Effect of Slag Composition on the Kinetics of Formation of Al 2 O 3 MgO Inclusions in Aluminum Killed Ferritic Stainless Steel

Transcription

1 , pp Effect of Slag Coposition on the Kinetics of Foration of Al 2 O 3 MgO Inclusions in Aluinu Killed Ferritic Stainless Steel Goro OKUYAMA, Koji YAMAGUCHI, Syuji TAKEUCHI and Ken-ichi SORIMACHI Technical Research Labs., Kawasaki Steel Corp., Kawasaki-Cho, Chuo-ku, Chiba-city, Japan. (Received on July 8, 1999; accepted in final for on Noveber 10, 1999) Kinetics of both slag/etal reactions and etal/inclusion reactions were investigated experientally using 20 kg vacuu induction furnace in order to clarify the echanis of the foration of MgAl 2 O 4 spinel inclusions in aluinu killed ferritic stainless steel (SUS430). The results obtained are suarized as follows : 1) By reducing CaO/SiO 2 and CaO/Al 2 O 3 ratio of top slag, MgO contents in Al 2 O 3 based inclusions decreased. 2) The two fil theory was eployed to analyze the rate deterining step of slag/etal reaction (reduction of MgO in top slag). By this odel, it was found that the rate deterining step of the reaction was the ass transfer of Mg through the fil in olten steel. The increase rate of Mg in olten steel is deterined by the activities of soluble oxygen and MgO at the slag/etal interface, and hence by slag coposition. 3) The unreacted core odel was eployed to analyze the rate deterining step of etal/inclusions reaction. The analysis showed that the rate deterining step of the reaction in the case of 20 kg vacuu induction furnace was the diffusion of Mg in olten steel. KEY WORDS: secondary steelaking; stainless steel; slag; inclusion. 1. Introduction With the requireents for high quality iron and steel products becoing increasingly strict, the requireents for high cleanliness in the olten steel have also becoe higher. Particularly with regard to high Ni alloys and stainless steels, a olten steel refining process which provides higher cleanliness in coparison with carbon steel has becoe an iportant topic in consideration of the applications and quality requireents of those products. In recent years, the FeO and chroe oxide content of slag has been reduced and high basicity slags have been adopted in order to achieve higher purity, and particularly lower oxygen levels. However, as a result, the foration of MgAl 2 O 4 spinel type inclusions in steel, which was rarely seen in the past, has becoe a proble. 1) Due to the fact that MgAl 2 O 4 spinel has a high elting point and displays a different deforation capacity fro that of steel, it exists as an inclusion in the for of C type inclusions with a sall aspect ratio, and thus reduces the fatigue strength of spring aterial and bearing aterials. Moreover, this type of inclusion has also becoe a cause of surface defects and other probles in high Ni alloy steels, which are processed by rolling into ultra thin sheets with thickness on the order of , as in shadow asks. Against this background, research on the foration of MgAl 2 O 4 spinel type inclusions has becoe active in recent years, and therodynaic studies of the subject 2,3) and reports on the influence of slag basicity on inclusion coposition change behavior 4) have been published. Based on these researches, it has been possible to obtain equilibriu constants for the foration of MgAl 2 O 4 spinel, interaction paraeters, and other nuerical values necessary for investigations based on equilibriu theory. However, study of the influence of slag basicity and siilar factors has been liited to qualitative explanations, and study fro the viewpoint of kinetics, which is iportant for practical purposes, has been insufficient. In the present research, in order to clarify the foration echanis of MgAl 2 O 4 spinel type inclusions which for in the VOD treatent for 16% Cr ferritic Al killed stainless steel, experients were carried out using a 20 kg high frequency, sall scale induction furnace, and the slag, etal, and inclusions were investigated. This research is expected to lead to an inclusion control technique which can be applied to actual VOD operation by controlling the slag coposition. 2. Experiental Procedure Experients were carried out using the 20 kg high frequency vacuu induction furnace shown in Fig. 1. The induction furnace is housed in a sealed chaber, and the interior of the chaber was aintained at Pa (780 Torr) with Ar gas during elting and the experients. MgO crucible with an inner diaeter of and a ISIJ

2 Table 1. Coposition of Molten steel used for 20 kg VIF experients. Table 2. Initial slag coposition used for 20 kg VIF experients. Fig. 1. Scheatic diagra of 20 kg vacuu induction furnace. depth of was placed in the furnace. The teperature of the olten steel was continuously easured and controlled to aintain at K using a therocouple installed in the crucible, while at the sae tie, consuable type therocouples were also iersed at appropriate ties and teperature adjustents were ade. The teperature in the experients was K. The experiental procedure was as follows. First, after reducing the pressure in the chaber, the air was replaced with Ar gas, and the atospheric pressure was adjusted to Pa. After elting electrolytic iron in the crucible, etallic Cr was added, and 20 kg of olten steel with a coposition of 16 ass% Cr was elted while aintaining a teperature at K. Next, the coponents C, Mn, Si, etc. were adjusted, and flux (equivalent to 25 kg/t) was added. After confiring elting of the flux, a prescribed aount of Al was added. Al addition was perfored by attaching an Al wire to a round carbon steel rod having a diaeter of and a length of approxiately and iersing the rod and wire in the olten steel. By preventing a direct reaction between the Al and slag, this ethod stabilized the addition yield. After Al addition, saples of the olten steel were taken successively and rapidly cooled. In order to investigate the changes in the coposition of the inclusions contained in the steel, saples were polished to a irror surface with a diaond abrasive, five to ten representative spots were selected at rando using a scanning electron icroscope (SEM), and a quantitative analysis of the coposition was perfored with an energy dispersive type X-ray analyzer (EDX). To deterine the concentration of Mg in the steel, a quantitative analysis of the extreely sall aounts of this substance was perfored by flaeless atoic absorption spectroetry. The copositions of the olten steel and slag used in these experients are shown in Tables 1 and 2, respectively. 3. Experiental Results As an exaple of the experiental results obtained with the 20 kg vacuu induction furnace, Fig. 2 shows the changes with tie in the coposition of the olten iron after Al addition in experient No. 4. The Al concentration of the steel decreased, beginning iediately after Al addition, while siultaneously, the Si concentration increased. Further, the Mg concentration also increased after Al addi- Fig. 2. Fig. 3. Changes of silicon, aluinu and agnesiu contents in the etal with tie after aluinu addition at K. Changes of MgO and Al 2 O 3 contents in inclusions with tie during the sae experient in Fig. 2. tion, reaching 0.8 ass pp after 30 in. Figure 3 shows the changes with tie in the coposition of the inclusions after Al addition during the sae experient as in Fig. 2. The coposition of the inclusions in the steel was siple Al 2 O 3 iediately after Al addition. However, after approxiately 2 in, the MgO concentration of the inclusions reached approxiately 10 ass%. Thereafter, the MgO concentration increased gradually, apparently corresponding to the increase behavior of the Mg concentration in Fig. 2. Figure 4 shows an SEM photograph of typical Al 2 O 3 MgO inclusions. The size of the observed inclusions was sall, having a diaeter of in alost all cases. In order to confir that the change in the coposition of the inclusions described above was a change in coposition fro siple Al 2 O 3 inclusions to Al 2 O 3 MgO, an experient was carried out by first perforing top addition of a flux with the sae coposition as in experient No. 3 on the olten steel, and then iersing a dense aluina plate 2000 ISIJ 122

3 in the steel for 40 in after Al addition. The results of an observation of the cross section of the aluina plate, which was slow cooled after this experient, are shown in Fig. 5. Fro these photographs, it can be understood that the coposition had changed fro Al 2 O 3 to Al 2 O 3 MgO in a range extending fro the surface of the aluina plate to a depth of approxiately It was also found that the concentration of MgO in this degraded layer was virtually unifor in the plate thickness direction, fro the olten steel contact surface, at ass%. These observations confired that Al 2 O 3 is cheically reduced by the Mg contained in the steel and is degraded into Al 2 O 3 MgO. It should be noted, however, that the absolute values of the concentration and thickness of the degraded layer were not identical to those at the tie of iersion of the aluina plate, because Mg diffusion also occurred during slow cooling after the experient. Fro the above, it is considered that the MgO in inclusions after Al addition is the result of the process in which the MgO contained in the slag is cheically reduced by the Al in the steel, and then the Mg fored by the reduction reacts with the deoxidation product Al 2 O 3 to for Al 2 O 3 MgO inclusions. Figure 6 shows the change with tie in the MgO concentration of inclusions after Al addition under various experiental conditions. Although the MgO concentration of the inclusions increases after Al addition, the MgO concentration tends to increase ore quickly when the CaO/SiO 2 or CaO/Al 2 O 3 of the slag is high (experients No. 1, 3). Moreover, because the rate of the increase in the MgO concentration becoes slow when the MgO concentration of the inclusions reaches ass%, it is considered that the coposition of the inclusions has changed fro Al 2 O 3 to MgAl 2 O 4 positive spinel (Al 2 O 3 : MgO 72 ass% : 28 ass%). Furtherore, although an MgO crucible was used in this research, the coposition of the inclusions was Al 2 O 3 throughout experients under slag-free conditions. Fro this fact, it is considered that the MgO concentration of the inclusions was not affected by the MgO crucible. 4. Discussion Fro the results described in the previous chapter, it was understood that the concentration of MgO in inclusions increases with the passage of tie after Al addition, and the rate of increase in the concentration of MgO in inclusions is influenced by the slag coposition. The foration of MgO Fig. 4. Typical SEM iage of MgAl 2 O 4 spinel inclusions. Fig. 6. Changes of MgO content in the inclusions with tie after aluinu addition at K. Fig. 5. SEM and EDX iages of distribution of Al and Mg eleents near the surface of aluina plate after keeping in the olten steel for 40 in ISIJ

4 in inclusions consists of two eleent processes, one being a reaction between the etal and the slag, in which the MgO in the slag is cheically reduced by the Al in the olten steel, and another being a reaction between the etal and inclusions, in which the deoxidation product Al 2 O 3 reacts with the Mg in the steel that was fored by cheical reduction of the slag. Figure 7 shows these two eleental processes in scheatic for. In order to estiate the rate-deterining step in these respective eleent processes, the slag etal reaction was investigated fro the viewpoint of kinetics in the following Sec. 4.1, and the etal inclusion reaction was siilarly investigated in Sec Kinetics of Reduction of MgO in Slag Slag Metal Reaction Model In order to analyze the reduction reaction of the MgO in slag in the 20 kg sall scale induction furnace experients fro the viewpoint of kinetics, the authors adopted a copeting reaction odel 5,6) based on two fil theory, which is frequently applied to dephosphorization/desulfurization reactions in olten iron and to reoxidation reactions in olten steel by slag. In the following, this will be referred to in abbreviated for as the reaction odel. It is assued that the concentrations of Al 2 O 3, SiO 2, and MgO in the slag side and of Al, Si, Mg, and O in the etal show respective concentration gradients in the double boundary fil layer at the slag etal interface, and have reached a therodynaic equilibriu at the interface. Assuing that the reactions in Eqs. (1) (3) have reached equilibriu at the slag etal interface, the equilibriu constants for these reactions can be expressed by Eqs. (4) (6). Further, AlO 1.5 is adopted for the sake of coputational siplicity, and because the concentrations of iron and chroiu oxides in the slag were extreely low in the experients with the sall scale induction furnace, these reactions are not considered. [Al] 1.5[O] (AlO 1.5 )...(1) [Si] 2[O] (SiO 2 )...(2) [Mg] [O] (MgO)...(3) K Al a* AlO1.5 /(a* Al a* 1.5 O )...(4) K Si a* SiO2 /(a* Si a* 2 O )...(5) K Mg a* MgO /(a* Mg a*) O...(6) If it is assued that the rate of the cheical reactions involving the respective coponents at the slag etal interface are sufficiently large, and therefore ass transfer is the rate-deterining step, the reaction rates can be expressed by the following equations. d[al] Ak Al (AlO [Al] W BAl a 1.5 * 15. O )...(7) Fig. 7. Scheatic diagra for reactions aong slag, etal, and inclusion and for Mg content in slag, etal, and inclusion. d[si] Ak Si (SiO2 [Si] W ) BSi a* 2 O...(8) d[mg] Ak Mg (MgO [Mg]...(9) W ) BMg ao* d[o] Ak O ao...(10) W [O] * fo* Ki fi C Bi...(11) M γ i n C (% O )...(12) ( MiO ) 1 1 MiOn k ρ k n B M ρ a k i...(13) Oxygen activity, a* O, at the slag etal interface can be obtained fro the above equations and the ass balance equation for oxygen at the interface, Eq. (14). Here, M is the olecular weight, and g is the activity coefficient. 15. d[al] 2 M M Al 1 d[mg] 1 d[o] 0...(14) M M Mg i Si io d[si] If this a* O and the appropriate ass transfer coefficients for olten steel and slag are given, it is possible to obtain the reaction velocities of the respective coponents between the slag and etal. It was assued that the ass transfer coefficient, k i, on the etal side has an identical value for all the coponents, including Mg. On the other hand, it was assued hypothetically that the ass transfer coefficients for SiO 2 on the slag side, k is, have different values fro the other coponents, as has been reported in connection with previous research. 6 8) Under these assuptions, the ass transfer coefficient for the etal side, k, and the ass transfer coefficient for the slag side, k s, were obtained so as to agree with the experiental results. As a result, it was possible to obtain the calculated result which showed the closest agreeent with the experiental results when the etal side ass transfer coefficient, k, was /s, the slag side ass transfer coefficient of the coponents other than SiO 2, k s, was /s, and the slag side ass transfer coefficient of SiO 2 was /s. i n n i i O s O is 2000 ISIJ 124

5 Fig. 8. Observed changes of Al and Si contents in olten steel in coparison with those calculated for experient No. 4. Fig. 10. Calculated relation between slag basicity, CaO/SiO 2 and activity of MgO in the slag, a MgO. Fig. 9. Observed change of soluble Mg content in the etal after Al addition in coparison with calculated ones. Fig. 11. Influence of slag basicity, CaO/SiO 2, on activity of dissolved oxygen in olten steel calculated at the slag/ etal interface, coparing with easured dissolved oxygen 10 in after Al addition. Table 3. Exaple of calculated values for ass transfer resistances (exp. No. 4). reaction in Eq. (3) is rate-deterining for ass transfer on the etal side, and the reaction velocity is expressed considering only the ass transfer on the etal side, then Eq. (15) can be deduced using the concentration gradient in the boundary fil on the etal side. Figure 8 shows the observed results of the change with tie in the concentration of Al and Si in the olten steel in experient No. 4, in coparison with the results calculated based on the odel described above. Figure 9 shows the observed results of the concentration of Mg in the olten steel, in coparison with the results obtained by calculation. Fro these figures, the calculated results of the change with tie in the concentrations of Al, Si, and Mg in the olten steel showed good agreeent with the experiental results. Based on the results described above, the ass transfer resistance of the respective coponents on the etal side and slag side in experient No. 4 was obtained using Eq. (13), as shown in Table 3. Fro this table, it can be inferred that the reactions in Eqs. (1) and (3), which are due to slag etal reactions, are the rate-deterining steps of ass transfer on the etal side, and the reaction in Eq. (2) is rate-deterining for ass transfer on the slag side Influence of Slag Coposition on Rate of Increase in Concentration of Mg in Molten Steel Due to Reduction Reaction of MgO in Slag If it is assued, based on the previous section, that the Fro this equation, it can be understood that the rate of increase in the Mg concentration of the olten steel depends on the Mg concentration, [Mg]*, at the slag etal interface. The slag coposition dependency of [Mg]* at the slag etal interface will be considered qualitatively in the following. [Mg]* can be deterined by the activity of MgO, a* MgO, and the activity of oxygen, a* O, at the slag etal interface using Eq. (6). Figure 10 shows the calculated relationship between the slag basicity, CaO/SiO 2 and CaO/Al 2 O 3, and the activity of MgO, a MgO, the latter being obtained using the therodynaic data base software Thero-calc. The value of a MgO increases as the basicity, CaO/SiO 2 and CaO/Al 2 O 3, of the slag increases. Figure 11 shows the relationship between the slag basicity, CaO/SiO 2, and the activity of the dissolved oxygen in the olten steel, a* O, which was calculated using Eqs. (1) through (14), together with the observed values of a O of the bulk etal, as easured using an oxygen probe. The value of a* O and the a O of the bulk etal decrease as CaO/SiO 2 ind[mg] Ak V ([Mg]* [Mg])...(15) ISIJ

6 Fig. 12. Mg content distribution in olten steel and an inclusion based on a odel in which rate deterining step is Mg diffusion in the inclusion. Fig. 13. Fig. 14. creases. Fro the points entioned above, it can be understood qualitatively that [Mg]* at the slag etal interface increases as the slag has higher basicity, as indicated by CaO/SiO 2 and CaO/Al 2 O 3, and consequently, the rate of increase in the Mg concentration of the olten steel due to the reduction reaction with the MgO in the slag also increases Kinetics of Metal Inclusion Reaction As discussed above, the change in the coposition of inclusions produced by Al deoxidation is the result of a process in which the deoxidation product Al 2 O 3 is degraded to an Al 2 O 3 MgO coposition by the reaction with the [Mg] in olten steel, the latter being fored when the MgO in the slag was cheically reduced by the Al. Analyses were perfored for the case in which the diffusion of Mg in the inclusion layer is rate-deterining, assuing hypothetically that the rate of the cheical reaction at the etal inclusion interface is sufficiently large, and for the case in which the diffusion of Mg in olten steel is rate-deterining. It is assued that the Mg in olten steel reacts with Al 2 O 3 inclusions fro outside the inclusions, foring a reaction product layer which is coposed of Al 2 O 3 MgO. Moreover, in order to siplify the odel, it is also assued that the shape of inclusion particles is spherical, with a radius of R 0, and the outer diaeter of the particles does not change over tie. The phase diagra for MgAl 2 O 4 spinel shows that the concentration of MgO is % at K; it was therefore assued that the MgO concentration is 10 % when the inclusions initially begin to for spinel, and the MgO concentration finally changes to 28 % spinel Case When Mg Diffusion in Inclusion Layer Is Rate-deterining Step Figure 12 shows a scheatic diagra of the distribution of the Mg concentration in an inclusion in the case when the diffusion of Mg in the inclusion layer is rate-deterining. In actuality, because expansion of the spinel layer progresses by diffusion of Mg and Al into a shell-like spinel layer, it is considered that the concentration profile takes a for such as that shown in Fig. 12. Here, however, for the sake of siplicity, it was thought that Mg is transferred by diffusion in an inclusion with an initial (Mg) concentration of 0 ass%. Therefore, the diffusion coefficient of Mg in MgAl 2 O 4 spinel was used as the diffusion coefficient in this case. The equation for diffusion in an inclusion can be expressed by Eq. (16). Changes of average MgO content in the inclusion calculated by a odel in which Mg diffusion in solid inclusion is rate deterining step. Mg content distribution in olten steel and an inclusion based on a odel in which rate deterining step is Mg diffusion in boundary layer of olten steel. d(mgo) D r d r dr s 2 2 d(mgo)...(16) dr It was assued that when t 0, r R 0, and (MgO) 28 ass%, and when r does not equal R 0, (MgO) 0 ass%. Further, it was assued that the MgO concentration at the boundary phase between the spinel phase and Al 2 O 3 is 10 ass%. Figure 13 shows the results when the change in the MgO concentration of the inclusion as a whole is obtained for each inclusion particle size by calculating the above equation by the calculus of finite differences. Here, D s ( 2 /sec) 9) was used as the inter-diffusion coefficient in MgAl 2 O 4 spinel. Fro the sae figure, it can also be understood that diffusion within inclusions progresses extreely rapidly, and at a inclusion particle size on the order of 3, as observed in these experients, the MgO concentration reaches saturation in approxiately 2 sec Case When Mg in Molten Steel Is Rate-Deterining Step The case when the MgO concentration distribution in the inclusion changes uniforly, under the assuption that the diffusion of Mg in inclusions is sufficiently rapid, can be represented as shown in Fig. 14. Fro the balance of Mg on the etal side and in the inclusions: 2000 ISIJ 126

7 Fig. 15. Changes of MgO content in the inclusions calculated by a odel in which Mg diffusion in olten steel is rate deterining step. Fig. 16. Changes of average MgO content in the inclusion calculated by a odel in which Mg diffusion in the boundary layer at slag/etal interface is rate deterining step. d 4π R 3 (Mg) ρ 0 3 s ρ 4π R D 0 2 (Mg)...(17) R0 [Mg] L (Mg) [Mg]...(18) L [Mg] is Mg concentration of etal at the etal inclusion interface. And (Mg) is Mg concentration of inclusion at the etal inclusion interface. Here, based on the fact that the inclusion particle size is extreely sall, at , only the diffusion within the boundary layer on the etal side was considered in ass transfer. The distribution ratio, L, is the equilibriu distribution ratio of Mg at the etal inclusion interface. Fro the phase diagra for an oxide phase in which Al and Mg in olten steel are in equilibriu, which was obtained by Hino et al., 2) a value of was used as the distribution ratio, this being obtained fro an [Mg] concentration of 0.25 pp at the boundary where the oxide phase changes fro Al 2 O 3 to MgAl 2 O 4 at [Al] 0.1 ass%, and an (Mg) concentration of 10 % in MgAl 2 O 4. D is the diffusion coefficient of Mg in olten steel, and as a value for the diffusion coefficient of Al, ( 2 /sec) 10) was used. The (Mg) concentration of inclusions, if calculated while holding the [Mg] concentration of the olten steel constant, is given by the following equation. 3D ρ (Mg) [Mg] L 1 exp t...(19) R0 2 L ρs Using the above equation, the change with tie in the concentration of MgO in an inclusion in the case of an inclusion particle radius of R was calculated under the conditions used in experients No. 3 and No. 4, and the results are shown in Fig. 15. At the inclusion particle radius of , which was observed in these experients, the MgO concentration of the inclusions reaches saturation in 200 sec when [Mg] 0.4 ass pp, and in 50 sec when [Mg] 0.8 ass pp. According to the phase diagra by Hino et al., the stable oxide phase is not MgO but MgAl 2 O 4 when [Mg] 40 ass pp. Here, therefore, it was thought that the concentration of (Mg) reaches saturation at the (Mg) concentration of spinel. Copared with the case discussed in the previous section, in which the diffusion of Mg in the inclusion layer was the rate-deterining step, the reaction rate here is slower, on the order of 1/25 to 1/100 than the previous case. It ay, therefore, be assued that the diffusion of Mg in the boundary layer on the olten steel side is the rate-deterining step. However, Fig. 9 showed that the behavior of Mg in olten steel due to the slag-etal reaction achieves equilibriu in approxiately 30 in. Based on this fact, it can be inferred that the slag etal reaction is the slowest aong the various eleent processes. Thus, in the syste as a whole, this reaction is the rate-deterining step for inclusion foration, including that of MgO. Therefore, Eq. (17) was calculated considering the tie related change in [Mg] in olten steel. If [Mg] is expressed as shown in Eq. (15), and assuing that the Mg concentration at the slag etal interface, [Mg]*, is constant, the tie related change in [Mg] in olten steel can be expressed by the following equation. t...(20) Here, assuing (Mg) 0 when t 0, the MgO concentration in inclusions can be expressed by the equation shown below. (Mg) [Mg] L [Mg]* L 3D ρ AK R L ρ V 0 2 AK [Mg] [Mg]* 1 exp V s 3D ρ R0 2 L ρ AK V s 0 2 s AK exp V 3D ρ exp t R L ρ t...(21) Figure 16 shows the tie related change in the MgO concentration in inclusions obtained using Eq. (21), together with the observed values. The calculated values can pro ISIJ

8 vide a rough explanation of the observed values. The calculated values and observed values do not show good agreeent in the initial stage of the reaction. This ay be attributed to the fact that the equilibriu distribution value, L, of Mg at the etal inclusion interface, and Mg concentration, [Mg]*, at the etal slag interface are assued to be constant; whereas, in actualy, the value of L in the initial stage of the reaction is larger than the value used in the calculation. 5. Conclusion In order to clarify the echanis by which Al 2 O 3 MgO inclusions for in chroe-bearing olten steel, experients were perfored with a 20 kg high frequency induction furnace, and the slag etal inclusion reaction was investigated fro the viewpoint of kinetics. The results were as follows. (1) An investigation of the influence of the slag coposition on the foration of MgO Al 2 O 3 inclusions showed that the Mg concentration of the olten steel increases with tie after the addition of Al, and accopanying this increase, the coposition of inclusions changes fro siple Al 2 O 3 to Mg Al 2 O 4 spinel having an MgO concentration of ass%. The rate of increase in the MgO concentration of the inclusions also increased as the basicity, CaO/SiO 2 and CaO/Al 2 O 3, of the top slag increased. (2) A coparison of the calculated results of a slag etal reaction odel based on two fil theory and the experiental results showed good agreeent between the two. In the coposition range used in these experients, it was inferred that the increase in the concentration of [Mg] in the olten steel is the rate-deterining step for ass transfer on the etal side. The results also showed that the influence of the slag coposition on the rate of increase in the Mg concentration of inclusions can be explained by changes in the [Mg] concentration at the slag etal interface due to the slag coposition dependency of MgO activity, a MgO, and oxygen activity, a O, at the interface. (3) As a result of a kinetic analysis of the respective conditions under which Mg diffusion in inclusions is the rate-deterining step for the etal inclusion reaction, and under which Mg diffusion in the olten steel is rate-deterining, it was inferred that the latter is the rate-deterining step. Furtherore, with the inclusion particle size observed in these experients, the etal inclusion reaction is sufficiently faster than the slag etal reaction. Consequently, it can be concluded that, in the syste as a whole, the slag etal reaction is the rate-deterining step for the rate of inclusion foration, including that of MgO. Noenclature A : Area of reaction interface ( 2 ) a i : Activity of coponent i (olten steel coponent a i f i [%i], slag coponent a io g i N i ) D i : Diffusion constant of coponent i ( 2 /s) f i : Activity coefficient of coponent i K i : Equilibriu constant of i no io n k i : Total ass transfer coefficient of coponent i (g/ 2 s) k : Mass transfer coefficient of etal side (g/ 2 s) k s : Mass transfer coefficient of slag side (g/ 2 s) L : Distribution ratio of Mg between etal and inclusions ( ) M i : Molecular weight of coponent i N i : Mole fraction of coponent i R o : Radius of inclusion particle () V : Volue of olten steel ( 3 ) W : Mass of olten steel (kg) g i : Activity coefficient of coponent i r : Density of etal (assued to be kg/ 3 ) r s : Density of slag (assued to be kg/ 3 ) REFERENCES 1) H. Matuno: CAMP-ISIJ, 7 (1994), ) H. Ito, M. Hino and S. Banya: CAMP-ISIJ, 8 (1995), 75. 3) R. Inoue and H. Suito: Metall. Mater. Trans. B, 25B (1994), ) T. Nishi, A. Ueno and K. Shine: CAMP-ISIJ, 7 (1994), ) D. G. C. Robertson, S. Ohguchi, B. Deo and A. Willis: Ironaking Steelaking, 11 (1984), No. 5, ) H. Ichihashi, Y. Higuchi, Y. Tago and M. Fukugawa: CAMP-ISIJ, 7 (1994), ) Physical Properties of Molten Iron and Molten Slag, ISIJ, Tokyo, (1972). 8) S. Shinozaki, K. Mori and Y. Kawai: Tetsu-to-Hagané, 68 (1982), No. 1, 72. 9) General Theory of Cheistry, Cheical Society of Japan, No. 9, (1975). 10) Y. Ono: Tetsu-to-Hagané, 63 (1977), No. 8, ISIJ 128