Reoxidation of Aluminum in Fe-Al-M (M = C,Mn, and Ti) melts with CaO-Al2 O3-Fe t O (3 mass pct) slags

An Fe-0.01 to 0.5 mass pctAl alloy and an Fe-0.003 to 0.71 mass pctAl-1 mass pctM (M = C, Mn, and Ti) alloy were reoxidized with the CaO-Al₂O₃-Fe_tO (3 mass pct) slags at 1873 K in an Al2O3 or CaO crucible for 5 and 60 minutes. The contents of acid-insoluble Al, total O, and alloying element M in metal as well as those of M and FetO in slag were measured as a function of total Al content. On the basis of the present and previous results for Fe-Al-Te alloys, the effect of alloying elements on the degree of supersaturation with respect to the Al2O3 precipitation was studied. As a result, the supersaturation phenomenon was observed in all experiments at 5 minutes, but in the experiments at 60 minutes, it was observed only in Fe-Al and Fe-Al-Ti alloys. No supersaturation was observed in the reoxidation of Si in Fe-0.13 to 0.98 mass pctSi alloys with the CaO-SiO2-FetO (3 mass pct) slags in a CaO crucible at 5 and 60 minutes.     

Enrichment Mechanism of Phosphate in CaO-SiO2-FeO-Fe2O3-P2O5 Steelmaking Slags

The phosphate-enrichment behavior has experimentally been investigated in CaO-SiO₂-FeO-Fe₂O₃-P₂O₅ steelmaking slags. The reaction ability of structural units in the slags has been represented the mass action concentration \( N_{i} \) from the developed ion and molecule coexistence theory (IMCT)- \( N_{i} \) model based on the IMCT. The defined enrichment possibility \( N_{{{\text{c}}i{\text{ {-}c}}j}} \) and enrichment degree \( R_{{{\text{c}}i{\text{{-}c}}j}} \) of solid solutions containing P₂O₅ from the developed IMCT- \( N_{i} \) model have been verified from the experimental results. The effects of binary basicity, the mass percentage ratio \( {{ ( {\text{pct Fe}}_{t} {\text{O)}}} \mathord{\left/ {\vphantom {{ ( {\text{pct Fe}}_{t} {\text{O)}}} { ( {\text{pct CaO)}}}}} \right. \kern-0pt} { ( {\text{pct CaO)}}}} \) , and mass percentage of P₂O₅ in the initial slags on phosphate-enrichment behavior in the slags has also been discussed. The results show that the P₂O₅ component can easily be bonded by CaO to form tricalcium phosphate 3 CaO·P₂O₅, and the formed 3CaO·P₂O₅ can react with the produced dicalcium silicate 2CaO·SiO₂ to generate solid-solution 2CaO·SiO₂-3CaO·P₂O₅ under fixed cooling conditions. The maximum value of the defined enrichment degree \( R_{{{\text{C}}_{ 2} {\text{S{-}}} {\text{C}}_{ 3} {\text{P}}}} \) of solid-solution 2CaO·SiO₂-3CaO·P₂O₅ is obtained as 0.844 under conditions of binary basicity as 2.5 and the mass percentage ratio \( {{ ( {\text{pct Fe}}_{t} {\text{O)}}} \mathord{\left/ {\vphantom {{ ( {\text{pct Fe}}_{t} {\text{O)}}} { ( {\text{pct CaO)}}}}} \right. \kern-0pt} { ( {\text{pct CaO)}}}} \) as 0.955 at fixed cooling conditions.     

Solubility of carbon in CaO-Al2O3 melts

Carbon distribution ratios between CaO-Al₂O₃ slags and Fe-0.0003 to 0.8 mass pct Al-0.2 to 5.6 mass pct C alloys were measured at 1873 K in an Al₂O₃, CaO, or graphite crucible. The carbon distribution ratios were dependent on the oxygen potential, determined by theAl/(Al₂O₃) equilibrium, not by theC/CO (P _co = 1 atm) equilibrium. The (mass pct C)/a _c ratios were proportional to the activity of Al in logarithmic form with a slope of 2/3, indicating that carbon in slag is dissolved as C^2? ion. Solubilities of carbon in CaO-Al₂O₃ slags were also measured at 1873 K under the CO-CO₂-Ar gas mixtures in an Al₂O₃ or graphite crucible. It was found that C^2? ion is present in the range of log $P_{O_2 } $ (atm) < ?15 and CO ₃ ^2? ion in the range of log $P_{O_2 } $ (atm) > ?7.     

The morphology and substructure of highly tetragonal martensites in Fe-7 pct Al−C steels

This investigation reports on an optical and electron microscope study of bct martensite formed in Fe-7 pct Al-1.5 pct C and Fe-7 pct Al-2.0 pct C alloys. In each case the martensite is plate-like containing \((112)[\bar 1\bar 11]\) transformation twins 100 to 200Å in width. The particular twin plane variant \((112)[\bar 1\bar 11]\) corresponds to the martensite habit plane variant (3, 15, 10)_F, which is predicted by the crystallography theory. The twins are uniformly spaced and extend completely from one martensite-austenite interface to the other as would be theoretically expected. The martensite plates are ideally lenticular in the 2 pct C alloy but those in the 1.5 pct C alloy frequently exhibit irregular interfaces which are attributed to impingement effects. All observations are in accordance with the phenomenological crystallography theory as applied to ferrous martensites with a {3, 15, 10}_F habit plane.     

Ti3Ga and αTi interdiffusion between 660° and 860°C

Diffusion experiments were conducted in vacuum with bimetallic couples of the Ti₃Ga (α₂) composition and unalloyed α titanium. The gallium-composition profiles after various timetemperature exposures were determined by microprobe analyzer transverses and evaluated by established techniques. Results from this evaluation include the definition of the α to α +α₂ and the α + α₂ to α₂ phase boundaries for the Ti?Ga system and the determination of the interdiffusion coefficients for gallium in the α Ti and Ti₃Ga (α₂) phases. The interdiffusion coefficients were found to conform to the relationships: $$\tilde D_{\alpha Ti} = 4.4 \times 10^{ - 4} \exp [ - (43.4 \pm 4.7)10^3 /RT]cm^2 /\sec $$ $$\tilde D_{\alpha Ti_3 Ga} = 7.4 \times 10^{ - 5} \exp [ - (43.8 \pm 10.7)10^3 /RT]cm^2 /\sec $$      

Iron redox equilibria in CaO-Al2O3-SiO2 and MgO-CaO-Al2O3-SiO2 slags

Measurements have been made of the ratio of ferric to ferrous iron in CaO-Al₂O₃-SiO₂ and MgO-CaO-Al₂O₃-SiO₂ slags at oxygen activities ranging from equilibrium with pCO₂/pCO≈0.01 to as high as air at temperatures of 1573 to 1773 K. At 1773 K, values are given by $\begin{gathered} \log {\text{ }}\left( {\frac{{Fe^{3 + } }}{{Fe^{2 + } }}} \right) = 0.3( \pm {\text{ }}0.02){\text{ }}Y + {\text{ }}0.45( \pm {\text{ }}0.01){\text{ }}\log \hfill \\ \left( {\frac{{pCO_2 }}{{pCO}}} \right) - 1.24( \pm {\text{ }}0.01) \hfill \\ \end{gathered} $ where Y=(CaO+MgO)/SiO₂, for melts with the molar ratio of CaO/SiO₂=0.45 to 1.52, 10 to 15 mol pct Al₂O₃, up to 12 mol pct MgO (at CaO/SiO₂≈1.5), and with 3 to 10 wt pct total Fe. Available evidence suggests that, to a good approximation, these redox equilibria are independent of temperature when expressed with respect to pCO₂/pCO, probably from about 1573 to 1873 K. Limited studies have also been carried out on melts containing about 40 mol pct Al₂O₃, up to 12 mol pct MgO (at CaO/SiO₂≈1.5), and 3.6 to 4.7 wt pct Fe. These show a strongly nonideal behavior for the iron redox equilibrium, with $\frac{{Fe^{3 + } }}{{Fe^{2 + } }} \propto \left( {\frac{{pCO_2 }}{{pCO}}} \right)^{0.37} $ The nonideal behavior and the effects of basicity and Al₂O₃ concentration on the redox equilibria are discussed in terms of the charge balance model of alumino-silicates and the published structural information from Mössbauer and NMR (Nuclear Magnetic Resonance) spectroscopy of quenched melts.     

Fabrication and Characterization of Naturally Selected Epitaxial Fe-{111} Y2Ti2O7 Mesoscopic Interfaces: Some Potential Implications to Nano-Oxide Dispersion-Strengthened Steels

The smallest features of ≈2 to 3 nm in nanostructured ferritic alloys (NFA), a variant of oxide dispersion-strengthened steels, include the Y₂Ti₂O₇ complex oxide cubic pyrochlore phase. The interface between the bcc Fe-Cr ferrite matrix and the fcc nanometer-scale Y₂Ti₂O₇ plays a critical role in the stability, strength, and damage tolerance of NFA. To complement other characterization studies of the actual nanofeatures (NF) themselves, mesoscopic interfaces were created by electron beam deposition of a thin Fe layer on a 5 deg miscut {111} Y₂Ti₂O₇ bulk single crystal surface. While the mesoscopic interfaces may differ from those of the embedded NF, the former facilitate characterization of controlled interfaces, such as interactions with point defects and helium. The Fe-Y₂Ti₂O₇ interfaces were studied using scanning electron microscopy, including electron backscatter diffraction, atomic force microscopy, X-ray diffraction, and transmission electron microscopy (TEM). The polycrystalline Fe layer has two general orientation relationships (OR) that are close to (a) the Nishiyama–Wasserman (NW) OR $ \left\{ {110} \right\}_{\text{Fe}} ||\left\{ {111} \right\}_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 110 Fe | | 111 Y 2 Ti 2 O 7 and $ \left\langle {100} \right\rangle_{\text{Fe}} ||\left\langle {110} \right\rangle_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 100 Fe | | 110 Y 2 Ti 2 O 7 and (b) $ \left\{ {100} \right\}_{\text{Fe}} ||\left\{ {111} \right\}_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 100 Fe | | 111 Y 2 Ti 2 O 7 and $ \left\langle {100} \right\rangle_{\text{Fe}} ||\left\langle {110} \right\rangle_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 100 Fe | | 110 Y 2 Ti 2 O 7 . High-resolution TEM shows that the NW interface is near-atomically flat, while the {100}_Fe grains are an artifact associated with a thin oxide layer. However, the fact that there is still a Fe-Y₂Ti₂O₇ OR is significant. No OR is observed in the presence of a thicker oxide layer.     

Deoxidation of titanium aluminide by Ca-Al alloy under controlled aluminum activity

Removal of oxygen in titanium aluminide (TiAl) by chemically active calcium-aluminum (Ca-AI) alloy was carried out around 1373 K with the purpose of obtaining extra-low-oxygen TiAl. The deoxidation experiments were preceded by an investigation of the phase equilibria of the system Ti-Al-Ca at 1273 and 1373 K. The compositions of the Ca-AI alloy deoxidant, which equilibrates with TiAl, and the experimental conditions suitable for the deoxidation were of particular interest. In experiments in which Ti-Al samples were submerged in liquid Ca-AI alloys at 1373 K, the surfaces of the samples severely deteriorated and became nodular. When TiAl powders were mixed with CaO and the deoxidant was supplied in vapor form, powders which initially contained 510, 1100, and 4200 ppm O were deoxidized to about 160, 490, and 670 ppm O after deoxidation at 1373 K in 86.4 ks (1 day). Among many conditions tested, the use of TiAl powders mixed with CaCl₂ was most effective for deoxidation at 1373 K. CaCl₂ was used as a flux to facilitate the deoxidation by decreasing the activity of the deoxidation product CaO. In the case that TiAl powders mixed with CaCl₂ and reacted with Ca-AI vapor at 1373 K for 86.4 ks, the powders initially containing 510, 1100, and 4200 mass ppm O were deoxidized to a level of 62, 140, and 190 mass ppm O, respectively. No significant change in morphology of the particle after deoxidation was observed. The titanium and nitrogen concentrations in the powders remained constant, whereas calcium, which was present only in trace amounts initially, increased up to 160 mass ppm after the deoxidation treatment.     

Activities in liquid Fe−Al−O and Fe−Ti−O alloys

The solubility and activity of oxygen in Fe?Al and Fe?Ti melts at 1600°C were measured. The activity was measured electrochemically using the following galvanic cells: Cr-Cr₂O₃(s) ? ThO₂(Y₂O₃) ? Fe-Al-O(l), Al₂O₃(s) Cr-Cr₂O₃(s) ? ThO₂(Y₂O₃) ? Fe-Ti-O(l, saturated with oxide) Cr-Cr₂O₃(s) ? ZrO₂(CaO) ? Fe-Ti-O(l, saturated with oxide) Aluminum and titanium decrease the solubility of oxygen in liquid iron to a minimum of 6 ppm at 0.09 wt pct Al and 40 ppm at 0.9 wt pct Ti, respectively. The value of the interaction coefficients ε ₀ ^(Al) and ε ₀ ^(Ti) are ?433 and ?222, respectively. the activity coefficient of aluminum at infinite dilution in liquid iron is 0.021, while that of titanium is 0.038. The value of the aluminum equilibrium constant, the solubility product at infinite dilution, is 5.6×10^?14 at 1600°C. The ThO₂(Y₂O₃) electrolyte exhibited insignificant electronic conductivity at 1600°C down to oxygen partial pressures of 10^?15 atm, which corresponds to about 0.3 ppm O in unalloyed iron.     

A mass-spectrometric study of the thermodynamics of the Fe−Cu and Fe−Cu−C(sat) systems at 1600°C

The Knudsen cell-mass spectrometer combination has been used to study the Fe?Cu and Fe?Cu?C_(sat) alloys at 1600°C. Activity coefficients in the Fe?Cu system are closely represented by the equations $$\begin{gathered} \ln \gamma _{Fe} = 1.86N_{Cu}^2 + 0.03, (0< N_{Fe}< 0.7) \hfill \\ \ln \gamma _{Cu} = 2.25N_{Fe}^2 - 0.19, (0.7< N_{Fe}< 1.0) \hfill \\ \end{gathered} $$ with an uncertainty in the quadratic terms of about 5 pct. For the iron-rich carbon-saturated alloys, the activity coefficient of copper is given by the equation $$\ln \gamma _{Cu} = 2.45(N'_{Fe} )^2 + 0.3N'_{Fe} + 0.03, (0< N'$$ to within an uncertainty of about 10 pct. N _Fe ^′ represents the fraction N_Fe/(N_Fe+N_Cu), etc. The activity coefficient of iron in this region is found to be essentially constant at 0.69±0.05.     

A Thermodynamic Model for Representation Reaction Abilities of Structural Units in Fe-S Binary Melts Based on the Atom-Molecule Coexistence Theory

A thermodynamic model for calculating the mass action concentrations of structural units in Fe-S binary melts based on the atom-molecule coexistence theory, i.e., AMCT-N _i model, has been developed and verified through a comparison with the reported activities of both S and Fe in Fe-S binary melts with changing mole fraction $ x_{\text{S}} $ of S from 0.0?to 0.095?at temperatures of 1773?K, 1823?K, and 1873?K (1500 °C, 1550 °C, and 1600 °C) from the literature. The calculated mass action concentration $ N_{\text{S}} $ of S is much smaller than the reported activity $ a_{\text{R, S}} $ of S in Fe-S binary melts with changing mole fraction $ x_{\text{S}} $ of S from 0.0?to 0.095. The calculated mass action concentration $ N_{\text{S}} $ of S can correlate the reliable 1:1?corresponding relationship with the reported activity $ a_{\text{R, S}} $ or $ a_{\%,\text {S}} $ of S through the introduced transformation coefficients with absolutely mathematical meaning or through the defined comprehensive mass action concentration of total S with explicitly physicochemical meaning. The calculated mass action concentrations $ N_{i} $ of structural units from the developed AMCT-N _i thermodynamic model can be applied to describe or predict the reaction abilities of structural units in Fe-S binary melts. The reaction abilities of Fe and S show a competitive relationship each other in Fe-S binary melts in a temperature range from 1773?K to 1873?K (1500 °C to 1600 °C). The calculated mass action concentration $ N_{{{\text{FeS}}_{ 2} }} $ of FeS_2?is very small and can be ignored because FeS_2?can be incongruently decomposed above 1016?K (743 °C). The very small values for the calculated mass action concentrations $ N_{{{\text{FeS}}_{ 2} }} $ of FeS_2?in a range of mole fraction $ x_{\text{S}} $ of S from 0.0?to 1.0?as well as a maximum value for the calculated mass action concentration $ N_{\text{FeS}} $ of FeS with mole fraction $ x_{\text{S}} $ of S as 0.5?are coincident with diagram phase of Fe-S binary melts. A spindle-type relationship between the calculated mass action concentration $ N_{i} $ and the calculated equilibrium mole number $ n_{i} $ can be found for FeS and FeS_2?in Fe-S binary melts. The Raoultian activity coefficient $ \gamma_{S}^{0} $ of S relative to pure liquid S(l) as standard state and the infinitely dilute solution as reference state in Fe-S binary melts can be determined as 1.0045?in a temperature range from 1773?K to 1873?K (1500 °C to 1600 °C). The standard molar Gibbs free energy change $ \Updelta_{\text{sol}} G_{{{\text{m, S }}({\text{l}}) \to [{\text{S}}]_{{ \, [{\text{pct \, S}}] = 1.0}} }}^{{\Uptheta,\%}} $ of dissolving liquid S for forming [pct S] as 1.0?in Fe-S binary melts relative to 1?mass percentage of S as standard state can be formulated as $ \Updelta_{\text{sol}} G_{{{\text{m, S }}({\text{l}}) \to [{\text{S}}]_{{ \, [{\text{pct \, S] }} = \, 1.0}} }}^{{\Uptheta,\, \%}} \,\, = -0.219\,-\,33.70T\,\,\left( {\text{J/mol}} \right).$      

A Reaction Between High Mn-High Al Steel and CaO-SiO2-Type Molten Mold Flux: Part II. Reaction Mechanism, Interface Morphology, and Al2O3 Accumulation in Molten Mold Flux

Following a series of laboratory-scale experiments, the mechanism of a chemical reaction $4[\rm{Al}] + 3(\rm{SiO}_2) = 3[\rm{Si}] + 2(\rm{Al}_2\rm{O}_3)$ between high-alloyed TWIP (TWin-Induced Plasticity) steel containing Mn and Al and molten mold flux composed mainly of CaO-SiO₂ during the continuous casting process is discussed in the present article in the context of kinetic analysis, morphological evolution at the reaction interface. By the kinetic analysis using a two-film theory, a rate-controlling step of the chemical reaction at the interface between the molten steel and the molten flux is found to be mass transport of Al in a boundary layer of the molten steel, as long as the molten steel and the molten flux phases are concerned. Mass transfer coefficient of the Al in the boundary layer ( $k_{\rm{Al}}$ ) is estimated to be 0.9 to 1.2 × 10^?4 m/s at 1773 K ( $1500\,^{\circ}$ C). By utilizing experimental data at various temperatures, the following equation is obtained for the $k_{\rm{Al}}; \ln k_{\rm{Al}} = -14,290/T - 1.1107.$ Activation energy for the mass transfer of Al in the boundary layer is 119 kJ/mol, which is close to a value of activation energy for mass transfer in metal phase. The composition evolution of Al in the molten steel was well explained by the mechanism of Al mass transfer. On the other hand, when the concentration of Al in the steel was high, a significant deviation of the composition evolution of Al in the molten steel was observed. By observing reaction interface between the molten steel and the molten flux, it is thought that the chemical reaction controlled by the mass transfer of Al seemed to be disturbed by formation of a solid product layer of MgAl₂O₄. A model based on a dynamic mass balance and the reaction mechanism of mass transfer of Al in the boundary layer for the low Al steel was developed to predict (pct Al₂O₃) accumulation rate in the molten mold flux.     

Nitrogen solubility in liquid Fe-V and Fe-Cr-Ni-V alloys

Nitrogen solubility in liquid Fe, Fe-V, Fe-Cr-V, Fe-Ni-V and Fe-18 pct Cr-8 pet Ni-V alloys has been measured using the Sieverts’ method for vanadium contents up to 15 wt pct and over the temperature range from 1775 to 2040 K. Nitrogen solution obeyed Sieverts’ law for all alloys investigated. Nitride formation was observed in Fe-13 pet V, Fe-15 pet V and Fe-18 pet Cr-8 pet Ni-10 pet V alloys at lower temperatures. The nitrogen solubility increases with increasing vanadium content and for a given composition decreases with increasing temperature. In Fe-V alloys, the nitrogen solubility at 1 atm N₂ pressure is 0.72 wt pet at 1863 K and 15 pct V. The heat and entropy of solution of nitrogen in Fe-V alloys were determined as functions of vanadium content. The first and second order interaction parameters were determined as functions of temperature as: $$e_N^V = \frac{{ - 463.6}}{T} + 0.148 and e_N^{VV} = \frac{{17.72}}{T} - 0.0069$$ The effects of alloying elements on the activity coefficient of nitrogen were measured in Fe-5 pet and 10 pet Cr-V, Fe-5 pet and 10 pet Ni-V and Fe-18 pet Cr-8 pct Ni-V alloys. In Fe-18 pet Cr-8 pet Ni-10 pet V, the nitrogen solubility at 1 atm N₂ pressure is 0.97 wt pet at 1873 K. The second order cross interaction parameters, e _N ^Cr,V and e _N ^Ni,V , were determined at 1873 K as 0.00129 and ? 0.00038 respectively.     

Dendritic Growth Morphologies in Al-Zn Alloys—Part I: X-ray Tomographic Microscopy

Upon solidification, most metallic alloys form dendritic structures that grow along directions corresponding to low index crystal axes, e.g., $\langle100\rangle$ directions in fcc aluminum. However, recent findings[1,2] have shown that an increase in the zinc content in Al-Zn alloys continuously changes the dendrite growth direction from $\langle100\rangle$ to $\langle110\rangle$ in {100} planes. At intermediate compositions, between 25 wt pct and 55 wt pct Zn, $\langle320\rangle$ dendrites and textured seaweeds were reported. The reason for this dendrite orientation transition is that this system exhibits a large solubility of zinc, a hexagonal metal, in the primary fcc aluminum phase, thus modifying its weak solid–liquid interfacial energy anisotropy. Owing to the complexity of the phenomenology, there is still no satisfactory theory that predicts all the observed microstructures. The current study is thus aimed at better understanding the formation of these structures. This is provided by the access to their 3D morphologies via synchrotron-based X-ray tomographic microscopy of quenched Bridgman solidified specimens in combination with the determination of the crystal orientation of the dendrites by electron-backscattered diffraction. Most interestingly, all alloys with intermediate compositions were shown to grow as seaweeds, constrained to grow mostly in a (001) symmetry plane, by an alternating growth direction mechanism. Thus, these structures are far from random and are considered less hierarchically ordered than common dendrites.     

Effect of Slag Composition on the Concentration of Al2O3 in the Inclusions in Si-Mn-killed Steel

The thermodynamic equilibria between CaO-Al₂O₃-SiO₂-CaF₂-MgO(-MnO) slag and Fe-1.5 mass pct Mn-0.5 mass pct Si-0.5 mass pct Cr melt was investigated at 1873 K (1600 °C) in order to understand the effect of slag composition on the concentration of Al₂O₃ in the inclusions in Si-Mn-killed steels. The composition of the inclusions were mainly equal to (mol pct MnO)/(mol pct SiO₂) = 0.8(±0.06) with Al₂O₃ content that was increased from about 10 to 40 mol pct by increasing the basicity of slag (CaO/SiO₂ ratio) from about 0.7 to 2.1. The concentration ratio of the inclusion components, \( {{X_{{{\text{Al}}_{2} {\text{O}}_{3} }} \cdot X_{\text{MnO}} } \mathord{\left/ {\vphantom {{X_{{{\text{Al}}_{2} {\text{O}}_{3} }} \cdot X_{\text{MnO}} } {X_{{{\text{SiO}}_{2} }} }}} \right. \kern-0pt} {X_{{{\text{SiO}}_{2} }} }} \) , and the activity ratio of the steel components, \( {{a_{\text{Al}}^{2} \cdot a_{\text{Mn}} \cdot a_{\text{O}}^{2} } \mathord{\left/ {\vphantom {{a_{\text{Al}}^{2} \cdot a_{\text{Mn}} \cdot a_{\text{O}}^{2} } {a_{\text{Si}} }}} \right. \kern-0pt} {a_{\text{Si}} }} \) , showed a good linear relationship on a logarithmic scale, indicating that the activity coefficient ratio of the inclusion components, \( {{\gamma_{{{\text{SiO}}_{2} }}^{i} } \mathord{\left/ {\vphantom {{\gamma_{{{\text{SiO}}_{2} }}^{i} } {\left( {\gamma_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{i} \cdot \gamma_{\text{MnO}}^{i} } \right)}}} \right. \kern-0pt} {\left( {\gamma_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{i} \cdot \gamma_{\text{MnO}}^{i} } \right)}} \) , was not significantly changed. From the slag-steel-inclusion multiphase equilibria, the concentration of Al₂O₃ in the inclusions was expressed as a linear function of the activity ratio of the slag components, \( {{a_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{s} \cdot a_{\text{MnO}}^{s} } \mathord{\left/ {\vphantom {{a_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{s} \cdot a_{\text{MnO}}^{s} } {a_{{{\text{SiO}}_{2} }}^{s} }}} \right. \kern-0pt} {a_{{{\text{SiO}}_{2} }}^{s} }} \) on a logarithmic scale. Consequently, a compositional window of the slag for obtaining inclusions with a low liquidus temperature in the Si-Mn-killed steel treated in an alumina ladle is recommended.