Thermodynamics of Titanium Oxide in Ladle Slags

ISIJ International, Vol. 41 (2001), No. 12, pp. 1447–1453

Sung-Mo JUNG and R. J. FRUEHAN1)

Formerly Postdoctoral research associate, at Department of Materials Science and Engineering, Carnegie Mellon University, now at Graduate School of Iron and Steel Technology, Pohang University of Science and Technology, Pohang 790-784, Korea. 1) Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA. (Received on May 17, 2001; accepted in ﬁnal form on August 27, 2001)

It is necessary to have information on the thermodynamic behavior of titanium oxide in ladle type slags in order to control the titanium content in several grades of steel. In the present study, the thermodynamics

was determined from the equilibrium between Fe–Csat–Ti and CaO–SiO2-–30%Al2O3–MgO–TiOx slags ϳ in equilibrium with CO and from the equilibrium between Fe–Csat–(16 18)%Cr–Si–Ti and CaO–SiO2– 20%Al2O3–MgO–TiOx slags in equilibrium with CO. From the experiment with Fe–Csat–Ti alloy, the activity coefﬁcients of TiO1.5 and TiO2 vary with basicity from 0.3 to 1.5 and from 0.5 to 2.3, respectively. And from ϳ the experiment with Fe–Csat–(16 18)%Cr–Si–Ti alloy, the activity coefﬁcients of TiO1.5 and TiO2 vary with basicity from 0.4 to 1.4 and from 0.6 to 3.5, respectively. The results obtained from the equilibrium between ϳ Fe–Csat–(16 18)%Cr–Si–Ti and CaO-SiO2–20%Al2O3–MgO–TiOx slags were used to estimate the titanium content of silicon-added stainless steel. Experiments were also conducted using Fe–Al–Ti melts in equilibri-

um with CaO–SiO2–Al2O3–TiOx slags saturated with MgO. In this case most of the titanium in the slag is 4ϩ present as TiO2(Ti ). The present results were used to predict the titanium content of aluminum-killed steel in equilibrium with ladle slags containing titanium oxide and the predictions agreed with plant data. KEY WORDS: ladle slags, titanium oxide, activity, silicon-added stainless steel, aluminum-killed steel.

the formation of titanium carbonitride using the thermody- 1. Introduction namic data obtained. But these slags are not relevant to the Titanium is one of the most important alloying elements ladle processes. for the production of several grades of steels. As examples, No information on the thermodynamic behavior of titani- titanium content should be controlled in the reﬁning of Ti- um oxide in ladle type slags is available. The objective of microalloyed HSLA steels, which are being produced for the present research was to obtain thermodynamic informa- line pipes, pressure vessels, and offshore oil constructions.1) tion on titanium oxide in ladle type slags for the control of Titanium is also used for the production of less expensive titanium in carbon steel, aluminum deoxidized steel, and ferritic grades of stainless steel which are suitable for auto- stainless steel. The composition ranges are given in Table motive exhaust application by replacing the use of expen- 1. This was achieved by investigating the equilibrium of Ti sive alloying elements such as nickel. Therefore, the addi- with carbon-saturated iron, Fe–Al alloy, or stainless steel tion of titanium to plain carbon steel and stainless steel in and the ladle type slags. the ladle for improving properties has increased in recent years. In order to predict the inclusions formed and the re- 2. Experimental lationship between titanium in the metal and slag, the thermodynamic activity of titanium oxides in ladle type slag 2.1. Experimental Equipment and Procedure must be known. A MoSi2-resistor furnace with an alumina tube was used The number of previous investigations dealing with the for the equilibrium experiments. The master slag was pre- equilibrium between metals and slags containing titanium pared by melting mixtures of reagent grade CaO, SiO2, oxide is limited. Benesch et al.2,3) studied the distribution of Al2O3, and MgO in a MgO crucible using an induction fur- titanium between CaO–SiO2–MgO–Al2O3–TiO2 slags and nace in open air and the master alloy, carbon-saturated iron, carbon saturated iron. However, the slag composition they was melted in a graphite crucible under a carbon monoxide investigated was in a relatively narrow range, i.e., the MgO content of 5 or 7% and the lime to silica ratio of about one. Table 1. The composition range of slags investigated at In addition, they assumed only TiO2 in the molten slags. 1 873 K. 4) Kishi et al. measured both TiO1.5 and TiO2 contents in their studies on the equilibrium between CaO–Al2O3–TiOx slags and iron–chromium alloys. Recently Morizane et al.5) measured the activities of TiO1.5 and TiO2 in CaO–SiO2– MgO–Al2O3–TiO2 blast furnace type slags and predicted

1447 © 2001 ISIJ ISIJ International, Vol. 41 (2001), No. 12 atmosphere at 1 923 K. By chemical analysis, it was found monoxide atmosphere at 1 873 K. In this case, the oxygen that the slag composition was 47.97%CaO–13.18%SiO2– partial pressure is determined by C/CO equilibrium as 30.97%Al2O3–7.88%MgO and the master alloy was Fe– shown in Eq. (2). C –0.20%Ti. And for the experiment study on ladle type sat 1 slags of stainless steel, another master slag and alloy with C( s)ϩϭ O (g) CO(g) ...... (2) 2 2 54.3%CaO–13.0%SiO2–19.9%Al2O3–7.6%MgO–4.5%TiO2 and Fe–C –17.8%Cr–0.64%Ti were prepared by melting, ϭϪ Ϫ 8) sat DG2° 111 700 87.65T (J/mol) repectively. In each experiment, proper amount of reagent grade chemicals were mixed with the master slag to adjust In the third set of experiments, where the ladle type slags were in equilibrium with Fe–Al–Ti alloys, the oxygen po- the initial TiO2 content and the slag basicity, i.e. the lime to tential is determined by Eq. (3). Therefore, it is necessary silica ratio. The initial slag compositions except for TiO2 to estimate the activity of Al O in the slag in order to cal- were chosen to be in the liquid region of CaO–SiO2–MgO– 2 3 6) culate the oxygen partial pressure. Al2O3 system at 1 873 K. For the equilibrium experiments between ladle type slags 3 and Fe–C –Ti alloys or Fe–C –18%Cr–Ti, 5.0 g of slag 2AlϩϭO (g) (Al O ) ...... (3) sat sat 2 223 was made by mixing the master slag and TiO2, and 10 g of ϭϪ ϩ 9) the master alloys were equilibrated in a graphite crucible at DG3° 1 503 630 379.63T (J/mol) 1 873 K for 24 hr under a CO atmosphere. And for the equi- In this study, the activity of Al2O3 was based on the values librium experiments between ladle type slags and Fe–Al–Ti 10) alloys, 8.0 g of slags uniformly mixed and 15–20 g of alloys calculated by Rein and Chipman. They computed the ac- were melted in a MgO crucible under a purified Ar atmo- tivity of Al2O3 by Gibbs–Duhem equation, regarding the sphere. Since the Fe–Al–Ti experiments were conducted in slag as consisting of the four major oxide components, MgO crucibles, the slags were saturated with MgO and CaO, SiO2, Al2O3, and MgO along with minor proportions contained significantly more MgO. Preliminary experi- of other oxides and of sulfur. ments indicated for these experiments that 4 hr was suffi- The following relations are derived by using the equilib- cient to achieve equilibrium. The crucible containing a rium constant K3 in the Reaction (3). sample was then pulled out of the furnace and rapidly aAl O D GRT°ϭϪ ln 23 ...... (4) quenched in an Ar gas stream. The ground slag samples 3 2 ⋅ 32/ aPAl O and the metals were chemically analyzed for CaO, SiO2, 2 Al O , MgO, TiO and TiO and for C, Si and Ti, respec- 2 3 1.5 2 aAl O tively. K ϭ 23 ...... (5) 3 2 ⋅ 32/ aPAl O 2.2. Chemical Analysis 2 ϭ O ϩ Al ϩ Ti The SiO2 content in the slag and silicon in metal was de- log fAl e Al[%O] e Al[%Al] e Al[%Ti]...... (6) termined gravimetrically by dehydration. The contents of CaO and MgO were determined by titration with KMnO In Eq. (6), the value fAl can be obtained by using the con- 4 centration of Al, O, and Ti, along with the related interac- and with EDTA, respectively. The Al2O3 content was deter- 11) mined by atomic emission spectrometry. The titanium in tion parameters. The computed oxygen potential in this metal and slag was analyzed by diantipyryl-methane ab- case is considerably less certain than that for the C–CO sorptiometry. The carbon in metal was analyzed by com- case. In particular, there are uncertainties in the activities of ϩ bustion infrared spectroscopy. The contents of the Ti3 and Al and Al2O3. Ti4ϩ ions in the slag were determined by the following 3.2. Activity and Activity Coefficient of TiO1.5 and method.7) A slag sample was dissolved under an Ar atmo- TiO ϩ ϩ 2 sphere into a mixture of hot HCl(1 1), HF(1 1), and the The experimental results for the first and second sets of 3ϩ ferric ammonium sulfate solution. The content of Ti was experiments are given in Table 2 and Table 3, respectively. 2ϩ obtained by titrating Fe ion, which was produced by the The activity and activity coefficient of one component in following ion exchange reaction, with potassium dichro- slags are usually determined by other oxides at a given tem- mate. perature under a specific atmosphere. However, the titanium Fe3ϩϩTi3ϩϭFe2ϩϩTi4ϩ...... (1) oxide contents of the slag system investigated in the present research as well as most ladle slags are relatively small 4ϩ 3ϩ The Ti content was calculated by subtracting the Ti ion compared with other components. Therefore, it can be as- content from the total Ti content. Not enough thermody- sumed that the activity and activity coefficient of titanium namic information on the TiO or Ti3O5 is available and oxide are mainly controlled by the slag compositions com- hence all reduced form of titanium was assumed as Ti3ϩ. posed of CaO, SiO2, MgO, and Al2O3. The equilibrium be- ϳ tween Fe–Csat–Ti, Fe–Csat–(16 18)%Cr–Ti, or Fe–Al–Ti 3. Results and Discussion alloy and a typical ladle slag was studied to evaluate the effect of the titanium oxide content on its activity. The initial 3.1. Calculation of the Oxygen Potential TiO2 content was varied in the range from 1 to 10%. In the first and second sets of experiments, the ladle type The activity and activity coefficient of titanium oxide slags were equilibrated with Fe–Csat–Ti alloys or Fe– with respect to the pure solid state were evaluated based ϳ Csat–(16 18)%Cr–Ti in a graphite crucible under a carbon on the oxygen partial pressures previously calculated.

Titanium–oxygen equilibrium is expressed using a general 2. However, the activity of TiO2 obtained for the ladle type form of titanium oxide, TiOx as slags of stainless steelmaking in equilibrium with Fe–Csat– ϳ x (16 18)%Cr–Ti exhibits a positive deviation in low TiO2 ϩϭ Ti O2 (g) (TiOx ) ...... (7) content and a negative deviation in relatively high TiO2 2 content. This indicates that the activity coefﬁcient of Ti ϭϪ ϩ ϭ 11,12) DG7° 714 928 171.27T (J/mol) (x 1.5) may be affected by the presence of silicon and chromium in ϭϪ ϩ ϭ 11,12) Fe–C –(16ϳ18)%Cr–Ti alloy. The results in Fig. 1 and DG7° 907 604 221.33T (J/mol) (x 2) sat Fig. 2 are in contrast to those obtained by Morizane et al.5) γ ⋅ TiOX TiO for 40% CaO–42% SiO –11% MgO–7% Al O –(1ϳ D GRT°ϭϪ ln xx...... (8) 2 2 3 7 ⋅ x / 2 8.5%)TiO . It is believed that the different tendency be- aPTi O 2 2 tween the two experimental results is due to the different γ ⋅ TiOX TiO slag composition where one is ladle type slags and the other K ϭ xx...... (9) 7 ⋅⋅x / 2 blast furnace type slags. The basicity (%CaO)/(%SiO2) of ([%fPTi Ti]) O 5) 2 the blast furnace slags in Morizane et al.’s work was about one compared to about 3.5 in the present work. The results log f ϭe Ti[%Ti]ϩe O [%O]ϩe Al[%Al]...... (10) Ti Ti Ti Ti for the experiment using Fe–Al–Ti melts are given in Table

For the ladle type slags in equilibrium with Fe–Csat–Ti and 4 in the case the oxygen potential is considerably higher ϳ ϳ Fe–Csat–(16 18)%Cr–Ti alloys, the activity of titanium than that for the Fe–Csat–Ti and Fe–Csat–(16 18)%Cr–Ti oxide in slags is determined by titanium content in carbon- experiments. Consequently the amount of TiO1.5 was low, saturated iron under 1 atm of CO gas atmosphere. The especially less than one weight percent. Therefore, the ther- 5) value of fTi is 0.023 as reported by Morizane et al. The ef- modynamics of TiO1.5 could not be determined with sufﬁ- fect of silicon and chromium in the metal on the activity co- cient precision to be reported. In computing the activity of Al efﬁcient of titanium was neglected since no information is TiO2, the value of e Ti is not known but it’s effect will be available and assumed to be small for the low Si and Cr small and can be neglected. There is considerable scatter in contents.

Figure 1 shows the activity of TiO1.5 as a function of its mole fraction for the slags not saturated with MgO but ϳ equilibrated with Fe–Csat–Ti or Fe–Csat–(16 18)%Cr–Ti and CO. It is indicated that the activity of TiO1.5 exhibits a negative deviation from Raoult’s law, while a positive deviation was obtained for the activity of TiO2 as shown in Fig.

Table 2. Experimental results for the CaO–SiO2–Al2O3– MgO–TiOx system in equilibrium with Fe–Csat–Ti at 1 873 K.

Fig. 1. The activity of TiO1.5 as a function of the mole fraction of TiO1.5 at 1 873 K.

ϳ Table 3. Experimental results for the CaO–SiO2–Al2O3–MgO–TiOx in equilibrium with Fe–Csat–(16 18)%Cr–Ti at 1 873 K.

1449 © 2001 ISIJ ISIJ International, Vol. 41 (2001), No. 12 the computed activity coefficient. The average value is almost independent of the titanium content in metal, there about 3 to 4. The scatter in part is due to the uncertainty in would be a linear relation between the X /X 3/4 values TiO1.5 TiO2 the calculation of the oxygen potential. The difference and log[%Ti] with a slope of 1/4, as expected from Eq. among the three sets of experiments in the activity coeffi- (12). And the results by Morizane et al.5) for blast furnace cient may be the result of the different slag compositions. type slags in Fig. 3 are showing a similar relationship. The value obtained using Fe–C –Ti and Fe–C –(16ϳ sat sat 3.4. Equilibrium Distribution of Titanium between 18)%Cr–Ti alloys may be more accurate due to less uncer- Slag and Metal tainty in the oxygen potential. When steels are deoxidized with aluminum and also con- 3.3. Redox Equilibria of Titanium in Ladle Type Slags tain titanium in ladle refining processes, the slag/metal It is well known that many transition cations exist in equilibrium is established for titanium by Eq. (13). That is, molten slags and glasses in two valency states, their relative the equilibrium distribution ratio in ladle practices depends proportions depending on temperature, pressure, composi- on the Al content of the metal for TiOx. From the thermo- 13) tion, and oxygen potential of the system. The redox reac- dynamics of TiOx and Al2O3 in slag and of Ti and Al in the tion of titanium cations in slags can be written by Eq. (11). metal, the distribution ratio can be calculated. Aluminum– ϭ ϩ titanium equilibrium is expressed by Eq. (13). 4TiO1.5 Ti 3TiO2 ...... (11) ϩ ϭ ϩ 2xAl 3TiOx(s) xAl2O3(s) 3Ti...... (13) Since the activity coefficients of TiOx are almost independent of the TiOx content of the slag and the titanium content The following relation is obtained using the equilibrium of the metal, a linear relationship between log[%Ti] and constant of the Reaction (13), K13. log(X /X 3/4 ) was obtained with the slope of 1/4, as TiO1.5 TiO2 Ϫ ϭ log[%Ti] log XTiO (2x/3) log[%Al] shown in Fig. 3. The result in Fig. 3 can be explained by x 13//⋅⋅ 2x 3 γ Eq. (12) deduced, using the equilibrium constant of the Kf13 TiO ϩlog Al x ...... (14) Reaction (11), K11. x / 3 ⋅ afTi Al23 O 3/4 ϭ log(XTiO /X TiO ) (1/4) log[%Ti] 1.5 2 where f is the activity coefficient of i component in a liquid ϩlog{( f 1/4·g 3/4 )/(K1/4·g )} .....(12) i Ti TiO2 11 TiO1.5 alloy with respect to an infinite dilute of one mass% state. If the second term of the right hand side of Eq. (12) were

Fig. 3. Relationship between log(X /X 3/4 ) and log[wt%Ti] TiO1.5 TiO2 for CaO–SiO2–30%Al2O3–MgO–TiOx in equilibrium with carbon-saturated iron and for CaO–SiO2–20%Al2O3– Fig. 2. The activity of TiO2 as a function of the mole fraction of MgO–TiOx in equilibrium with carbon-saturated stainless TiO2 at 1 873 K. steel at 1 873 K.

Table 4. Experimental results for the CaO–SiO2–Al2O3–MgO–TiOx in equilibrium with Fe–Al–Ti at 1 873 K.

ϫ 15 (%TiO ) (706 . 10 )(PO ) 2 ϭ 2 [%Ti] γ TiO2 for stainless slag in ladle process...... (17)

Duplicating the similar procedure for Ti–TiO1.5 equilibrium, the following equations can be obtained:

ϫ 13 3/4 (%TiO ) (109 . 10 )(PO ) 1.5 ϭ 2 [%Ti] γ TiO1.5

for ladle slag/Fe–Csat–Ti ...... (18)

ϫ 13 3/4 (%TiO ) (111 . 10 )(PO ) 1.5 ϭ 2 [%Ti] γ TiO1.5 for stainless slag in ladle process...... (19) In the interpretation of plant data on titanium oxide in ladle slags, the titanium oxide is usually assumed to be

Fig. 4. Relation between titanium and aluminum in Fe–Al–Ti TiO2 for the sake of simplicity because the information alloy equilibrated with CaO–SiO2–Al2O3–MgO–TiO2 at about the various suboxides of titanium oxide is not clear, 1 873 K. as mentioned in the description of the chemical analysis 5) principle. The total “TiO2” can be deﬁned as follows. g TiO is the activity coefﬁcient of TiOx in slag with respect x MTiO ϭϩ ⋅ 2 to pure solid state. As discussed in the present work, the (%“TiO2 ”) (%TiO 2 ) (%TiO 1.5 ) ...... (20) MTiO amount of TiO1.5 is small and not accurately examined. For 1.5 TiO2 the results are plotted in accordance with Eq. (14) where MTiO and MTiO are the molecular weights of TiO2, along with the results of Kishi et al.4) in Fig. 4. The slope is 2 1.5 79.9 g/mol, and TiO1.5, 71.9 g/mol, respectively. Combining 4/3 as predicted by Eq. (14). Eqs. (16) to (20), the equilibrium distribution ratio in terms The relationship between the titanium content of the of the weight percentage of titanium in the metal and that of metal and the titanium oxide content of the slag can be esti- hypothetical “TiO2” in the slag at 1 873 K can be expressed mated using thermodynamic information obtained in the as follows. present work. The equilibrium ratio between carbon-satu- ϫ 15 ϫ 13 3/4 rated iron and the slag for the given slag basicity and the (%“TiO ”) (6.92 10 )(PO ) (1.21 10 )(PO ) 2 ϭ 2 ϩ 2 partial pressure of carbon monoxide was computed. [%Ti] γγ TiO2 TiO1.5 Starting with the Ti–TiO2 equilibrium, the equilibrium constant for the Reaction (7) is represented by Eq. (9). for ladle slag/Fe–Csat–Ti ...... (21) Using the free energy of the Reaction (7), to calculate the ϫ 15 (1.23ϫ 1013 )(P3/4 ) ϭ (%“TiO2 ”) (7.06 10 )(PO ) O equilibrium constant, K7, x 2, the following equation can ϭ 2 ϩ 2 be derived: [%Ti] γγ TiO2 TiO1.5 ⋅ for ladle type stainless slag...... (22) (%TiO ) ()(Kn7 total M TiO )()() f Ti P O 2 ϭ 22...... (15) γ Eqs. (21) and (22) can be used to estimate the titanium con- [%Ti] TiO 2 tent in steels and stainless steels, respectively, based on the

Considering that the activity coefficient of titanium in car- activity coefficients of TiO2 and TiO1.5 obtained for ladle bon steel is in the Henrian region, the values of fTi can be type slags in the present work along with the information assumed to be unity. If the slag systems in equilibrium with on the oxygen partial pressure in ladle processes. The oxy- ϳ Fe–Csat–Ti and Fe–Csat–(16 18)%Cr–Ti alloys in Table 1 gen partial pressure is usually determined by Al/Al2O3 or are considered as the ladle type slags for carbon steel and Si/SiO2 equilibrium depending on the steel grades produced stainless steel, the total number of moles of the constituent in ladle refining. For the ladle slags in equilibrium with Al oxides per 100 g of slags is about 1.52 to 1.56 for Fe–Csat– deoxidized steel the oxygen partial pressure is determined ϳ Ti alloy and about 1.44 to 1.66 for Fe–Csat–(16 18)%Cr–Ti by the Al–(Al2O3) equilibrium. Using Eqs. (3)–(6) for com- alloy. Taking the average value, 1.54 for Fe–Csat–Ti alloy puting PO , it can be shown that the total “TiO2” content is ϳ 2 and 1.57 for Fe–Csat–(16 18)%Cr–Ti alloy, the distribution given by Eq. (23). ratios can be expressed as: 23// 12 (%“TiO ”) (12 . 72 )(aaAl O ) ( 107 . 4 )(Al O ) 2 ϭϩ23 23 ϫ 15 [%Ti] γ ⋅[%Al]4/3 γ ⋅[%Al] (%TiO ) (692 . 10 )(PO ) TiO2 TiO1.5 2 ϭ 2 [%Ti] γ ...... (23) TiO2

for ladle slag/Fe–Csat–Ti ...... (16) Equation (23) can be applied to estimate the titanium content in aluminum deoxidized steels based on the activity

Fig. 6. The estimated Ti content in aluminum deoxidized steel as Fig. 5. Titanium distribution ratio between CaO–SiO2–Al2O3– a function of Al content at 1 873 K. MgO–TiO2 slags and Fe–Al–Ti alloys as a function of Al content at 1 873 K. Eq. (22) is expressed by Eq. (27). coefficients of TiO and TiO obtained for ladle type slags 2 1.5 ϩ ϭ Si O2(g) (SiO2) ...... (26) in ladle processes along with the activity of Al2O3. The data about the activity of Al O are available in several research- ϭϪ ϩ 9,14) 2 3 DG26° 821 000 220.0T (J/mol) es as described previously.10) As discussed previously most ϫ 4434ϫ / of Ti in the slag is TiO2 given by the first term of the right- (%“TiO ”) (.2 78 10 )(aaSiO ) (. 3 44 10 )(SiO ) 2 ϭ 2 ϩ 2 hand side in Eq. (23) and the contribution of the second γ ⋅ γ ⋅ 3/4 [%Ti]TiO [%Si] TiO [%Si] term to the titanium distribution ratio is relatively small 2 1.5 compared to that of the first term. The calculated titanium ...... (27) distribution ratio by Eq. (23) for aluminum deoxidized steel is plotted as a dashed curve in Fig. 5 based on the estimated Equation (27) can be applied to estimate the titanium activity of Al O and the measured activity coefficients of content in silicon-added stainless steels based on the activi- 2 3 ty coefficients of TiO and TiO obtained for stainless TiO and TiO . The dashed curve can approximately be 2 1.5 2 1.5 slags in ladle processes along with the activity of SiO . The formulated by Eq. (24). 2 activity of SiO2 in Eq. (27) was calculated by the standard (%“TiO ”) 097. Gibbs free energy change of Eq. (26) based on the silicon 2 ϭ ...... (24) contents in melts and the oxygen partial pressure controlled [%Ti] [%Al]4/3 by C/CO equilibrium. The obtained values of a are SiO2 As can be seen in Fig. 5, the titanium distribution ratio found to be in good agreement with those estimated by measured in the present work are in reasonable agreement Rein and Chipman10) at the compositions corresponding to 9) with the data observed in practice. The empirical relation- saturation with both dicalcium silicate (2CaO·SiO2) and 9) ship from plant data is given by Eq. (25). The difference lime (CaO) in CaO–SiO2–Al2O3 slags at 1 873 K, as shown in Eqs. (24) and (25) may be due to uncertainty in the activ- in Table 3. Therefore, it may be concluded that most of the ities of Al, Ti, and Al2O3. It may also be due to variation in slag compositions investigated in the present study are satu- the activity coefficient of TiO2 with slag composition. rated with both dicalcium silicate and lime. For the sake of Considering this uncertainty, the agreement is reasonable. interpretation most of Ti in the slag can be assumed to be TiO given by Eq. (27) and the contribution of the first term (%“TiO ”) 055. 2 2 ϭ ...... (25) of the right-hand side to the titanium distribution ratio is [%Ti] [%Al]4/3 relatively small compared to that of the second term. The calculated titanium distribution ratio by Eq. (27) for silicon- The titanium content in liquid steel can be controlled by added stainless steel is plotted as a curve in Fig. 7 based on adjusting the amount of aluminum addition for deoxidation the mean values of aSiO and the activity coefficients of TiO2 and the concentration of titanium oxide in the ladle slags as 2 and TiO1.5 measured for the slag compositions studied in shown in Fig. 6. For example for a typical steel with 0.04% the present work. The curve in Fig. 7 can approximately be Al the Ti content in the metal increase from 0.15 to 0.4 for formulated by Eq. (28). slags containing 5 and 15% “TiO2”, respectively. And for the ladle slags in equilibrium with silicon-added (%“TiO ”) 31. 4 2 ϭ ...... (28) stainless steel the oxygen partial pressure is determined by [%Ti] [%Si]3/4 the Si–(SiO2) equilibrium. Considering the activity coefficient of silicon in carbon-saturated stainless steel is in the As indicated in Fig. 7, the titanium distribution ratio be- Henrian region to compute P , the total “TiO ” content in tween ladle type stainless slag and Fe–C –(16ϳ18)%Cr– O2 2 sat

MgO–TiOx, were investigated at 1 873 K. From the ﬁnd- ings, the following conclusions were obtained. (1) By equilibrating the typical ladle slags with Fe–

Csat–Ti alloys and CO the activity coefﬁcients of TiO1.5 and TiO2 were found to be 0.3 to 1.5 and 0.5 to 2.3, respectively. (2) By equilibrating the ladle type stainless slags with ϳ Fe–Csat–(16 18)%Cr–Si–Ti alloys and CO the activity co- efﬁcients of TiO1.5 and TiO2 were found to be 0.4 to 1.4 and 0.6 to 3.5, respectively.

(3) For the experiments with Fe–Csat–Ti and Fe–Csat– (16ϳ18)%Cr–Si–Ti equilibration the slag contained about equal amount of Ti3ϩ and Ti4ϩ and the relative amounts varied with Ti content in the metal as expected. (4) For Fe–Al–Ti alloys in equilibrium with MgO satu-

rated slags most of the Ti in the slag is TiO2. The activity

Fig. 7. Titanium distribution ratio between CaO–SiO2–20%Al2O3– coefﬁcient could not be precisely as for the Fe–Csat–Ti and MgO–TiO slags and Fe–C –(16ϳ18)%Cr–Ti alloys as a ϳ 2 sat for Fe–Csat–(16 18)%Cr–Si–Ti cases because of uncertain- function of silicon content at 1 873 K. ties in the computed oxygen potential. However, the activity also showed positive deviations and the activity coefﬁcient is about 3ϳ4. (5) From the present results it is probable to predict the Ti content of Fe–Al steel in equilibrium with ladle slags

containing “TiO2”. The predictions are in agreement with plant data. (6) The titanium distribution ratio was calculated based

on the activity of SiO2 and the activity coefﬁcients of TiO2 and TiO1.5. Acknowledgements The member companies of the Center for Iron and Steelmaking Research (CISR) of Carnegie Mellon Uni- versity are greatly acknowledged for their ﬁnancial support of this research.

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