Coupled Experimental Study and Thermodynamic Modeling of the Al₂O₃–Ti₂O₃–TiO₂ System

Abstract

A complete critical evaluation and re-optimization of phase diagrams and thermodynamic properties of the Al₂O₃–Ti₂O₃–TiO₂ system at 1 atm pressure has been performed. Equilibration and quenching experiment in the Al₂O₃–TiO₂ system in air was also performed to constrain the solubility limit of Al₂O₃ in TiO₂ rutile solution at high temperatures. The molten oxide phase was described by the Modified Quasichemical Model considering the short-range ordering in molten oxide. While Al₂TiO₅ and Ti₃O₅ were treated as separate stoichiometric phases in the previous optimization, they were described in this study, using the Compound Energy Formalism, as part of pseudobrookite solid solution with a miscibility gap based on new experimental data. Corundum and rutile solutions were also described based on their crystal structures. New high temperature phase, Al₆Ti₂O₁₃, was also considered for the first time. A set of optimized model parameters of all phases was obtained, which reproduces all available and reliable literature data within experimental error limits from 25°C to above the liquidus temperatures under oxygen partial pressures from metallic saturation to 1 atm. The newly optimized database was applied to calculate the inclusion diagram and reoxidation of Al-killed and Ti bearing steels.

1. Introduction

Titanium addition to steel creates various forms of non-metallic inclusions such as oxide, nitride, carbide, and sulphide, depending on the steel composition. The effect of these non-metallic inclusions to microstructure and mechanical properties of solid steel is quite important to understand to produce steel with desired properties.¹⁾ Moreover, TiO_x inclusions easily get agglomerate and forms clusters by decreasing the final steel properties and causes a severe submerged entry nozzle clogging problem during continuous casting of Ti-bearing steel. To understand this phenomenon thoroughly, accurate knowledge on thermodynamics and phase equilibria in the Al–Ti–O and Fe–Al–Ti–O system is crucial. The present author (Jung et al.²⁾) already performed the comprehensive critical evaluation and optimization of the Al–Ti–O (Al₂O₃–Ti₂O₃–TiO₂) system and presented the inclusion stability diagram of the Fe–Al–Ti–O system for better understanding the inclusion chemistry in Ti-bearing and Al-killed steel. In the previous study, Al₂TiO₅ and Ti₃O₅ were treated as separate stoichiometric phases. However, it is found out that both solid phases belong to pseudobrookite solid solution, which will be discussed later.

In the present study, all the experimental thermodynamic properties and phase diagram data for the Al₂O₃–TiO₂–Ti₂O₃ system at 1 atm total pressure with oxygen partial pressures from metallic saturation to 1 atm were critically evaluated and re-optimized to obtain the models with a set of model parameters which will be able to reproduce all reliable experimental data in the system. In order to assist the optimization, equilibration and quenching experiment in the Al₂O₃–TiO₂ system in air was also performed at high temperatures. In the end, a revised inclusion diagram of the Fe–Al–Ti–O system was calculated based on the revised thermodynamic database. All the thermodynamic calculations in the present study were performed using the FactSage thermochemical software.³⁾

2. Equilibrium Phases and Thermodynamic Models

The list below shows all the solutions and stoichiometric compounds that are observed in the Al₂O₃–Ti₂O₃–TiO₂ system:

(i) Liquid phase (Liq): AlO_1.5–TiO_1.5–TiO₂ in the molten state

(ii) Pseudobrookite solid solution (Psb): (Al³⁺, Ti³⁺, Ti⁴⁺)^4c[Al³⁺, Ti³⁺, Ti⁴⁺]₂^8f O₅

(iii) Ilmenite solid solution (Ilm): (Al³⁺, Ti³⁺)^A [Al³⁺, Ti³⁺, Ti⁴⁺]^B O₃

(iv) Corundum (Cor) solid solution: (Al, Ti)₂O₃

(v) Rutile solid solution (Rut): TiO₂–TiO_1.5–AlO_1.5

(vi) Stoichiometric compounds: Several Magnéli phases (Ti_nO_2n−1, n ≥ 4) and Al₆Ti₂O₁₃

Cations shown within a set of brackets occupy the same sublattice. The abbreviation of solution phase name was used throughout this study. The metallic phases and gas phases are taken from FACT pure substance database.³⁾ The optimized model parameters for each phase are listed in Table 1.

Table 1. Optimized model parameters in the Al₂O₃–TiO₂–Ti₂O₃ system (J/mol and J/mol·K).

Liquid phasea: AlO1.5–TiO1.5–TiO2
${\text{q}}_{{\text{TiO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{2}}}^{\text{00}}\text{=}-\text{11},\text{715}\text{.20}$ ${\text{q}}_{{\text{AlO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{2}}}^{\text{01}}=\text{13},\text{388}\text{.80}$ ${\text{q}}_{{\text{TiO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{2}}}^{\text{20}}=\text{16},\text{736}\text{.00}$			${\text{q}}_{{\text{AlO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{1}\text{.5}}}^{\text{00}}=\text{16},\text{736}\text{.00}$ ${\text{q}}_{{\text{TiO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{2}}}^{\text{01}}=\text{25},\text{104}\text{.00}$ ${\text{q}}_{{\text{AlO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{1}\text{.5}}}^{\text{01}}=\text{16,736}\text{.00}$				${\text{q}}_{{\text{AlO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{2}}}^{\text{00}}=\text{5},\text{230}\text{.00}$ ${\text{q}}_{{\text{AlO}}_{\text{1}\text{.5}}\text{,}\mathrm{\hspace{0.17em} }{\text{TiO}}_{\text{1}\text{.5}}{\text{(TiO}}_{\text{2}}\text{)}}^{\text{001}}=\text{20},\text{920}\text{.00}$
Coordination numbers (CN) of Al3+, Ti3+ and Ti4+ was set to be ZAl3+ = 2.0662, ZTi3+ = 2.0662 and ZTi4+ = 2.7548, respectively.
Pseudobrookite solutionb, Al2TiO5–Ti3O5: ${\text{(Al}}^{\text{3+}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}^{\text{3+}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}^{\text{4+}}{\text{)}}^{\text{4c}}{\text{(Al}}^{\text{3+}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}^{\text{3+}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}^{\text{4+}}{\text{)}}_{\text{2}}^{\text{8f}}{\text{O}}_{\text{5}}$
GAT = 2 G°(Al2TiO5)α – 4 RT ln (0.5) – GAA GTA = G°(Al2TiO5)α + 20, 920.00 – 4.60 T ΔAA:TT = (GAA + GTT) – (GTA + GAT) = 0					ΔTAG = (GTA + GAG) – (GAA + GTG) = 0 ΔGTA = (GTT + GGA) – (GGT + GTA) = 154, 808.00
Ilmenite solutionc, Ti2O3-rich: ${\text{(Al}}^{\text{3+}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}^{\text{3+}}{\text{)}}^{\text{A}}{\text{(Al}}^{\text{3+}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}^{\text{3+}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}^{\text{4+}}{\text{)}}_{\text{2}}^{\text{B}}{\text{O}}_{\text{5}}$
GAA = G°(Al2O3)β + 1000 GAG = 0.5 GAA + 0.5 GGG + 41, 840					ΔGA:AG = (GGA + GAG) – (GGG + GAA) = 89, 956 ΔAT:GA = (GAT + GGA) – (GAA + GGT) = 0
Corundum: (Al, Ti)2O3
G°(Al2O3) = G°(Al2O3)β			G°(Ti2O3) = G°(Ti2O3)δ + 1000				${\text{q}}_{{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{,}\mathrm{\hspace{0.17em} }{\text{Ti}}_{\text{2}}{\text{O}}_{\text{3}}}^{\text{00}}=46,024.00$
Rutile: TiO2 – TiO1.5 – AlO1.5
G°(TiO2) = G°(TiO2)φ			G°(Ti2O3) = G°(Ti2O3)δ + 45,185.94 + 5.18 T				G°(Al2O3) = G°(Al2O3)β + 96, 232.00
Stoichiometric compounds
G°(Al2TiO5)α = – 2,620,616.52 – 5400.40 T0.5 + 1724.43 T – 249.29 TlnT – 24,03,050.06 T−1 – 86005000.00 T−2 (298.15 K < T < 2500 K) G°(Al2O3)β = – 1,703,961.42 – 3313.55 T0.5 + 1099.96 T – 155.02 TlnT + 1,930,681.50 T−1 – 68,180,607.70 T−2 (298.15 K < T < 2327 K) G°(Ti2O3)δ = – 1,547,548.01 – 3000.87 T0.5 + 1155.33 T – 169.96 TlnT – 8,04,824.47 T−1 – 260,920,167.33 T−2 (298.15 K < T < 2115 K)      = – 1,589,513.65 + 1009.76 T – 156.90 TlnT (2115 K < T < 2500 K) G°(TiO2)φ = – 2,33,505.41 + 155.85 T – 18.60 TlnT – 402,466.66 T−1 – 16,050,855.33 T−2 (298.15 K < T < 2130 K)      = – 2,44,632.37 + 162.52 T – 24.00 TlnT (2130 K < T < 3000 K) G°(Al6Ti2O13) = – 6,921,257.59 – 9940.64 T0.5 + 4183.74 T – 620.73 TlnT + 9,159,885.53 T−1 – 338,855,380.52 T−2 (298.15 K < T < 2115 K)

^* Notations A, G, T are used for Al³⁺, Ti³⁺, and Ti⁴⁺, respectively.

^a The Gibbs energies pure liquid AlO_1.5 (= 0.5 Al₂O₃), TiO₂ and TiO_1.5 (= 0.5 Ti₂O₃) were taken from and Eriksson and Pelton.^4,5)

^b The Gibbs energy of pseudobrookite end-members in the Ti-O system were taken from Panda and Jung.⁶⁾

^c The Gibbs energy of ilmenite end-members in the Ti–O system were taken from Panda et al.⁷⁾

^β,δ,φ The Gibbs energies of pure solid AlO_1.5 (= 0.5 Al₂O₃), TiO₂ and TiO_1.5 (= 0.5 Ti₂O₃) were taken from Eriksson and Pelton.^4,5)

^ψ The Gibbs energies of pure rutile TiO_1.5 (= 0.5 Ti₂O₃) were taken from Kang et al.⁸⁾

2.1. Liquid Oxide Phase (Molten Slag)

The Modified Quasichemical Model (MQM)^9,10,11,12) which takes into account short-range ordering of second–nearest–neighbor cations in the oxide melt, was used for describing the molten slag. For example, for the Al₂O₃–TiO₂–Ti₂O₃ slag, the interactions between the cations such as Al³⁺, Ti³⁺, and Ti⁴⁺ are considered in the MQM with O²⁻ as a common anion. The components of the slag are taken as AlO_1.5–TiO_1.5–TiO₂. The brief description of the MQM is given elsewhere.⁴⁾

The binary liquid TiO₂–Ti₂O₃ parameters⁸⁾ were revised to reproduce the liquidus and melting point of the new Ti₃O₅-rich pseudobrookite solid solution. The Al₂O₃–TiO₂ and Al₂O₃–Ti₂O₃ binary liquid parameters²⁾ were modified to better reproduce all experimental data in air and reducing atmosphere for the Al₂O₃–TiO₂–Ti₂O₃ system. The ‘coordination numbers’ of Al³⁺ and Ti³⁺ are identical to each other, which is ¾ of Ti⁴⁺ (see Table 1).

Once binary interactions for all the binary systems are determined, then parameters can be used to predict the Gibbs energy of ternary system. The Gibbs energy of ternary AlO_1.5–TiO_1.5–TiO₂ melt was calculated using a Kohler type ‘symmetric’ interpolation method.¹³⁾ A small ternary adjustable model parameter was added to destabilize the liquid slag within Al₂TiO₅–Ti₃O₅ system to reproduce the phase diagram, which will be discussed later. It should be noted that a Toop type ‘asymmetric’ interpolation method was used in the previous optimizations: Jung et al.²⁾ adopted TiO₂ as an asymmetric component without any ternary parameter, and Kang and Lee¹⁴⁾ adopted AlO_1.5 as an asymmetric component with a ternary parameter. Because the sub-binary liquid solutions within Al₂O₃–TiO₂–Ti₂O₃ system have similar Gibbs energy of mixing values (about −12 to −20 kJ/mol at 1873 K) and show reasonably regular solution behavior, the choice of interpolation method would not influence largely to the Gibbs energy of ternary liquid solution and phase diagram involving liquid phase. So, the symmetric Kohler type interpolation method¹³⁾ was chosen in the present study.

2.2. Pseudobrookite Solid Solution

As mentioned above, in the previous thermodynamic optimization by Jung et al.,²⁾ the Al₂TiO₅ and Ti₃O₅ were treated as separate stoichiometric phases, which is obviously wrong. This mistake is corrected in this study.

In general, pseudobrookite oxides AB₂O₅ are thermodynamically stable at high temperature under 1 atm total pressure. Well known pseudobrookites are Fe₂TiO₅ (pseudobrookite), FeTi₂O₅ (ferropseudobrookite), MgTi₂O₅ (karrooite), MnTi₂O₅, Al₂TiO₅, (Mg,Fe)Ti₂O₅ (armalcolite), Ti₃O₅, etc. Pseudobrookite compounds have usually orthorhombic structure and belong to the Cmcm space group.¹⁵⁾ A two-sublattice pseudobrookite model⁷⁾ in the framework of the Compound Energy Formalism (CEF) (Hillert et al., 1988¹⁶⁾) was developed in the present study to describe the Gibbs energy (G^m) of pseudobrookite solution:   

$$G^m=\sum _{\text{i}}\sum _{\text{j}}{Y}_i{}^{\text{4}c}{Y}_j{}^{\text{8}f}{G}_{ij}-T{S}^{config}+G^{excess}$$(1)

where $Y_i^{4c}$ and $Y_j^{\text{8}f}$ represent the site fractions of constituents ‘i’ and ‘j’ on the 4c and 8f octahedral sublattices, respectively (see above for the cations in each sublattice); G_ij is the Gibbs energy of an “end member [i]^4c[j]₂^8fO₅” in which 4c and 8f sites are occupied only by i and j cations, respectively; G^excess is the excess Gibbs energy; and S^config is the configurational entropy which takes into account the random mixing of cations on each sublattice. The detail description of the Gibbs energy of pseudobrookite solution can be found elsewhere.⁷⁾ The model parameters are listed in Table 1 where the notation A, G and T are used for Al³⁺, Ti³⁺ and Ti⁴⁺, respectively.

The Gibbs energies of nine end-members are required for the present model. Among them, the Gibbs energies of four end-members (G_GG, G_TT, G_GT, and G_TG) were previously determined in the Ti–O system.⁹⁾ The Gibbs energies of the remaining five end-members (G_AT, G_AA, G_TA, G_AG, G_GA) were obtained in the present study (see Table 1). The Gibbs energy of stoichiometric end-member, TA (TiAl₂O₅) was optimized by slightly adjusting the ΔH°_298K and S°_298K of G°(Al₂TiO₅) to reproduce the experimental cation distribution data. The Gibbs energy G_GA was set positive to form a miscibility gap between Al₂TiO₅–Ti₃O₅ (for detail, see the discussion in section (3). In the present study, no excess Gibbs energy parameter, G^excess, was required.

2.3. Corundum and Ilmenite Solid Solutions

The corundum phase is an Al₂O₃-rich solid solution, with a trigonal structure and belongs to R3c space group.¹⁸⁾ Ti₂O₃ is iso-structural with corundum Al₂O₃ with approximate hexagonal close packing of the oxygens and metal ions in 2/3 of the octahedral sites.¹⁹⁾ Therefore, ideally Al₂O₃-rich corundum and Ti₂O₃-rich should be considered as one solid solution. However, Ti₂O₃ forms a complete solid solution with ilmenite compounds in the Fe–Ti–O (FeTiO₃),⁶⁾ Mn–Ti–O (MnTiO₃)⁷⁾ and Mg–Ti–O (MgTiO₃)²⁰⁾ systems at high temperatures, while Al₂O₃ has no solid solution with such ilmenite compounds. Therefore, in the present study, two different solid solutions were considered: Ti₂O₃-rich ilmenite solid solution (space group: R3) and Al₂O₃-rich corundum solid solution (space group: R3c).

No TiO₂ solubility in corundum solution was detected by previous authors.^23,24) The Gibbs energy of the corundum was described using the Bragg-Williams random mixing model¹¹⁾ considering Al₂O₃ and Ti₂O₃ as components.   

$$\begin{array}{l}{\text{G}}_{\text{m}}={\text{(X}}_{\text{A}}\text{G}°{}_{\text{A}}+{\text{X}}_{\text{B}}\text{G}°{}_{\text{B}}\text{)}+{\text{nRT(X}}_{\text{A}}{\text{lnX}}_{\text{A}}+{\text{X}}_{\text{B}}{\text{lnX}}_{\text{B}}\text{)}\\ \hspace{1em}\hspace{1em}+\sum _{\text{i,j}\ge \text{0}}\text{(q}{}_{\text{AB}}^{\text{ij}}{\text{X}}_{\text{A}}{}^{\text{i}}{\text{X}}_{\text{B}}{}^{\text{j}}{\text{)X}}_{\text{A}}{\text{X}}_{\text{B}}\end{array}$$(2)

where A and B are Al₂O₃ and Ti₂O₃ (pseudo-end member), and their Gibbs energies $G{°}_i$ are listed in Table 1. As two moles of Al and Fe are assumed to be randomly mixed per mole of formula solution, ‘n’ is ‘2’ in this case. One binary model parameter was used to reproduce the Ti₂O₃ solubility in corundum solution in reducing atmosphere.

Similar to pseudobrookite solutions, the Gibbs energy of the ilmenite solution is expressed using the CEF considering their cation structure (see above). The model is detailed elsewhere,⁷⁾ and their model parameters are listed in Table 1.

2.4. Rutile Solid Solution

TiO₂ rutile has a body-centered tetragonal structure which has non-stoichiometry toward the Ti₂O₃ direction and is usually expressed as TiO_2−δ. Eriksson and Pelton⁴⁾ was first to model the rutile solid solution using the simple Henrian solution model. Then, Kang et al.⁸⁾ further modified the solution by assigning a temperature dependent term to the Henrian activity coefficient of TiO_1.5 in order to reproduce all experimental data over wide range of temperatures. In the present study, the solubility of Al₂O₃ in the rutile solution was also considered for the first time.

Like the corundum solid solution, the rutile solution is modeled using the Bragg-Williams random mixing model¹¹⁾ considering TiO₂, TiO_1.5 and AlO_1.5 as the components. In the cation sites, random mixing of Ti⁴⁺ (TiO₂), Ti³⁺ (TiO_1.5) and Al³⁺ (AlO_1.5) was considered, and cation vacancies were assumed to remain associated with Ti³⁺ and Al³⁺ to maintain electrical neutrality and so do not contribute to the configurational entropy. Table 1 shows the assembly of Gibbs energy of rutile solution. The Gibbs energy of AlO_1.5 (pseudo-endmember) was modified to reproduce Al solubility in rutile from the present experimental data, and the Gibbs energy of ternary solution was calculated using the Kohler interpolation technique.¹³⁾ No ternary excess ternary parameter was required.

2.5. Stoichiometric Compounds, Metallic Phases and Gas Phases

In this study, the Gibbs energies of several stochiometric Magnéli phases (Ti_nO_2n−1, n ≥ 4) were taken from previous studies by Kang et al.⁸⁾ (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.³⁾ The Gibbs energy of Al₆Ti₂O₁₃ stoichiometric compound is evaluated in the present study.

3. Experimental Procedure and Results

Although phase equilibria in the oxidizing atmosphere (mostly in the Al₂O₃–TiO₂ system) are reasonably well known, the solubility of Al₂O₃ in TiO₂-rich rutile solution at high temperature is unexplored. Therefore, phase diagram study in air was conducted in this study mainly to obtain such solubility data.

Reagent grade powders of Al₂O₃ from Sigma Aldrich (99.99%) and TiO₂ from Sigma Aldrich (99.99%) were used to prepare the starting materials. These oxides were employed to guarantee the purity of the starting materials, which can exist in multivalent oxidation states (for example, Ti₂O₃). To remove hydroxide impurities or Ti₂O₃ from the TiO₂ reagent, Al₂O₃ and TiO₂ powders were heated overnight (16 hours) 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 powders were then removed from the ST–1700C furnace and allowed to cool down in a drying oven set at 393 K (120°C). To confirm the purities and oxidation states of starting materials, X-ray diffraction (XRD) analyses of pre-dried powders were conducted using Bruker Discover D8 X-ray diffractometer with a Co-Kα source (λ = 1.79 Å) equipped with HiSTAR area detector at McGill University.

Batch of 1 gram of starting material was prepared by mixing in appropriate proportions the reagents in an alumina mortar filled with isopropyl alcohol (<0.02 vol.% H₂O) for 30 minutes. 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 was taken out from the drying oven and allowed to reach room temperature in a desiccator. To prevent any contamination from crucible materials, 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 40–50 mg of starting material was tightly packed into each Pt capsule. 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.

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 Pt capsules were placed in a small porous alumina boat, suspended in the hot zone using a Pt–Rh wire and kept at the target temperature (1640 and 1660°C) for enough time to fully equilibrate the samples. After equilibration, the capsules were quenched in a bath filled with ice–cold water.

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 seconds 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). Spot analysis were performed with beam diameter kept at 3 μm. Raw data were reduced with the ZAF correction using corundum (Al) 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, all titanium was safely assumed in quadrivalent state, Ti⁴⁺ as the experiments were performed in air.

The experimental results for the key experiments at 1640 and 1660°C are summarized in Table 2 and the BSE images of one equilibrated sample (AT1) from EPMA are presented in Fig. 1. The small standard deviation (2σ) in the composition of each phase determined by EPMA indicates the samples were well equilibrated. No Al and Ti solubility in Pt crucible was detected and no Pt was detected in oxide phases.

Table 2. Result of the present quenching experiment for Al₂O₃–TiO₂ in air.

Sample	Starting mixture mole fraction		Temperature	Annealing time hours	Phases* (#analysis)	Phase composition mole fraction
	Al2O3	TiO2	°C			Al2O3	TiO2
AT1	0.334	0.667	1640	24	Psb (7)	0.495 ± 0.004	0.505 ± 0.004
					Rut (10)	0.981 ± 0.009	0.019 ± 0.009
AT2	0.334	0.667	1660	24	Psb (6)	0.499 ± 0.002	0.501 ± 0.002
					Rut (6)	0.981 ± 0.001	0.019 ± 0.001

*  Psb: Pseudobrookite, Rut: Rutile

Fig. 1.

Backscattered electron images of the equilibrated sample, AT1. (a) overview, and (b) close-up view.

4. Critical Evaluation/optimization of Experimental Data

All the thermodynamic property and phase diagram data of the Al₂O₃–Ti₂O₃–TiO₂ system available in the literature were first reviewed. New phase diagram experimental data from this study and all reliable experimental data (with known atmospheric conditions) from the literature^{23,24,25,26,27,28,29,30,31,32,33,34)} were then simultaneously considered to obtain a set of Gibbs energy functions for all the phases. The optimized model parameters in this study are listed in Table 1.

4.1. Ti₂O₃–TiO₂ Binary System

Figure 2 shows the calculated phase diagram of Ti–O (TiO₂–Ti₂O₃) system. The liquid parameters of the TiO₂–Ti₂O₃ system were revised from the previous study,⁸⁾ where the liquid solution was described by old Modified Quasichemical Model using equivalent fraction expression. In the current optimization, it was replaced with new Modified Quasichemical Model using pair fraction expression. This helped in better prediction of liquidus along the Ti–O region with less parameters and increase the predictive ability of Ti–containing multicomponent oxide system. The description of rutile solution for Ti–O system was taken directly from the previous study.⁸⁾ The Ti₃O₅ was initially treated as stoichiometric compound,^2,4,8) which is replaced in this study with pseudobrookite solid solution.⁶⁾ The details of the thermodynamic modeling and model parameters of Ti₃O₅ pseudobrookite solid solution can be found elsewhere.⁶⁾ Iso-oxygen partial pressure lines in the liquid phase are also calculated and plotted in Fig. 3. As can be seen, the equilibrium amount of Ti₂O₃ and TiO₂ in the liquid phase varies significantly with oxygen partial pressure and temperature.

Fig. 2.

Calculated optimized phase diagram of the Ti–O (Ti₂O₃–TiO₂) system along with iso oxygen pressure lines in the liquid slag.

Fig. 3.

Optimized heat capacity of Al₂TiO₅ from pseudobrookite solid solution along with the experimental data by King.³⁵⁾

4.2. Al₂O₃–Ti₂O₃–TiO₂ System

4.2.1. Thermodynamic Data

The optimized heat capacity of Al₂TiO₅ from the present pseudobrookite solution is shown in Fig. 3 along with the experimental data between 52.74 and 298.15 K measured by King³⁵⁾ using low temperature adiabatic calorimetry (Nernst Method⁴⁶⁾). Using Simpson rule integrations and Debye & Einstein function³⁷⁾ (below 52.74 K), King³⁵⁾ determined the entropy S°_{298.15 K} to be 109.42 ± 0.84 J mol⁻¹ K⁻¹. However, the current optimized entropy was set to be 121.82 J mol⁻¹K⁻¹ which takes into consideration the configurational entropy, ΔS_mix = – 2R (0.5ln0.5 + 0.5ln0.5) = 11.526 J mol⁻¹K⁻¹ of Al₂TiO₅ at 298.15 K, generated due to random mixing of cations (Al³⁺, Ti⁴⁺) in the second sublattice (8f) of Al₂TiO₅ at room temperature, i.e. (Al³⁺)^4c(Al³⁺, Ti⁴⁺)₂^8fO₅. Figure 4 shows the calculated heat content (H_T – H_298.15) of Al₂TiO₅ from the current pseudobrookite solution along with the experimental data by Bonnickson³⁸⁾ between 411 and 1803.2 K using drop calorimetry. The enthalpy of Al₂TiO₅ at 298.15 K (ΔH°_298.15) was estimated using the Neumann–Kopp (N–K) rule from its constituent oxides (Al₂O₃ and TiO₂) and modified to reproduce its phase stability region in air atmosphere (all values listed in Table 1).

Fig. 4.

Calculated heat content (H_T – H_298.15) of Al₂TiO₅ from the present pseudobrookite solid solution along with the experimental data by Bonnickson.³⁸⁾

The thermodynamic properties of stoichiometric Al₆Ti₂O₁₃ have been rarely studied. No low-temperature and high-temperature heat capacities were measured and, therefore, the enthalpy and entropy at 298.15 K (ΔH°_298.15, S°_298.15) and heat capacity were estimated from its constituent oxides (Al₂O₃ and TiO₂) using the Neumann–Kopp (N–K) rule¹⁷. The estimated H°_298.15 and S°_298.15 were then revised (ΔH°_298.15 = – 677.20 kJ mol⁻¹ and S°_298.15 = 339.00 J mol⁻¹K⁻¹) during the optimization to fix the high-temperature stability suggested by different authors.^39,40,41)

4.2.2. Structural Data

The calculated cation distribution of Al₂TiO₅ from the present study is shown in Fig. 5. Recently, Ohya et al.⁴²⁾ determined the cation distribution in Al₂TiO₅ pseudobrookite compound at 600–1500°C using XRD Rietveld analysis. They found partial decomposition of Al₂TiO₅ to corundum (Al₂O₃) and rutile (TiO₂) when annealed at 1100 and 1200°C for 1 hour and complete decomposition at 1200°C after 10 hours of annealing time. No decomposition was found at 600°C after 100 hours of annealing time. After water quenching, Rietveld analysis were performed on Al₂TiO₅ XRD pattern for all temperatures. It is well-known from Jung et al.^43,44) that the cation distribution can be frozen at low temperature due to the slow kinetic of cation-exchange reactions. Therefore, the experimental data collected at 600°C can most probably be in non-equilibrium state. Similarly, Skala et al.⁴⁵⁾ synthesized Al₂TiO₅ from Al₂O₃ and TiO₂ at 1550°C and then performed XRD Rietveld analysis for the furnace-cooled sample. They reported about 0.4 occupancy of Ti⁴⁺ in 4c site. It should be noted that the experimental data from Ohya et al.⁴²⁾ and Skala et al.⁴⁵⁾ are consistent each other, and they are reasonably well reproduced in the present study. As discussed above in section 2, the end member Gibbs energy of G_TA was determined to reproduce this cation distribution data.

Fig. 5.

Calculated cation distribution in Al₂TiO₅ pseudobrookite solution along with the experimental data.^42,45)

4.2.3. Phase Diagram Data

The phase equilibria of the Al₂O₃–TiO₂–Ti₂O₃ system strongly dependent on temperature and oxygen partial pressure.

(1) Air Atmosphere

The calculated phase diagram of the Al₂O₃–TiO₂ system in air atmosphere is shown in Fig. 6 along with the experimental data^{23,24,28,29,30,34)} and current experimental data discussed below. The Al₂O₃–TiO₂ was first studied by von Wartenberg and Reusch²³⁾ and by Bunting²⁴⁾ using thermal analysis (TA) technique and petrographic microscope (PM). The former gave the intermediate compound to be Al₂Ti₂O₇, while the later reported Al₂TiO₅ (tialite). Later, Gulamova and Sarkisova³⁰⁾ conducted similar experiments using TA signifying Al₂TiO₅ as intermediate compound. Goldberg²⁸⁾ preformed phase equilibrium experiments using quenching technique (QT) and optical microscopic (OM) analysis and reported the eutectic at 1703°C and 80.13 mole% TiO₂. Slepetys and Vaughan²⁹⁾ determined the Al₂O₃ solubility in TiO₂ from 1200 to 1426°C ranging from 0.49 mol% to 1.55 mol%. They provided a temperature error range of 30–60°C. Recently, Ilatovskaia et al.³⁴⁾ performed thermal analysis (TA–DSC/DTA) and quenching experiments along with XRD and SEM/EDX for phase analysis between 1060 to 1840°C.

Fig. 6.

Calculated phase diagram of the Al₂O₃–TiO₂ in air along with the experimental data from the literature^{23,24,28,29,30,34)} and current experimental data.

Unfortunately, as the solubility of Al₂O₃ in TiO₂ rutile solution is not available near the eutectic temperature between Al₂TiO₅ and TiO₂ at about 1710°C, we performed the phase equilibrium experiments at the present study to constrain the solubility limit of Al₂O₃ in TiO₂ rutile solution. Two samples were prepared for equilibration at 1640 and 1660°C. From the current experimental data, 2 mol% Al₂O₃ solubility in rutile solid solution was found at this high temperature. As Ti₃O₅ is not stable in air, no measurable inhomogeneity range of Al₂TiO₅ pseudobrookite phase was detected at 1640 and 1660°C. Wartenburg and Reusch,²³⁾ Goldberg²⁸⁾ and Ilatovskaia et al.³⁴⁾ experimental measurements were used to fix the liquidus between Al₂O₃ and TiO₂. To fix the Al₂O₃ solubility in TiO₂, measurements performed from the current study and from Sleptys and Vaughan²⁹⁾ were used. Ilatovskaia et al.³⁴⁾ measurements were used to fix the eutectic temperature and decomposition temperature of Al₂TiO₅. The optimized eutectic (L → Al₂TiO₅ + TiO₂) temperature and composition are 1710°C and 81.80 mole% TiO₂, respectively which is close to the experimental data of Goldberg²⁸⁾ (1703°C and 81.13 mole% TiO₂) and Ilatovskaia et al.³⁴⁾ (1715°C and 83.70 mole% TiO₂), as shown in Fig. 6.

The melting temperature (between 1850 and 1863°C) and decomposition temperature (between 1240 and 1295°C) of Al₂TiO₅ pseudobrookite solution in air atmosphere were determined by many authors using different techniques,^{24,25,28,29,33,46,47,48,49,50)} as shown in Table 3. There was a dispute on the presence of a high temperature compound or a high allotropic form of Al₂TiO₅ close to its decomposition temperature. Lang et al.⁴⁶⁾ performed experiments by visually measuring the melting temperatures for different compositions combined with petrographic and XRD studies of unquenched samples and suggested the presence of high allotropic form of Al₂TiO₅ between 1820 to 1860 ± 10°C. Due to the extreme experimental conditions of high temperature and high melt viscosity, they propose two versions of their phase diagrams with distinct invariant points: one with a eutectic point (L → Al₂TiO₅ + Al₂O₃), the other with a peritectic point (L + Al₂O₃ → Al₂TiO₅). The optimized melting and decomposition temperatures of Al₂TiO₅ are 1860 and 1279°C, respectively, in the present study.

Table 3. Optimized melting and decomposition temperature of Al₂TiO₅ (tialite) compared with experimental data.^{24,25,28,29,33,50,51,52,53,54)}

Temp., °C	Technique	Reference	Temp., °C	Technique	Reference
Al2TiO5 → Liq (Melting)			AlTi2O5 → Al2O3 + TiO2 (Decomposition)
1860	TA, PM	24)	1240	QM, XRD	29)
1850 ± 30	TA	25)	1280	QM, XRD	33)
1860	QM, OM	28)	1262 ± 7	QM, PM, XRD	47)
1850	DTA	29)	1295	IH	48)
1863	VT, OM, XRD	46)	1280	QM, XRD	49)
1860	Optimized	Present Study	1280	In-situ ND	50)
			1279	Optimized	Present Study

QM: Quenching Method, OM: Optical Microscopy, DTA: Differential Thermal Analysis, VT: Visual Technique, XRD: X-Ray Diffraction, TA: Thermal analysis, PM: Petrographic Microscopy, IH: Isothermal Heating, ND: Neutron Diffraction

Apart from Al₂TiO₅, Lejus et al.⁵¹⁾ found two new compounds with compositions between 33 and 40 mol% TiO₂ which are stable in the approximate temperature range between 1800 and 1900°C. In the previous optimization, Jung et al.²⁾ adopted Al₄TiO₈ as the high temperature compound. However, Hoffman et al.,³⁹⁾ Norberg et al.,⁴⁰⁾ and Berger et al.⁴¹⁾ suggested the high temperature phase to be Al₆Ti₂O₁₃. Norberg et al.⁴⁰⁾ was first to synthesize single crystal Al₆Ti₂O₁₃ and confirmed by energy-dispersive XRD. They proposed a refined structure of Al₆Ti₂O₁₃ and indicated the crystal structure to be orthorhombic and space group Cm2m which is similar to mullite, Al₆Si₂O₁₃. Later on, Berger et al.⁴¹⁾ perform directional solidification experiments at three compositions (0.11, 0.26, 0.439 mole fraction of TiO₂) at Al₂O₃ rich side using laser heat floating zone method along with microstructural characterization using XRD, WDX, SEM, HRTEM and STEM-EDX. From their observations, they suggested the formation of high temperature phase, Al₆Ti₂O₁₃ and the invariant reaction to be eutectic (L → Al₂TiO₅ + Al₆Ti₂O₁₃) and peritectic (L + Al₂O₃ → Al₆Ti₂O₁₃), which confirms the suggestion made by Lang⁵⁰⁾ but with different invariant reactions. Berger et al.⁴¹⁾ could not able to measure the exact temperature of the eutectoid or solidification reaction. In the present study, Al₆Ti₂O₁₃ is believed to be stable at high temperature between 1797°C to 1857°C as shown in Fig. 6.

(2) Reducing Atmosphere

The calculated phase diagram of the Al₂O₃–Ti₂O₃ system in reducing atmosphere (p_O2 = 10^-16 atm) is shown in Fig. 7 along with the experimental data discussed below. McKee and Aleshin²⁵⁾ determined the solubility of Ti₂O₃ in the Al₂O₃ corundum solution in H₂ gas atmosphere at 1400, 1600, 1700°C. The used lattice parameter data from X-ray diffraction measurements of quenched samples to measure the Ti₂O₃ solubility in corundum. No solubility of Al₂O₃ in Ti₂O₃ was found in their study. Later, Belon and Forestier²⁷⁾ investigated the phase diagram under vacuum using both X-ray diffraction technique and optical pyrometer. They reported a maximum solubility of Ti₂O₃ in Al₂O₃ of 12.5 mol% near 1700°C. The eutectic temperature was found to be about 1695°C from high temperature optical pyrometer, which was well reproduced in our present optimization within experimental error limits. Horibe and Kuwabara²⁶⁾ used experimental technique to determine the solubility of Ti₂O₃ in Al₂O₃ corundum solution under high purity Ar gas atmosphere along with liquidus measurements throughout the whole composition range. They prepared the Ti₂O₃ by reducing TiO₂ under CO gas at 1400°C. They reported the solubility of Ti₂O₃ in Al₂O₃ to be 2.7 mol % at 1710°C. Yasuda et al.³¹⁾ performed XRD measurements on Al₂O₃-3 mol% Ti₂O₃ quenched samples in order to determine the phases and calculated the Ti₂O₃ solubility in Al₂O₃ corundum solid solution using lattice constant measurements. Equilibrium experiments were performed at Ar-5% H₂ gas (reducing atmosphere) for 1400, 1500, 1600 and 1700°C. As, the oxygen partial pressure is not accurately known for pure gases (H₂, Ar, Ar-5%H₂) and vacuum for above experimental data, therefore, are being compared at reducing atmosphere (p_O2 = 10^-16 atm) as shown in Fig. 7. Recently, Ohta and Morita³²⁾ determined the reciprocal solid solubility of Ti₂O₃ and Al₂O₃ in corundum and ilmenite solid solution at 1600°C in oxygen partial pressure, respectively at (p_O2 = 10^-16 atm). The XRD lattice parameter data (d-spacing) of quenched sample (using Ar gas) at 50 mass% TiO₂ was used to determine the reciprocal solubility. They reported solubility of 4.57 mol% Ti₂O₃ in Al₂O₃ corundum solid solution and 5.07 mol% Al₂O₃ in Ti₂O₃-rich ilmenite solid solution. Mizoguchi and Ueshima³³⁾ performed ternary phase equilibrations in the CaO–Ti₂O₃–Al₂O₃ system at p_O2 = 10⁻¹⁴ – 10⁻¹⁵ atm and reported 21.3 and 17.6 mol% Al₂O₃ solubility in the Ti₂O₃ ilmenite solid solution at 1550 and 1600°C, respectively. The samples were quenched using Ar gas and phases were analyzed by SEM-EDS.

Fig. 7.

Calculated phase diagram of the Al₂O₃–Ti₂O₃ in reducing atmosphere (p_O2 = 10^-16 atm) along with the experimental data.^{26,27,28,31,32,33)}

In Fig. 7, the phase diagram was calculated at p_O2 = 10⁻¹⁶ atm. In the present evaluation, more preference was given to solubility data by Ohta and Morita³²⁾ due to its well-controlled oxygen partial pressure in the experiments. The solubility data by Mizoguchi and Ueshima³³⁾ are strangely much larger than other studies.^25,26,31,32) The eutectic temperature and liquidus in the present study are consistent with the experimental data by Belon and Forestier²⁷⁾ and Horibe and Kuwabara,²⁶⁾ respectively.

(3) Al₂TiO₅–Ti₃O₅ Section

As pointed out in the thermodynamic model, both Al₂TiO₅ and Ti₃O₅ belong to pseudobrookite solid solution. Matsuura¹⁾ equilibrated liquid Fe–Al–Ti metal with Al₂TiO₅ pellet in Al₂O₃ crucible at 1600°C for 3 hours under Ar-3%H₂ atmosphere. Then, the interface between metal and Al₂TiO₅ was analyzed using SEM-EDS, which showed the formation of Ti oxide phase containing about 10 mol% Al and Al₂O₃ phase containing about 3 mol%Ti. This Ti oxide phase is believed to be Ti₃O₅ phase containing a considerable amount of Al₂TiO₅. In fact, this is the only literature data which revealed the solubility of Al in Ti₃O₅ phase. Figure 8 shows the calculated isopleth of Al₂TiO₅–Ti₃O₅ in this study. The result of Matsuura¹⁾ is plotted in the figure. In order to reproduce the experimental data, a large miscibility gap between Al₂TiO₅ and Ti₃O₅ was considered in the pseudobrookite solid solution.

Fig. 8.

Calculated isopleth of the Al₂TiO₅–Ti₃O₅ along with the experimental data by Matsuura.¹⁾

(4) Liquidus Projection

The calculated liquidus projection of Al₂O₃–TiO₂–Ti₂O₃ system from the present study is shown in Fig. 9 and the invariant reaction points are listed in Table 4. A small adjustable ternary model parameter is used in the Al₂O₃–Ti₂O₃–TiO₂ liquid oxide phase in the present study to make sure that there is no liquid phase forming between Al₂TiO₅ and Ti₃O₅ at 1600°C (see Fig. 8). There is no phase diagram measurement available in the literature for this ternary system. No ternary solid phases have been reported in the literature. Pseudobrookite solid solutions containing Al₂TiO₅-rich and Ti₃O₅-rich phase can be clearly seen in the liquidus projection.

Fig. 9.

Calculated (predicted) liquidus projection of the Al₂O₃–TiO₂–Ti₂O₃ system.

Table 4. Invariant reactions in the Al₂O₃–TiO₂–Ti₂O₃ system involving liquid phase, calculated from the present optimization.

No.a	Phases in equilibrium with liquid*	Composition (mole fraction)			Temp., (°C)
		Al2O3	Ti2O3	TiO2
1	Cor + Psb + Al6Ti2O13	0.566	0.028	0.406	1829
2	Rut + Ti10O19 + Ti20O39	0.005	0.210	0.785	1714
3	Rut + Ti9O17 + Ti10O19	0.044	0213	0.743	1675
4	Rut + Ti8O15 + Ti9O17	0.101	0.205	0.693	1639
5	Ilm + Cor + Psb	0.242	0.440	0.318	1611
6	Psb + Rut + Ti8O15	0.153	0.196	0.651	1610
7	Psb + Ti7O13 + Ti8O15	0.153	0.203	0.644	1607
8	Cor + 2 Psb	0.257	0.287	0.456	1602
9	Psb + Ti6O11 + Ti7O13	0.154	0.222	0.624	1599
10	Psb + Ti5O9 + Ti6O11	0.155	0.243	0.602	1591

^a  The number index of the invariant reaction points are the same as the ones in Fig. 8.

*  Cor: Corundum, Psb: Pseudobrookite, Ilm: Ilmenite, and Rut: Rutile phase

Figure 10 predicts the isothermal phase diagram between Al₂O₃–TiO₂–Ti₂O₃ at 1600°C. Although the phase diagram between Al₂O₃–TiO₂ at air (see Fig. 6) and Al₂O₃–Ti₂O₃ at p_O2 = 10⁻¹⁶ atm (see Fig. 7) shows no stable liquid phase at 1600 °C, the ternary liquid interpolation technique (without any parameter) used in current modeling predicts the stability of liquid phase up to 1590°C. Therefore, a small positive ternary liquid parameter was used for reproducing the experimental data of Matsuura¹⁾ at 1600°C, which shows immiscibility within Al₂TiO₅–Ti₃O₅ system (see Fig. 9). As, there are no direct phase equilibrium experiments to confirm the phase equilibria between Al₂O₃–Ti₂O₃–TiO₂ at 1600°C (shown in Fig. 10), few indirect experiments confirmed the stability of oxides. Doo et al.⁵²⁾ reported the inclusions in Al-killed Ti-bearing steel in the RH process at 1600°C. They found rugged-surface spherical complex oxide inclusions, composed of Al₂O₃ corundum and Al–Ti–O phase with Ti/Al ratio of 1.0 to 2.3 found using EPMA. The inclusion data support the existence of pseudobrookite phase complex phase (Ti_3−xAl_xO₅, 0 ≤ x ≤ 2) in equilibrium with Al₂O₃-rich corundum phase, as shown as shaded area in Fig. 10.

Fig. 10.

Calculated (predicted) isothermal phase diagram of the Al₂O₃–TiO₂–Ti₂O₃ system at 1600°C.

5. Inclusion Stability Diagram and Nozzle Clogging of Al-killed Ti Bearing Steel

During the continuous casting of Al-killed Ti bearing steel, the steel consisting of non-metallic inclusions (Al₂O₃, Ti₂O₃, Al₂TiO₅, Ti₃O₅) and solidified liquid oxide (Al₂O₃–TiO_x) causes severe clogging of submerged entry nozzle.^53,54) Numerous researchers^51,54,55) have investigated the inclusions causing nozzle clogging in Al-killed Ti-bearing steel and Al-killed Ti-free steel and found the difference to be the existence of complex Al–Ti–O inclusion covering Al₂O₃. They reported the reason behind the nozzle clogging is due to reoxidation of molten steel (Al and Ti) by liquid tundish slag containing high SiO₂ content, or the reducible oxide (FeO and MnO) contained in ladle slag after Al-killing. Another important reason of nozzle clogging found by various authors^54,56,57) is the carbothermic reduction of impurities (SiO₂, Na₂O) present within Al₂O₃–C SEN refractories at continuous casting temperature (< 1600°C). It releases SiO and CO gases which can oxidize Al and Ti in molten steel, and formin-situ Al₂O₃ corundum and Al₂TiO₅ pseudobrookite phase on SEN surface during casting process. Therefore, accurate knowledge on thermodynamics and phase equilibria in the Al–Ti–O and Fe–Al–Ti–O system is a crucial step to predict the oxide phases in equilibrium with liquid steel for different steel compositions.

Ruby-Meyer et al.⁵⁸⁾ was first to propose the “inclusion stability diagram” in the Fe–Al–Ti–O system at 1580°C using the CEQSI code based on slag model.⁵⁹⁾ They showed the formation of Al₂TiO₅ (stoichiometric compound), and liquid (TiO_x–Al₂O₃) phase between Al₂O₃ and Ti₂O₃ stable phase. Although Ti₃O₅ pseudobrookite should exist in low Al region, it was shown in the calculated diagram. Jung et al.⁶⁰⁾ proposed a new stability diagram at 1600°C by using oxide database (FToxid) from FactSage 5.3 version, to perform similar calculations and found Ti₃O₅ phase and Al₂TiO₅ phase stable between Al₂O₃ and Ti₂O₃ stable phases, and no liquid phase was calculated. Later, Jung et al.²⁾ revised the thermodynamic database of the Al₂O₃–Ti₂O₃–TiO₂ system (FactSage 6.3–7.2 version) and calculated the inclusion diagram again. Their new diagram indicated the formation of liquid phase between Ti₃O₅ and Al₂O₃ corundum phase, but no Al₂TiO₅ phase was calculated. Kim et al.⁶¹⁾ also reported the phase stability diagram of oxides by equilibrating with Fe–Al–Ti melt at 1600°C in which the stable oxide phases are Al₂O₃, Ti₂O₃ and Ti₃O₅. Matsuura¹⁾ and Choi et al.⁶²⁾ experimentally measured the inclusion in Al killed and Ti bearing steel at 1600°C and proposed the formation Al₂O₃ phase containing TiO_x and TiO_x phase containing Al₂O₃ as stable phase for steels containing O < 60 ppm. Jo⁶³⁾ found out the formation of only Ti₃O₅ and Al₂O₃ stable phases for steels containing O < 40 ppm. He equilibrated the liquid Fe–Al–Ti alloy in an Al₂O₃ crucible at 1600°C and used ICP for analysis of Al and Ti concentrations in the liquid alloy, LECO for O concentrations, and SEM and EBSD for interface between the liquid alloy and Al₂O₃ crucible. Recently, Kang and Lee¹²⁾ slightly revised the thermodynamic database of the Al₂O₃–Ti₂O₃–TiO₂ system from Jung et al.¹⁾ and made the liquid oxide phase slightly less stable. As result, their inclusion stability diagram showed the formation of liquid oxide phase only at low Al and Ti region where [O] > 50 ppm and the formation of Al₂O₃ and Ti₃O₅ oxides at high Al and Ti region where [O] < 50 ppm. In general, most of the available inclusion diagrams in the Fe–Al–Ti–O system can be summarized into two groups: (i) diagram containing only solid Al₂O₃, Ti₂O₃, Ti₃O₅, and Al₂TiO₅ phases, and (ii) diagram containing Al₂O₃, Ti₂O₃, Ti₃O₅ and liquid phases.

Based on the present optimization results of the Al–Ti–O oxide system, the inclusion stability diagram for Fe–Al–Ti–O system has been re-calculated in Fig. 11. In order to construct this diagram, both oxide and liquid steel databases containing all the elements are necessary. For the oxide database, the present model parameters for Al–Ti–O system were combined with the newly optimized parameters for Fe–Ti–O system⁶⁾ (Fe₂O₃–Ti₂O₃–TiO₂) and Fe–Al–O (FeO–Fe₂O₃–Al₂O₃)⁶⁴⁾ systems. For the molten steel phase, the FactSage FTmisc (FeLQ) database³⁾ was used.

Fig. 11.

Calculated (predicted) oxide stability diagram of the Fe–Al–Ti–O system at 1600°C in the present study along with the experimental data.^1,58,61,63) Thin lines are iso-O (wt. ppm) lines. (Online version in color.)

Figure 11 show inclusion stability diagram of Fe–Al–Ti–O system at 1600°C along with the experimental data.^1,58,61,63) Thin lines denote the calculated iso-oxygen line (ppm) and thick lines denote the phase boundaries between two different oxide inclusion phases. The most stable oxide inclusions formed during the production Al-killed Ti bearing steel are Al₂O₃-rich corundum phase and Ti₃O₅-rich pseudobrookite phase. A small stability region of Al₂TiO₅-rich pseudobrookite is calculated in low Al and Ti region. Most of the low Al and Ti region is occupied by liquid oxide phase mainly of FeO–Al₂O₃–Ti₂O₃–TiO₂. Compared to the previous stability diagram by the present author²⁾ the stability region of liquid oxide phase is shrunk a lot because the liquid slag phase optimized in this study is less stable than the previous one by about 50°C, as mentioned in Fig. 9. A small region of the Al₂TiO₅-rich pseudobrookite is calculated because this phase is described as a pseudobrookite solution phase rather than a stoichiometric Al₂TiO₅ solid phase as in the previous study, and its Gibbs energy is relatively more stable than the previous study. Both Ti₃O₅-rich pseudobrookite and liquid oxide phase contain noticeable amount of FeO in low Al and Ti region of the diagram.

Compared to the inclusion diagrams in the previous works, one of the main differences of the present diagram is the existence of both liquid and Al₂TiO₅ phases. The only diagram containing both phases was drawn by Ruby-Meyer et al.,⁵⁸⁾ but Ti₃O₅ phase was not considered in their diagram, and the liquid oxide phase always existed between Ti₂O₃ and Al₂O₃. In many Al/Ti complex deoxidation experiments,^65,66,67) Al₂O₃/TiO_x complex inclusions were frequently found in high Al and Ti content region of molten steel, and the Al–Ti–O inclusions (cluster-type Al–Ti–O inclusions (solid Al₂TiO₅ inclusions), and random compositional Al–Ti–O inclusions (liquid oxide inclusions)) were observed in low Al and Ti region of molten steel. The occurrence of such inclusions can be more easily explained by the present inclusion diagram in Fig. 11, than the previous diagrams. That is, the formation of complex Al₂O₃/TiO_x (TiO₂ or Ti₃O₅) inclusions where TiO_x inclusion covered by Al₂O₃ layer tells that the inclusion diagram should have Al₂O₃ and TiO_x (TiO₂ or Ti₃O₅) phase boundary without liquid phase in-between. This is well explained by the present diagram but not from the one by Ruby-Meyer et al.⁵⁸⁾ The liquid inclusion of Al₂O₃–Ti₂O₃–TiO₂(–FeO) and solid Al₂TiO₅ phase calculated in the present diagram are also well matching with Al–Ti–O inclusion in low Al and Ti region.

In order to simulate the reoxidation of Al-killed and Ti bearing steel by CO gas in SEN at 1550°C, thermodynamic calculations were performed, and the results are given in Fig. 12. The partial pressure of CO gas was varied from 0.1 to 1 atm, and Ti content and Al content are fixed at 400 and 100 wt. ppm, respectively. As can be seen in Fig. 12, CO gas produced by carbothermic reduction process can form liquid slag, Al₂TiO₅ pseudobrookite, Ti₃O₅ pseudobrookite and Al₂O₃ phase depending on the degree of reoxidation of molten steel. That is, the original Al-killed and Ti bearing steel where Al = about 400 wt. ppm and Ti = about 800 wt. ppm can contain Al₂O₃ inclusions, but the chemistry of inclusions can be changed with decreasing soluble Al and Ti by reaction with CO gas (as shown in Fig. 12). This can be also understood from the inclusion diagram in Fig. 11. Such oxide products from reoxidation can be deposited on SEN which results in nozzle clogging.

Fig. 12.

Reoxidation of Al-killed Ti bearing steel by CO gas at 1550°C, (a) Ti = 400 wt. ppm and (b) Al = 100 wt. ppm.

6. Conclusions

A complete review and critical evaluation of all available phase diagrams, thermodynamic and structural data for the Al₂O₃–TiO₂–Ti₂O₃ system at a total pressure of 1 atm has been carried out. The equilibrium experiments of Al₂O₃–TiO₂ in air were also performed and revealed about 2 mol% solubility of Al₂O₃ in TiO₂ rutile solution. The thermodynamic model with optimized parameters can reproduce most of reliable experimental data from room temperature to above liquidus under the oxygen partial pressures ranging from 10⁻²⁴ to 1 atm within ± 10°C and ± 1 mol% compositional range. The unexplored phase equilibria and thermodynamic properties of the system are also predicted. Compared to the previous optimization, the major update of this study is the modeling of Al₂TiO₅ and Ti₃O₅ as part of pseudobrookite solid solution. The stability diagram of Fe–Al–Ti–O system was calculated using the new optimization results. In addition, the possible reoxidation phenomenon of Al-killed and Ti bearing steel by CO gas is calculated. The present database containing optimized parameters along with general thermodynamic software, such as FactSage, can calculate phase equilibria and thermodynamic properties at any given set of conditions under 1 atm total pressure.

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 are gratefully acknowledged. This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF- 2015R1A5A1037627). One of the authors (S. K. Panda) would like to thank the McGill Engineering Doctorate Award (MEDA) program.

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