Coupled experimental study and thermodynamic modeling of the MnO-Mn2O3-Ti2O3-TiO2 system

Calphad 66 (2019) 101639

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Coupled experimental study and thermodynamic modeling of the MnO-Mn2O3-Ti2O3-TiO2 system

T

Sourav Kumar Pandaa, Pierre Hudona, In-Ho Jungb,* a

Department of Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, QC, H3A 0C5, Canada Department of Materials Science and Engineering, and Research Institute of Advanced, Materials (RIAM), Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, South Korea

b

ARTICLE INFO

ABSTRACT

Keywords: MnO–Mn2O3–TiO2–Ti2O3 Pseudobrookite Ilmenite Spinel Phase diagram Thermodynamic modeling

A coupled experimental study and thermodynamic modeling of the MnO-Mn2O3-Ti2O3-TiO2 system at 1 bar total pressure is presented. Classical equilibration and quenching experiments followed by the phase analysis using electron probe microanalysis (EPMA) and X-ray diffraction (XRD) were employed to obtain equilibrium compositions of the liquid and solid solutions in air. The molten oxide phase was described by using the Modified Quasichemical Model which considers short-range ordering, and the Gibbs energies of the solid solutions (pseudobrookite, ilmenite and spinel) were described using the Compound Energy Formalism based on their crystal structures. A set of optimized model parameters of all phases was obtained, which reproduces all available and reliable thermodynamic data and phase diagrams within experimental error limits from 298 K (25 °C) to above the liquidus temperatures over the entire range of composition under oxygen partial pressures from metallic saturation to 1 bar. The complex phase relationships in the system have been elucidated and discrepancies among the experimental data have been resolved. The database of the model parameters can be accessed by FactSage software with the Gibbs energy minimization to calculate any phase diagrams and thermodynamic properties of the MnO-Mn2O3-Ti2O3-TiO2 system.

1. Introduction The MnO–Mn2O3–TiO2–Ti2O3 system is significant in steelmaking and advanced ceramics. Titanium-containing steels are used for making corrugated plate type heat exchangers (PHE) for marine applications [1]. It is also used in the heat transfer tubes for the multi-stage flash (MSF) and multi-effect desalination (MED) process for seawater desalination and condensers in power plants. However, the press patterns used by PHE makers are so complicated that the titanium sheet requires good formability and toughness. For this reason, acicular ferrite microstructure is preferred which forms on the interior of original austenite grains by nucleating heterogeneously on non-metallic inclusions produced during deoxidation of steel [2–5]. Depending upon the deoxidants (Mn/Si, Al etc.), different kinds of Ti oxide inclusions can be formed in Ti containing steel, and the chemistry, size and distribution of these inclusions must be well controlled to produce a uniform acicular ferrite microstructure. One of the likely mechanisms for intergranular ferrite (IGF) is the development of a Mn-depleted zone (MDZ) around the non-metallic inclusions by Mn absorption into the inclusions [6–12]. As Mn is one of the austenite stabilizing elements, depletion of

*

Mn around the inclusions can lead to decrease of the thermodynamic stability of austenite, which increase the driving force of ferrite nucleation. Therefore, information on phase equilibria and stability of Ticontaining oxide inclusions at any oxygen potential and temperature is important to control the nucleation of acicular ferrite and produce flat, beautiful and uniform Ti containing steel sheets. In the present study, all the experimental thermodynamic properties and phase diagram data for the MnO-Mn2O3-TiO2-Ti2O3 system at 1 bar total pressure with oxygen partial pressures from metallic saturation to 1 bar were critically evaluated and optimized to obtain the models with a set of model parameters able to reproduce all reliable experimental data in the system. In addition, phase equilibration experiments of the Mn-Ti-O system in air atmosphere were performed using the classical equilibration and quenching method followed by phase identification and analysis using the Electron Probe Micro-Analyzer (EPMA) and Xray diffraction (XRD) to provide more accurate description of the entire oxide system. This is part of a wide research project to extend and replace the current FACT oxide database (FToxid) in FactSage thermochemical software [13] toward higher Mn and Ti oxide regions. All the thermodynamic calculations of the present study were performed using

Corresponding author. E-mail address: [email protected] (I.-H. Jung).

https://doi.org/10.1016/j.calphad.2019.101639 Received 21 November 2018; Received in revised form 23 June 2019; Accepted 25 June 2019 0364-5916/ © 2019 Elsevier Ltd. All rights reserved.

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Table 1 Summary of the previous experimental phase diagram studies for the MnO-Ti2O3-TiO2 system. Technique

Atmosphere

Temperature, K (°C)

Crucible

Reference

TA, OM QM, XRD, CA

N2 or Vacuum CO2/H2 (log pO2 = −14 to −18 bar)

1573–1773 (1300–1500) 1473 (1200)

Mo Mo

[16] [17]

1773 (1500)

Pt

[21]

1723 (1450)

Mo

[24]

QM, XRD, EPMA, CA DTA, QM, XRD QM, XRD, EMF

QM, XRD, AAS, GA, CA

Air and CO/CO2 (up to 10−5 bar) N2, FeO-Fe3O4 buffer Air and Ar/H2/H2O (log pO2 = – 2 to −21 bar)

1473 (1200) 1473–1873 (1200–1600) 1273 (1000)

CO/CO2 = 0.1 (log pO2 = −5 bar)

QM, XRD, CA QM, XRD, CA

Ar and Saturating Oxide CO/CO2 = 10, 30 (log pO2 = – 10.64, – 9.72 bar)

1673 (1400) 1673, 1873 (1400, 1600)

QM, EPMA

CO/CO2 = 1, 9 (log pO2 = – 8.62, −16.13 bar) and C/CO (log pO2 = −16.13 bar)

1573–1823 (1300–1550)

QM, XRD, CA, AAS

CO/CO2 (log pO2 = – 12.14 bar)

Al2O3 Pt ZrO2

Pt Ni, Pt Mo, Pt

[18] [19] [20]

[22] [23] [15]

TA: Thermal Analysis, OM: Optical Microscopy, DTA: Differential Thermal Analysis, QM: Quenching Method, XRD: X-Ray Diffraction, EPMA: Electron Probe Micro Analysis, CA: Chemical Analysis, AAS: Atomic Absorption Spectroscopy, GA: Gravimetric Analysis.

the FactSage thermochemical software [13].

isopropyl alcohol (< 0.02 vol% H2O) for 30 min. The alcohol was driven off under a lamp and the starting materials were stored in the drying oven at 393 K (120 °C). Prior to usage, the starting material were taken out from the drying oven and allowed to reach room temperature in a desiccator. In order to prevent any contamination from crucible materials, all the experiments were carried out using pure Pt capsules (length = 10 mm, inner diameter = 2.87 mm, outer diameter = 3 mm). The capsules were sealed from one end with a three-corner weld using a PUK 04 micro-welder (Lampert, Germany) and their integrities were checked using an optical microscope. About 50–90 mg of starting materials were tightly packed into each Pt capsule, depending upon the size and density of the starting material. The other side of the Pt capsule was crimped slightly to prevent any spilling of the starting material during the run and to make sure the equilibration under air atmosphere.

2. Previous studies The MnO–Mn2O3–TiO2–Ti2O3 system was first reviewed by Eriksson and Pelton [14] and then discussed thoroughly by Kang and Lee [15]. The experimental conditions of all previous phase diagram studies [15–24] are summarized in Table 1. Due to the multiple oxidation states of Mn and Ti (Mn2+, Mn3+, Mn4+, Ti2+, Ti3+ and Ti4+), the specification of oxygen partial pressure is very important in the experiments. However, atmospheric condition was not clearly defined in several studies, and there are controversies between experimental data. For example, Grieve and White [16] and Leusmann [19] reported different melting point of MnTiO3 and eutectic reactions (incongruent melting at 1633 K (1360 °C) by Greive and White and congruent melting at 1683 K (1410 °C) by Leusmann). The phase diagram studies by Grieve and White [16], Leusmann [19] and Ito et al. [22] did not specify the actual oxygen partial pressures and did not consider solid solutions. The detail discussion of the previous experiments can be found in Kang and Lee [15].

3.2. Equilibration/quenching experiments The quenching experiments were conducted in a vertical tube furnace (DelTech®, USA) equipped with a dense alumina reaction tube. In order to make the samples be equilibrated in air, the end of the reaction tube was open. A Pt30Rh-Pt6Rh (type B) thermocouple connected to a PID (Proportional-Integral-Differential) controller was used to keep the temperature within ± 1 K. Another Pt30Rh-Pt6Rh (type B) thermocouple was inserted inside the alumina tube from the top of the furnace to determine the temperature immediately above the Pt capsules. The capsules were placed in a small porous alumina boat and suspended in the hot zone using a Pt-Rh wire. To ensure complete homogeneity, the capsules were first kept for 15 min at a temperature 1873–1923 K (1600–1650 °C) higher than the target temperature of the experiment to completely melt and homogenize the starting materials. The temperature was then lowered to the target temperature and kept for sufficient time to fully equilibrate the samples. After equilibration, the capsules were quenched in a bath filled with ice-cold water. After the experiments, no swelling, spilling or bursting of the crucibles were observed. The quenched samples were mounted in epoxy and polished using an oil-based diamond suspension to avoid any moisture pick up. To remove any oil or dust particles on the surface of the polished sections, samples were cleaned 3 times in an ultrasonic bath using isopropyl alcohol (< 0.02 vol% H2O) for about 60 s each time. Phase identification and composition analysis were conducted by EPMA with the help of the JEOL 8900 (Tokyo, Japan) superprobe at McGill University using an accelerating voltage of 15 kV and a 20 nA beam current. Phase identification was conducted using the backscattered electron (BSE) images produced by the scanning electron microscope (SEM) of the EPMA and phase analysis using wavelength dispersive spectrometry (WDS). The beam diameter was varied between 1 and 10 μm depending on the size of each phase. Even after rapid quenching, exclusion could not be fully prevented in the liquid phase;

3. Experimental procedure Unfortunately, phase equilibria in the oxidizing atmosphere (mostly for MnO-Mn2O3-TiO2 system) is still less known. As the phase equilibria in both reducing and oxidizing conditions are essential to develop accurate thermodynamic database for the entire MnO-Mn2O3-Ti2O3-TiO2 system, new phase diagram study in air was conducted in this study using classical equilibration and quenching method. 3.1. Starting materials Reagent grade powders of MnO from Sigma Aldrich (≥99.99%) and TiO2 from Alfa Aesar (99.9%) were used to prepare the starting materials. These oxides were employed to guarantee the purity of the starting materials, which can exist in multivalent states (Mn2O3 and Ti2O3) and to avoid any possible contamination from carbonates (MnCO3). In order to remove hydroxide impurities or Ti2O3 from the TiO2 reagent, the TiO2 powder was heated overnight (16 h) at 873 K (600 °C) in air in an ST-1700C box furnace (Sentro Tech, USA; inner dimensions: 10 cm × 10 cm × 20 cm) equipped with MoSi2 heating elements. The powder was then removed from the ST-1700C furnace and allowed to cool down in a drying oven set at 393 K (120 °C). The oxidation states of Mn and Ti reagent oxide powders are important to prepare proper starting compositions. To confirm their purities and oxidation states, X-ray diffraction (XRD) analyses of all reagents were also conducted. Batches of 2 g of starting materials were prepared by mixing in appropriate proportions the reagents in an alumina mortar filled with 2

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Table 2 Optimized model parameters in the MnO-Mn2O3-TiO2-Ti2O3 system, J/mol and J/mol-K. Liquid solutiona,b: MnO–MnO1.5–TiO2–TiO1.5 gMnO1.5, TiO2 = –5020.4

gMnO, TiO2 = –41421.60 + 23012.00XMn2 +

–5857.60XTi4 + Ti 4 + Mn2 +

gMnO, TiO1.5 = +8368.00

Coordination numbers (CN) of Mn2+ and Mn3+ were taken from Kang and Jung [26] (ZMn2 +, Mn2 + = 1.3774; ZMn3 +, Mn3 + = 2.0662). CN of Ti3+ and Ti4+ were taken from Panda and Jung [27], ZTi3 +, Ti3 + = 2.0662 and ZTi4 +, Ti4 + = 2.7548.

Pseudobrookite solutionc: MnTi2O5–Ti3O5 (Mn2+, Ti3+, Ti4+)4c[Mn2+, Ti3+, Ti4+]28f O5* GJT = G°(MnTi2O5)α IJT = (GTT + GTJ )–2GJT = 33 4720.00 JJ : TT = (GJJ + GTT )–(GTJ + GFT ) = 1 46 440.00 JTG = (GTT + GJG )–(GTG + GJT ) = 0 GJT = ( GJJ + GGT ) – ( GGJ + GJT ) = 0 Cubic spinel solutiond: Mn3O4-Mn2TiO4-MnTi2O4 (Mn2+)T [Mn2+, Mn3+, Mn4+, Ti3+, Ti4+ Va]2O O4* , GJG = G°(MnTi2O4)ᵝ GJT = 2 G°(Mn2TiO4)ᵞ – 4 RT ln(0.5) - GJJ Tetragonal spinel solutiond: Mn3O4-Mn2TiO4 2+ (Mn , Mn3+)T [Mn2+, Mn3+, Ti4+ Va]2O O4* , GJT = 2 G°(Mn2TiO4)ᵟ – 4 RT ln(0.5) - GJJ KJT = (GKJ + GJT )–(GJJ + GKT ) = 0 Ilmenite solutionb: MnTiO3-Ti2O3 (Mn2+, Ti3+)A [Ti3+, Ti4+]B O3* GGG = G°(Ti2O3)b GJT = G°(MnTiO3)τ GGT = G°(Ti2O3)b + ΔHc ΔHc = 5184 JT : GG = (GJT + GGG )–(GJG + GGT ) = – 57 739.20 + 18.41T Manganosite solutiona,b: MnO-MnO1.5- TiO1.5-TiO2 G(TiO2) = G°(TiO2)b + 22175.20 G(Ti2O3) = G°(Ti2O3)b + 1000.00

Fig. 1. Schematic diagram of the MnO-Mn2O3- TiO2-Ti2O3 system presenting spinel, ilmenite and pseudobrookite solid solutions.

consequently, 5 to 10 different areas (10 μm) were analyzed to accurately determine the equilibrium liquidus composition. Raw data were reduced with the ZAF correction using garnet (Mn) and rutile (Ti) standards. The EPMA provides information only on the metal content in a phase and does not distinguish between multivalent cations. In the current study, manganese in air is present as Mn2+ and Mn3+, while, all titanium can be assumed in quadrivalent state, Ti4+ [25]. The equilibrium samples were also identified by X-ray diffraction (XRD) using the Bruker Discover D8 X-ray diffractometer with a Co-Kα source (λ = 1.79 Å) equipped with HiSTAR area detector at McGill University. All the peaks recorded in the XRD scans were identified with the Power Diffraction Files (PDF) of the International Centre for Diffraction Data (ICDD) using the Bruker AXS DIFFRAC.EVA (Bruker AXS, Karlsruhe, Germany, 2000) software package.

00 qMnO , TiO = –4184 .00 2

00 qMnO , TiO1.5 = 29288 .00

Rutile solutiona,b MnO-TiO1.5-TiO2 G(MnO) = G°(MnO)a + 1000.00 00 qMnO , TiO = 33472 .00 2

End-members of solid solutions Compounds ΔH°298.15K S°298.15K (kJ (J mol−1 −1 mol ) K−1) – 2285.33 163.66 MnTi2O5α

4. Equilibrium phases and thermodynamic models Fig. 1 shows the intermediate solid solutions in the MnO-Mn2O3TiO2-Ti2O3 system at 1 bar. The solutions existing in this system are: (a) Liquid phase (Liq): MnO-MnO1.5-TiO1.5-TiO2 in the molten state. (Mn2+,Ti3+,Ti4+) 4c (b) Pseudobrookite solution (Psb): [Mn2 +,Ti3 +,Ti4 +]8f O 5 2 (c) Cubic spinel solution (CSpi): (Mn2 + )T[Mn2 +,Mn3 +,Mn4 +,Ti3 +,Ti4 + ,Va]O2 O4 (Mn2+,Mn3 +)T (d) Tetragonal spinel solution (Tspi): [Mn2 +,Mn3 +,Ti4 + ,Va]O2 O4 (e) Ilmenite solution (Ilm): (Mn2+,Ti3+) A [Ti3 +,Ti4 +]B2 O3 (f) Manganosite solution (Mono): MnO-MnO1.5- TiO1.5- TiO2 (g) Rutile solution (Rut): TiO2-MnO1.5-TiO1.5

MnTi2O4ᵝ

– 1921.36

140.65

Mn2TiO4ᵞ

−1730.92

181.65

Mn2TiO4ᵟ

−1764.81

140.83

MnTiO3

−1358.23

108.41

τ

Cp (J mol−1 K−1) 247.154–4502759.630T−2 – 1026.149T−0.5 + 455515895.808T−3 213.794 + 9.288E-3T + 2.789E+6T−2 – 750.219T−0.5 – 1.968E+9T−3 170.806 + 1.6234E-2T – 4.10E+6T−2 + 4.029E+86T−3 170.806 + 1.6234E-2T – 4.10E+6T−2 + 4.029E+86T−3 121.670 + 9.290E-3T – 2.19E+6T−2 + 3.46E-13T2

*

Notations J, K, L, G, T and V are used for Mn2+, Mn3+, Mn4+, Ti3+, Ti4+, and Va, respectively. a The Gibbs energies of pure solid and liquid MnO were taken from Wu et al. [28], and those of solid Mn2O3 and pure liquid MnO1.5 (= 0.5 Mn2O3) were taken from Kang and Jung [26]. b The Gibbs energies of pure solid and pure liquid TiO2 and TiO1.5 (= 0.5 Ti2O3) were taken from and Eriksson and Pelton [14]. c The Gibbs energy of pseudobrookite end-members in the Ti-O system were taken from Panda and Jung [30]. d The Gibbs energy of spinel end-members (cubic and tetragonal) in the MnO system were taken from Kang and Jung [26].

Cations shown within a set of brackets occupy the same sublattice, and Va represents vacancy. The abbreviation of solution phase name was used throughout this study. The optimized model parameters for each phase are listed in Table 2. 4.1. Stoichiometric oxide compounds, metallic and gas phases

The Gibbs energy of stoichiometric compound is described as:

In this study, the Gibbs energies of Magnéli phases (TinO2n-1, n ≥ 4) and other stoichiometric oxides (MnO2, α-Mn2O3, β-Mn2O3) were taken from previous studies by Kang et al. [26,29] (now stored in FACT pure substance database) and Gibbs energies of all metallic phases and gasses species were taken from the FACT pure substance database [13].

T

GTo =

o H298.15 K +

T

Cp dT T = 298.15 K

o T S298.15 K + T = 298.15 K

Cp T

dT (1)

3

Calphad 66 (2019) 101639

S.K. Panda, et al. ° where H298.15 K is standard enthalpy of formation from stable pure ° elements at 298.15 K, S298.15 K is the entropy at 298.15 K and CP is the heat capacity. The heat capacity expression of each compound can be determined by fitting heat capacity data. The Gibbs energies of stoichiometric compounds which are used for the end-members of the solutions are also described using Eq. (1). In ° ° order to determine the Gibbs energy of compound, H298.15 K , S298.15K and CP should be determined based on the experimental data. If no reliable experimental data on CP are available, CP expression can be predicted using the Neumann-Kopp (N-K) rule which assumes the CP of AxBy oxide compound is a stoichiometric sum of CP of A and B com° ° pound [31]. Then, H298.15 K and S298.15K are determined to reproduce available experimental data such as thermodynamic properties and phase equilibria.

better reproduce new phase diagram data in air obtained in the present study (in air condition, nearly all Ti cations in liquid oxide can be assumed as Ti4+ state). One small binary parameter was also introduced for each binary liquid MnO-TiO1.5 and MnO1.5–TiO2 solution in order to reproduce the liquidus data within the experimental error limit. The Gibbs energy of the ternary liquid systems can be predicted with proper geometric interpolation technique based on the binary model parameters for reaction (1). For example, the symmetric ‘Kohler’ or asymmetric ‘Toop’ type of interpolation can be used. The details of the ternary interpolation technique and calculation for higher order system are explained elsewhere [35]. A Kohler-like “symmetric approximation” [35] was used for all 4 ternary systems within MnOMnO1.5-TiO2-TiO1.5 system. No ternary model parameters were required in the present study for all ternary systems. This tells a predictive ability of the MQM for the Gibbs energy of liquid solution at high order system from the binary model parameters.

4.2. Liquid oxide phase (molten slag) The Modified Quasichemical Model (MQM) [32,33], which considers short-range ordering of second-nearest-neighbor cations in the oxide melt, was used to describe the MnO-Mn2O3-Ti2O3-TiO2 molten slag. In the present study, the interactions between the cations such as Mn2+, Mn3+, Ti3+, and Ti4+ were considered in the MQM with O2− as a common anion. That is, MnO, MnO1.5, TiO1.5, and TiO2 were considered as the components in liquid slag. In the MQM, the quasichemical reaction between A and B is described as:

(A

A) + (B

B) = 2 (A 2+

B) 3+

4.3. Pseudobrookite solid solution The pseudobrookite compounds generally have an orthorhombic structure and belong to the Cmcm space group [36]. The solid solution has the general formula AB2O5, where all the A and B cations are distributed in two non-equivalent octahedrally coordinated cation sites, the 4c (or M1 or A) sites and the 8f (or M2 or B) sites, producing AO6 and BO6 octahedra, respectively [37,38]. Well known pseudobrookites are Fe2TiO5 (pseudobrookite), FeTi2O5 (ferropseudobrookite), MgTi2O5 (karrooite), MnTi2O5, Al2TiO5, (Mg,Fe)Ti2O5 (armalcolite), Ti3O5, etc. In fully ordered pseudobrookite, all the A cations reside in the 4c site while all the B cations reside in the 8f site. In fully disordered pseudobrookite, the composition of both 4c and 8f site are (A0.33B0.67). This structural information was properly implemented in the development of the present thermodynamic models for the pseudobrookite solid solution in the MnO-Mn2O3-Ti2O3-TiO2 system. A two-sublattice model in the framework of the Compound Energy Formalism (CEF; Hillert et al., 1988 [39]) was developed in the present study to describe the Gibbs energy of the pseudobrookite solution. The pseudobrookite solid solution in the Mn-Ti-O system can be structurally formulated as:

(2)

gAB 3+

4+

where A and B are Mn , Mn , Ti , and Ti , and (A – B) represents a second-nearest-neighbor A-B pair with O2− as a common anion. The Gibbs energy of the above reaction gAB is the model parameter which can be expanded as an empirical function of composition and temperature. The Gibbs energy of the solution is given by:

Gm = (nA gAo + nB gBo)–T S config +

nAB 2

gAB

(3)

are the number of moles and molar Gibbs energies of where ni and the pure component, respectively, and nAB is the number of moles of (A – B) bonds at equilibrium. S config is the configurational entropy of mixing of random distribution of the (A – A), (B – B) and (A – B) pairs in the one-dimensional Ising approximation [34]:

gio

(Mn2+,Ti3+,Ti4+) 4c [Mn2+,Ti3+,Ti4+]8f 2 O5 where ions enclosed in parentheses and brackets occupy the same octahedral 4c and 8f sublattice, respectively. In the present model, Mn2+, Ti3+ and Ti4+ cations are assumed to enter both 4c and 8f octahedral sublattice. There is no evidence of the existence of Mn3+ and Mn4+ in pseudobrookite. The notation J, G and T are used for Mn2+, Ti3+ and Ti4+, respectively, to simplify the description below. The Gibbs energy of the pseudobrookite solid solution is expressed, in the CEF, as

S config = –R (nA lnXA + nB lnXB )–R nAA ln ln

XAA X + nBB ln BB + nAB YA2 YB2

XAB 2YA YB

(4)

o gAB = gAB +

i 1

i0 i gAB X AA +

j 1

0j j gAB XBB

Yi4 c Y 8j f Gij

Gm =

gAB is expanded in terms of the pair fractions:

i

TS config + Gexcess

j

(6)

where and represent the site fractions of constituents ‘i’ and ‘j’ on the 4c and 8f octahedral sublattices, respectively, Gij is the Gibbs energy of an “end member [i]4c[j]28fO5” in which 4c and 8f sites are occupied only by i and j cations, respectively, Gexcess is the excess Gibbs energy, and S config is the configurational entropy, which takes into account the random mixing of cations on each sublattice:

Y 8j f

Yi4c

(5)

0j i0 o where gAB , gAB and gAB are the parameters of the model which may be functions of temperature. Optimized parameters for the binary liquid MnO-MnO1.5 and TiO2TiO1.5 solutions were obtained previously [26,27], and they were adopted in the present study without any modification. The secondnearest-neighbor ‘coordination numbers’ of Mn2+, Mn3+, Ti3+ and Ti4+ used in the present study are the same as the previous studies [26,27]. In other words, the coordination numbers of Mn3+ and Ti3+ are identical to each other, which is 3 2 of Mn2+ and 3 4 times of Ti4+. The binary liquid parameters of MnO–TiO2 were first model by Erikssen and Pelton [14], which was reoptimized by Kang et al. [26] to reproduce their own experimental data at reducing condition (MnO-TiO2Ti2O3 system). However, in the present study, the binary liquid MnO–TiO2 parameters by Kang et al. [26] were further modified to

S config =

Y 8j f ln Y j8f

Yi4c ln Yi4c + 2

R i

j

(7)

The Gibbs energies of end-members are the most important model parameters for the present solid solution. For a fully normal pseudobrookite, for example, GAB = Go(AB2O5) is the (measurable) Gibbs energy of pure normal AB2O5, which can be used directly as a Gibbs energy of one end-member. Unfortunately, it is not possible to determine the Gibbs energies of the other end-member, GBA from the experimental 4

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S.K. Panda, et al.

data alone. Therefore, certain logical and physically meaningful assumptions are needed to find the other end-members Gibbs energies. In the present model, physically meaningful linear combinations of the end-members pertaining to certain cation site exchange reactions are used to determine the Gibbs energies of the other end-members. The Gibbs energy of these cation site exchange reactions between the M1 and M2 sites are the model parameters; they are denoted by Δ and I parameters and described elsewhere [30]. From our experience, this approach helps in increasing the predictive ability and stability of the model for large solid solutions such as pseudobrookite, ilmenite and spinel. The Gibbs energies of nine end-member are required for the model. Among them, the Gibbs energies of four end-members (GGG, GTT, GGT, and GTG) were previously fixed in the Ti-O system [30]. The Gibbs energies of the remaining five end-members (GJJ, GJG, GJT, GGJ, GTJ) were obtained in the present study, as described below (see also Table 2). The Gibbs energy of JT (MnTi2O5), GJT, was originally taken from Pelton et al. [40] and its enthalpy (ΔH°298.15K) and entropy (S°298.15K) were slightly modified in order to reproduce the phase diagram data, especially the three phase equilibria of pseudobrookite, ilmenite and rutile at 1473 K (1200 °C) (for detail, see the discussion in section 6). The Gibbs energies of other two end-members, TJ (TiMn2 O52 ) and JJ (Mn3 O54 ) were fixed by the following site exchange reactions below and pre-determined, GTT [30]:

2JT = TT + TJ IJT = (GTT + GTJ )–2GJT

(8)

TJ + JT = JJ + TT

(9)

JJ : TT

= (GJJ + GTT )–(GTJ + GJT )

cation distribution is well studied for cubic spinel solution. At high temperature, spinel compounds generally have a cubic (isometric) structure and belongs to Fd3m space group [44]. The ideal structural formulas of the Mn-Ti-O cubic spinel end-members are Mn2TiO4: (Mn2+)[Mn2+Ti4+]O4 and MnTi2O4: (Mn2+)[Ti3+]2O4, where the parentheses indicate cations in tetrahedrally coordinated A sites and square brackets indicate cations in octahedrally coordinated B sites. Note that, MnTi2O4 is a 2–3 spinel with normal structure while Mn2TiO4 is a 2–4 spinel with almost inverse spinel [45,46]. Intermediate compositions are complex spinels (space group Fd3m), with cations occupy 1/8 of all tetrahedral sites and ½ of all octahedral sites, yielding a total of 8 tetrahedral and 16 octahedral interstices together with 32 O sites per cell [47]. With decreasing temperature, cubic spinel undergoes at low temperature the phase transition to tetragonal spinel having P4122 space group, which occurs because of long range ordering of cations in octahedral site [48,49]. Low-temperature tetragonal ordering has been experimentally observed in Ti-containing spinel such as Mg2TiO4 [48–50], Zn2TiO4, and Mn2TiO4 [49,51,52] inverse spinel [53]. The Mn2TiO4 tetragonal spinel, (Mn2+)[Mn2+,Ti4+]O4, and Mn3O4 spinel by Kang et al. [26] were taken into account to describe tetragonal spinel solution in the present Mn-Ti-O system. Similar to pseudobrookite solid solution explained above, the Gibbs energy of the spinel solution (cubic and tetragonal) is described using the CEF [39], as shown in Eqs. (6) and (7). Site exchange reactions and Gibbs energy of end-members are determined similarly as shown in Eqs. (8)–(11). Details of the linear combination of Gij parameters of both cubic ad tetragonal spinel are given in Table 2. The cubic and tetragonal spinel solution in the MnO-Mn2O3-Ti2O3-TiO2 system can be structurally formulated as: Cubic spinel solution: (Mn2+)T [Mn2+, Mn3+, Mn4+, Ti3+, Ti4+, Va]2O O4 Tetragonal spinel solution: (Mn2+, Mn3+)T [Mn2+, Mn3+, Ti4+, Va]2O O4 For modeling the Mn3O4 cubic spinel, Kang and Jung [26] took the idea from Dorris and Mason [43] in which they concluded that Mn2+ is the only constituent in the tetrahedral site while Mn2+, Mn3+ and Mn4+ mix each other in the octahedral site. Dorris and Mason [43] developed their structural idea based on sudden increases of electrical conduction when passing from tetragonal-to-cubic transformation which is due to hopping of electrons between Mn3+ and Mn4+ on octahedral sites. Electrical conductivity measurements by Lu et al. [54] (MnCr2O4), and Gillot et al. [55] (CuMn2O4, NiMn2O4) also confirmed the findings of Dorris and Mason. Cation distribution and magnetic moments of Ti-doped cubic spinel ferrites by different authors [56–60] conclude all Ti cations (Ti3+ and Ti4+) going only into the octahedral sites. With decrease in temperature, the cubic spinel undergoes tetragonal distortion to P4122 because of long-range ordering of Ti4+ with other divalent cations in octahedral site [48,49,53]. The above structural information was properly implemented in the development of the present thermodynamic models for the spinel phases in the MnOMn2O3-Ti2O3-TiO2 system. In the current CEF model for Mn-Ti-O system, the Gibbs energies of six end-members and eight end-members are required for the cubic and tetragonal spinel, respectively. In the description of spinel end-members below, the notation J, K, L, G, T and V are used for Mn2+, Mn3+, Mn4+, Ti3+, Ti4+, and Va, respectively. Among all the end-members, the Gibbs energies of four end-members (GJJ, GJK, GJL and GJV) for cubic spinel and six end-members (GJJ, GJK, GJV, GKJ, GKK, and GKV) for tetragonal spinel were already optimized from the previous thermodynamic optimization of the Mn-O system [26]. In the present study, the Gibbs energies of other two end-members in cubic spinel (GJG, GJT) and two in tetragonal spinel (GJT and GKT) were optimized, as described in the following sections (see also Table 2). For cubic MnTi2O4, there are no thermodynamic data available in the literature. Consequently, GJG (G° of MnTi2O4) was first estimated by

The I parameter was mainly used to reproduce the solubility range of pseudobrookite from Ti3O5 toward MnTi2O5 at all temperatures and Δ parameter was used to destabilize the solubility of pseudobrookite towards Mn-rich region. In addition, other site exchange reaction model parameters (Δ) were used to find GJG and GGJ, which were set to be zero:

TG + JT = TT + JG

GJ + JT = JJ + GT

JTG

GJT

= (GTT + GJG )–(GTG + GJT )

= (GJJ + GGT )–(GGJ + GJT )

(10) (11)

In the present study, no excess Gibbs energy parameter, expressed in Eq. (6), was required. The solution models for pseudobrookite solid solutions are also successfully expanded to the Fe–Ti–O [30], Al–Ti–O [27], and Mg–Ti–O [41] systems. 4.4. Spinel solid solution A simple spinel contains two different cations in the ratio of 1:2 and has a general formula AB2O4, where A resides in tetrahedral site and B reside in octahedral site. Cationic distribution between these sublattices is important for determining the physical and thermodynamic properties of spinel. Theoretically, spinel minerals can be classified into three classes: normal, inverse and mixed based on their ordering structures. A normal spinel is one in which all the A cations reside in the tetrahedral sites and all the B cations reside in the octahedral site. A fully inverse spinel is one in which the B cations are evenly split between the tetrahedral and octahedral sites and all the A cations reside in the octahedral site. A mixed spinel has the cations A and B cations present in both the tetrahedral and octahedral sites. There are two types of spinel phases in the Mn–Ti–O system: cubic and tetragonal. Kang and Jung [26] and Grundy et al. [42] reviewed experimental data of pure Mn3O4 and reported that tetragonal spinel transforms to cubic spinel at about 1448 K (1175 °C) in air. The ionic configuration of both tetragonal and cubic Mn3O4 spinel was determined by Dorris and Mason [43] using the electrochemical ‘Seebeck’ experimental technique. This structural information was properly implemented in the development of the present thermodynamic models for the cubic and tetragonal spinel phases in the Mn–Ti–O system. The 5

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combining the Gibbs energy of MnO and Ti2O3 and then slightly modified the enthalpy ΔH°298.15K to reproduce the phase boundary between spinel and ilmenite at reducing condition. The cubic spinel compound Mn2TiO4, which has the inverse structure (Mn2+) [Mn2+ 0.5 , Ti4+ 0.5 ]2O5 at room temperature, is assumed to be an equimolar ideal (Mn2 + )[Mn2 + ]2O 4 , and JT, mixture between JJ, (Mn2 + ) [Ti 4 + ]2O 4 ; that is:

G° (Mn2 TiO4) =

1 1 (GJJ + GJT ) + 2RT ln 2 2

combinations of Gij parameters for the ilmenite solid solution are given in Table 2. The Gibbs energies of four end-member are required for the model. Among them, the Gibbs energies of two end-members (GGG and GGT) were previously fixed in the Ti-O system [30]. The Gibbs energies of the other two end-members (GJG and GJT) were obtained as described below (see also Table 2). JT (MnTiO3) was first prepared by summing the energies of MnO and TiO2 and its ΔH°298.15 K and S°298.15 K were slightly modified to reproduce the liquidus at reducing condition. The Gibbs energy of other end-member, JG (MnTiO31 ) was fixed by the reciprocal reaction given below:

(12)

where G° (Mn2 TiO4) is the Gibbs energy of pure Mn2TiO4 whose thermodynamic properties was first estimated from its constituent oxides (2MnO + TiO2) using the Neumann–Kopp (N–K) rule [31] (ΔH°298.15 K = - 1714.60 kJ mol−1 and S°298.15 K = 170.12 J mol−1 K−1) and then was modified slightly. The N-K estimated values are comparable to the value recommended in Barin's compilation [61], ΔH°298.15 K = - 1750 kJ mol−1, and S°298.15 K = 170.43 J mol−1 K−1. However, to take in to account the random mixing entropy of cations in = – 2R the octahedral sublattice (ΔSmix (0.5ln0.5 + 0.5ln0.5) = 11.526 J mol−1K−1) for the structure of 4+ O (Mn2+ )T[Mn20.5+,Ti 0.5 ]2 O4 , the optimized entropy of Mn2 TiO4 was set to be 181.65 J mol−1K−1 at room temperature. Then, ΔH°298.15 K was slightly adjusted (−16.317 kJ mol−1) from the N-K estimated value in order to reproduce the homogeneity range of spinel in Mn3O4-Mn2TiO4 obtained in the present experimental study in air. That is, the GJT was determined from the optimized G° (Mn2 TiO4) as shown in Eq. (12). No excess Gibbs energy parameter was required in the optimization of cubic spinel solution. Likewise, the Gibbs energy of tetragonal spinel end-member GJT was fixed using Eq. (12), followed by modification of ΔH°298.15 K and S°298.15 K of Mn2TiO4 to predict the homogeneity range of Mn3O4Mn2TiO4 tetragonal spinel at 1473 K (1200 °C) at air [20]. The Gibbs energy of other end member (GKT) was fixed by site exchange reaction between cations in the tetrahedral and octahedral sites, which is denoted by Δ parameter and set to be zero:

JJ + KT = KJ + JT

KJT

= (GKJ + GJT )–(GJJ + GKT )

JG + GT = JT + GG

JGT

= (GJT + GGG )–(GJG + GGT )

(14)

where parameter was optimized to reproduce the homogeneity range of ilmenite MnTiO3-Ti2O3 solution at all temperatures. A temperature dependent term was needed in order to form the three phase equilibria of ilmenite solution with spinel and pseudobrookite solid solution at 1473 K (1200 °C). 4.6. Manganosite (monoxide) solid solution The manganosite solution is part of monoxide solution with rocksalt structure, which was modeled previously [26,29]. It is assumed that the cation vacancies associate with Mn3+, Ti3+ and Ti4+ cations in order to maintain electrical neutrality; consequently, they do not contribute independently to the configurational entropy in manganosite solution. (MnO, MnO1.5, TiO1.5, TiO2) The manganosite solution is described using the Bragg-Williams random mixing model considering MnO, MnO1.5, TiO1.5 and TiO2 as components. The molar Gibbs energy of the solution is described by:

Gm =

Xi ln Xi + Gexcess

Xi G°i + RT i

i

(15)

where Xi is the mole fraction, G°i is the standard molar Gibbs energy of pure component i and Gexcess is the excess Gibbs energy of solution. In the binary system, the excess molar Gibbs energy of the system can be often expressed as:

(13)

No excess Gibbs energy parameter was required in the optimization of cubic and tetragonal spinel solution.

Gexcess =

4.5. Ilmenite solid solution

AB XA XB

(16)

where AB parameter may be expanded as a polynomial of the mole fraction of components:

The ilmenite compound has a trigonal (distorted hexagonal) structure and belongs to the R 3 space group [62–65]. The solid solution within ilmenite compounds has a general formula of XYO3, where all the cations (X and Y) are distributed in two non-equivalent octahedrally coordinated cation sites (A and B) occupying 2/3 of the interstices. At high temperature (above the critical ordering temperature, Tc) cations get randomly distributed within A and B cation sites and the space group symmetry change from R 3 to R 3 c [66,67]. The order-disorder transition for general ilmenite solution are still not well known, therefore, the transition to disordered structure was not considered in this study. The structure of ilmenite solid solution in the Mn-Ti-O system is described below:

AB

= i 0 j 0

ij qAB X Ai XBj

(17)

ij where qAB

is the binary interaction parameter which can be temperature dependent. Gibbs energy of pure components were taken from earlier studies, MnO [28], MnO1.5 [26], TiO1.5 [14] and TiO2 [14]. The binary model parameters of MnO–MnO1.5 were taken from Kang et al. [26]. 00 One small model parameter for MnO–TiO2 (qMnO , TiO2 = – 4184 J) and 00 another parameter for MnO-TiO1.5 (qMnO, TiO1.5 = + 29 288 J) was required to form the solubility range of manganosite at all temperatures and oxygen partial pressures. The Gibbs energy of ternary monoxide MnO–MnO1.5–TiO2 and MnO-TiO1.5-TiO2 solution was calculated from the binary parameters with the Kohler-like “symmetric approximation” [35]. No ternary excess parameter was necessary for this solution in this study.

(Mn2+, Ti3+)A [Ti3+, Ti4+]BO3 where cations enclosed in parentheses and brackets occupy the same octahedral (A and B) sublattice. In the present model, Mn2+ and Ti3+ cations are assumed to mix randomly on A sublattice, while Ti3+, Ti4+ mix randomly on the B sublattice. The notations J, G and T are the same as those of pseudobrookite and spinel solution. As for the pseudobrookite and spinel solutions, the Gibbs energy of the ilmenite solution is expressed using the CEF as shown in Eqs. (6) and (7). Site exchange reactions and Gibbs energy of end-members are determined similarly as shown in Eqs. (8)–(11). Details on the linear

4.7. Rutile solid solution Rutile TiO2 has a body-centered tetragonal structure which has small solubility of Ti2O3 and is usually expressed as TiO2-δ. Eriksson and Pelton [14] was first to model the rutile solid solution using the simple Henrian solution model. Then, Kang et al. [29] further modified the solution by assigning a temperature dependent term to the Henrian 6

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Table 3 Experimental phase diagram results for the MnO-Mn2O3-TiO2 system in air in the present study. Sample

Starting mixture (mole fraction)

Temperature

Annealing time

MnO

TiO2

K (°C)

(hours)

MT1 MT2

0.5 0.7

0.5 0.3

1723 (1450) 1723 (1450)

12 12

MT3

0.3

0.7

1723 (1450)

9

MT4

0.7

0.3

1623 (1350)

12

MT5

0.3

0.7

1773 (1500)

12

MT6

0.7

0.3

1673 (1400)

9

MT7

0.3

0.7

1673 (1400)

9

MT8

0.7

0.3

1623 (1350)

40

MT9

0.3

0.7

1573 (1300)

40

MT10

0.5

0.5

1673 (1400)

40

a

Phasesa (#analysis)

Glass (8) Glass (9) CSpi (10) Glass (9) Rut (10) CSpi (10) Ilm (10) Glass (6) Rut (10) Glass (10) CSpi (10) Glass (9) Rut (5) Spi (10) Ilm (10) Spi (10) Ilm (10) Glass (10)

Phase composition (mole fraction) Mn

Ti

0.496 ± 0.006 0.632 ± 0.01 0.796 ± 0.004 0.373 ± 0.015 0.005 ± 0.001 0.787 ± 0.012 0.520 ± 0.009 0.332 ± 0.006 0.004 ± 0.001 0.5850 ± 0.009 0.774 ± 0.009 0.396 ± 0.013 0.007 ± 0.001 0.793 ± 0.008 0.523 ± 0.007 0.812 ± 0.011 0.528 ± 0.008 0.503 ± 0.007

0.504 0.368 0.204 0.627 0.995 0.213 0.480 0.668 0.996 0.415 0.226 0.604 0.993 0.207 0.477 0.188 0.472 0.497

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.006 0.01 0.004 0.015 0.001 0.012 0.009 0.006 0.001 0.009 0.009 0.013 0.001 0.008 0.007 0.011 0.008 0.007

CSpi: Cubic Spinel, Rut: Rutile, Ilm: Ilmenite phase.

activity coefficient of TiO1.5 in order to reproduce all experimental data over wide range of temperatures. Like the manganosite (monoxide) solid solution, the rutile solution is modeled using the Bragg-Williams random mixing model [32] considering TiO2, TiO1.5 and MnO as the components. The Gibbs energy of pure components were taken from earlier studies, MnO [28], TiO2 [14] and Ti2O3 [14]. One small binary model 00 parameter for MnO-TiO2 (qMnO , TiO2 = - 8368 J) was required to form the solubility range of rutile at all temperature and oxygen partial pressure.

According to many authors [71,75–78], the exsolution within the solid solutions occurs very quickly during quenching and is due to the fast exchange of cations (Mn2+ + Ti4+ → Mn3+) and some vacancy relaxation in the spinel solid solution (Mn3O4-Mn2TiO4). For quantitative analysis of these samples (MT4, MT8 and MT9), five spot analyses are performed at primary phase area (host) and five at secondary phase area (guest) to have better experimental error range. The standard deviation (2σ) was found to be less than 0.01 mol % for each case. 6. Critical evaluation and optimizations

5. Experimental results

All the thermodynamic property, structural data, liquid activity, and phase diagram data of the MnO-Mn2O3-Ti2O3-TiO2 system available in the literature were first critically reviewed. New phase diagram experimental data from this study and all reliable experimental data (with known atmospheric conditions) from the literature [15,17,18,20–24] were then simultaneously considered to obtain a set of Gibbs energy functions for all the phases. In particular, among the previous experimental data, more weight was given to the experimental results by Kang and Lee [15] as they performed the experiments in controlled atmosphere and used EPMA for phase composition analysis. The liquid model parameters for the Ti-O system were taken directly from Panda and Jung [27]. The Magneli phases and rutile solution were taken from Kang et al. [29]. While Eriksson and Pelton [14] and Kang et al. [29] modeled the solid solutions (spinel, ilmenite and pseudobrookite) in the MnO-Ti2O3-TiO2 system at reducing atmosphere, the current work aimed for the entire oxygen pressure range from metallic saturation to 1 bar pressure. That is, the present thermodynamic model for solid solutions and liquid can supersede the previous results. The optimized model parameters in this study are listed in Table 2. The phase equilibria in the Mn-Ti-O system can be presented in different way due to the multiple oxidation states of Mn and Ti. For example, the calculated phase diagrams in the MnO-Mn2O3-TiO2 and MnO-TiO2-Ti2O3 systems at 1673 K (1400 °C) are shown in Fig. 3, where the oxygen isobars are indicated by dashed lines. At this temperature, all the phases are stable but the pseudobrookite solid solution in the MnO-Mn2O3-TiO2 system and the liquid in the MnO-TiO2-Ti2O3 system. In the MnO-Mn2O3-TiO2 phase diagram (Fig. 3(a)), the manganese has two valences (Mn2+ and Mn3+) and titanium has one valence (Ti4+). Depending upon the oxygen partial pressure, each isobar starts at the TiO2 end-member, passes through distinct locations within the

The purpose of the present experimental phase diagram study was to determine the liquidus and sub-solidus phase equilibria in air. The experimental results are summarized in Table 3, and the BSE images of several equilibrated samples from EPMA are presented in Fig. 2. As mentioned in section 3, all the samples (MT1 to 10) were first equilibrated at higher temperature, 1873–1923 K (1600–1650 °C) for 15 min to fully melt the MnO and TiO2 powders to achieve fast homogenization. The small standard deviation (2σ) in the composition of each phase determined by EPMA indicates the samples were well equilibrated. Area analysis (20 μm × 20 μm) was performed for liquid (glass) phase, and spot analysis of 1–3 μm in diameter was performed for solid phases. No Mn and Ti solubility was detected in Pt crucible and no Pt was detected in oxide phases. EPMA cannot distinguish different oxidation states of metals, so the experimental composition results are only summarized as Mn and Ti metallic composition in Table 3. As can be seen in the microstructures in Fig. 2(a)–(d), the equilibrium solid phases (spinel and rutile crystals) are very well developed in each sample. The clean glass phase formed during quenching gives a clear indication of fast quenching speed. In the present experimental study, about 0.5 mol % of MnO solubility was detected in rutile TiO2 (from the sample MT3). In Fig. 2(e) and (f), the phase equilibria in equilibrium temperature shows the presence of spinel and ilmenite solid solution. Micro-intergrowth textures can be observed in the spinel and ilmenite phase by formation of rims and trellis-like lamellae due to exsolution effect [68–74]. The ilmenite lamellae observed inside the spinel crystals are often continuous, broad and in the form of a trellis whereas the spinel blebs seen inside the ilmenite crystals are always discontinuous and forms small oval bodies. Similar microstructures were reported by Lattard [71] in spinel and ilmenite crystals in their study of the Fe-Ti-Cr-O system at 1573 K (1300 °C) and log PO2 = −8.5. 7

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Fig. 2. Backscattered electron images (BSE) of the equilibrated samples (a) MT1 (900×), (b) MT3 (40×), (c) MT6 (40×), (d) MT7 (40×), (e) MT9 (40×), and (f) MT9 (150×).

Fig. 3. Calculated isothermal sections in the MnO-Mn2O3-TiO2 and MnO-Ti2O3-TiO2 systems at 1673 K (1400 °C).

8

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phase fields, and ends at a different location along the MnO-Mn2O3 binary. When the oxygen partial pressure decreases from 1 bar to 0.01 bar, the isobars end on the spinel (Mn3O4-rich) phase field of the binary MnO-Mn2O3; when the oxygen partial pressure decreases further, the terminal points shift towards the monoxide (MnO-rich) phase field. In other words, the isobar lines of oxygen shift towards the MnOTiO2 side of ternary system at 1673 K (1400 °C) with decreasing oxygen partial pressure; the liquid and spinel phase fields get narrower and the ilmenite (MnTiO3-rich) phase starts to become stable. In the MnO-TiO2-Ti2O3 phase diagram (Fig. 3(b)), manganese has only one valence (Mn2+) while titanium has two (Ti3+ and Ti4+). As a result, all the isobars of oxygen start at the MnO end-member and terminate at different locations along the TiO2-Ti2O3 binary. When the oxygen partial pressure decreases from 1 bar to log PO2 (bar) = −9 (these isobars are barely visible on Fig. 3(b)), the isobars of oxygen cross the MnO phase field, then the spinel (Mn2TiO4-rich) plus ilmenite (MnTiO3-rich) phased field and terminate in the rutile (TiO2-rich) phase field. At such oxygen partial pressures, it is reasonable to consider the MnO-TiO2 binary system as a good analog of the MnO-TiO2-Ti2O3 system. However, when the oxygen partial pressure decreases further, the oxygen isobars are shifted towards the Ti2O3 side of the phase diagram. The phase fields crossed are the MnO phase field, the spinel (Mn2TiO4-rich) plus ilmenite (MnTiO3-rich) phased field, the ilmenite plus pseudobrookite (MnTi2O5-Ti3O5) phase field, and the pseudobrookite plus rutile phase field. Below log PO2 = −13, the limiting point moves towards the pseudobrookite (Ti3O5-rich) phase and the stable region of spinel plus ilmenite solid solutions starts getting wider than previous conditions.

(below 31 K), Stephenson and Smith [79] determined the entropy S°298.15 K to be 104.934 J mol−1 K−1. The heat capacity of MnTiO3 was later measured by Cherian et al. [81] from 0 to 125 K using QD (Quantum Design) - Physical Property Measurement System (PPMS). Using the heat capacity data of Stephenson and Smith [79] and Cherian et al. [81], the entropy of MnTiO3 could be calculated to be 108.70 J mol−1 K−1; this value was later adjusted to 108.41 J mol−1 K−1 to reproduce the phase diagram data in this study. The enthalpy of MnTiO3 at 298.15 K (ΔH°298.15) was estimated using the Neumann–Kopp (N–K) rule [31] from its constituent oxides (MnO and TiO2) and modified to reproduce the melting temperature and solid solubilities in ilmenite in oxidizing atmosphere. The thermodynamic properties of stoichiometric Mn2TiO4, MnTi2O4 and MnTi2O5 compounds were rarely studied. Neither enthalpy nor low- and high-temperature heat capacity data exist and therefore, the enthalpy at 298.15 K (ΔH°298.15), entropy at 298.15 K (S°298.15) and heat capacity Cp were estimated from the constituent oxides (MnO, Ti2O3 and TiO2) of the compounds using the Neumann–Kopp (N–K) rule [31]. The estimated ΔH°298.15 of Mn2TiO4 and MnTi2O4 in the spinel and MnTi2O5 in the pseudobrookite were then slightly modified during the optimization to reproduce the experimental phase diagram ( pO2 - composition, melting point, and solid solubilities) data. 6.2. Structural data – spinel solution The Ti4+/Ti3+ ratio in the cubic spinel solution in equilibrium with manganosite at 1573 K (1300 °C) as a function of oxygen partial pressure is depicted in Fig. 5. Amitani et al. [21] measured, with the help of wet chemical analysis, the Ti distribution in cubic spinel (open symbols in Fig. 5) by equilibrating Cu-Mn alloy, manganosite, and spinel at 1573 K (1300 °C). They estimated the oxygen partial pressure from the equilibrium reaction Mn (in Cu) + 0.5O2 (g) = MnO (s) by assuming the activity of MnO (s) to be one and by analysing the Mn content in Cu alloys. In their calculation, the activity coefficient of Mn in Cu-Mn alloy, ° Mn (Cu) , was derived from the activity measurements of Spencer and Pratt [82] at high Mn concentrations and the ° Mn (Cu) given by

6.1. Thermodynamic property data The optimized heat capacity of MnTiO3 from the present ilmenite solution is shown in Fig. 4 along with the experimental data. The heat capacity of MnTiO3 was first measured by Stephenson and Smith [79] using low temperature adiabatic calorimetry between 31 and 298.15 K. Using Simpson rule integrations and Debye & Einstein function [80]

Fig. 4. Calculated heat capacity of MnTiO3 ilmenite solid solution along with the experimental data [79,81]. 9

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Fig. 5. Distribution of Ti valences (Ti3+ and Ti4+) in the spinel solid solution in equilibrium with the manganosite solid solution at 1573 K (1300 °C) as a function of oxygen partial pressure. The original experimental data (open symbols) of Amitani et al. [21] were re-evaluated (half filled symbols) by Kang et al. [29]. The line is calculated from the current model.

Fig. 6. Activity of MnO (with respect to pure solid MnO) in the MnO-TiOx system [23,24,85–87]. Lines are calculated using the current model under the same pO2 employed in the experiments.

Oishi and Ono [83] at low Mn concentrations. Unfortunately, as shown in Fig. 5, the Ti distribution data of Amitani et al. [21] are rather discontinuous when reported as a function with Log PO2 and no phase transformation is known to explain this behaviour. For this reason, the

oxygen partial pressures of Amitani et al. [21] were recalculated by Kang et al. [29] (half-filled symbols in Fig. 5) using the consistent set of ° Mn (Cu) taken from the thermodynamic optimization of the Cu-Mn by Liu et al. [84]. Our calculated line agrees with the data corrected by 10

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Martin and Bell [85] previously used the values of ° Mn (Pt ) of Smith and Davies [88], which are considerably lower than the other investigations, whereas Karsud [87] misinterpreted the ° Mn (Pt ) provided by Abraham et al. [89] (with respect to solid Mn) and calculated the activity of Mn with respect to pure liquid Mn; detailed information can be found in Kang et al. [29]. All the re-evaluated values were used in our study and are in good agreement with our calculated lines at different temperatures and oxygen partial pressures.

Table 4 Experimental conditions for activity measurements in the MnO-TiOx system. Experimental study Reference #

Temperature K (°C)

[24] [85] [86] [87] [86] [23]

1723 1773 1773 1773 1823 1873

(1450) (1500) (1500) (1500) (1550) (1600)

Source of Mn activity coefficient, Mn

Reference metal

Used in original analysis

Used in this study

Ag Pt Pt Pt Pt Cu

[22] [89] [87] [90] [87] [23]

[26] [26] [86] [26] [86] [23]

Atmosphere log pO2 (bar)

−12.137 −7 −6 to −7 −7 −6.155 −9.721

6.4. Phase diagram data The calculated phase diagram of the Mn-Ti-O system in air condition is presented in Fig. 7 along with the experimental data from previous studies [18,20] and this study. As shown in Fig. 3, there is a nonnegligible amount of Mn2O3 in the system at about 1400 °C in air atmosphere. Unfortunately, the amount of Mn2O3 cannot be analyzed in EPMA, the experimental results are projected to MnO-TiO2 section. According to experimental data, molten oxide (glass), cubic spinel, ilmenite and rutile phase are observed in air, but pseudobrookite and monoxide solid solution are unstable in air. The liquidus of the Mn-Ti-O system in air was well determined in the present experimental study. The maximum solubility of Ti in cubic spinel is up to 22 mol% at around 1648 K (1375 °C). Around 5 mol% Ti solubility in tetragonal spinel at 1273 K (1000 °C) was measured by Garcia-Rosales et al. [20] which is very well predicted in the present optimization too. The ilmenite shows almost stoichiometric MnTiO3 composition with excess 2 mol% solubility towards Mn-rich side. The simplification of current ilmenite model (as explained earlier) restricts the reproduction of this result. Ilmenite is disassociated into tetragonal spinel and rutile at about 1240 K (967 °C). In the present experimental studies, 0.7 mol% Mn solubility in rutile solid solution was found. Except a small non-stoichiometry of ilmenite, the phase diagram is well reproduced in the present optimization. The change of equilibrium phases in the MnO-Mn2O3-Ti2O3-TiO2 system depending on the partial pressure of oxygen is calculated in Fig. 8. All lines are calculated from the current thermodynamic models

Kang et al. [29]. 6.3. Activity data in liquid solution Fig. 6 shows the calculated activities of MnO with respect to pure solid MnO in the MnO-TiOx system at different temperatures and oxygen partial pressures along with experimental data [23,24,86–88]; experimental conditions are summarized in Table 4. All the investigations were performed using the gas/metal/slag equilibration technique at high temperature with various reference metals (Pt, Cu, Ag). Note that at 1723 K (1450 °C), the original activities of MnO determined by Kim et al. [24] were recalculated by Kang et al. [29] using the more accurate activity coefficient measurements of Mn in Ag alloy ( ° Mn (Ag ) ) by Jung et al. [90]. Kim et al. [24] employed originally the ° Mn (Ag ) calculated by Ito et al. [22], whom reported a value of 0.395 at 1723 K (1450 °C) (with respect to liquid Mn standard state), which is quite different from the value of 0.596 obtained by Jung et al. [90]. Note also that at 1773 K (1500 °C), the data of Martin and Bell [85] and Karsud [87] were also re-evaluated by Kang et al. [29] by replacing the activity coefficient of Mn in Pt by a newly evaluated activity-composition relation in Pt-Mn alloy published in Appendix A of Kang et al. [29].

Fig. 7. Calculated phase diagram of the Mn-Ti-O system in air along with the experimental data from previous studies [18,20] and present study. 11

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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 [15,17,18,20–24] and current experiments.

with optimized parameters. The experimental techniques employed in all phase diagram studies are summarized in Table 1. In the optimization, all these data were considered, but certain preference was given to the specific studies when there were discrepancies between existing experimental data. This is explained here. The liquidus data of rutile solution reported by Amitani et al. [21] and Ohta and Morita [23] at 1773 K (1500 °C) and 1873 K (1600 °C), respectively, match well with the results of Kang and Lee [15] and present experiments. The calculated liquidus shows reasonable agreement with all available

experimental data. There are inconsistencies among the available experimental data on the liquidus of manganosite (monoxide phase) by Ohta and Morita [23], Amitani et al. [21], Kim et al. [24] and Kang and Lee [15]. Ohta and Morita [23], Amitani et al. [21] and Kim et al. [24] used chemical equilibration technique in which they saturated MnO phase with molten oxide and found the saturation limit (liquidus) by chemical analysis. However, this technique might suffer the overestimate of the saturation composition due to the contamination by small solid oxide MnO particles in molten oxide. In the case of Kang and 12

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Fig. 8. (continued)

Lee [15], the quenching method was also employed but Mo and Pt crucibles were used, and samples were analyzed with the help of EPMA. Consequently, their manganosite liquidus has a lower Mn content than the ones determined by Ohta and Morita [23], Amitani et al. [21] and Kim et al. [24]. Therefore, in the present optimization, more preference was given to the results by Kang and Lee [15] who employed EPMA for the quenched samples. Amitani et al. [21] found the spinel and manganosite phase boundary at 1573 K (1300 °C) which are shown as open diamonds in Fig. 8(c). The recalculated oxygen partial pressure values (half-filled diamond) by Kang et al. [29] using the newly evaluted ° Mn (Cu) in the same study (as discussed earlier) were in good agreement

with the current optimization. The phase equilibria measurements performed by Grieve and White [16] and Leusmann [19] (described in Table 1) were carried out by differential thermal analysis and optical microscopy to determine the phase transformation temperatures and the phases present, respectively. In these studies, the solid solutions were assumed to be stoichiometric and oxygen partial pressures (in vacuum and N2 atmospheres) were not well controlled. Moreover, Grieve and White [16] employed Mo crucibles, which are known to dissolve in the molten oxide at high oxygen partial pressures [15]. Consequently, in the current optimization, the data of Grieve and White [16] and Leusmann 13

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Fig. 9. Liquidus projections of the MnO-Mn2O3-TiO2 and MnO-Ti2O3-TiO2 system calculated from the present study. Thin lines are isothermal lines and thick lines are invariant lines. Temperatures are in K. Table 5 Invariant reactions involving liquid phase in the MnO-Mn2O3-TiO2 and MnO-TiO2-Ti2O3 systems calculated from the present optimization. No.a

Phases in equilibrium with liquid

Composition (mole fraction)

1 2 3 4 5 MnO-Ti2O3-TiO2

Cubic Spinel + Tetragonal Spinel + β-Mn2O3 β-Mn2O3 + MnO2 + Rutile β-Mn2O3 + Tetragonal Spinel + Rutile Ilmenite + Rutile + Tetragonal Spinel Cubic Spinel + Tetragonal Spinel + Ilmenite

TiO2 0.257 0.625 0.593 0.586 0.580

MnO 0.132 0.034 0.158 0.253 0.260

Mn2O3 0.611 0.341 0.250 0.161 0.160

1715 1583 1547 1553 1558

(1442) (1310) (1274) (1289) (1285)

6 7 8 9 10 11 12 13 14 15

Pseudobrookite + Ti5O9 + Ti6O11 Pseudobrookite + Ti6O11 + Ti7O13 Pseudobrookite + Ti7O13 + Ti8O15 Pseudobrookite + Ti8O15 + Ti9O17 Pseudobrookite + Ti9O17 + Ti10O19 Pseudobrookite + Ti10O19 + Ti20O39 Cubic Spinel + Ilmenite + Liq metal Pseudobrookite + Rutile + Ti20O39 Cubic Spinel + Monoxide + Liq metal Ilmenite + Pseudobrookite + Rutile

MnO 0.033 0.070 0.100 0.119 0.133 0.157 0.368 0.180 0.706 0.376

TiO2 0.671 0.680 0.690 0.697 0.702 0.711 0.313 0.714 0.263 0.620

Ti2O3 0.296 0.250 0.210 0.184 0.165 0.132 0.319 0.106 0.031 0.004

1932 1922 1913 1907 1901 1891 1936 1881 1861 1702

(1659) (1649) (1640) (1634) (1628) (1618) (1663) (1608) (1588) (1429)

MnO-Mn2O3-TiO2

a

Temp., K (°C)

The number index of the invariant reaction points are the same as the ones in Fig. 9.

[19] were not taken into consideration. All reliable available experimental data from different studies are well reproduced in the present calculations. Cubic spinel (CSpi) and ilmenite (Ilm) solid solution encompass from Mn3O4 to MnTi2O4, and from MnTiO3 to Ti2O3, respectively, depending on the partial pressure of oxygen. In both CSpi and Ilm solutions, the solubility of Ti oxide at constant temperature is increasing with decreasing oxygen partial pressure. This can be interpreted as a decrease of Mn3+ and Ti4+ stabilization and an increase of Mn2+ and Ti3+ stabilization with the decrease of pO2 . It should be also noted that the Ti oxide solubility in MnO monoxide is very small and nearly independent of oxygen partial pressure. Pseudobrookite (Psb) solution exists only at low oxygen partial pressure [15] and its composition lies between hypothetical ‘MnTi2O5’ and Ti3O5. Interestingly, the ilmenite solution is discontinued at 1473 K (1200 °C) because of the relatively less stability against the mixture of CSpi and Psb. The three phase equilibria of Psb + Ilm + CSpi measured at 1473 and 1573 K (1200 and 1300 °C) are very sensitive to the Gibbs energies of MnTiO3 (Ilm) and MnTi2O5 (Psb), and therefore these data were specially used for the fine

calibration of the standard enthalpy of formation of the corresponding end-members in the solution phases. It should be also noted that in the previous optimization of Eriksson and Pelton [14] and Kang et al. [29], the cubic spinel was calculated only between Mn2TiO4 to MnTi2O4 due to the limitation of the spinel model, so the experimental data at high oxygen partial pressure in high Mn oxide region are not reproduced. This is well overcome in the present study. Thanks to a large amount of available phase equilibrium data in sub-solidus state at different temperatures and oxygen partial pressures, and also well-known Gibbs energies of stoichiometric Mnoxides and Ti-oxides, the Gibbs energies of solid oxide solutions in the Mn-Ti-O system can be reasonably well constrained. In the present optimization, the liquidus in Fig. 8 in middle oxygen partial pressure range to air, and Fig. 7 in air were roughly optimized using the liquid MQM model parameters of MnO-TiO2. Then, MQM binary parameters for MnO-TiO1.5 and MnO1.5-TiO2 were introduced to better reproduce the activity data of MnO at reducing atmosphere (see Fig. 6) and phase diagram in air (Fig. 7), respectively. Of course, the final optimization of all model parameters of solids and liquid phase was conducted to 14

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simultaneously reproduce all available and reliable data. Overall, the error in reproduction of the experimental phase diagram data by the present optimization is less than 2 mol % and 10 K. The calculated liquidus projections of the MnO-Mn2O3-TiO2 and MnO-Ti2O3-TiO2 systems from the present study are shown in Fig. 9 and the invariant reaction points are listed in Table 5. The stability of all the solid solutions with the isothermal lines can be clearly seen. As discussed above and as shown in Fig. 3, the pseudobrookite solid solution is stable only at reducing conditions (MnO-TiO2-Ti2O3).

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7. Summary A complete review and critical evaluation of all available phase diagram, thermodynamic and structural data for the MnO-Mn2O3-TiO2Ti2O3 system at a total pressure of 1 bar has been carried out. Due to lack of phase equilibrium data in oxidized atmosphere, new phase diagram experiments were performed in the MnO-Mn2O3-TiO2 system in air using the quenching method followed by phase characterization with the help of XRD, BSE, and EPMA. The thermodynamic models with optimized parameters can reproduce all the reliable experimental data from room temperature to above liquidus under the oxygen partial pressures ranging from metallic saturation to 1 bar within ± 10 K and ± 1 mol %. Unexplored phase equilibria and thermodynamic properties of the system are also predicted. Thermodynamic software such as FactSage can be used together with new database to calculate phase equilibria and thermodynamic properties at any given set of conditions under 1 bar total pressure. Conflicts of interest All the authors of this paper confirm that the content of this paper is original and hasn't published elsewhere. The authors whose names are listed in the manuscript certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Data availability The raw/processed data required to reproduce these findings cannot be shared at this time due to confidential and also forms part of an ongoing study. Acknowledgements Financial support from Hyundai Steel, JFE Steel, Nippon Steel and Sumitomo Metals Corp., Nucor Steel, POSCO, RHI, RioTinto Iron and Titanium, RIST, Schott A.G., Tata Steel Europe, Voestalpine Stahl, and the Natural Sciences and Engineering Research Council of Canada (CRDPJ 469115 - 14) are gratefully acknowledged. This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF2015R1A5A1037627). One of the authors (S.K. Panda) would like to thank the McGill Engineering Doctorate Award (MEDA) program. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.calphad.2019.101639. 15

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