Reduction Rate of Cr 2 O 3 in a Solid Powder State and in CaO SiO 2 Al 2 O 3 CaF 2 Slags by Fe C Si Melts

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1 , pp eduction ate of Cr 3 in a Solid Powder State and in Ca Si l 3 CaF Slags by Fe C Si Melts Takaitsu NKSUG, Haiping SUN, 1) Kunihiko NKSHIM and Katsui MI Graduate School of Engineering, Kyushu University, Hakozaki, Higashi-ku, Fukuoka Japan. E-ail: nakasuga@zaiko.kyushu-u.ac.jp 1) Forerly at Kyushu University, now at School of Materials Science and Engineering, The University of New South Wales. (eceived on February 16, 001; accepted in final for on May 18, 001) In order to understand effective conditions to recover chroiu fro stainless steel-aking slags, the kinetic behavior of Cr 3 reduction by iron carbon elts were investigated at various conditions by using solid Cr 3 powder and Cr 3 Ca Si l 3 CaF slags. The effect of teperature on the reduction rate of solid Cr 3 was fairly large and the apparent activation energy was about 180 kj ol 1. The overall reduction of solid Cr 3 was considered to be controlled by a cheical reaction step. For reduction of Cr 3 in slag, the addition of CaF to slag and of silicon to iron elt prooted the reduction rate, but the reduction of Cr 3 powder was retarded by the silicon addition. The kinetic behavior of reduction of Cr 3 in slag could be well siulated by the kinetic reaction odel proposed previously. s a result, it was found that the overall reduction rate of Cr 3 in slag was controlled by the ass transport in the slag phase. KEY WDS: ironaking; steelaking; stainless steel; Cr 3 ; slag etal reaction; reduction; kinetics; echanis; odeling. 1. Introduction Chroiu is one of the ost iportant alloying eleents for special steel products and also one of harful eleents whose contents in wasted aterials are regulated. The affinity of chroiu to oxygen is relatively large, so that soe chroiu transfer into slag occurs in stainless steel-aking process. Therefore, a high recovery of expensive chroiu fro the refining slags is an essential issue fro both the econoical and the environental points of view. reduction of Cr 3 by carbon and/or silicon dissolved in iron elt is a basic reaction for chroiu recovery as well as decarburization of stainless steel-aking. Thus, uch attention has been directed to the clarification of this reaction so far. 1 4) However, different conclusions have been reported on a rate-deterining step. For instance, Suzuki et al., 1) who exained the reduction rate of solid Cr 3 in a cylinder shape by carbon in iron elt, concluded that the reduction rate was controlled by the diffusion of oxygen in iron. Whereas, Fruehan ) concluded that the diffusion of carbon in iron was a rate-deterining step in the decarburization of stainless steel-aking. lso, Taoka et al. 3) said that the decarburization rate was prooted by l 3 addition to slag, but Nakao et al. 4) reported that lower contents of l 3 and Mg in slag were favorable for Cr 3 reduction. Furtherore, in order to save the consuption of expensive ferro-chroiu alloy required for stainless steel products, a chroiu-containing iron elt was produced by reducing chroiu ore in a stainless steel-aking furnace and was directly used as it was. However, a kinetic study on the Cr 3 reduction by high carbon iron elts was just begun and then its reduction features haven t been sufficiently understood. Therefore, it is very iportant to clarify its kinetic behavior and reaction echanis for an increase of reaction efficiency. In the present work, the reduction rates of Cr 3 in a solid powder state and in Ca Si l 3 CaF slags by Fe C Si elts were investigated at various conditions. The experiental results on the reduction behavior of Cr 3 in slag were analyzed based on the previous kinetic reaction odel. 5). Experiental Procedures The sae experiental apparatus as in the previous work 5) was used. bout 0.1 kg of Fe C or Fe C Si alloy was first elted in a graphite crucible or an aluina crucible (0.036 I.D.) under argon atosphere. fter the experiental teperature was attained, an initial etal saple was taken by using a quartz tube. Then, about 0.01 kg of Cr 3 powder ( ) or 0.0 kg of liquid slag containing Cr 3 elted in a pure iron slag holder was placed on the etal surface, the oent of which was taken as a starting point of the reaction. Soe etal saples were taken at certain tie intervals during the reaction. The progress of the reaction was followed by cheical analysis of these etal saples. t the end of each experient, the final slag saple for cheical analysis and X-ray diffraction analysis was taken by sticking slag to a fine iron ISIJ

2 Table 1. Coposition of initial slags (ass%). Table. Experiental conditions and copositions of initial and final iron of each experient for reduction of solid Cr 3 powder (ass%). Fig. 1. Effect of teperature on the reduction rate of Cr 3 powder by carbon-saturated iron elts. Table 3. Experiental conditions and copositions of initial and final iron of each experient for reduction of Cr 3 in slag (ass%). Fig.. Effect of teperature on the initial reduction rate, k i of solid Cr 3 powder by carbon-saturated iron elts. wire. s a source of Cr 3, solid Cr 3 powder reagent and Cr 3 Ca Si l 3 CaF synthetic slags were used. l 3 and CaF were added to lower the liquidus teperature of slags. Slags were prepared by preelting a ixture of appropriate aount of cheical reagent grade oxide powders. The coposition of initial slags are listed in Table 1. In the present work, the effects of teperature, CaF content in slag, Ca/Si ratio of slag, carbon content in iron elt, and addition of silicon and sulfur to iron elt were exained. The experiental conditions and copositions of initial and final iron of each experient for reduction of solid Cr 3 powder and Cr 3 in slag are suarized in Tables and 3, respectively. The alphabetical letter of un No. indicates the slag type shown in Table Experiental esults 3.1. eduction of Solid Cr 3 Powder Effect of Teperature Figure 1 shows the results of the reduction of Cr 3 powder by carbon-saturated iron elt at 1 500, and C. The chroiu content in iron elt increases rapidly with reaction tie at the early stage, but the slope of its curve gradually decreases with decreasing aount of powders, and the content reains constant after all powders reacted with iron elt. It is evident that the reduction rate increases with increasing teperature. The overall reduction reaction of solid Cr 3 by carbon in iron elt can be expressed: Cr 1.5 (s)1.5ccr1.5c(g)...(1) The initial slope of curves shown in Fig. 1, defined by k i {(d[cr]/dt) t0 }, is taken as the index of reduction rate of solid Cr 3 to copare effects of various factors on the reduction rate, because the effect of back reaction can be ignored and the reaction area reains constant at that tie. Fro rrehnius plots of log k i vs. 1/T shown in Fig., a value of 181 kj ol 1 for apparent activation energy, E i, was calculated. Since the value of k i obtained here is that for overall reduction rate of Cr 3, the teperature dependence of rate coefficient and driving force is also included in it. So, the value of E i should be considered as an index for teperature dependence of the initial reduction rate. The apparent activation energy was fairly large, so that the overall reduction of solid Cr 3 by carbon in iron elt was considered to be controlled ainly by a cheical reaction step at the interface Effect of Metal Coposition Figure 3 shows the effect of carbon content in iron elt on the reduction rate. It is found that the carbon content in iron elt has only a little influence on the initial reduction rate of Cr 3 powder and also that the final chroiu contents slightly increase as the initial carbon content increases. This difference in final chroiu content ay be attributed to the residual carbon content. For the run with the ini- 001 ISIJ 938

3 Fig. 3. Effect of initial [C] content in iron elt on the reduction rate of Cr 3 powder at C. Fig. 5. Effect of teperature on the reduction rate of Cr 3 in slag. Fig. 4. Effect of initial [Si] content in iron elt on the reduction rate of Cr 3 powder at C. tial carbon content of 1.76 ass%, the larger part of carbon is used at first 3 in, and thereafter, the iron elt has alost no reducing power. Figure 4 shows the variation of chroiu content in iron elt with reaction tie during the reduction reaction between Cr 3 powder and Fe ass%c elt with different silicon contents. In runs with silicon addition, the progress of Cr 3 reduction was retarded. The reason for this phenoenon is that for Fe C Si elts, silicon is oxidized siultaneously with carbon to produce silica at the early period of reaction, which leads to the obstacle for the contact of Cr 3 powder and iron elt. s the aount of silicon addition increases, the silica volue generated is also increased. Therefore, the final chroiu content in iron elt was decreased. 3.. eduction of Cr 3 in Slag Explanation of eduction Behavior During the reduction reaction, the slag foaing due to C gas evolution was observed, and it was confired that the higher the initial carbon content in iron elt was, the ore intensively the C gas evolved. The reduction rate of Cr 3 is relatively fast, so that alost all of Cr 3 in slag is reduced within about 10 in, and thereafter, the chroiu content in iron elt reains constant. The carbon content in iron elt decreases linearly with reaction tie at first, but it gradually decreases even after the Cr 3 reduction ceases, because soe of carbon is used for the reduction of Si in slag, as seen fro the increase in the silicon content in iron elt at the later stage of a run. The solid lines in Figs. 5 through 8 show the calculational results based on the kinetic analysis discussed in Sec. 4, and those are generally in good agreeent with the experiental results Effect of Teperature Figure 5 shows the effect of teperature on the reduction rate of Cr 3 in slag. It is found that the reduction of Cr 3 proceeds ore rapidly and up to higher chroiu content in final iron elt as the teperature is higher. Higher teperature also favors the reduction of Si in slag, and therefore, it is seen that the final silicon content in iron elt is higher in a run at higher teperature. In the reduction of Cr 3 in slag by Fe ass%c elt, its apparent activation energy was as high as 151 kj ol 1. This value was the nearly sae as that for the reduction of solid Cr 3. This eans that the reduction of Cr 3 in slag is considered to be controlled by a cheical reaction step at the early stage, so that it is better for its kinetic analysis that the dissociation reaction of Cr 3 at the interface is taken into consideration Effect of Slag Coposition Figure 6 shows the effect of CaF content in slag on the reduction rate. It is found that the reduction rate and the chroiu content in final iron elt increase with an increase in CaF content in slag, and also that the lower the CaF content in slag is, the higher the silicon content in final iron elt is. Since the viscosity of slag tends to decrease with the addition of CaF to slag, such an increase in the reduction rate ay be attributed to the increase of ass transport coefficient in the slag. Figure 7 shows the effect of Ca/Si ratio of slag on the reduction rate. It is found that the reduction rate increases in order of slag G, F, H. The difference between ISIJ

4 Fig. 6. Effect of CaF content in slag on the reduction rate of Cr 3 in slag at 1600 C. Fig. 8. Effect of [Si] and [S] in iron elt on the reduction rate of Cr 3 in slag at C. Fig. 9. X-ray diffraction patterns of initial and final slag saples. Fig. 7. Effect of Ca/Si ratio of slag on the reduction rate of Cr 3 in slag at C. these runs ay be attributed to an decrease of the activity coefficient of Cr 3 in the case of slag F, because the higher the Ca/Si ratio of slag is, the lower the activity coefficient of Cr 3 is, 6) and to an increase of the viscosity of slag in the case of slag H, because Si content in the slag is high. Consequently, the reduction rate was the fastest in the case of slag G (Ca/Si 1.11) in these runs Effect of Metal Coposition Figure 8 shows the effect of silicon and sulfur in iron elt on the reduction rate. It is found that the reduction rate and the chroiu content in final iron elt increase rearkably by the addition of silicon, which is oxidized doinantly, because reducing power of silicon is superior to that of carbon under the present experiental conditions. n the other hand, it is found that the reduction rate decreases by the addition of surface active sulfur, although it does not directly involve in the reaction. This ay be attributed to a decrease in the effective reaction area by the adsorption of sulfur on the interface X-ray Diffraction nalysis In order to exaine the state of chroiu oxide in slag, the X-ray diffraction analysis was ade on initial and final slag saples. Exaples of the diffraction patterns of these slags are shown in Fig. 9. The diffraction peaks of Cr 3 are observed for the initial slags. This fact indicates that soe of Cr 3 particles still reained as undissolved in slag owing to the low solubility of Cr 3 in Ca Si l 3 slags, and therefore, slags used in this study were saturated with Cr 3 at the early period of reaction. n the other hand, the diffraction peaks of l 3 instead of Cr 3 are observed for the final slags. l 3 content of final slags was ass% fro the cheical analysis. It is considered fro this fact that l 3 content increased close to its saturation value due to the dissolution of crucible aterial, l 3, into slag during a run, and l 3 was precipitated on cooling. 001 ISIJ 940

5 4. Discussion 4.1. ate Equations for Cr 3 eduction fro Slag The kinetic reaction odel based on two-fil theory has been applied to the analysis of the present experiental results on the reduction behavior of Cr 3 in slag. The following reactions are considered to take place siultaneously at the slag-etal interface when Cr 3 Ca Si l 3 CaF slags contact Fe C Si S elts. In addition, sall aounts of Fe was contained in the initial slags, because the Fe dissolution into the slag occurred on holding near the etal surface for about 5 in to allow the slag to elt, and Fe content also changed according to the change of oxygen content in the etal. The equilibriu constant, K, for each reaction is given as function of the absolute teperature, T, as follows 7) : (Cr 1.5 )Cr1.5...() Cr 1.5 log KCr a a log...(3) a 00 Cr 1.5 T 971. CC(g)...(4) log log P C KC...(5) aa 1160 C T. 003 (Si )Si...(6) Si log KSi a a log...(7) a Si T (Fe)Fe...(8) Fe log KFe a a log...(9) a 6150 Fe T. 604 where a is the activity; P is the partial pressure, at. Here, because the activity of oxygen in iron elt is used in the siulation of the kinetic behavior, an electrocheical expression is used for eaction (10) on sulfur, and its equilibriu relation can be given with the sulfide capacity, C S, defined by Eq. (11). 8) The sulfide capacity, C S, defined by ichardson et al. 9) was used 10) for the evaluation of C S in this study. S( )(S )...(10) (S) a 769 log C Slog log CS (11) a T P log CS log (S) / 1 / P S 1 S 1.79(Ca) 1.4(Mg) (Si ) 0.33(l ) 3 T...(1) Several researches 11 13) on the kinetics of the slag etal reactions have suggested that the reaction of C foration is controlled by the cheical reaction at the interface, and other reactions are controlled by the ass transport in the slag and/or etal phases. In this study, the ass transport of carbon in the etal phase, and the dissociation reaction of oxides at the interface for chroiu and silicon, were also taken into consideration. The changes of chroiu, carbon, silicon, sulfur and oxygen contents in the etal, and Fe content in the slag with reaction tie can be written as follows: d[ Cr]...(13) dt W k {( Cr) B [Cr] a * Cr Cr 15. } BCra k k ρ k k ρ Cr s s r,cr d[c] dt W k f a P* C C C[ C] * KC 1 1 fca* k k k ρ C...(14)...(15)...(16) d[si]...(17) dt W k Si{ (Si) B Si[Si] a * } B a* k k ρ k k ρ Si s s r,si d[s] dt W k [S] BS S (S) a* 1 1 BS k k ρ k ρ a* S s s d[] dt W k * ρ af...(18)...(19)...(0) []...(1) d(fe) dt W k sρ s{ (Fe) B Fe a Fe a *} s r,c...() where t is the reaction tie, s; is the reaction area, ; W and W s is the weight of etal and slag, kg; k and k s is the ass transport coefficient in etal and slag, s 1 ; r and r s is the density of etal and slag, kg 3 ; k Cr, k C, k Si and k S are the overall ass transport coefficients for each reactions, kg s 1, and they are given by Eqs. (14), (16), (18) and (0); k r,cr, k r,c and k r,si are the rate constants for each reaction, kg s 1 ; B is the apparent equilibriu constant; f is the activity coefficient in etal; a superscript, * indicates the slag etal interface; [ ] and ( ) indicate coponent in etal and slag phase, ass%. The interfacial distribution ratio of each eleent between slag and etal, L*, can be defined as a function of the interfacial oxygen activity, a*, and the apparent equilibriu constant, B, as follows: (Cr)* LCr * BCra*. [Cr]* (Si)* L* Si BSia* [Si]* (S)* BS L* S [S]* a* Si 15 *....(3)...(4)...(5) ISIJ

6 (Fe) * L* B a* Fe...(6) The activity of oxygen in etal, a, is referred to an infinite dilution. In the calculation of the activity coefficient of coponents in etal, f i, the literature values 7) of interaction coefficients, e j i, between i and j eleents were used. Then, a Fe was assued to be equal to the ole fraction of iron. For siplification, it was assued that the ass transport coefficients of each eleent are equal with each other in the etal or in the slag phase. Slags used in this study were saturated with Cr 3 at the early period of reaction. Therefore, during that period, the Cr 3 content dissolved in slag reains constant, i.e. the chroiu content in slag is its saturation value, (Cr) sat. But after the Cr 3 content in slag decreases less than its saturation value, the chroiu content in slag decreases as the reduction proceeds. Therefore, a value of (Cr) sat is necessary for the present kinetic analysis, but its values in slags with CaF have not been sufficiently deterined, so it was taken as a fitting paraeter, here. In the calculation, the changes in the coposition and weight of slag and etal due to the slag etal reaction and the dissolution of crucible aterial, l 3, into the slag during a run were also taken into consideration on the assuption that the l 3 dissolution rate is controlled by the ass transport in the slag phase. 4.. ate Calculation ssuing that no accuulation of oxygen at the slag etal interface occurs, the following ass balance equation of oxygen can be obtained: 3W M Cr d[cr] W d[c] W d[si] dt M dt M dt W d[s] W d[] Ws d( Fe) M dt M dt M dt S C...(7) Si Fe Fig. 10. Table 4. Variation of calculated oxygen activity at the slag etal interface with reaction tie in run B-8. The paraeters deterined by odeling calculation. where M is the olecular weight, kg ol 1. Given the values of, k r, k s r s, k r,cr, k r,c, k r,si, B Cr, B Si, B Fe, B S and (Cr) sat as entioned later, the value of oxygen activity at the interface, a*, can be deterined fro Eq. (7). n exaple of the variation of its value during a run is shown in Fig. 10. It is found fro this figure that a* increases with reaction tie in the beginning of reaction, which indicates that the rate of C foration is slower than that of Cr 3 dissociation, so that the oxygen content at the interface becoes oversaturated. But it gradually decreases after the Cr 3 content in slag decreases less than its saturation value. By using these interfacial values of oxygen activity, concentration changes of each eleent in the etal and the slag with reaction tie can be calculated fro Eqs. (13) (). The pressure of C gas evolved at the interface, P* C, was taken as 1 at to solve Eq. (15). In order to reduce the nuber of paraeters, the values of k r 1.4 kg s 1 obtained by Mori et al. 14) and B S obtained by Shibata et al. 15) were used, respectively. The other paraeters k s r s, k r,cr, k r,c, k r,si, B Cr, B Si, B Fe and (Cr) sat were deterined by coparing the calculated results with the experiental results for each run. It was also assued that the values of these paraeters were constant during the entire period of reaction Paraeters The paraeters deterined by odeling calculation are shown in Table 4. The solid lines in Figs. 5 through 8 are the results calculated by using these paraeters, and these figures show the kinetic behavior of Cr 3 reduction fro slag can be siulated by the present odel. The values of k s r s in the range of 0.1 to 0.6 kg s 1 were greater than the literature values. This is believed to be attributed to a decrease of the viscosity of slag by the addition of CaF to slag, and oreover, the stirring effect of slag by C gas evolution. The values of k r,cr were not reported, and were obtained in this study, as shown in Table 4. The values of k r,c were also greater than those obtained in the previous work. 15) The values of B Cr, B Si, B S and B Fe can be theoretically calculated fro the therodynaic data. 7) Using the equilibriu constants or capacity, the theoretical values of B Cr, B Si, B S and B Fe are given as follows 5) : ( Mx ) MCr fcr MM...(8) x BCr KCrγ Cr1.5 ( Mx ) MSi fsi MM...(9) x BSi KSiγ Si ( Mx ) MFe MM...(30) x BFe K γ Fe Fe 001 ISIJ 94

7 Fig. 11. Coparison of the values obtained fro the present work, B (paraeter), with those calculated fro the therodynaic data, B (theoretical). B S C S f S...(31) where M x indicates oxides and fluoride (Cr 3, Ca, Si, l 3, CaF and Fe) in slag, and g Mx is the activity coefficient of oxide in slag. B Si and B S were calculated using the initial and final copositions of slag due to the difference in the initial and the final copositions of slag. The values of g Cr1.5 and g Si in the initial slags were estiated fro the literature values, 16) and the values of g Si and g Fe in the final slags were estiated fro the following relation based on the regular solution odel 17) for slag. T ln γ α N ( α α α ) N N i ij j ij ik jk j k j j k...(3) where i, j and k indicate oxides (Ca, Si, l 3 and Fe) in slag, and N is the ole fraction of oxides in slag. a ij are the ion ion interaction energies in slag suggested by Banya, 17) and were used in this calculation. CaF was also taken into consideration as the calciu ion. Figure 11 shows the coparison of the values obtained fro the kinetic analysis of the experiental results, B (paraeter), as given in Table 4, with the theoretical values calculated fro Eqs. (8) (31) using the therodynaic data, B(theoretical). s seen fro Fig. 11, the theoretical and the calculated values agree well with each other, although the values of B Cr deviate slightly for the lack of the literature values of g Cr1.5 in slag studied ate-deterining Step(s) The total resistance for the transfer reaction of each eleent i (icr, C, Si, S) between slag and etal, i, is defined by the reciprocal of the overall ass transport coefficient, k i, i.e.; i 1 k...(33) The relative contributions to the total resistance of the transport in the slag phase, i s, and that in the etal phase, i, and the cheical reaction at the interface, i r, are defined by the following equations, respectively: i Fig. 1. s Cr B a r Cr 1, Cr 1, Cr k ρ k k ρ s Si Coparison of the relative contributions of each eleent for the reduction of Cr 3 in slag in run B-8. s s Cr 1 C r, kr,cc 1 1 BSia* r, Si, Si k ρ k k ρ s s Si 1 k ρ S s s s S, r,cr r,si S B S k ρ a* S...(34)...(35)...(36)...(37) The coparison of these relative contributions of each eleent, s i, r i, i, gives a good suggestion on which step(s) controls the overall reaction. n exaple of the changes of these relative contributions during a run are shown in Fig. 1. s Cr is uch larger than r Cr and Cr, this fact indicates that the overall rate of Cr 3 reduction is controlled by the ass transport in the slag phase. The result of our odeling calculation is practically the sae as the one Yokoyaa et al. 18) concluded fro the experients of selting reduction of chroite ore by the dissolved carbon in liquid iron. But Cr is relatively large at the early period of the reaction, so that it can be said that the ass transport in the etal phase is not negligible at that tie. For reaction on silicon, when silicon content in iron elt is low and Si reduction proceeds, it can be said that its rate is controlled by the cheical reaction at the interface as seen fro Fig. 1. n the other hand, when silicon content in iron elt is high and silicon oxidation proceeds at the early stage for run B-7, its rate was found to be controlled by the ass transport in the etal phase. But, after the oxidation of silicon in iron elt ceased, the rate-deterining step was Cr Si fa* k ρ C C C * 15. Cr Si ISIJ

8 siilar to run B-8. It also suggests that the rate of C foration is controlled by the cheical reaction at the interface, but the rate of eaction (10) on sulfur is controlled by the ass transport in the slag phase. 5. Conclusions In order to clarify the kinetic behavior and the reaction echanis of Cr 3 reduction, the effect of various factors on the reduction rates of Cr 3 in a solid powder state and in Ca Si l 3 CaF slags by Fe C Si elts were investigated at teperatures fro to C. The effect of teperature on the reduction rate of solid Cr 3 was fairly large and the apparent activation energy was about 180 kj ol 1. The overall reduction of solid Cr 3 was considered to be controlled by a cheical reaction step at the interface. For reduction of Cr 3 in slag, the reduction rate and the chroiu content in final iron elt increased with an increase in CaF content in slag, which ight be attributed to an increase in the ass transport coefficient in the slag. The addition of silicon to iron elt prooted the reduction rate rearkably, although it retarded the reduction of Cr 3 powder. The reduction rate decreased by the addition of surface active sulfur to iron elt, such a decrease was attributed to a decrease in the effective reaction area by the adsorption of sulfur on the interface. The kinetic behavior of reduction of Cr 3 in slag could be well siulated by the kinetic reaction odel based on two-fil theory. It was found fro the present odeling study that the transfer rate of chroiu fro slag to etal was controlled by the ass transport in the slag phase during the entire period of reaction. cknowledgeents ne of authors would like to express his sincere gratitude to Nippon Steel Corporation for the financial support. EFEENCES 1) K. Suzuki, K. Mori and T. Ito: Tetsu-to-Hagané, 65 (1979), ). J. Fruehan: Metall. Trans. B, 8B (1977), 49. 3) K. Taoka, H. Noura, K. Koaura, K. Eoto, F. Sudo and T. Fujii: Kawasaki Steel Tech. ep., 17 (1985), 0. 4). Nakao, S. Tanaka and H. Takao: Tetsu-to-Hagané, 80 (1994), 30. 5) E. Shibata, H. Sun and K. Mori: Metall. Mater. Trans. B, 30B (1999), 79. 6) Y. kabe, I. Tajia and K. Ito: Metall. Mater. Trans. B, 9B (1998), ) ecoended Equilibriu Value of Steel-Making, Japan Society for Prootion of Science and Technology 19th Coittee on Steelaking, Tokyo, (1984), 49, 83, 99, 131, ) J. F. Elliott, M. Gleiser and V. aakrishna: Therocheistry for Steelaking, Vol., ddison Wesley Pub. Co., eading, Mass, (1963). 9) F. D. ichardson and C. J. B. Fincha: J. Iron Steel Inst., 178 (1954), 4. 10). S. Venkatradi and H. B. Bell: Trans. Metall. Soc. IME, 45 (1969), ) Y. Kawai,. Nakao and K. Mori: Trans. Iron Steel Inst. Jpn., 4 (1984), ) S. Kitaura, N. Sato and K. kohira: Trans. Iron Steel Inst. Jpn. 8 (1988), ) K. Mori, Y. Kawai and Y. Fukai: Trans. Iron Steel Inst. Jpn. 8 (1988), ) K. Mori, S. Hiwasa and Y. Kawai: J. Jpn. Inst. Met., 44 (1980), ) E. Shibata, H. Sun and K. Mori: Tetsu-to-Hagané, 8 (1996), ) Y. P. Xiao and L. Holappa: Proc. of the 5th Int. Conf. on Molten Slags, Fluxes and Salts, ISS, Warrendale, P, (1997), ) S. Ban-ya: ISIJ Int., 33 (1993),. 18) S. Yokoyaa, M. Takeda, K. Ito and M. Kawakai: Tetsu-to- Hagané, 78 (199), ISIJ 944