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Communications Evaluation of a Process that uses Phosphate Additions to Upgrade Titania Slag J.P. VAN DYK and P.C. PISTORIUS Thermal reduction is the oldest ilmenite concentration process and involves smelting ore in an electric arc furnace to produce pig iron and a TiO2-rich slag.[1] The resulting TiO2-rich slag is a suitable feed material for the chloride process if the ilmenite feed material is low in alkaline earth impurities. While the thermal reduction process is successful in upgrading ilmenite ore, some practical difficulties remain: (1) the operating temperature during reduction is very high (in excess of 1600 8C) as a result of the absence of flux additions; (2) the quality of the slag product is limited by the impurity level in the ilmenite feed; and (3) there is a minimum particle size limitation on the crushed slag imposed by the chloride process. The phosphate process was developed by the United States Bureau of Mines in the 1970s[2] and is in essence a modified version of the normal thermal reduction process that can potentially provide solutions to the listed problems. It consists of the following three stages (Figure 1): ● reduction of ilmenite ore, ● synthesis of rutile crystals in the slag, and ● liberation of the rutile crystals from the slag. Reduction is accomplished is an electric arc furnace with the use of 5 pct lime and 3 to 5 pct FeO as fluxing agents. This lowers the melting point of the slag to some 1300 8C. The main phases present in the slag are perovskite (CaTiO3), ferrous pseudobrookite, and glass. Rutile crystals are synthesised from these phases by oxidizing the slag and fluxing the impurities, adding a phosphate compound such as P2O5. Following this procedure, the slag consists of rutile crystals in a phosphate glass matrix that contains all the impurities. The rutile crystals are then recovered through a combination of grinding and leaching in dilute phosphoric acid. The resulting rutile concentrate typically has a TiO2 content higher than 94 pct TiO2 and recovers 77 to 88 pct of the TiO2 in the original slag. Some fines below th stated minimum size of 49 mm2 for the chloride process are produced during the liberation of the rutile crystals. The Bureau of Mines proposed a way of handling these fines by reacting them with phosphoric acid to produce TiP2O7, which can be used in place of P2O5 as a fluxing agent. The first aim of this study was to test the applicability of the Phosphate Process to South African feed materials. A

J.P. VAN DYK, Chief Engineer, is with Iscor Ltd., Pretoria 0001, South Africa. P.C. PISTORIUS, Professor, is with the Department of Materials Science and Metallurgical Engineering, University of Pretoria, Pretoria, South Africa 0001. Manuscript submitted August 5, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS B

typical South African titania slag was used as the feed material. Table I gives the composition of this slag. It closely matched the slag composition specified by the original process, except for the lower lime content. For this reason, additional lime was added at the later process step of fluxing. The as-reduced slag was ground to 2220 mm before further processing. For the oxidation step, 20 g batches of slag were placed in alumina crucibles and oxidized in air for 6 hours at 1000 8C in a box furnace, passing oxygen through the furnace at a rate of 0.05 m3/min. After oxidation, the slag was cooled to room temperature. Following oxidation, the slag was mixed with CaO and P2O5 to give final contents of 4 pct CaO and 10 pct P2O5. Tests were also conducted with an equivalent mixture of TiP2O7. The mixtures were reacted at 1400 8C for 1 hour. After cooling, rutile was recovered by grinding the slag to 21700 mm and leaching it in a stirred reactor, using 8.5 pct phosphoric acid at 95 8C for 1 hour. Examination by X-ray diffraction indicated that the phosphate process is successful at recovering rutile from the starting materials (Table II). The microstructure of the slag after the various process stages is illustrated in Figures 2 through 4. The feed slag consists primarily of ferrous pseudobrookite. Oxidation changed the phase structure to a mixture of fine rutile and ferric pseudobrookite. The fluxing procedure altered the structure of the slag to rutile crystals in a phosphate glass matrix. Almost all of the impurities partitioned to the glass phase. It was found that leaching did remove the impurity-containing glass phase. In this way, leaching yielded a product with a TiO2 content in excess of 95 pct TiO2. With TiP2O7 as a fluxing agent, the TiO2 content increased to 98 pct after leaching. This higher TiO2 content may be explained by the introduction of extra TiO2 into the slag by the TiP2O7. Phosphate losses were insignificant and were on average 5 pct of the weight of phosphate added to the slag. The residual P2O5 and CaO contents of the slag were both below 0.05 pct after leaching. The second aim of this study was to quantify the two important process steps, crystal growth during fluxing and leaching. Sulfuric acid was considered as an alternative leachant. The oxidized titania slag used previously was mixed with the fluxing agents to yield a mixture containing 4 pct CaO and 16 pct TiP2O7. The samples were reground and formed into a paste by adding water. Samples weighing 1 g were placed in a platinum wire basket inside a vertical tube furnace to conduct isothermal and continuous cooling tests in air. The crystal sizes were determined with an image analysis program using polished samples set in resin. The rutile crystals exhibited near spherical shapes for which the relationship D 5 1.5 L holds3. This relationship was used to convert the measured average crystal diameter (L) to the spatial crystal diameter (D). The results of the crystal growth experiments are presented in Figure 5. The results are for isothermal experiments at 1400 8C, 1440 8C, and 1470 8C and for continuous cooling from 1440 8C at 20 8C/h (point J) and 80 8C/h (point K), respectively. The times for the continuous cooling experiments are arbitrarily plotted as the total time above 1000 8C, including an initial holding time of 30 minutes at 1440 8C. X-ray diffraction revealed that two phases, rutile and glass, were present in all the samples treated, even for the VOLUME 30B, AUGUST 1999—823

Fig. 1—Flow diagram of the phosphate process as developed by the United States Bureau of Mines.

Fig. 2—The microstructure of the slag from ilmenite reduction, which was used as the starting material for the process evaluation. The structure contains pseudobrookite-type crystals (“M3O5”) in a glass matrix.

Table I. Composition (in Mass Percent) of the Slag Which Was Used as the Feed Material for the Experiments* TiO2

FeO SiO2 A12O3 CaO MnO MgO Cr2O3 V2O5

90.00 5.93 1.38

1.38

0.23

1.28

1.11

0.08

0.43

*The slag had been produced by thermal reduction of ilmenite in a plasma furnace. The titanium content is expressed as an equivalent amount of TiO2, although some Ti31 is expected to be present.

Table II. Phase-Chemical Composition of the Slag after Each Process Stage of the Phosphate Process, as Determined by X-ray Diffraction

Slag

Main Component (.30 Pct)

Minor Component (,30 Pct)

Feed slag Oxidized slag Fluxed slag Leached slag

FeTi-Oxide rutile rutile rutile

— FeTi-oxide — —

Trace Component (,10 Pct) rutile — — —

Note: rutile—TiO2; and FeTi-Oxide—pseudobrookite solid solution.

shortest treatment time of 1 hour. The results indicate that crystal growth occurs during isothermal and continuous cooling treatments. Only in the case of the shortest treatment at the lowest fluxing temperature (1 hour at 1400 8C) was the average crystal diameter smaller than the minimum of 49 mm required by the chloride process. Figure 6 indicates that the crystal sizes after the continuous-cooling treatments are similar, despite very different cooling rates (points J and K in the figure). This suggests that most of the crystal growth in these samples occurred during the initial holding period of 30 minutes at 1440 8C rather than during subsequent cooling. Leaching tests were performed to investigate the effects 824—VOLUME 30B, AUGUST 1999

Fig. 3—The microstructure of the slag of Fig. 2, following oxidation at 1000 8C for 6 h. The structure contains rutile, with residual pseudobrookite (“M3O5”) and glass.

of stirring rate, particle size, temperature, and acid concentration. For the leaching tests, 1.5 kg of slag was oxidized and fluxed with CaO and TiP2O7. The fluxed slag was ground and separated into different size fractions. The experiments were performed in a baffled stirred tank glass reactor with a total volume of 0.5 dm3. Temperature was controlled with a water bath and stirring was done with a variable speed stirring head. The extent of leaching was quantified by analyzing the residual solids with inductively coupled plasma analysis. Very little particle degradation occurred during leaching, as is illustrated by Figures 6 and 7. Figure 6 indicates that the rutile particles within ground slag fragments remain agglomerated even after substantial leaching (as comparison with Figure 8 shows, the TiO2 content of the particles shown in Figure 6 had increased from 87 to 97 pct during leaching). The size distribution in Figure 7 confirms that little size degradation occurred during leaching. This figure gives the size distribution of leached slag particles, which had been METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 4—The microstructure of the slag of Fig. 3, following fluxing by P2O5 at 1400 8C for 1 hour.

Fig. 5—Growth of rutile crystals during phosphate fluxing. The results are for isothermal experiments at 1400 8C, 1440 8C, and 1470 8C and for continuous cooling from 1440 8C at 20 8C/h (point J) and 80 8C/h (point K), respectively. The times for the continuous cooling experiments are arbitrarily plotted as the total time above 1000 8C, including an initial holding time of 30 minutes at 1440 8C.

in the 1300 to 600 mm size range before leaching; the size distribution indicates that, after leaching, only some 20 wt pct of the particles are smaller than the lower limit of the original size range. In all of the tests, the maximum achievable grade after extended leaching was below 100 pct TiO2, and typically ranged from 94 pct TiO2 to 97 pct TiO2. This effect is thought to be due to a combination of the presence of inaccessible (occluded) glass phase between the rutile crystals and the limited purity of the rutile crystals. The latter effect was investigated by analyzing the rutile crystals in the slag chemically with the energy dispersive system of an electron microscope. This showed that the TiO2 content of the crystals METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 6—Particles of the 1300 to 600 mm size fraction of the slag, after leaching for 2 hours in 6 pct H2SO4 at 50 8C, with a stirring rate of 300 rpm. It is apparent that the rutile particles remain in contact even after substantial removal of the leachable glass.

Fig. 7—The size distribution of leached slag particles after leaching for 2 hours in 6 pct H2SO4 at 50 8C, with a stirring rate of 300 rpm. The weight percentages of particles in each size range are shown. Before leaching, the particles had been in the size range 1300 to 600 mm.

varied between 98 and 99 pct. (The impurities in the crystals were iron and occasionally manganese.) The results of the leach tests indicated that stirring speed did not change the leaching rate (only stirring speeds that gave full suspension of the solids were considered). All further experiments were conducted at 200 rpm. In contrast with stirring speed, slag particle size did have a definite effect on the rate of leaching: Figure 8 shows that the rate of leaching increases with decreasing particle size. In addition to the kinetic effect, there is apparently also an “equilibrium” effect (the maximum amount of impurities leachable at long times) of particle size, in that the composition of the smaller particles plateaus at a lower grade of TiO2 (about 94 pct) during leaching. As noted previously, this is thought VOLUME 30B, AUGUST 1999—825

Fig. 8—The particle size does have a strong effect on the leaching rate. Leaching conditions: stirring speed, 300 rpm; leaching solution, 6 pct H2SO4; and temperature, 50 8C.

Fig. 9—The temperature of the leaching solution affects the leaching rate. Leaching conditions: particle size range, 1300 to 600 mm; stirring speed, 300 rpm; and leaching solution, 6 pct H2SO4.

to be the result of the presence of occluded glass between the rutile particles. This glass is not exposed to the leaching solution, thereby limiting the maximum attainable grade. Please note that in Figure 8 it is assumed (in the absence of experimental data to the contrary) that particle size does not have an effect on the composition before leaching. Temperature (in the range 30 8C to 70 8C) has a pronounced effect on the leaching rate in this system (Figure 9). Almost all of the glass was leached from the slag after only 50 minutes at 70 8C, but a substantial amount of the glass phase was still present after the slag was leached for 240 minutes at 30 8C. The effect of an increase in acid concentration is not as pronounced as the temperature effect, but Figure 10 does show that a higher acid concentration leads to a higher TiO2 content in the leached slag; there also appears to be some equilibrium effect, similar to that found with varying particle sizes. This study has shown that the phosphate process provides possible solutions to limitations of the traditional thermal

826—VOLUME 30B, AUGUST 1999

Fig. 10—An increase in acid concentration does give some increase in leaching rate. Leaching conditions: particle size range, 1300 to 600 mm; stirring speed, 300 rpm; and temperature, 50 8C.

reduction process. The high operating temperature in excess of 1600 8C can be lowered to around 1300 8C through the addition of CaO to the slag. The CaO, along with most of the other impurities, is removed through a combination of oxidation, fluxing, and leaching. In addition, all fines generated by crushing the slag can be recycled by using the fines to produce TiP2O7, which can be used as the phosphate fluxing agent. Although the crystal growth study indicated that it is possible to increase the rutile crystal size in the slag substantially, large crystal sizes do not appear to be a prerequisite for the process, as very little/particle degradation occurs during leaching. Either phosphoric acid or sulfuric acid can be used to leach the phosphate glass phase from the slag. Stirring is only necessary to keep the particles in suspension, and vigorous agitation should be avoided, as this may lead to the formation of excessive fines during leaching. A particle size distribution of 1300 to 600 mm proved the most suitable. Higher temperatures and higher acid concentrations enhanced the rate of leaching considerably. The most suitable conditions for leaching therefore seem to be temperatures around 70 8C with the sulfuric acid concentration at 8 pct. It is concluded that the phosphate process potentially holds many advantages, but a detailed economic evaluation as well as trials on a pilot plant scale would be necessary before the phosphate process could be considered as a viable alternative to the traditional thermal reduction process.

REFERENCES 1. W.W. Minckler and E.F. Baroch: Metallurgical Treatises, USA-China Bilateral Conf., J.K. Tien and J.F. Elliot, eds., TMS-AIME, Warrendale, PA, 1981, pp. 171-85. 2. G.W. Elger, D.E. Kirby, S.C. Rhoads, and W.A. Stickney: Bureau of Mines Report RI 7985, United States Department of the Interior, Washington, DC, 1974. 3. E.E. Underwood: Metals Handbook, ASM, Metals Park, OH, 1985, pp. 131-34.

METALLURGICAL AND MATERIALS TRANSACTIONS B

Rate of Reduction of FetO-SiO2-TiO2 Melts with CO Gas KENJI MATSUZAKI, TAKASHI MAKI, TASUKU HAMANO, and KIMIHISA ITO The FetO-SiO2-TiO2 systems are produced when titaniferous iron ores are smelted. The kinetic study of titania-containing slag is valuable if we consider the use of titaniferous iron ores in smelting reduction processes, because the liquid slag-gas reaction plays an especially important role in these processes. Several investigations of the reaction have been made. For example, Nagasaka et al.[1] measured the rate of reduction for various liquid slags containing FetO in equilibrium with solid iron with an Ar-CO mixture by thermobalance technique. Sasaki et al.,[2] El-Rahaiby et al.,[3] Sun et al.,[4] and Mori et al.[5] measured the rate of dissociation of CO2 on liquid melts by the isotope exchange technique. Surprisingly few studies of titania-containing slag, however, exist in the literature. In the present work, the rate of reduction for liquid FetOSiO2-TiO2 and FetO-SiO2-TiO2-MOx (MOx 5 CaO, MgO, AlO1.5) melts in equilibrium with solid iron with CO was measured using the thermobalance. The mechanisms of the reaction are discussed based on the results obtained. The thermobalance consists of an electric balance, and a SiC electric resistance furnace was used in the experiment. The temperature was controlled by a proportional-integraldifferential (PID) controller, which maintained it within 61 K. The temperature was measured by Pt/Pt-13 pct Rh thermocouple located just above the crucible. The slag sample of about 2.5 g charged in an iron crucible (16-mm i.d., 5mm depth) was heated and melted under Ar atmosphere. After equilibrium between the liquid slag and the iron crucible had been attained at the selected temperature, Ar-CO mixture of a desired composition was blown onto the surface of the sample through a stainless steel nozzle (2.7-mm i.d.) from a distance of 10 mm above the surface. The PCO and the gas flow rate were controlled by a mass flow controller. The slag samples were prepared by mixing the synthesized wustite, FetO, reagent grade SiO2, TiO2, CaO, MgO, and Al2O3. The rate of reduction was measured by reading the decrease in weight of the sample in the iron crucible connected to the electric balance by Pt wire. The rate of reduction was calculated by Eq. [1] from the experimental results of the initial stage of the reduction, in which change in the slag composition was negligible. r 5 2(dnO /dt)/S

[1]

where r is the apparent rate of reduction (mol/cm2?s), nO is the number of moles of oxygen in the sample (mol), t is the reduction time (s), and S is the surface area of the slag sample (cm2). Figure 1 shows dependence of the apparent rate of reduction on flow rate for the pure FetO (PCO 5 3.5 3 1022 atm)

and 80 mol pct FetO-10SiO2-10TiO2 (PCO 5 3.5 3 1022, 1.2 3 1022 atm) melts at 1673 K. This apparent rate increases with the flow rate at less than 0.6 L/min and then gradually approaches a constant value. At the flow rate of more than about 1 L/min, the rate of reduction becomes independent of the flow rate within the experimental scatter. All the experiments, therefore, were carried out at the flow rate of 2 L/min, in which the effect of mass transfer in the gas phase would be negligible for the overall rate of reduction for most slags. The addition of a basic oxide such as CaO and MgO to the sample, however, increased the reaction rate. In such cases, the effect of mass transfer in the gas phase was not neglected. The gas phase mass-transfer coefficient was estimated[6] and subtracted from the apparent rate of reduction. Figure 2 shows the dependence of the apparent rate of reduction on PCO at 1673 K. The rates are proportional to PCO in a low pressure region: r 5 kaPCO

where ka is the apparent rate constant (mol/cm ?s?atm). However, as PCO increases, the rates gradually decrease from the linear relation because of the effect of mass transfer in the liquid phase.[1] Therefore, the rate of reduction at very low PCO (3.8 3 1023 to 1.2 3 1022 atm), in which Eq. [2] is valid, was measured to minimize the effect of mass transfer in the liquid phase. Figure 3 shows the apparent rate constants, ka , as a function of XTiO2 /(XTiO2 1 XSiO2) for the FetO-SiO2-TiO2 melts at 1673 K, where XFetO 5 0.7. The constants slightly increase when TiO2 is substituted for SiO2. Figure 4 shows the apparent rate constants as a function of XFetO at 1673 K. They increase with XFetO and are a little higher for the FetO-SiO2TiO2 melts than for FetO-SiO2 and FetO-TiO2 melts.[1] They also increase with the addition of MOx (MOx 5 CaO, MgO, AlO1.5). Figure 5 shows the effect of the addition of MOx to the FetO-SiO2-TiO2 melts on the apparent rate constants at 1673 K, where XFetO 5 0.7 and XTiO2 /XSiO2 5 1. The addition of CaO increases these constants significantly, while MgO and AlO1.5 have less effect on raising them. When CaO is added to the slag, ka exceeds that of pure FetO, which means that the reaction rate cannot be described simply by using aFetO. The overall reaction for the reduction is expressed in Eq. [3]. However, Min and Fruehan[7] suggested that the slaggas reaction can be further broken down, and Eq. [4] is the rate-determining step. (FetO) 1 CO (g) 5 tFe 1 CO2 (g) CO (on the surface) 1 O

22

(on the surface)

5 CO2 (g) 1 2e2


[3] [4]

If the overall reaction is governed by Eq. [4], the rate of reduction is described by Eq. [5], in which the effect of surface coverage is assumed to be negligible. R 5 k4PCOaO22 2 k84PCO2

KENJI MATSUZAKI, Research Associate, TAKASHI MAKI and TASUKU HAMANO, Graduate Students, and KIMIHISA ITO, Professor, are with the Department of Materials Science and Engineering, Wasada University, Tokyo 169-8555, Japan. Manuscript submitted October 21, 1998.

[2] 2

[5]

where R is the overall rate of reduction (mol/cm2 s); k4 and k84 are the forward and reverse rate constants of Reaction [4] (mol/cm2 s atm), respectively; and aO22 is the activity of O22 on the surface. In the present work, PCO2 can be

VOLUME 30B, AUGUST 1999—827

Fig. 1—Dependence of the apparent rate of reduction on flow rate at 1673 K.

Fig. 2—Dependence of the apparent rate of reduction on PCO at 1673 K.

defined as 0, since the Ar-CO mixture was used. Thus, R becomes: R 5 k4 PCO aO22

[6]

Here, if we assume that the aO22 at the surface is proportional to that in a bulk phase, the equilibrium between ferric and ferrous in basic slags is expressed by Eq. [7].[8] Fe21 1 1/4O2 1 3/2O22 5 FeO22

[7]

Since the melts are in equilibrium with solid iron in this study, Reaction [8] is suitable to evaluate aO22 in a bulk slag. 3Fe21 1 4O22 5 Fe (s) 1 2FeO22

[8]

Equation [8] is valid in the melts of the present work because 828—VOLUME 30B, AUGUST 1999

Fig. 3—The apparent rate constants as a function of XTiO2 /(XTiO2 1XSiO2) for the FetO-SiO2-TiO2 melts at 1673 K, where XFetO 5 0.7.

Fig. 4—The apparent rate constants as a function of XFetO at 1673 K.

XFe31 /XFe21 increases with the addition of a basic oxide such as CaO and MgO.[9] If O22 on the surface is governed by O22 in the bulk as assumed before, the activity of O22 should be proportional to (XFe31)2/(XFe21)3 to the one-fourth power, assuming that the activity coefficients of FeO22 and Fe21 can be regarded as a constant: aO22 } [(XFe31)2/(XFe21)3]1/4

[9]

If the apparent rate of reduction, r, can be identified as R, the apparent rate constant, ka , becomes ka } [(XFe31)2/(XFe21)3]1/4

[10]

Thus, [(XFe31)2/(XFe21)3]1/4 is considered

to be proportional to the driving force of the reduction, aO22. Figure 6 shows the apparent rate constants as a function of (XFe31)2/(XFe21)3 at METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 5—Effect of the addition of MOx to the FetO-SiO2-TiO2 melts on the apparent rate constants at 1673 K, where XFetO 5 0.7 and XTiO2 /XSiO2 5 1.

Fig. 7—Temperature dependence of the apparent rate constants for the 80 mol pct FetO-10SiO2-10TiO2 melts.

Figure 7 shows the temperature dependence of the apparent rate constants for 80 mol pct FetO-10SiO2-10TiO2 melts together with the data of Nagasaka et al.[l] and Tsukihashi et al.[11] and with the converted data of Sasaki et al.[2] and El-Rahaiby et al.,[3] who measured the rate of CO2 dissociation. The best straight line is given by Eq. [11], and the apparent activation energy is 169 kJ/mol. log ka 5 28800/T 1 0.10

[11]

ACKNOWLEDGMENTS The authors gratefully acknowledge the “Research for the Future” Program of The Japan Society for the Promotion of Science for their financial support and Professor T. Nagasaka, Department of Metallurgy, Tohoku University, for his helpful comments and suggestions. REFERENCES

Fig. 6—The apparent rate constants as a function of (XFe31)2/(XFe21)3 at 1673 K.

1673 K. The values of XFe31 and XFe21 for each slag in equilibrium with solid iron were estimated from the correlations in the literature.[9,10] The plots of data agree well with a straight line whose slope is 0.25; ka can be explained by Eq. [10]. The data are also close to those of Nagasaka et al.,[1] who employed the regression analysis to the data for various FetO-containing melts and reported that ka is directly proportional to [(XFe31)2/(XFe21)3]1/3. The discrepancy between the theoretical value (1/4) and the empirical one (1/3) can be recognized as the effects of surface coverage and the variation of activity coefficients of Fe ions.


1. T. Nagasaka, Y. Iguchi, and S. Ban-ya: Proc. 5th Int. Iron and Steel Congr., ISS-AIME, Warrendale, PA, 1986, vol. 3, pp. 669-78. 2. Y. Sasaki, S. Hara, D.R. Gaskell, and G.R. Belton: Metall. Trans. B, 1984, vol. 15B, pp. 563-71. 3. S.K. El-Rahaiby, Y. Sasaki, D.R. Gaskell, and G.R. Belton: Metall. Trans. B, 1986, vol. 17B, pp. 307-16. 4. S. Sun, Y. Sasaki, and G.R. Belton: Metall. Trans. B, 1988, vol. 19B, pp. 959-65. 5. M. Mori, K. Morita, and N. Sano: Iron Steel Inst. Jpn. Int., 1996, vol. 36, pp. 624-30. 6. S. Ban-ya, Y. Iguchi, and T. Nagasaka: Tetsu-to-Hagane´, 1984, vol. 70, pp. 1689-96. 7. D.-J. Min and R.J. Fruehan: Metall. Trans. B, 1992, vol. 23B, pp. 29-37. 8. N. Sano, W.-K. Lu, P.V. Riboud, and M. Maeda: Advanced Physical Chemistry for Process Metallurgy, Academic Press Inc., London, 1997, pp. 72-74. 9. K. Matsuzaki, Y. Higano, K. Katsumata, and K. Ito: Iron Steel Inst. Jpn. Int., 1998, vol. 38, pp. 1147-49. 10. K. Matsuzaki and K. Ito: Iron Steel Inst. Jpn. Int., 1997, vol. 37, pp. 562-65. 11. F. Tsukihashi, K. Kato, K. Otsuka, and T. Soma: Trans. Iron Steel Inst. Jpn., 1982, vol. 22, pp. 668-95.

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