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Transient Evolution of Inclusions during Al and Ti Additions in Fe-20 Mass pct Cr Alloy

The transient evolution of inclusions during Al and Ti additions in a Fe-20 mass pct Cr alloy was investigated using polished cross sections and electrolytic extraction. After Al addition, the evolution of Al2O3-based inclusions based upon the area and particle size passed through the following three main stages with time: Particle agglomeration, inclusion floating, and a slow decrease of the remaining Al2O3-based inclusions. Titanium wire was fed into the steel at the end of the floating stage after Al addition when the Ostwald ripening process was finished. Immediately after Ti addition, the transient phase of Ti oxide was readily generated on the existing Al2O3-based inclusion and disappeared due to Al reduction as time progressed. The formation of the transient TiOx phase was affected by the low disregistry between Al2O3 and TiOx and the local Ti supersaturation, which cannot be predicted by the equilibrium relations of Ti–O–N or Ti–Al–O in the high-Cr-containing melt. Because of the local supersaturation of dissolved [%Ti] and [%N] shortly after Ti addition, TiN associated with existing inclusions and three types of individual TiN including single cubes, twinned inclusions, and clusters were identified. In order to minimize the Ti loss caused by the formation of Ti-rich zones during the transient stages, the removal of large Al2O3-based particles including aggregates, clusters, and flower-shaped inclusions should be promoted by stirring before Ti addition. After Ti addition, Brownian and turbulent were the major factors affecting the collision of particles smaller than the threshold of 2.7 μm. The agglomeration of inclusions larger than this threshold was mainly dominated by turbulent and Stokes’ collisions.


Introduction
Aluminum and titanium are both important alloying elements in steels. Aluminum provides one of the most economical and efficient approaches for deoxidation in steels. However, the Al 2 O 3 inclusions formed as deoxidation products are likely to deteriorate the steel castability due to their high hardness and high melting point [1,2]. Titanium has a strong affinity with carbon and nitrogen and, therefore, is commonly added into steels, as a stabilizing alloying element, to improve the mechanical properties via grain refinement during hot rolling. In particular, fine TiN and TiO x as second-phase particles with a dispersive distribution can raise the percentage of equi-axed cast structure in steels [3][4][5][6]. On the other hand, these Ti-bearing particles including TiN, TiO x , and TiO x -Al 2 O 3 are also the possible cause of deposits [7][8][9][10][11][12][13]. Thus, the presence of titanium in liquid steel, unfortunately, is a risk factor for clogging in submerged nozzles during continuous casting.
There are two aspects embodied in the complexity of the transient inclusion evolution during Al and Ti additions in Cr-rich stainless steels. with oxide cores covered by TiN, only the inner phase was measured for inclusion characterization during the two-dimensional investigations in the previous work [20,34]. In the case of Ti-stabilized stainless steel containing 0.025 mass pct N, Yin et al. [44] found that three different three-dimensional morphologies of TiN inclusions, including single particles, twinned particles, and clusters, were extracted from the sample after Ti addition.
In light of the complexity of inclusion behaviors during Al and Ti additions, further research into the transient evolution of inclusions in high-chromium melts is required. In the current work, laboratory experiments in a Fe-20 mass pct Cr alloy were carried out to clarify the evolution mechanisms of inclusion behaviors by taking samples at various times during Al and Ti additions. Electrolytic extraction was employed to extract intact inclusions from the steel matrix, allowing three-dimensional investigations of inclusion characteristics including composition, morphology, and structure during the transient stage after Ti wire feeding. The thermodynamic calculation in the Fe-20 mass pct Cr-Al-Ti-O-N system was performed to predict the formation of inclusions in stainless steels. The agglomeration mechanism of inclusions after Ti addition was also discussed in this paper.

Experimental Procedure
In order to obtain the Fe-20 mass pct Cr alloy, high-purity electrolytic iron (~99.99%) and superalloy degassed chromium (~99.8%) were melted in a high-frequency induction furnace (Jinzhou electric furnace Co., Ltd., Jinzhou, China) under Ar atmosphere. The original oxygen content and nitrogen content in Fe-20 mass pct was approximately 0.0113% and 0.0009%, respectively. Subsequently, approximately 450 g of Fe-20 mass pct Cr steels were melted in a MgO crucible (40 mm inner diameter, 48 mm outer diameter, and 130 mm depth) at 1873 K in a Si-Mo high-temperature tube furnace. The schematic of the experimental furnace is shown in Figure 1. Two sets of experiments (No. 1 and No. 2) were carried out under Ar atmosphere. After melting, Fe 2 O 3 powders (99.999 pct) were added to the melt to adjust oxygen content to approximately 0.03%. As depicted in Figure 2, the Al alloy (>99.9%) was added into the molten steel after 30 min stabilization of the melt in experiments No. 1 and No. 2, while Ti wire (>99.5%) was added into the melt in experiment No. 2 at 20 min after Al addition. In experiment No. 1, the first sample was taken before Al addition, and other five samples were collected at 5 min, 10 min, 15 min, 20 min, and 30 min after Al addition. In experiment No. 2, the first sample was taken before Ti addition, and other three samples were collected at 2 min, 5 min, and 10 min after Ti addition. All steel samples in the present work were taken by using quartz tubes and quenched into water at room temperature.
Metals 2019, 9, x FOR PEER REVIEW 3 of 22 work [20,34]. In the case of Ti-stabilized stainless steel containing 0.025 mass pct N, Yin et al. [44] found that three different three-dimensional morphologies of TiN inclusions, including single particles, twinned particles, and clusters, were extracted from the sample after Ti addition.
In light of the complexity of inclusion behaviors during Al and Ti additions, further research into the transient evolution of inclusions in high-chromium melts is required. In the current work, laboratory experiments in a Fe-20 mass pct Cr alloy were carried out to clarify the evolution mechanisms of inclusion behaviors by taking samples at various times during Al and Ti additions. Electrolytic extraction was employed to extract intact inclusions from the steel matrix, allowing three-dimensional investigations of inclusion characteristics including composition, morphology, and structure during the transient stage after Ti wire feeding. The thermodynamic calculation in the Fe-20 mass pct Cr-Al-Ti-O-N system was performed to predict the formation of inclusions in stainless steels. The agglomeration mechanism of inclusions after Ti addition was also discussed in this paper.

Experimental Procedure
In order to obtain the Fe-20 mass pct Cr alloy, high-purity electrolytic iron (~99.99%) and superalloy degassed chromium (~99.8%) were melted in a high-frequency induction furnace (Jinzhou electric furnace Co,.Ltd , Jinzhou, China) under Ar atmosphere. The original oxygen content and nitrogen content in Fe-20 mass pct was approximately 0.0113% and 0.0009%, respectively. Subsequently, approximately 450 g of Fe-20 mass pct Cr steels were melted in a MgO crucible (40 mm inner diameter, 48 mm outer diameter, and 130 mm depth) at 1873 K in a Si-Mo high-temperature tube furnace. The schematic of the experimental furnace is shown in Figure 1. Two sets of experiments (No. 1 and No. 2) were carried out under Ar atmosphere. After melting, Fe2O3 powders (99.999 pct) were added to the melt to adjust oxygen content to approximately 0.03%. As depicted in Figure 2, the Al alloy (>99.9%) was added into the molten steel after 30 min stabilization of the melt in experiments No. 1 and No. 2, while Ti wire (>99.5%) was added into the melt in experiment No. 2 at 20 min after Al addition. In experiment No. 1, the first sample was taken before Al addition, and other five samples were collected at 5 min, 10 min, 15 min, 20 min, and 30 min after Al addition. In experiment No. 2, the first sample was taken before Ti addition, and other three samples were collected at 2 min, 5 min, and 10 min after Ti addition. All steel samples in the present work were taken by using quartz tubes and quenched into water at room temperature.

Chemical Analysis
Each steel sample collected at different sampling locations was machined into three specimens, as shown in Figure 3. The specimen A was analyzed to obtain the chemical composition of steel. In this work, the aluminum and titanium contents were determined by inductively coupled plasma atomic emission spectrometry (ICP-AES, NCS, Beijing, China). Inert gas fusion-infrared absorptiometry (LECO, St. Joseph, MI, USA) was applied to measure the total oxygen and nitrogen contents of steel. The results are listed in Table 1.

Inclusion Characterization
For two-dimensional inclusion analysis, one-half of a vertical section cut from the center of specimen B was polished. Afterwards, the two-dimensional characteristics (composition, number,

Chemical Analysis
Each steel sample collected at different sampling locations was machined into three specimens, as shown in Figure 3. The specimen A was analyzed to obtain the chemical composition of steel. In this work, the aluminum and titanium contents were determined by inductively coupled plasma atomic emission spectrometry (ICP-AES, NCS, Beijing, China). Inert gas fusion-infrared absorptiometry (LECO, St. Joseph, MI, USA) was applied to measure the total oxygen and nitrogen contents of steel. The results are listed in Table 1.

Chemical Analysis
Each steel sample collected at different sampling locations was machined into three specimens, as shown in Figure 3. The specimen A was analyzed to obtain the chemical composition of steel. In this work, the aluminum and titanium contents were determined by inductively coupled plasma atomic emission spectrometry (ICP-AES, NCS, Beijing, China). Inert gas fusion-infrared absorptiometry (LECO, St. Joseph, MI, USA) was applied to measure the total oxygen and nitrogen contents of steel. The results are listed in Table 1.

Inclusion Characterization
For two-dimensional inclusion analysis, one-half of a vertical section cut from the center of specimen B was polished. Afterwards, the two-dimensional characteristics (composition, number,

Inclusion Characterization
For two-dimensional inclusion analysis, one-half of a vertical section cut from the center of specimen B was polished. Afterwards, the two-dimensional characteristics (composition, number, and Metals 2019, 9, 702 5 of 21 size distribution) of inclusions were determined using an automated inclusion analysis system (ASPEX Explorer, 20 kV, Thermo Fisher Scientific, Waltham, MA, USA). The scanning area of each sample was approximately 10 mm 2 . The working magnification and distance were set at ×450 and 18 mm, respectively. Inclusions larger than 1 µm in each sample were analyzed in the backscatter electron imaging mode. In this work, the area fraction (AF) and number density (ND) were used to describe the two-dimensional characteristics of non-metallic inclusions, which can be defined by Equations (1) and (2), respectively: where AF is the area fraction of inclusions (ppm), A inclusion is the total area of detected inclusions (µm 2 ), and A total is the total analysis area (mm 2 ); ND is the number of inclusions per unit area (per mm 2 ) and N inclusion is the number of detected inclusions within the area of A total .
To manifest the three-dimensional morphologies, non-metallic inclusions were extracted by dissolving specimen C in a 10%AA (10 v/v% acetylacetone-1 wt/v% tetramethylammonium chloride-methanol) electrolyte. Figure 4 presents the schematic of the electrolysis cell. The steel sample was the anode, while a platinum loop was used as the cathode. The current density and temperature during the extraction were set at 40-50 mA·cm −2 and 0-5 • C, respectively. Approximately 0.15 g of metal was dissolved in the electrolyte with an electrolysis time of 6 h. After extraction, the solution was filtered through a polymer filter membrane with 0.2 µm openings. Subsequently, the membrane was mounted on an aluminum stub and sputter coated with gold. The three-dimensional characteristics of the inclusions were investigated using scanning electron microscopy (SEM, Supra 55, Zeiss, Oberkochen, Germany) combined with energy dispersive spectroscopy (EDS, INCA, Oxford, UK). At least 30 typical inclusions were observed using secondary electron image mode (instrument conditions: 10~15 keV, 18 mm working distance, and lithium drifted silicon detector at 45 deg elevation). and size distribution) of inclusions were determined using an automated inclusion analysis system (ASPEX Explorer, 20 kV, Thermo Fisher Scientific, Waltham, MA, USA). The scanning area of each sample was approximately 10 mm 2 . The working magnification and distance were set at ×450 and 18 mm, respectively. Inclusions larger than 1 μm in each sample were analyzed in the backscatter electron imaging mode. In this work, the area fraction (AF) and number density (ND) were used to describe the two-dimensional characteristics of non-metallic inclusions, which can be defined by Equations (1) and (2), respectively: where AF is the area fraction of inclusions (ppm), Ainclusion is the total area of detected inclusions (μm 2 ), and Atotal is the total analysis area (mm 2 ); ND is the number of inclusions per unit area (per mm 2 ) and Ninclusion is the number of detected inclusions within the area of Atotal.
To manifest the three-dimensional morphologies, non-metallic inclusions were extracted by dissolving specimen C in a 10%AA (10 v/v% acetylacetone-1 wt/v% tetramethylammonium chloride-methanol) electrolyte. Figure 4 presents the schematic of the electrolysis cell. The steel sample was the anode, while a platinum loop was used as the cathode. The current density and temperature during the extraction were set at 40-50 mA·cm −2 and 0-5 °C, respectively. Approximately 0.15 g of metal was dissolved in the electrolyte with an electrolysis time of 6 h. After extraction, the solution was filtered through a polymer filter membrane with 0.2 μm openings. Subsequently, the membrane was mounted on an aluminum stub and sputter coated with gold. The three-dimensional characteristics of the inclusions were investigated using scanning electron microscopy (SEM, Supra 55, Zeiss, Oberkochen, Germany) combined with energy dispersive spectroscopy (EDS, INCA, Oxford, UK). At least 30 typical inclusions were observed using secondary electron image mode (instrument conditions: 10~15 keV, 18 mm working distance, and lithium drifted silicon detector at 45 deg elevation).

Two-Dimensional Characteristics of Inclusions after Al Addition
By scanning an area of approximately 10 mm 2 , inclusions larger than 1 μm were characterized using ASPEX. Figure 5 shows the area fraction (AF) and mean size of inclusions after Al addition. Since the AF of inclusions after melting was approximately 0.87 ppm, the influence of existing after melting on the inclusion behaviors after Al addition could be ignored. Meanwhile, the size statistical analysis after Al addition as a function of holding time is presented in Figure 5. The solid symbols in Figure 6 represent the number density and mean size of each size group. The distribution curves based on the lognormal distribution model were also plotted in the figure, which are consistent with

Two-Dimensional Characteristics of Inclusions after Al Addition
By scanning an area of approximately 10 mm 2 , inclusions larger than 1 µm were characterized using ASPEX. Figure 5 shows the area fraction (AF) and mean size of inclusions after Al addition. Since the AF of inclusions after melting was approximately 0.87 ppm, the influence of existing after melting on the inclusion behaviors after Al addition could be ignored. Meanwhile, the size statistical analysis after Al addition as a function of holding time is presented in Figure 5. The solid symbols in Figure 6 represent the number density and mean size of each size group. The distribution curves based on the lognormal distribution model were also plotted in the figure, which are consistent with the experimental observations. On the basis of the statistical data collected in Figures 5 and 6, the evolution of inclusions after Al addition was classified into three stages as follows: Metals 2019, 9, x FOR PEER REVIEW 6 of 22 the experimental observations. On the basis of the statistical data collected in Figures 5 and 6, the evolution of inclusions after Al addition was classified into three stages as follows:  (1) In the early stage after Al addition, the AF of inclusions decreased dramatically, while the opposite trend was observed for inclusion size. Notably, the percentage of inclusions in the size range of 5~10 μm increased with time, revealing the effect of particle collision and agglomeration on inclusion growth within the first stage. Consequently, the average size of inclusions reached a peak value of approximately 4.2 μm at the end of stage I (10 min after Al addition).
(2) From 10 to 20 min after Al addition, the statistical results including the AF and average size of Al2O3 inclusions exhibited a downward trend. With rapidly decreasing inclusions in the size range of 5~10 μm due to the removal by preferential floatation, the mean size of inclusions declined to approximately 3.7 μm at the end of stage II. Therefore, the inconsistency between the AF and particle size during the first two stages after Al addition indicates that the floatation of particles was accompanied by the dramatic aggregation of inclusions in the first stage and then became dominant in the next stage.
(3) Within stage III, the AF and ND of inclusions experienced a continuous but slow decrease, whereas no significant changes in the particle size were observed. the experimental observations. On the basis of the statistical data collected in Figures 5 and 6, the evolution of inclusions after Al addition was classified into three stages as follows:  (1) In the early stage after Al addition, the AF of inclusions decreased dramatically, while the opposite trend was observed for inclusion size. Notably, the percentage of inclusions in the size range of 5~10 μm increased with time, revealing the effect of particle collision and agglomeration on inclusion growth within the first stage. Consequently, the average size of inclusions reached a peak value of approximately 4.2 μm at the end of stage I (10 min after Al addition).

Three-Dimensional Characteristics of Inclusions after Al Addition
(2) From 10 to 20 min after Al addition, the statistical results including the AF and average size of Al2O3 inclusions exhibited a downward trend. With rapidly decreasing inclusions in the size range of 5~10 μm due to the removal by preferential floatation, the mean size of inclusions declined to approximately 3.7 μm at the end of stage II. Therefore, the inconsistency between the AF and particle size during the first two stages after Al addition indicates that the floatation of particles was accompanied by the dramatic aggregation of inclusions in the first stage and then became dominant in the next stage.
(3) Within stage III, the AF and ND of inclusions experienced a continuous but slow decrease, whereas no significant changes in the particle size were observed. (1) In the early stage after Al addition, the AF of inclusions decreased dramatically, while the opposite trend was observed for inclusion size. Notably, the percentage of inclusions in the size range of 5~10 µm increased with time, revealing the effect of particle collision and agglomeration on inclusion growth within the first stage. Consequently, the average size of inclusions reached a peak value of approximately 4.2 µm at the end of stage I (10 min after Al addition).

Three-Dimensional Characteristics of Inclusions after Al Addition
(2) From 10 to 20 min after Al addition, the statistical results including the AF and average size of Al 2 O 3 inclusions exhibited a downward trend. With rapidly decreasing inclusions in the size range of 5~10 µm due to the removal by preferential floatation, the mean size of inclusions declined to approximately 3.7 µm at the end of stage II. Therefore, the inconsistency between the AF and particle size during the first two stages after Al addition indicates that the floatation of particles was accompanied by the dramatic aggregation of inclusions in the first stage and then became dominant in the next stage.
(3) Within stage III, the AF and ND of inclusions experienced a continuous but slow decrease, whereas no significant changes in the particle size were observed.

Three-Dimensional Characteristics of Inclusions after Al Addition
The electrolytic extraction technique offers an effective means of elucidating the three-dimensional characterization of Al 2 O 3 -based inclusions by eliminating the interference associated with the steel  Figure 7 shows the three-dimensional morphologies of typical inclusions in the sample with a holding time of 10 min after Al addition. Aggregated, faceted, and plate-like inclusions were identified among the dominant morphologies. It is also noted that at this moment, a neck, resulting from the sintering process and leading to the densification of the aggregate, was found between the colliding inclusions, as shown in Figure 7c. This observed result indicates that the diffusion of pseudomolecules was not yet completed at the end of the first stage after Al addition. Additionally, a small number of coral-like clusters were extracted from the steel sample (see Figure 7f). By contrast, in an Al-deoxidation experiment performed in the melt containing 0.293 mass pct Al with an initial O content = 297 ppm, Yang et al. reported [45] that there were plenty of spherical and dendritic inclusions within 9 min after Al addition under no-stirring conditions. containing 0.293 mass pct Al with an initial O content = 297 ppm, Yang et al. reported [45] that there were plenty of spherical and dendritic inclusions within 9 min after Al addition under no-stirring conditions.
In view of the grain growth, the morphology of Al2O3 inclusions depends on the growth conditions of the particles, i.e., the supersaturation degree of the dissolved Al and O contents, holding time, liquid flow conditions, grain surface roughness, and impurity particles [46,47]. Upon increasing the initial supersaturation in the melt, the generation sequence of alumina inclusions is polyhedral first, then plate-like, dendritic, and spherical successively [48] on the basis of the classification of inclusion morphologies by Braun et al. [46] and Dekkers et al. [47]. Therefore, in a previous Al deoxidation study under the condition of higher supersaturation by Yang et al. [45], unstable growth along with variable supersaturation gradient directions was the leading cause of the dendritic particles, whereas the presence of spherical Al2O3-based inclusions was due to the coarsening and breaking of dendrite arms [49]. In turn, the polyhedral and plate-like particles obtained in the current work are the consequences of the low supersaturation of dissolved Al and O. With respect to dendritic inclusions observed in samples, their formation may be likely attributed to a local high supersaturation degree after Al addition. In the sample with a holding time of 20 min after Al addition, aggregated and single inclusions were by far the dominant morphologies. Looking at Figure 8a-d, it is apparent that the surface contours of inclusions became smoother due to the Ostwald-ripening effect [46] (the diffusion of pseudomolecules). That is, small inclusions and the sharp edges of inclusions were dissolved, In view of the grain growth, the morphology of Al 2 O 3 inclusions depends on the growth conditions of the particles, i.e., the supersaturation degree of the dissolved Al and O contents, holding time, liquid flow conditions, grain surface roughness, and impurity particles [46,47]. Upon increasing the initial supersaturation in the melt, the generation sequence of alumina inclusions is polyhedral first, then plate-like, dendritic, and spherical successively [48] on the basis of the classification of inclusion morphologies by Braun et al. [46] and Dekkers et al. [47]. Therefore, in a previous Al deoxidation study under the condition of higher supersaturation by Yang et al. [45], unstable growth along with variable supersaturation gradient directions was the leading cause of the dendritic particles, whereas the presence of spherical Al 2 O 3 -based inclusions was due to the coarsening and breaking of dendrite arms [49]. In turn, the polyhedral and plate-like particles obtained in the current work are the consequences of the low supersaturation of dissolved Al and O. With respect to dendritic inclusions observed in samples, their formation may be likely attributed to a local high supersaturation degree after Al addition.
In the sample with a holding time of 20 min after Al addition, aggregated and single inclusions were by far the dominant morphologies. Looking at Figure 8a-d, it is apparent that the surface contours of inclusions became smoother due to the Ostwald-ripening effect [46] (the diffusion of pseudomolecules). That is, small inclusions and the sharp edges of inclusions were dissolved, whereas larger inclusions grew. The three-dimensional features of the Al 2 O 3 -based particles in Figure 8 show that Ostwald-ripening can be finished within 20 min, which is in agreement with Yang's findings [45]. The dendritic morphology of the particles was hardly observed in the sample at 20 min after Al addition. In addition to the floatation of inclusions, Van Ende et al. [50] reported that the dendritic Al 2 O 3 inclusion that usually appeared in the early deoxidation stage could subsequently change into a polyhedral shape with the decrease of supersaturation. Considering the smaller rising velocity and the transformation from dendrites, small polyhedral inclusions, therefore, could be observed long after Al addition. whereas larger inclusions grew. The three-dimensional features of the Al2O3-based particles in Figure 8 show that Ostwald-ripening can be finished within 20 min, which is in agreement with Yang's findings [45]. The dendritic morphology of the particles was hardly observed in the sample at 20 min after Al addition. In addition to the floatation of inclusions, Van Ende et al. [50] reported that the dendritic Al2O3 inclusion that usually appeared in the early deoxidation stage could subsequently change into a polyhedral shape with the decrease of supersaturation. Considering the smaller rising velocity and the transformation from dendrites, small polyhedral inclusions, therefore, could be observed long after Al addition.

Two-Dimensional Inclusion Characteristics after Ti Addition
Since titanium is an expensive alloying element, in commercial production, titanium is commonly added after Al deoxidation to diminish the Ti loss due to oxidation [51]. In this study, the Ti wire was fed into the melt at 20 min after Al addition, when most of the Al2O3-based inclusions had reached the melt surface and the Ostwald-ripening had almost been completed. Figure 9 shows the changes of the AF and average size of inclusions after Ti addition. As shown in Figure 9, the evolution of inclusion behaviors after Ti addition consisted of two main stages. (I) Within 5 min after Ti addition, the AF of inclusions first peaked at 2 min and then decreased drastically. The changes of the mean size of inclusions were approximately synchronous with those of the AF of inclusions. (II) Thereafter, no considerable changes in the AF were observed over time in contrast with the particle size, which gradually decreased.

Two-Dimensional Inclusion Characteristics after Ti Addition
Since titanium is an expensive alloying element, in commercial production, titanium is commonly added after Al deoxidation to diminish the Ti loss due to oxidation [51]. In this study, the Ti wire was fed into the melt at 20 min after Al addition, when most of the Al 2 O 3 -based inclusions had reached the melt surface and the Ostwald-ripening had almost been completed. Figure 9 shows the changes of the AF and average size of inclusions after Ti addition. As shown in Figure 9, the evolution of inclusion behaviors after Ti addition consisted of two main stages. (I) Within 5 min after Ti addition, the AF of inclusions first peaked at 2 min and then decreased drastically. The changes of the mean size of inclusions were approximately synchronous with those of the AF of inclusions. (II) Thereafter, no considerable changes in the AF were observed over time in contrast with the particle size, which gradually decreased.  Figure 10 shows the particle size distribution of the inclusion population as a function of holding time after Ti addition. In the figure, the open symbols correspond to the number density and mean size of each size group, which are in reasonable agreement with the fitted curves based on the lognormal distribution model. As presented in Figure 9, the value of ND at each holding time passed  Figure 10 shows the particle size distribution of the inclusion population as a function of holding time after Ti addition. In the figure, the open symbols correspond to the number density and mean size of each size group, which are in reasonable agreement with the fitted curves based on the lognormal distribution model. As presented in Figure 9, the value of ND at each holding time passed through a peak and tended towards zero with increasing inclusion size. In other words, the number of inclusions in the size range of 2-3 µm was much larger than the number of inclusions in the other size distributions. Besides, the value of ND experienced an increase shortly after Ti addition, followed by a rebound at a holding time of 5 min after Ti addition.  Figure 10 shows the particle size distribution of the inclusion population as a function of holding time after Ti addition. In the figure, the open symbols correspond to the number density and mean size of each size group, which are in reasonable agreement with the fitted curves based on the lognormal distribution model. As presented in Figure 9, the value of ND at each holding time passed through a peak and tended towards zero with increasing inclusion size. In other words, the number of inclusions in the size range of 2-3 μm was much larger than the number of inclusions in the other size distributions. Besides, the value of ND experienced an increase shortly after Ti addition, followed by a rebound at a holding time of 5 min after Ti addition. Distributions of the inclusion composition during Al and Ti additions are shown in Figure 11. Since the nitrogen content in oxide-nitride duplex inclusions cannot be quantitatively determined by ASPEX system [52], the inclusion composition data were collected in the Mg-Al-Ti system. Previous studies [53,54] have confirmed that small amounts of Mg and Al can lead to the generation of magnesium aluminate spinel in liquid steel, and thus, the magnesium-containing oxide phase in inclusions was identified as MgO·Al2O3. Accordingly, the dashed line in the figure corresponds to the mass ratio of titanium and aluminum in xMgAl2O4·yAl2TiO5.
Before titanium addition, the inclusion compositions were mainly concentrated close to the Al2O3 corner of the MgO-Al2O3 binary system, as visible in Figure 11a. According to ASPEX results, the Mg content in inclusions, which was normalized in the Mg-Al-Ti system ([Mass pct Ti] = 0) was Distributions of the inclusion composition during Al and Ti additions are shown in Figure 11. Since the nitrogen content in oxide-nitride duplex inclusions cannot be quantitatively determined by ASPEX system [52], the inclusion composition data were collected in the Mg-Al-Ti system. Previous studies [53,54] have confirmed that small amounts of Mg and Al can lead to the generation of magnesium aluminate spinel in liquid steel, and thus, the magnesium-containing oxide phase in inclusions was identified as MgO·Al 2 O 3 . Accordingly, the dashed line in the figure corresponds to the mass ratio of titanium and aluminum in xMgAl 2 O 4 ·yAl 2 TiO 5 .
Before titanium addition, the inclusion compositions were mainly concentrated close to the Al 2 O 3 corner of the MgO-Al 2 O 3 binary system, as visible in Figure 11a. According to ASPEX results, the Mg content in inclusions, which was normalized in the Mg-Al-Ti system ([Mass pct Ti] = 0) was 3.97% on average and varied from 2.22% and 23.88% before Ti addition, indicating that a little MgO was formed in inclusions because of reactions between soluble Al and MgO in the crucible. It should be pointed out that, according to the FactSage predictions, the Al 2 O 3 -based inclusions can be fully transformed into spinels when the Mg content in the Mg-Al system exceeds approximately 18.33%. Thus, in addition to a small number of spines, most of existing inclusions were Al 2 O 3 -based inclusions before Ti addition. Figure 11b shows a dramatic increase in the Ti content in inclusions at a holding time of 2 min after Ti wire feeding. In addition, there were a few smaller inclusions (≤3 µm) located close to the dashed line in the diagram but no pure titanium-containing particles were observed. This suggests the possibility of the discrete Al 2 TiO 5 particle after Ti feeding. Figure 12 exhibits the two-dimensional composition mappings of typical Ti-bearing inclusions at 2 min after Ti addition. The mapping pattern in Figure 12a confirms the inference about the presence of Al 2 TiO 5 from ASPEX results. As can be seen from Figure 12b-d, the zones of concentrated Ti were present in association with Al 2 O 3 -based body. Taken together, these results clearly point to the existing Al 2 O 3 -rich inclusions providing the major heterogeneous nucleation sites for the Ti-bearing phase. system used in this study. Third, the phase of TiN were not distinguishable according to the inclusion chemistry in this study because the typical particles in the previous work were Al-Ti-O oxides covered by a rectangular nitride phase in lieu of the irregular distribution of Ti-rich zones associated with Al2O3-based inclusions shown in Figure 11, and thus the Ti content determined by ASPEX represents the whole content in inclusions.

Three-Dimensional Characteristics of Inclusions after Ti Addition
One principal aim of this work is to establish a better understanding of the impact of existing Al2O3-based inclusions on the transient inclusion evolution during Ti addition. The electrolytic extraction technique provides revealing insight into the actual size and morphology of inclusions, with emphasis on the distribution of the Ti-bearing particles on the surface of Al2O3-based inclusions

Three-Dimensional Characteristics of Inclusions after Ti Addition
One principal aim of this work is to establish a better understanding of the impact of existing Al2O3-based inclusions on the transient inclusion evolution during Ti addition. The electrolytic extraction technique provides revealing insight into the actual size and morphology of inclusions, with emphasis on the distribution of the Ti-bearing particles on the surface of Al2O3-based inclusions and the joining of individual particles during agglomeration. In the steel sample taken at 5 min after titanium wire feeding as shown in Figure 11c, the chemistry of inclusions shifted back towards MgO-Al 2 O 3 binary system, implying that the Ti in inclusions was re-dissolved into the bulk steel. Consequently, the critical factor behind the rapid change in the Ti content is the presence of the Ti-bearing phase that functions as a transient product after Ti addition.
With increasing holding time, there were slight increases in the contents of Ti and Mg as presented in Figure 11d. As a result, the mean inclusion chemistry contained up to approximately 18 mass pct and 12 mass pct Ti (in Mg-Al-Ti system) at the ends of stage I and stage II after Ti addition, respectively. Strikingly, Matsuura et al. [20] reported that at 4 min after Ti addition, approximately 5 to 20 mol% Ti could be detected in the Al-Ti deoxidation experiments performed in IF steels ([mass pct Ti] = 0.12). This discrepancy can be partially attributed to the influence of the melt composition, including from Cr, N, and Mg. A second possible explanation for this difference is that the inclusion chemistry in the previous work was normalized in the Ti-Al-O system, rather than in the Ti-Al-Mg system used in this study. Third, the phase of TiN were not distinguishable according to the inclusion chemistry in this study because the typical particles in the previous work were Al-Ti-O oxides covered by a rectangular nitride phase in lieu of the irregular distribution of Ti-rich zones associated with Al 2 O 3 -based inclusions shown in Figure 11, and thus the Ti content determined by ASPEX represents the whole content in inclusions.

Three-Dimensional Characteristics of Inclusions after Ti Addition
One principal aim of this work is to establish a better understanding of the impact of existing It should first be pointed out that even though the N content was controlled to approximately 0.0020 mass pct, individual TiN inclusions were still identified after extraction from steel samples. As shown in Figure 13a-c, on the basis of the three-dimension morphologies, the individual TiN particles at 2 min after Ti addition can be classified into three general types: Single cubes, twinned inclusions, and clusters. In Figure 13a, a single TiN inclusion lying on the surface of the membrane exhibited a cubic habit. Twinned TiN with an irregular shape was also observed, as presented in Figure 13b, which is likely to originate from the growth of two nucleates [55]. Furthermore, the extracted TiN clusters comprised of sub-micron Ti-bearing particles (Figure 13c) were significantly smaller than Al 2 O 3 -based aggregates before Ti addition ( Figure 8). The present classification of TiN based upon their three-dimensional morphologies is similar to that applied in stainless steel containing 0.307 mass pct Ti and 0.0251 mass pct N (Figure 13d-f) [44]. By comparison, the typical TiN inclusions observed in the current melt containing a lower N concentration are relatively smaller than those observed in the high-N liquid steel. This difference is probably due to the excessive concentrations of Ti and N for TiN formation in the previous work.
The three-dimensional morphologies of typical Ti-containing particles associated with Al 2 O 3 -based inclusions at 2 min after Ti addition are illustrated in Figure 14. In contrast to the sharp edges of TiN aggregates (Figure 14c), the curved boundary lines of these Ti-rich regions in Figure 14 combined with EDS results indicate the existence of TiO x . However, considering the interference from the Al 2 O 3 matrix, it is exceedingly difficult to identify the accurate form of Ti in these regions according to the irregular inclusion shape or the semi-quantitative EDS analysis. So, the region of Ti-bearing particles adhering on the surface of the Al 2 O 3 -based body was simply considered to be the Ti-rich zone (TZ) during three-dimensional investigations.
smaller than Al2O3-based aggregates before Ti addition (Figure 8). The present classification of TiN based upon their three-dimensional morphologies is similar to that applied in stainless steel containing 0.307 mass pct Ti and 0.0251 mass pct N (Figure 13d-f) [44]. By comparison, the typical TiN inclusions observed in the current melt containing a lower N concentration are relatively smaller than those observed in the high-N liquid steel. This difference is probably due to the excessive concentrations of Ti and N for TiN formation in the previous work. The three-dimensional morphologies of typical Ti-containing particles associated with Al2O3-based inclusions at 2 min after Ti addition are illustrated in Figure 14. In contrast to the sharp edges of TiN aggregates (Figure 14c), the curved boundary lines of these Ti-rich regions in Figure 14 combined with EDS results indicate the existence of TiOx. However, considering the interference from the Al2O3 matrix, it is exceedingly difficult to identify the accurate form of Ti in these regions according to the irregular inclusion shape or the semi-quantitative EDS analysis. So, the region of Ti-bearing particles adhering on the surface of the Al2O3-based body was simply considered to be the Ti-rich zone (TZ) during three-dimensional investigations. Figure 13a-c exhibits the three-dimensional morphologies of Ti-rich zones associated with Al2O3-based clusters. This type of Ti-Al-containing inclusion may be the result of the growth of clusters by collision with separate inclusions or with other clusters during their ascension to the liquid surface (Figure 14a,b). Figure 14c is an enlarged partial view of the Ti-rich zone shown in Figure 14b. As seen from Figure 14c, a sintering process, driven by minimization of the surface energy [56], took place between Ti-rich particles and the Al2O3-based body, which led to densification of the aggregate. Figure 14d-f shows the three-dimensional features of the Ti-bearing Al2O3-based aggregates after Ti addition. The Al2O3-based aggregate originated from the agglomeration of inclusions. Because of the diffusion of pseudomolecules, the aggregating boundary line almost disappeared, and the surface of the aggregate became smoother. After Ti feeding, small Ti-rich zones were readily observed on the surface of existing aggregates, but the sites of these zones tended to be random and unpredictable (Figure 14d-f). Moreover, larger aggregates appeared to provide more advantageous sites for Ti-rich zones (Figure 14d).
As shown in Figure 14g,h, the experimental results obtained from the three-dimensional investigations revealed the presence of polygonal inclusions in association with the Ti-bearing particles after Ti wire addition. There were small concentrated Ti zones scattered on the body of the   (Figure 14a,b). Figure 14c is an enlarged partial view of the Ti-rich zone shown in Figure 14b. As seen from Figure 14c, a sintering process, driven by minimization of the surface energy [56], took place between Ti-rich particles and the Al 2 O 3 -based body, which led to densification of the aggregate. Figure 14d-f shows the three-dimensional features of the Ti-bearing Al 2 O 3 -based aggregates after Ti addition. The Al 2 O 3 -based aggregate originated from the agglomeration of inclusions. Because of the diffusion of pseudomolecules, the aggregating boundary line almost disappeared, and the surface of the aggregate became smoother. After Ti feeding, small Ti-rich zones were readily observed on the surface of existing aggregates, but the sites of these zones tended to be random and unpredictable (Figure 14d-f). Moreover, larger aggregates appeared to provide more advantageous sites for Ti-rich zones ( Figure 14d).
As shown in Figure 14g,h, the experimental results obtained from the three-dimensional investigations revealed the presence of polygonal inclusions in association with the Ti-bearing particles after Ti wire addition. There were small concentrated Ti zones scattered on the body of the polyhedral inclusions. This type of Ti-Al-containing inclusion might have been attributed to the collision between the Al 2 O 3 -based polyhedron and small-sized Ti-containing particles or to the simple generation of Ti-bearing particles onto the polyhedron.
The plate-like Al 2 O 3 -based inclusions can, likewise, provide a direct site for Ti-based particle formation. At a holding time of 2 min after Ti wire feeding, for an individual plate-like inclusion as depicted in Figure 14i, titanium was concentrated around the periphery rather than in the interior. Also, the Ti-rich zone was frequently located at the end of a single elongated platelet (i.e., bar shape during two-dimensional investigations) as shown in Figure 14j. Additionally, the outer edges of the base and the plate-like arms of flower-shaped Al 2 O 3 -based inclusions could act as nucleation sites for Ti-rich particles (Figure 14k,l).
As presented in Figure 14, compared with small aggregates with smooth surface contours and single polyhedral inclusions, larger Al 2 O 3 -based inclusions, including clusters, aggregates, and some flower-shaped inclusions, can provide favorable sites for Ti-rich zones during the transient stage. These newly produced Ti-bearing particles may increase the Ti loss because of the adsorption of refining slag in practical production. Hence, along with the steel chemistry (Al, Ti, and O contents) [39], the morphology of existing Al 2 O 3 -based inclusions is a contributing factor affecting the Ti yield. This means the large Al 2 O 3 -based particles including larger aggregates, clusters, and some flower-shaped inclusions, should be eliminated by stirring to the extent possible before Ti addition. polyhedral inclusions. This type of Ti-Al-containing inclusion might have been attributed to the collision between the Al2O3-based polyhedron and small-sized Ti-containing particles or to the simple generation of Ti-bearing particles onto the polyhedron.
The plate-like Al2O3-based inclusions can, likewise, provide a direct site for Ti-based particle formation. At a holding time of 2 min after Ti wire feeding, for an individual plate-like inclusion as depicted in Figure 14i, titanium was concentrated around the periphery rather than in the interior. Also, the Ti-rich zone was frequently located at the end of a single elongated platelet (i.e., bar shape during two-dimensional investigations) as shown in Figure 14j. Additionally, the outer edges of the base and the plate-like arms of flower-shaped Al2O3-based inclusions could act as nucleation sites for Ti-rich particles (Figure 14k,l).  (d-f) Ti-rich zones associated with aggregated inclusions; (g,h) Ti-rich zones associated with faceted inclusions; (i-l) Ti-rich zones associated with plate-like inclusions. Figure 15 exhibits the three-dimensional morphologies of Ti-rich zones associated with Al 2 O 3 -based inclusions at 10 min after Ti feeding. Note that Al 2 O 3 -based clusters containing Ti-rich zones almost disappeared long after Ti feeding. This is due to the preferential floatation of larger inclusions. As depicted in Figure 15, aggregated, faceted, and plate-like inclusions with Ti-rich zones were identified among the dominant morphologies. Even though no nitrogen was detected in inclusions by EDS, compared with the irregular boundary lines of the Ti-rich zones at 2 min after Ti addition, the sharp edges and right angles of these zones, shown in Figure 15, provided an indication of the TiN phase long after Ti feeding. Moreover, most of the Ti-rich zones in Figure 15 were in sub-micrometer. Figure 15 exhibits the three-dimensional morphologies of Ti-rich zones associated with Al2O3-based inclusions at 10 min after Ti feeding. Note that Al2O3-based clusters containing Ti-rich zones almost disappeared long after Ti feeding. This is due to the preferential floatation of larger inclusions. As depicted in Figure 15, aggregated, faceted, and plate-like inclusions with Ti-rich zones were identified among the dominant morphologies. Even though no nitrogen was detected in inclusions by EDS, compared with the irregular boundary lines of the Ti-rich zones at 2 min after Ti addition, the sharp edges and right angles of these zones, shown in Figure 15, provided an indication of the TiN phase long after Ti feeding. Moreover, most of the Ti-rich zones in Figure 15 were in sub-micrometer.

Thermodynamic Conditions in the Fe-20 Mass pct Cr-Al-Ti-O-N System
The calculated deoxidation equilibria for Al in high-Cr stainless steel and pure iron at 1873 K by using thermodynamic software FactSage 7.0 (ThermFact LTD, Montreal, QC, Canada and GTT-Technologies, Herzogenrath, Germany) is shown in Figure 16. The equilibrium curve in the Fe-20 mass pct Cr-Al-O system is higher than that in pure iron, suggesting that the deoxidation power of aluminum in stainless steel is reduced by the addition of chromium. One deeper reason for this difference may be the strong attraction between chromium and oxygen (e Cr O = −0.032 [30]), particularly in a Fe-Cr alloy containing up to 20 mass pct Cr.

Thermodynamic Conditions in the Fe-20 Mass pct Cr-Al-Ti-O-N System
The calculated deoxidation equilibria for Al in high-Cr stainless steel and pure iron at 1873 K by using thermodynamic software FactSage 7.0 (ThermFact LTD, Montreal, QC, Canada and GTT-Technologies, Herzogenrath, Germany) is shown in Figure 16. The equilibrium curve in the Fe-20 mass pct Cr-Al-O system is higher than that in pure iron, suggesting that the deoxidation power of aluminum in stainless steel is reduced by the addition of chromium. One deeper reason for this difference may be the strong attraction between chromium and oxygen (e Cr O = −0.032 [30]), particularly in a Fe-Cr alloy containing up to 20 mass pct Cr.  Figure 17 shows the equilibrium relationship between Ti and N for TiN formation in the Fe-20 mass pct Cr-Ti-N-O melt. According to the thermodynamic prediction, the contents of titanium and nitrogen play a crucial role in the formation of TiN in molten steel and, therefore, should be controlled at levels below the equilibrium values to avoid the generation of stable TiN. Within the range of Ti content studied here, the concentrations of Ti and N in the bulk melt containing 0.0020 mass pct N at 1873 K are located in the area below the Ti-N equilibrium curve. Hence, it is believed    Figure 17 shows the equilibrium relationship between Ti and N for TiN formation in the Fe-20 mass pct Cr-Ti-N-O melt. According to the thermodynamic prediction, the contents of titanium and nitrogen play a crucial role in the formation of TiN in molten steel and, therefore, should be controlled at levels below the equilibrium values to avoid the generation of stable TiN. Within the range of Ti content studied here, the concentrations of Ti and N in the bulk melt containing 0.0020 mass pct N at 1873 K are located in the area below the Ti-N equilibrium curve. Hence, it is believed that the observed TiN in this work was not a thermodynamically stable compound. Additionally, in the case of [mass pct N] = 0, Ti2O3 becomes dominated when the Ti content exceeds a threshold of approximately 0.21% in the Fe-20% Cr-Ti-O melt and this threshold slightly increased with the nitrogen content. The stability diagram in Fe-20 mass pct Cr-Al-Ti-O melt at 1873 K was calculated by using FactSage 7.0 with the FactPS, FToxid, and FSstel databases, as presented in Figure 18. The experimental data listed in Table 1 are located in the region of Al2O3, indicating that Al2O3 was the thermodynamically stable phase in the current deoxidization tests. In this figure, there lies a liquid region among Al2O3, Ti2O3, and Ti3O5 at 1873 K, which narrows to disappearance with increasing [mass pct Al]. Furthermore, the value of the critical Ti content between the Ti2O3 and Ti3O5 regions slightly decreases with increasing Al content. Nevertheless, the threshold of the Ti content between The stability diagram in Fe-20 mass pct Cr-Al-Ti-O melt at 1873 K was calculated by using FactSage 7.0 with the FactPS, FToxid, and FSstel databases, as presented in Figure 18. The experimental data listed in Table 1  the Ti-bearing inclusion region and the stable Al2O3 region shows an opposite trend. That is, with increasing Ti addition, more aluminum should be added into the liquid steel to prevent Ti oxidation.

Formation Mechanism of Transient Inclusions after Ti Addition
Note that various non-stable products were observed during two-dimensional and three-dimensional investigations, indicating that the melt shortly after Ti addition was a non-equilibrium thermodynamic system. Therefore, the equilibrium calculations in Section 3.5 are

Formation Mechanism of Transient Inclusions after Ti Addition
Note that various non-stable products were observed during two-dimensional and three-dimensional investigations, indicating that the melt shortly after Ti addition was a non-equilibrium thermodynamic system. Therefore, the equilibrium calculations in Section 3.5 are not suitable for the prediction of inclusion behaviors during the transient stage.
With respect to Ti oxide observed shortly after Ti addition, according to the observed findings from the two-dimensional and three-dimensional investigations, there are two possible interpretations for their formation: First, discrete TiO x particles can be directly formed by reactions between dissolved but not dispersed titanium and soluble oxygen, which can be expressed as follows: [Ti] The two-dimensional statistical data and three-dimensional features revealed a small number of discrete TiO x or Al 2 TiO 5 particles after Ti feeding. It is noted that in this mechanism, the source of oxygen for TiO x formation is offered by the current high-Cr-containing melt, wherein the equilibrium soluble oxygen concentration estimated by FactSage was approximately 3 ppm. These findings suggested a limited impact of the first mechanism by reactions (3) and (4) on the transient product generation.
The second formation mechanism of Ti oxide inclusions is that, shortly after Ti addition, TiO x can be generated onto the existing Al 2 O 3 -basedinclusions. Two factors may be linked to this mechanism: (1) Due to the low lattice disregistry between alumina and titanium oxide [57], the existing alumina can act as a heterogeneous nucleation core of titanium oxide.
(2) Another contributing factor is the reactions between the local high titanium and existing Al 2 O 3 -based inclusions, which can be understood by the following reactions: On the basis of the stability diagram of inclusions seen in Figure 18, the occurrence of two mechanisms is, in essence, a result of local Ti supersaturation after Ti feeding but the existing Al 2 O 3 -based inclusion can provide the site and oxygen for Ti-containing oxides through the second manner. The two-dimensional and three-dimensional characteristics of inclusions after Ti addition highlighted the direct effects of the second mechanism on the generation of TiO x during the transient stage. It can be concluded that the low lattice disregistry between alumina and titanium oxide and the local Ti supersaturation play leading roles in the formation of transient TiO x . Hence, for the minimization of Ti loss during the transient stage, the removal of existing Al 2 O 3 -based particles, especially larger aggregates, clusters, and some flower-shaped inclusions, should be enhanced before Ti addition.
The newly produced TiO x phase observed immediately after Ti feeding was, by nature, not thermodynamically stable; thus, the Ti in TiO x phase was eventually re-dissolved into the molten steel by Al reduction according to the following reaction: Consequently, the Ti content in inclusions underwent a rapid change after Ti addition. Notably, the inclusion chemistry displayed no significant changes during stage II after Ti feeding. It is concluded, therefore, that the transient evolution of most TiO x can be finished within 5 min after titanium feeding.
Considering the N content of approximately 20 ppm and the transient non-uniform nature of soluble Ti in the melt shortly after titanium wire feeding, the generation of TiN by the local supersaturation of dissolved [%Ti] and [%N] that exceeded the equilibrium value was very likely. However, long after Ti feeding, multiphase inclusions containing TiN and Al 2 O 3 became dominant, whereas the observed TiN was not the stable phase in the current thermodynamic system, as predicted in Figure 17. Hence, the observed TiN in the sample was expected to be the secondary inclusions formed during sampling. Rapid cooling of the liquid steel primarily provided high supersaturation with respect to Ti and N and uniform growth conditions. In addition, the existing inclusions in the melt, which have low lattice disregistry with TiN (see Table 2), could act as heterogeneous nucleation cores for TiN, thereby promoting the nucleation of TiN during sampling. It should be pointed out that, due to the comparably fast solidification, the TiN formed on existing inclusions during sampling had no time to grow and, hence, maintained sub-micrometer scale as presented in Figure 15.

Agglomeration Mechanism of Inclusions after Ti Addition
According to the obtained results from three-dimensional investigations, after Ti addition, inclusion collisions took place among single inclusions, aggregates, and clusters. In this study, three major types of collisions were taken into account during the collision-agglomeration process after titanium feeding: Brownian, turbulent, and Stokes' collisions. Brownian collision, β B ij , describes the random movement of very small particles suspended in liquid steel; turbulent collision, β T ij , originates from the turbulence flow caused by convection or stirring; and Stokes' collision, β S ij , occurs in liquid steel as a consequence of the large difference in inclusion size, or to be more specific, larger inclusions have a higher settling velocity and collide with smaller ones during ascension. For a certain collision phenomenon, the collision volume (m 3 /s), namely, the number of inclusion collisions in molten steel per unit time, is considered to be a significant parameter relative to collision rate. The total collision volume can be expressed as the sum of each type of collision, and the separate values of β B ij , β T ij , and β S ij can be determined by calculation from the following equations [58,59]: In these equations, k B is the Boltzmann constant (J/K), T is the thermodynamic temperature (K), µ is the absolute viscosity of steel (kg/m·s), r i and r j are the radii of the two colliding inclusions (m), g is the gravitational acceleration (m/s 2 ), and ρ Fe and ρ i are the densities of the steel and inclusion, respectively (kg/m 3 ). The parameters for the calculation are given in Table 3. The value of r i in the computation corresponds to the mean size in the size range of 2-3 µm in Figure 10, which was set to 2.4 µm. It was assumed that the irregular particle is a sphere and can collide with other sized particles within the radius. In this case, the average size of the particle determined by ASPEX system was considered to be the inclusion diameter. Since individual particles including TiN, TiO x , and Al 2 O 3 -based inclusions and their aggregations were observed after Ti feeding, the contribution of the particle density to the collision volume should be assessed.  Figure 19 provides the predicted contribution of each type of collision to inclusion growth in terms of the collision volume. When the diameter of the particle is less than 2.7 µm, Brownian and turbulent collisions play primary roles in particle growth. Moreover, the value of β B ij experiences a substantial increase with decreasing inclusion size, suggesting an increasing effect of Brownian collision on the particle growth. Consequently, the TiN clusters observed shortly after Ti addition (Figure 13c) probably results from Brownian and turbulent collisions. Note the little influence of Stokes' collision upon inclusion growth if the two colliding inclusions have the same size. Hence, the collision between the most frequently observed particles in this study, which have a mean size of 2.4 µm, can also be associated with the same reason. computation corresponds to the mean size in the size range of 2-3 μm in Figure 10, which was set to 2.4 μm. It was assumed that the irregular particle is a sphere and can collide with other sized particles within the radius. In this case, the average size of the particle determined by ASPEX system was considered to be the inclusion diameter. Since individual particles including TiN, TiOx, and Al2O3-based inclusions and their aggregations were observed after Ti feeding, the contribution of the particle density to the collision volume should be assessed.  Figure 19 provides the predicted contribution of each type of collision to inclusion growth in terms of the collision volume. When the diameter of the particle is less than 2.7 μm, Brownian and turbulent collisions play primary roles in particle growth. Moreover, the value of β B ij experiences a substantial increase with decreasing inclusion size, suggesting an increasing effect of Brownian collision on the particle growth. Consequently, the TiN clusters observed shortly after Ti addition (Figure 13c) probably results from Brownian and turbulent collisions. Note the little influence of Stokes' collision upon inclusion growth if the two colliding inclusions have the same size. Hence, the collision between the most frequently observed particles in this study, which have a mean size of 2.4 μm, can also be associated with the same reason. When the inclusion diameter exceeds the threshold of approximately 2.7 μm, the particle growth becomes controlled by turbulent and Stokes' collisions. As shown in Figure 19, the collision When the inclusion diameter exceeds the threshold of approximately 2.7 µm, the particle growth becomes controlled by turbulent and Stokes' collisions. As shown in Figure 19, the collision volume for Stokes' collision shows an upward trend as a function of increased size (more than 2.4 µm), whereas turbulent collision increases over the whole range. Thus, under the influence of turbulent and Stokes' collisions, the particle with a given size can be captured by larger Al 2 O 3 -based inclusions, especially clusters or aggregates, and then grow into larger ones. Moreover, compared with the particle density, the collision type and the inclusion diameter appear to be the predominant factors in the collision growth of inclusions.

Conclusions
In this manuscript, the transient inclusion evolution during Al and Ti additions in a Fe-20 mass pct Cr alloy was investigated by two-dimensional and three-dimensional methods. The main conclusions obtained are as follows: (1) Although the characteristics of Al 2 O 3-based inclusions are not new for low-carbon Al-killed steels, the current laboratory experiments identified that the deoxidation products in a liquid Fe-20 mass pct Cr alloy passed through three main stages with time: Particle agglomeration, inclusion floating and a slow decrease of remaining Al 2 O 3 -based inclusions.
(2) After Ti addition, TiO x was immediately generated onto the existing Al 2 O 3 -based inclusion as a transitional product and thermodynamically reduced into Al 2 O 3 by Al as time progressed. The generation of transient TiO x could hardly be predicted by the equilibrium relations of Ti-O-N and Ti-Al-O in the high-Cr-containing melt but was attributed to the low disregistry between Al 2 O 3 and TiO x and the local Ti supersaturation during the transient stages.
(3) Because of the local supersaturation of dissolved [%Ti] and [%N] shortly after Ti addition, TiN associated with existing inclusions and three types of individual TiN including single cubes, twinned inclusions, and clusters were identified.
(4) The formation of Ti-rich zones during transient stages was affected by the morphology of existing Al 2 O 3 -based inclusions. In order to minimize the Ti loss caused by the formation of Ti-rich zones, the removal of large Al 2 O 3 -based particles including aggregates, clusters, and flower-shaped inclusions should be promoted by stirring before Ti addition.
(5) After Ti addition, Brownian and turbulent collisions were the primary factors in the collisions of particles smaller than the threshold of 2.7 µm. The agglomeration of inclusions larger than this threshold was mainly dominated by turbulent and Stokes' collisions. The collision types and inclusion diameters produced more significant effects than did the inclusion densities on the collision process.