Evolution of the Non-metallic Inclusions Influenced by Slag-Metal Reactions in Ti-Containing Ferritic Stainless Steel

Laboratory experiment and thermodynamic calculation for the Ti-containing 24 mass pct Cr ferritic stainless steel with a CaO-SiO2-Al2O3-MgO system slag were performed to investigate the effect of slag addition on the inclusion characteristics in molten steel. The morphology, composition, and size evolution of inclusions in steel samples were analyzed in three-dimensional by the electrolytic extraction method and in two-dimensional by the automatic analysis method. The results showed that the Ti content significantly decreased after the slag addition. However, the change of the Si content showed an opposite tendency. The decrease of the Ti content in steel was due to the reduction of SiO2 and Al2O3 in the slag by dissolved Ti in steel. An increase of the TiO2 content in the slag can decrease the Ti loss in steel based on the slag-steel kinetic analysis. The total O content in the steel melt decreased from 62 to 26 ppm, and the steel cleanliness was improved, since the number density of inclusions decreased after the slag refining. The results of a kinetic analysis showed that the rate-determining step of the oxidation of Ti in the steel and the reduction of SiO2 in the slag were the mass transfer on the slag side. In addition, high Ti2O3-containing inclusions were found to be transformed to Cr2O3-Ti2O3-Al2O3 and Cr2O3-Ti2O3-SiO2 system inclusions after the slag addition. The Al2O3 contents in inclusions increased while the Ti2O3 contents decreased with time. However, there were some amount of high melting point inclusions with high Al2O3 content, which were not what we expected. When plotted on logarcxithmic scales, the mole ratio XAl2O3/(XTi2O3·XCr2O3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_{{{\text{Al}}_{2} {\text{O}}_{3} }} /(X_{{{\text{Ti}}_2 {\text{O}}_{3} }} \cdot X_{{{\text{Cr}}_{2} {\text{O}}_{3} }} )$$\end{document} values of the inclusions were expressed as a linear function of the aAl2/(aTi2·aCr2·aO3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{\text{Al}}^{2} /(a_{Ti}^{2} \cdot a_{\text{Cr}}^{2} \cdot a_{\text{O}}^{3} )$$\end{document} values of the steel melts with a slope of unity, which was theoretically expected.


I. INTRODUCTION
TITANIUM-CONTAINING ferritic stainless steels are widely used in various applications which require both high-temperature mechanical properties and excellent oxidation and corrosion resistance in an aggressive environment. [1] However, the presence of non-metallic inclusions, i.e., titanium oxides and nitrides, caused by the alloy addition can seriously affect the production process as well as the quality of the final steel products, for example, clogging of the submerged entry nozzle. [2,3] Normally, inclusions need to be removed or modified to achieve the optimal steel properties. The objective of inclusion modification techniques is to convert the existing solid inclusions to liquid inclusions that can be removed by coalescence and floatation. [4,5] Further, liquid inclusions would be easy to deform thus preventing failure during casting and rolling. [6][7][8] Therefore, it is crucial to control the formation of oxide inclusions in Ti-containing stainless steel during the steelmaking process.
For inclusions in Ti-stabilized ferritic stainless steels, many studies focused on the behaviour of Al 2 O 3 , Al 2 O 3 -TiO x , MgO-Al 2 O 3 -TiO x and TiN inclusions at different refining and casting stages. [1,9,10] Calcium treatment of Ti-bearing inclusions in steel contributes to the production of high-quality steel with fewer defects caused by inclusions. [11,12] Li et al. [9,13] and Chen et al. [14] have shown that a small amount of Ca in Al-killed Ti-bearing stainless steel effectively modified Al 2 O 3 -TiO x inclusions into liquid oxides and reduced the stability of the spinel by modifying the solid Al 2 O 3 inclusions into liquid calcium aluminates. Seo et al. [15] investigated the effect of the Ca and Ti addition sequence on the inclusion behavior in Al-killed Ti-bearing stainless steels. They reported that a Ca treatment after the Ti addition was not an effective way to minimize the spinel formation. However, a Ca treatment before the Ti addition efficiently prevented the formation of MgAl 2 O 4 spinel because of the depletion of available Al 2 O 3 by the earlier Ca operation. Kruger et al. [3] reported that the spinel inclusions were modified to spherical dual-phase spinel-liquid matrix inclusions by Ca treatment in a Ti-stabilized 11 mass pct Cr (409) stainless steel, which eliminated the clogging of SEN for this grade. In summary, these studies have investigated the effect of a Ca treatment on the modification of inclusions in molten steel.
Meanwhile, it is well known that the refining slag having a proper composition and excellent physicochemical properties can effectively modify and remove the inclusions. [16][17][18][19][20][21][22][23] It is a significant advantage that a good contact between metal and slag makes the steel chemically refined. [24] Park et al. [25] investigated the effect of CaO-Al 2 O 3 -MgO slags on the formation of MgO-Al 2 O 3 inclusions in a Si deoxidized 16 mass pct Cr ferritic stainless steel. They found that the MgO-rich spinel solid solutions were formed in the steel melt equilibrated with the highly basic slags saturated by CaO or MgO. Later, Park et al. [10] also investigated the equilibrium between CaO-SiO 2 -MgO-Al 2 O 3 -CaF 2 -(TiO 2 ) slag and a Si deoxidized Ti-stabilized ferritic stainless steel containing 11 mass pct Cr. They reported that the inclusions in the steel melt equilibrated with the basic slags (basicity=[CaO+MgO]/[SiO 2 +Al 2 O 3 ]>1.7) were located in the spinel+liquid multiphase region, while those in equilibrium with the less basic slags (basicity<1.7) were mostly located in the fully liquid region. Kim et al. [26] investigated the formation of complex oxide inclusions in Al-Ti deoxidized 304 stainless steel. They concluded that a decrease in the slag basicity was the most effective way to reduce the crystallization of the harmful CaO-TiO 2 phase in inclusions. Li et al. [27] investigated the effect of CaO-MgO-SiO 2 -Al 2 O 3 -TiO 2 -CaF 2 slags containing different CaF 2 contents on the inclusion characteristics in a Al deoxidized Ti-stabilized 20 mass pct Cr stainless steel. They concluded that the lower the CaF 2 content in slag, the lower MgO content of inclusions in steel, which made most of the inclusions located in or close to the liquid phase field.
High basicity slags have commonly been used in Al-killed steels to reach a high cleanliness and inclusions having low melting temperature. [28][29][30] Nevertheless, the effect of slag on the high TiO x contained inclusions in Ti-containing stainless steel has been under discussion. Therefore, in the present study, the refractory-slag-metal reaction experiments were performed to investigate the effect of the CaO-SiO 2 -Al 2 O 3 -MgO slag on the evolution of oxide inclusions in Ti-containing 24 mass pct Cr stainless steel.

A. Experimental Procedures
The experiment was carried out using a high-frequency induction furnace, which is shown in Figure 1(a). The quartz reaction chamber was initially evacuated using a mechanical rotary pump prior to performing the experiments; the chamber was subsequently filled with a highly purified Ar-3 pct H 2 gas mixture controlled using a mass flow controller. Impurities in the ArÀ3 pct H 2 gas mixture were removed by passing the gas through Drierite (W.A. Hammond Drierite Co. Ltd., Xenia, OH), silica gel, and Mg turnings at 723 K (450°C). The 430 steel ingot (500 g) was melted in a fused MgO crucible (99.9 pct purity, 60 9 50 9 120 mm) with a graphite heater for induction heating; the heater was surrounded by insulation. The experimental temperature was 1873 K (1600°C), which was controlled within ± 2 K (2°C) using a B-type (Pt-30Rh/Pt-6Rh, mass pct) thermocouple and a proportional integral differential controller. After the temperature was stabilized for 30 min, 85 g FeCr alloy was added through the quartz tube (149129500 mm) under an Ar-3 pct H 2 atmosphere. The chemical compositions of the steel and FeCr alloy are shown in Table I.
Several steel samples were taken after the FeCr addition, and the inclusion characterization results were reported elsewhere. [31] After 30 min of the alloy addition, sample S0 was taken from the molten steel using a quartz tube (ID=4 mm). Thereafter, 50 g slag was added on the surface of molten steel under an Ar-3 pct H 2 atmosphere. The slag was prepared by melting reagent grades of SiO 2 , Al 2 O 3 , MgO and CaO in advance in a vertical resistance tube furnace under a purified Ar atmosphere. Here, CaO was obtained from a reagent grade of CaCO 3 , which was calcined at 1273 K (1000°C) for 12 hours. Then, steel samples were taken at predetermined times after the slag addition (S1-5 min, S2-15 min, S3-25 min) and rapidly quenched in water. Slag samples were also taken using stainless steel rods at the predetermined times (Slag 1-5 min, Slag 2-15 min, Slag 3-25 min), as shown in Figure 1 (b).

B. Analysis and Characterization
The chemical compositions of the steel and slag samples were determined using inductively coupled plasma atomic emission spectrometry (ICP-AES, ACROS, SPECTRO) and X-ray fluorescence spectroscopy (XRF, Bruker, model S4 Explorer). The oxygen and nitrogen contents were determined by using a LECO combustion analyzer. Three-dimensional observations using the electrolytic extraction method were used to observe the exact morphology and composition of inclusions in the steel samples. For this experiment, a 10 pct AA solution (10 pct acetylacetone, 1 pct tetramethylammonium chloride, and methanol) was used as the electrolyte, and a 750 mA current was applied for 3 h. The extracted inclusions were filtered out by using a vacuum pump and laid on a membrane filter with a pore size of 0.1 lm. Once completely dried, the filter was coated with platinum. Next, the inclusions on the filter were investigated using field emission scanning electron microscopy analysis (FESEM; TES-CAN model MIRA 3) with an energy-dispersive X-ray spectroscope (EDS). Besides, the characterization of inclusions in two-dimensional, i.e., number density, size and composition, in the steel samples was performed using the automated inclusion analysis system. The following settings were applied: accelerating voltage 20 KV, magnification 500 times and a 1 lm limit diameter for inclusion detection in a 10 mm 2 area.

A. Characterization of Inclusions
SEM images of typical inclusions found in the samples before and after the slag addition are shown in Figure 2. To get stable TiO x and TiO x -CrO x based inclusions, FeCr alloys were added into the Ti-containing steels. The inclusion characteristics can be found from previous work, [31] where Ti 2 O 3 and Cr 2 O 3 were chosen to represent the Ti oxide and Cr oxide in inclusions. Before the slag addition, the main inclusions were Ti 2 O 3 -Cr 2 O 3 based systems containing a small amount of Al 2 O 3 content. It should be pointed out that the Ti 2 O 3 -Cr 2 O 3 based inclusions have rarely been reported before. They can further be divided into two groups based on their morphologies and compositions: irregular shapes with lower Cr 2 O 3 contents (Figure 2(a)) and globular shapes with higher Cr 2 O 3 contents (Figure 2(b)). In addition, a small number of spherical Ti 2 O 3 -Cr 2 O 3 -SiO 2 inclusions (Figure 2(c)) were also observed.
In sample S1 taken after 5 min of the slag addition, the number of inclusions significantly increased due to the slag-steel reactions. A relatively larger amount of inclusions were located together on the film filters, as shown in Figure 2 (Figure 2(l)). In addition, they were found in all the following samples.  In sample S2 taken after 15 min of the slag addition, the number of inclusions significantly reduced, which is discussed in detail in Figure  started to form in sample S1 (5 min) and that the Al 2 O 3 contents in these inclusions obviously increased with time. In the final sample S3 taken after 25 min of the slag addition, the types of inclusions were similar to those found in sample S2, but with some composition changes.
To investigate the evolution of inclusions, the compositions of inclusions in different samples were projected onto the CrO x -Ti 2 O 3 -Al 2 O 3 and CrO x -Ti 2 O 3 -SiO 2 ternary phase diagrams, as shown in Figure 4. The phase diagrams were calculated with the aid of FactSage 7.1 software using the FactPS and FToxid databases at 1873 K (1600°C) and p(O 2 )=10 -15 atm, which was calculated based on the measured oxygen content. The details of the calculation to determine the oxygen partial pressure in the present system is given elsewhere. [31] It can be seen from Figure 4(a) that the main compositions of inclusions are concentrated in the single liquid and Ti 2 O 3 +liquid regions before the slag addition. After 5 min of the slag addition (S1), the number of inclusions significantly increases, as shown in Figure 4 The number density and area fraction variations of different types of inclusions show similar tendency, which are illustrated in Figure 5. Before the slag addition (S0), the major type is the Ti 2 O 3 -Cr 2 O 3 -Al 2 O 3 system inclusions. After 5 min of the slag addition (S1), the number of this type of inclusions has increased by about 5 times. A large number of inclusions have been formed due to the slag-steel reactions. Thereafter, their number continues to decrease with time due to the inclusion floatation and absorption of inclusions by slag.
Finally, their number approximately reduces by half in sample S3 (25 min) compared to that in sample S0 before the slag addition.
The number of Ti 2 O 3 -Cr 2 O 3 -SiO 2 inclusions (multiphase and homogeneous) also greatly increases in sample S1. The number density of Ti 2 O 3 -Cr 2 O 3 -SiO 2 inclusions is almost twice more than that of

Composition change of molten steel and slag
After the slag addition, it took about 3 min for the slag to be fully melted, as shown in Figure 7. The compositions of the initial premelted slag, and the slag and steel samples taken at different times are shown in Table II and Figure 8. A high basicity ((CaO)/(SiO 2 ) % 6) MgO saturated slag was used in the present study. After the slag addition, the CaO and SiO 2 contents slightly decreased, while the Al 2 O 3 content increased (but not significant) with time. It should be noted that titanium oxide generated after the slag-steel reactions and continuously increased with time, indicating the oxidation of Ti in the steel. Here, the titanium oxide is assumed to be TiO 2 for the sake of simplicity. In terms of the steel compositions, the Ti content significantly decreased while the Al content only gradually decreased with time. The Si content showed an increasing tendency with time but with a small fluctuation, which increased  3992-VOLUME 52B, DECEMBER 2021 greatly during the first 5 min. The total O content decreased from 62 to 26 ppm after the slag addition, which indicated that the cleanliness of the steel had been improved due to the slag refining. The changes in the slag and steel compositions were due to the slag-steel reactions.
The activities of the slag components at the initial and final compositions were calculated with an aid of FactSage 7.1 software using the FToxide database, the results are shown in Figure 9. The activity of CaO decreases with time, whereas the activities of Al 2 O 3 , SiO 2 and TiO 2 all increase with time. Besides, the activity of Al 2 O 3 is much higher than those of SiO 2 and TiO 2 . This can be explained by the fact that the TiO 2 in the slag is an acidic oxide which has a strong affinity with CaO. Thus, the activity of CaO decreases with an increased TiO 2 content. Therefore, the relative attraction between SiO 2 , Al 2 O 3 and CaO decreases, which further increases the SiO 2 and Al 2 O 3 activity. [32] Therefore, the activity changes of slag component not simply depend on their compositions, but also the attractive force between different components. The activity changes of the slag components have a significant influence on the Al, Ti and Si contents in the steel melts.
During the refining process of Ti-bearing stainless steel, the slag-steel reaction could lead to the loss of titanium in molten steel. [27,33] The SiO 2 and Al 2 O 3 in slag can react with Ti in molten steel according to Eqs. [1] and [4], which would cause a loss of Ti in steel. [10,27,32,34] Moreover, considering the mass balance of the decrease of SiO 2 and the increase of TiO 2 in the slag, both reactions happened in the present study. Also, the increase of Al 2 O 3 in the slag might be due to the reaction between SiO 2 in the slag and Al in the molten steel based on Eq. [7].
where a TiO 2 , a SiO 2 and a Al 2 O 3 are the activities of TiO 2 , SiO 2 and Al 2 O 3 in the slag; f Ti , f Si and f Al are the Henrian activity coefficients of Ti, Si and Al in the steel. According to Eqs. [3], [6] and [9], the dependence of the composition ratios of steel on the activity ratios of slag in different samples can be calculated, as shown in Figure 10. Based on Eq. [3], the increase of logða TiO 2 =a SiO 2 Þ in the slag could cause an increase of log½%Ti=½%Si in the molten steel. This, in turn, can result in higher Ti contents and lower Si contents in the steel melt. It indicates that an increased TiO 2 activity can lead to a higher Ti content in the steel melt, which is also obtained in the following kinetics analysis. However, it should be pointed out that the increased TiO 2 activity should be obtained in the original slag before  the slag-steel reactions. The measured values of log½%Ti=½%Si decrease when the logða TiO 2 =a SiO 2 Þ of slag increases, which is due to the fact that the TiO 2 is formed after the slag-steel reactions in the present study ( Figure 10(a)). Similarly, in the case of Eq. [6], the decrease of logða 2 Al 2 O 3 =a 3 TiO 2 Þ slag could cause a decrease of logð½%Al 4 =½%Ti 3 Þ in the molten steel, but the experimental results also showed the opposite tendency ( Figure 10(b)). Moreover, both the Al and Ti contents decreased with time as shown in Figure 8(b). Therefore, the reduction of the Ti content was greater than that of Al in the molten steel, which indicated that Eq. [4] might not be the main reaction. The decrease of logða 2 Al 2 O 3 =a 3 SiO 2 Þ of slag could cause a decrease of logð½%Al 4 =½%Si 3 Þ in the molten steel according to Eq. [9], where a similar tendency of the measured values of logð½%Al 4 =½%Si 3 Þ was obtained as shown in Figure 10(c). Based on these discussions, the final steel composition changes depend on these coupled reactions.

C. Kinetics of Slag-Steel Reactions
The coupled-reaction model and two film theory have frequently been applied to describe the kinetics of slag-steel reactions. [30,32,35,36] It is assumed that the concentrations of Al 2 O 3 , TiO 2 , SiO 2 in the slag side and Al, Ti, Si and O in the steel show respective concentration gradients in the boundary film layer at the slag-steel interface, and have reached a thermodynamic equilibrium at the interface, as shown in Figure 11.
In the present study, the reactions [10], [12] and [14] were simultaneously considered to take place at the slag-steel interface. Assuming that these reactions occur rapidly during the present conditions, and local equilibrium reaches at the slag-steel interface. The corresponding equilibrium constants K for each reaction can be calculated. [37][38][39] To simplify the computation, AlO 1.5 is used. Apparent equilibrium constant B i can be expressed by Eq. [16].
where a i is the activity of element i in the metal, f i is the Henrian activity coefficient of element i referred to 1 pct standard state with mass percentage [% i] as the concentration unit, which can be calculated by the classical Wagner formulation [17], using the first-(e j i ) and second-order (r j i ) interaction parameters, which are listed in Table III Because the rates of the chemical reactions involving the respective component at the slag-steel interface are extremely large. Thus, mass transfer is the rate-determining step, which can be controlled by the mass transfer of metal in the steel side and slag component in the slag side. Therefore, the respective mass transfer resistance of metal (R M i ) and slag component (R M i O n ) can be expressed by Eq. [18], which can express the controlling step in the reactions. During the transfer of component i from molten steel to slag, the flux density should be constant, this can be expressed by Eq. [19]. The modified mass transfer coefficients can be illustrated by Eqs. [20] and [21]. Therefore, the flux density of Al, Ti, Si and O can be derived by combing Eqs. [22] through [25].
where J i , F i , and F M i O n stand for the is the molar flux density (mol/m À2 s À1 ), modified mass transfer coefficients of metal and slag (m/s), respectively. Superscript '*' and 'b' represent the slag-steel interface and bulk phase, respectively. q m and q s are the density of steel and slag (kg/m À3 ), k M i ;m and k M i O n ;s are the mass transfer coefficients of element i and M i O n in slag (m/ s), and M i is molecular weight of element i in steel. The oxygen activity a Ã O at the slag-steel interface can be determined by Eq. [26]. Then, the concentrations of each element in the metal as a function of time can be calculated by Eq. [27] when the calculated a Ã O value is 2.6 ppm. The parameters used in the calculations can be found in Table IV. Figure 12(a) shows the measured and calculated results of the concentrations of Ti,Si and Al in the steel as a function of time. It can be seen that the Si and Ti contents change more drastically during the first 5 min than during a later stage. Moreover, the calculated results of the contents of Al, Si, and Ti in the molten steel show relatively good agreement with the experimental results. Based on Eq. [18], the mass transfer resistance of the respective components on the slag side can be obtained. The calculated values for mass transfer resistances of Al 2 O 3 , TiO 2 and SiO 2 are 0.23, 44 and 2.3910 4 m 2 s/kg, respectively. The mass transfer resistance in molten steel is 0.71 m 2 s/kg. Therefore, the rate-determining step of the oxidation of Ti in the steel and the reduction of SiO 2 in the slag are the mass transfer on the slag side. Thus, the Ti content change can be expressed by Eq. [28].
It is indicated that the Ti content change depends on the difference between the TiO 2 content in the slag and the TiO 2 * value at the slag-steel interface. According to a previous work, [32] an increased TiO 2 content in slag can prevent a loss of titanium by the reaction of dissolved Ti in steel with alumina and silica in slag. Therefore, different TiO 2 contents in the original slag were considered, and the corresponding oxygen activity (a Ã O ) values were calculated by Eq. [26]. It should be pointed out that this calculation was simply performed by increasing the TiO 2 content while keeping the proportion of other slag components unchanged. As a result, the Ti content change can be calculated by Eq. [27] when an a Ã O value is obtained. The calculated results are shown in Figure 12(b). As can clearly be seen that an increased TiO 2 content in the original slag results in a less decreased Ti content in the melt. This can be explained by the fact that a higher TiO 2 content in the slag can suppress reactions [1] and [4] to the right. From another point of veiw, the activities of SiO 2 and Al 2 O 3 decrease with an increased TiO 2 content. Thus, reactions [1] and [4] become weakened due to the lower activities of SiO 2 and Al 2 O 3 on the left side of the Mass transfer coefficient of Al, Si, Ti and O in steel 2 9 10 -4 m/s [30] Density of steel, q steel 7000 kg/m À3 [41] Mass transfer coefficient of Al 2 O 3 , TiO 2 in slag 1 910 -5 m/s [30] Density of slag, q slag 3000 kg/m À3 [41] Mass transfer coefficient of SiO 2 in slag 2910 -6 m/s [30] Weight of steel, W steel 500 g Reaction area between the steel and slag, A p AE(0.025) 2 m 2 Weight of slag, W slag 50 g reactions. Therefore, TiO x or complex inclusions containing TiO x due to the reactions between Ti and SiO 2 and Al 2 O 3 will be reduced. It was reported that there was an optimum TiO 2 content of about 8 mass pct due to the different combining affinity between TiO 2 and other components. [32] However, because this kind of experimental work was not carried out in the present study, future work needs to investigate the optimum slag composition to get a low Ti loss in the steel melt.

D. Thermodynamic Calculations of Inclusion Formations
The effect of the activity of alumina in the slag on the mole fraction of alumina in the inclusions is shown in Figure 13. After the slag addition, the Ti 2 O 3 and Cr 2 O 3 contents decreased in the Ti 2 O 3 -Cr 2 O 3 -Al 2 O 3 inclusions. This might be due to the fact that they were reduced by dissolved Al in the steel melts based on Eqs. [29] and [31]. [39,40,42] Thus, the composition of inclusions can be deduced as a function of the activities of Al, Ti, Cr and O as given in Eq. [33] and [34].
where a i denotes the activity of component i in steel, X MO and c MO are the mole fraction and the activity coefficient of MO in the inclusions.
Therefore, it can be expected that on a logarithmic scale the mole ratios of the inclusion components are in direct proportion to the logarithmic activity ratios of Al, Ti, Cr and O in the steel melts with a slope of unity, by assuming that the activity coefficient ratio c Al 2 O 3 =c Ti 2 O 3 and c Al 2 O 3 =ðc Ti 2 O 3 Á c Cr 2 O 3 Þ in Eqs. [33] and [34] would not be significantly affected by the compositions at a fixed temperature. Their relationships are given in Figure  14.  [10,25,43] In terms of the SiO 2 -containing inclusions, the typical multiphase and homogeneous inclusions formed after the slag additions have been mentioned in Figure 2. These inclusions were spherical in shape but with varied Si-Ti-Cr contents. Figure 15 shows possible evolutions of these SiO 2 -containing inclusions after the slag additions. The dissolved Si content increased in the melt after the slag additions, which originated from the reduction products of the slag-steel reactions as discussed before. They reacted with the Ti 2 O 3 -Cr 2 O 3 inclusions to form a Ti 2 O 3 -Cr 2 O 3 -SiO 2 phase, resulting in the formation of multiphase inclusions. The oxide inclusions transformed by gaining SiO 2 and losing Ti 2 O 3 , Cr 2 O 3 or both can be expressed by Eqs. [35] and [36]. In addition, the drop in the Ti content was higher than the Cr content in the inclusions, which suggested that Si reduced Ti 2 O 3 more severely than Cr 2 O 3 .
In terms of the multiphase inclusions, they can be divided into two groups: type 1 containing inclusions and were then transformed into type 3 homogeneous Ti 2 O 3 -Cr 2 O 3 -SiO 2 inclusions. This was also applied to the Ti 2 O 3 -Cr 2 O 3 -SiO 2 phases in type 2 inclusions. Moreover, the SiO 2 -rich phases in type 2 inclusions were attributed to the enrichment of Si. Thereafter, the higher chemical potential of Si in the SiO 2 -rich phases may have resulted in the diffusion of Si into the low melting Ti 2 O 3 -Cr 2 O 3 -SiO 2 phases. Conversely, the Ti and Cr contents in the low melting phases diffused into the SiO 2 -rich phases. When the diffusion reached a certain extent, a distinct interface between the low melting phases and SiO 2 -rich phases disappeared and spherical homogeneous type 3 Ti 2 O 3 -Cr 2 O 3 -SiO 2 inclusions were formed. Further, due to the increased activity of Al 2 O 3 in the slag, the Ti 2 O 3 , Cr 2 O 3 , and also SiO 2 contents in the inclusions were simultaneously reduced by dissolved Al in the steel melts based on the Eqs. [29], [31] and [37]. [38,40,42]

IV. CONCLUSIONS
In the present study, the equilibration between a CaO-SiO 2 -Al 2 O 3 -MgO slag and a Ti-containing ferritic stainless steel melt was investigated at 1873 K (1600°C) to clarify the effect of the slag composition on the modification of high Ti 2 O 3 -containing inclusions. Moreover, the slag-steel reaction was investigated from the viewpoint of kinetics. The following conclusions were obtained.

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