the activity of MnO in oxide, the following reaction can be considered. Mn(s, in Pt–Mn alloy) + 1/2O2 (gas) ◦ = MnO(s, in oxide) ∆gA.1 ◦ ∆gA.1 aMnO . K A−1 = = exp − RT aMn ( pO2 )1/2
(A.1) (A.2)
◦ can be found in literature or thermodynamic databases ∆gA.1 and pO2 is usually controlled during experiments. Therefore, the activity of Mn in the Pt–Mn alloy must be known as a function of composition and temperature. Several researchers have investigated the activity–composition relation in Pt–Mn alloy at various temperatures [54,55,60–65]. However, some results of those researches are sometimes inconsistent with each other, and temperatures at which the activity–composition relation can be applied are discrete at 1300 ◦ C, 1400 ◦ C, 1500 ◦ C, 1550 ◦ C, 1600 ◦ C and 1650 ◦ C. Therefore this study attempted to compare all available experimental data and to express the activity–composition relation as a function of composition and temperature. The Gibbs free energy of Pt–Mn solid solution in the Pt-rich region can be expressed as follows, assuming that it behaves as a regular solution: ◦ ◦ ◦ G = n Pt gPt + n Mn (gMn + RT ln γMn(s) ) + RT(n Pt ln X Pt + n Mn ln X Mn ) + αn Pt n Mn /(n Pt + n Mn )
(A.3)
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Fig. A.1. Activity coefficients of Mn(relative to pure solid Mn) in Pt–Mn alloys at several temperatures. Experimental data are taken from several sources. The lines are calculated in the present study [54,55,60–65]. ◦ where γMn(s) is a Henrian activity coefficient of Mn in the Ptrich solution relative to pure solid Mn and α is a regular solution parameter. The purpose of this appendix is an evaluation of ◦ the Henrian activity coefficient, γMn(s) , and the regular solution parameter α in a wide range of temperatures to express the activity coefficient of Mn in Pt–Mn alloy by fitting the available and reliable experimental data. The partial Gibbs free energy of Mn can be derived from Eq. (A.3) as follows: ◦ ◦ gMn = gMn + RT ln X Mn + α(1 − X Mn )2 + RT ln γMn(s) .
(A.4) The last two terms in the above equation correspond to the excess partial free energy of Mn, i.e., RT ln γMn(s) . Thus, RT ln γMn(s) is linearly proportional to (1− X Mn )2 if we assume ◦ α and RT ln γMn(s) are composition independent. In this work, it was further assumed that α is a temperature independent pa◦ rameter and RT ln γMn(s) is expressed as a form of A + BT . All available experimental data (ln γMn(s) ) at several temperatures ◦ are shown in Fig. A.1. In order to determine α and RT ln γMn(s) , all experimental data which have been reported in the literature were examined but it was subsequently found that the data of Smith and Davies [54] were inconsistent with others at 1500 ◦ C and 1600 ◦ C, as seen in Fig. A.1. Therefore, the data of Smith et al. [54] were not considered for further evaluation. The effect of non-stoichiometry of pure MnO on the activity of MnO was considered from the result of Davies and Richardson [66] and the Gibbs free energy of the reaction (A.1) was taken from the FactSage thermochemical computing system [32]. After the optimization, it was found that the following parameters gave the best fit to the experimental data (J/mol): α = −151 463,
◦ RT ln γMn(s) = −(18 476.5 + 1.33716T ). (A.5)
Fig. A.2 summarizes the agreement between experimental and calculated activity coefficients for approximately 85
Fig. A.2. Agreement between experimental and calculated activity coefficients of Mn in the Pt–Mn alloys. The solid line represents the 1:1 corresponding line and dashed lines are ±25 pct error range.
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