The Reduction of Iron Oxides by Volatiles in a Rotary Hearth Furnace Process: Part I. The Role and Kinetics of Volatile Reduction I. SOHN and R.J. FRUEHAN With iron ore reduction processes using coal-ore pellets or mixtures, it is possible that volatiles can contribute to reduction. By simulating the constituents of the individual reducing species in the volatiles, the rates for H2 and CO were investigated in the temperature and reduction range of interest; hydrogen is the major reductant and was studied in detail. The kinetics of the reduction by H2 has been found to be a complex mechanism with, initially, nucleation and growth controlling the rate. There is a catalytic effect by the existing iron nuclei, followed by a mixed control of chemical kinetics and pore diffusion. This results in a topochemical reduction of these iron oxide particles. Up to 1173 K, reduction by H2 is considerably faster than by carbon in the pellet/mixture or by CO. It was also found that H2S, which is involved with the volatiles, does not affect the rate at the reduction range of interest.
I. INTRODUCTION
WITH the world’s iron and steel demand on the rise and the growing restriction of coke as the reducing agent due to environmental and economic factors, there has been an increased interest for the implementation of new ironmaking technologies with less capital investment. Natural gas–based processes such as Midrex and HYL are relatively proven technologies with a combined market share of 90 pct for direct reduced iron (DRI)/hot briquetted iron (HBI). Since these processes can only be used where natural gas is relatively inexpensive, a family of coal-based processes using a rotary hearth furnace (RHF) such as FASTMET, INMETCO, Sidcomet, and ITmk3 have been developed. These RHF technologies combine low material costs with simplicity and flexibility of operation. The unprocessed coals may contain large amounts of volatiles, and the evolution of volatiles consumes the energy needed for the reduction of the iron oxides. The amount and type of volatiles that evolve varies with the rank and heating rate of the coal.[1,2] At low temperatures of up to 350 °C, superheated water vapor evolves, and from 350 °C to 600 °C, light gases of CO, CO2, H2, CH4, and C2H6 occur. Above 600 °C, small amounts of complex hydrocarbons are observed. Thus, in the devolatilization of high- and medium-volatile–containing coals, the majority of gases evolved have been found to be H2, CO, H2O, CO2, and CH4, where the possible reducing species are CO, H2, and CH4. Previous studies[3,4] done with volatiles for a single-layer RHF have shown that the short retention time of the volatiles in the pellets and the lower temperatures at which these volatiles are released results in negligible amounts of reduction by the volatiles. However, with multiple layers of three or more, the bottom layers are at a lower temperature and retain their volatiles longer compared to the upper layers. This allows the delayed release of volatiles to react with the I. SOHN, Graduate Student, and R.J. FRUEHAN, Professor, are with the Materials Science and Engineering Department, Carnegie Mellon University, Pittsburgh PA, 15213. Contact e-mail:
[email protected] Manuscript submitted February 8, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS B
top layers, which are at higher temperatures when the kinetics are favored. Thus, by simulating the individual reducing gaseous species, it may be possible to gain some information on the effects of volatile reduction. In addition, although the RHF process uses pellets, the intrinsic rates of the reduction with the simulated reducing gases must be measured, and in this study, the reduction of iron oxide powders has initially been investigated. The emphasis will be on the first 50 pct of reduction by H2, where reduction by volatiles will occur, and the effect of H2S, CO, and carbon is compared to the role of H2 in the temperature range of interest. For higher reduction degrees, devolatilization will have been completed, and the reduction by carbon will be dominant. II. EXPERIMENTAL The rates were measured using standard thermogravimetric analysis (TGA) and shown in Figure 1. A monolayer of various iron oxides (100/200 mesh), which were preheated to 200 °C in air for at least 72 hours, were spread on an alumina crucible. High-purity gases (99.998 pct) were used for the simulated volatiles, and the furnace temperature was controlled by a proportional integral derivative (PID) controller with a deviation of 2 °C. The temperature was varied from 400 °C to 1000 °C, which is assumed to be the temperature profile for the initial reaction with volatiles in the early stages of the RHF process. Preliminary experiments using different flow rates from 1 to 9 Lpm showed the effect of flow rate on the mass transfer to be negligible above 7 Lpm. However, as pointed out by Warner,[5] this alone does not rule out the possible effects of gas-phase mass transfer. Thus, by measuring the vaporization of Mg under identical flow conditions and estimating the masstransfer coefficient, the approximate calculation of the bulk gas-phase mass transfer was obtained, which can be used to determine the possible contribution of mass transfer to the overall rate. Details of this are given in the Appendix. Furthermore, fluidization was not observed for up to 13 Lpm. When working with high flow rates, the cooling of the crucible and sample by the gas is possible, but measurements VOLUME 36B, OCTOBER 2005—605
Fig. 2—Schematic illustration of devolatilization according to position. Temperature of the lower layer (TL) temperature of the upper layer (TU).
Fig. 1—Schematic of the TGA experimental apparatus.
Table I. Chemical Composition of Ore Samples by X-Ray Fluorescence Ore Type SiO2 Al2O3 MgO MnO TiO2 P2O5 K2O MNC CVRD Wabush PAH HFIO
1.27 0.48 3.07 Tr Tr
0.63 0.89 0.2 Tr Tr
0.02 0.01 Tr Tr Tr
0.06 0.46 0.91 0.01 Tr
0.03 0.03 Tr Tr Tr
Fe
0.08 0.02 67.60 0.07 0.02 67.79 0.0 0.02 65.56 0.02 Tr 69.80 Tr Tr 69.88
Tr: trace amounts.
of the temperature directly above and below the bottom of the crucible found negligible differences. Morphological examination of partially reduced oxides was conducted with secondary and backscattered field-emission gun scanning electron microscopy. Qualitative analysis using energydispersive spectroscopy (EDS) was employed to verify the gradient of oxygen content along the topochemical layers. The chemical compositions of the iron oxide specimens of Porous Analytical Hematite (PAH), chemical grade; Mt. Newmann Concentrate (MNC), from Western Australia; Companhia Vale do Rio Doce (CVRD), from Brazil; Wabush, from Wabush Mines, Canada; and Highly Faceted Iron Oxide (HFIO), synthetically produced, are given in Table I. The densities of these oxides are PAH MNC CVRD WABUSH HFIO. III. RESULTS AND DISCUSSION A. Mechanisms Controlling Volatile Reduction The possible reducing species in volatiles have been found to be H2, CO, and CH4, where CH4 has been known to either 606—VOLUME 36B, OCTOBER 2005
crack to C and H2[6] or be reformed to H2 and CO.[7] Thus, volatile reduction is essentially the reduction by H2 and CO. Figure 2 illustrates a multilayer RHF, where the temperature decreases with increased distance from the upper layer and, hence, volatiles evolve more slowly in the lower layers. The extent of reaction in a multilayer RHF by these relatively slowly evolving volatiles depends upon the rate of H2 and CO reduction. Considering the reduction of solids by gases, several mechanisms are possible as rate-controlling mechanisms and have been studied individually or as a mixed control. The possible rate-controlling mechanisms can be nucleation and growth, mass transfer (bulk diffusion or pore diffusion), chemical kinetics (complete, uniform internal reduction or a topochemical receding interface), and heat transfer. The barrier to nucleation can cause the nucleation and growth of metallic Fe to be rate-controlling. This is the socalled incubation region.[8] Beyond the controlling mechanisms of nucleation and growth, studies done on the reduction with reducing gases for small particles have shown several mechanisms that could be rate-controlling. One such mechanism is the transfer of H2, CO, H2O, and CO2 to and from the reacting interface through a porous reduced layer or through a bulk gas-boundary layer.[9–11] Another is the reaction of the reducing gases at the receding interface[12] or the bulk of the particle.[13] The final mechanism is a heattransfer-controlled reaction,[14] which is relatively fast for small samples. Considering these mechanisms and by plotting the results of the F (fraction reduced) vs time plots into various plots of ln (1 F), 1 (1 F)1/3, and 3 2F 3(1 F)2/3, which have been previously derived in the aforementioned literature, it may be possible to determine the controlling mechanisms. Furthermore, by comparing the bulk flux of gas-phase mass transfer through the external gas-boundary layer to the reaction rate, the function of the bulk gas mass transfer can also be determined. B. Reduction Mechanism by H2 The external mass transfer was estimated by measuring the rate of vaporization of Mg for a similar geometry. As shown in the Appendix, it is an order higher than the measured rates at temperatures below 500 °C, and it can be assumed to not influence the rate. At temperatures higher than 500 °C, the external mass transfer is faster than the measured reaction rates, but may slightly affect the rate and, therefore, at moderately higher temperatures, it should be considered. The reduction of iron oxides with H2 can be complicated by the chemical composition of the oxides, surface morphology, METALLURGICAL AND MATERIALS TRANSACTIONS B
initial density, and temperature. The reduction of porous PAH at 400 °C is shown in Figure 3. Similar results were observed below 600 °C. The complete reduction to Fe3O4 or 11.13 pct is observed in region I. Region II[8,16] is a nucleation-inhibited region termed the incubation region. The incubation region decreases with increased temperature due to a higher driving force for nucleation. As the nuclei grow, the existing nuclei catalyzes the formation of new nuclei and a catalytic region III is observed. Beyond the effects of nucleation and growth, a somewhat steady-state region IV is observed. Figure 4 shows region IV replotted according to the equations derived in Table II. One should understand that although the full regime of reduction is important, considering the amount of volatiles evolved and the reaction rate of these gases with the oxides, as previously mentioned, the reduc-
tion by volatiles will be below a 50 pct reduction and is the focus of the present research. Although the 1 (1 F)1/3 vs time plot is close to linearity, indicating a topochemical receding interface, the slope is not completely linear, which implies that the rate is not controlled by one single mechanism, but a mixed control of, possibly, chemical kinetics and mass transfer. The results of PAH have shown the reduction to be a complex mechanism that is complicated by the highly porous irregular surface characteristics, which have been observed from microscopic observations. Further studies have been done with iron ores of more controlled surface morphologies and higher densities, such as MNC, CVRD, Wabush, and HFIO. Unlike PAH, the aforementioned iron ores do not show complete uniform internal reduction to Fe3O4. The higher density inhibits the uniform internal reduction to Fe3O4. In Figure 5, the reduction of MNC shows a region I of nucleation and growth followed by an increased rate. A steadystate region III follows region II and continues to a 50 pct reduction. Similar observations can also be made with the HFIO, but the so-called mixed region III ends at approximately a 40 pct reduction compared to that of 50 pct with MNC. It is possible that the higher density of HFIO increases the importance of mass transfer at an early stage. Table II. Corresponding Equations of Controlling Mechanisms General Category Chemical kinetics Mass transfer
Fig. 3—The reduction of PAH (40 mg) with H2 (9 Lpm) at 400 °C.
Fig. 4—The reduction of PAH (40 mg) with H2 (9 Lpm) at 400 °C replotted as various controlling mechanisms. METALLURGICAL AND MATERIALS TRANSACTIONS B
Heat transfer
Specific Category
Equations
complete uniform internal reduction[13,15] topochemical receding interface[12] bulk gas mass transfer[15] porous gas mass transfer[15] conductive heat transfer[14]
ln (1 F) r t 1 (1 F)1/3 r t Frt 3 2F 3(1 F)2/3 r t 3 2F 3(1 F)2/3 r t
Fig. 5—The reduction of MNC (40 mg) with H2 (9 Lpm) at 400 °C. VOLUME 36B, OCTOBER 2005—607
Region III for MNC is replotted in Figure 6 and exhibits a tendency toward the receding interface–controlled reaction. However, the curve corresponding to the pore mass transfer–controlled reaction (Y 3 2F 3(1 F)2/3) shows some linearity, which cannot be ignored. Thus, most likely it is a mixed control of mass transfer in the pores and chemical kinetics at the receding interface. At a moderate temperature of 600 °C, the results in Figure 7 indicate a shorter-nucleation and growth-dependent region, but nonlinear curves for each individual controlling mechanism are observed in region III that suggest a mixed control of chemical kinetics and mass transfer. Although at higher temperatures the effects of nucleation and growth diminish, which could simplify the mechanism of reduction, sintering of the particles can have a significant impact on reduction. The results of varying the temperature from 400 °C to 600 °C show the rates to be highly dependent upon tem-
Fig. 6—The reduction of MNC (40 mg) with H2 (9 Lpm) at 400 °C replotted as various controlling mechanisms.
perature changes, suggesting that chemical kinetics is a dominant factor. From the temperature-dependence curves, the activation energies of each iron ore seem to show comparable values between 55 and 67 kJ/mole, which corresponds to literature values.[8,13,17,18] However, the activation energies do not prove chemical kinetics to be solely controlling. Reactions initially assumed to be controlled by chemical kinetics were found to be a mixed control of gas mass transfer and chemical kinetics or a nucleation-andchemical kinetics–controlled reaction. If the chemical kinetics was solely controlling, the reactionrate equation suggests the rate to be directly proportional to the internal surface area and, hence, the weight of the sample. The rates of reduction for PAH, MNC, CVRD, Wabush, and HFIO with varying weights are given in Table III. At low temperatures, the rate is not directly proportional to the weight, which supports the conclusion of a mixedcontrol mechanism. However, from the proportionality and the temperature dependence, chemical kinetics does play a major role in the reduction mechanism. At higher temperatures of 650 °C, where the sintering phenomenon comes into play, there is a marked decrease in the proportionality of the samples, which highlights the role of mass transfer to the reduction mechanism. Since the Wabush and HFIO samples behave similarly and the CVRD and MNC samples are similar as well, the following can be concluded. For the highly porous materials (PAH), the slope is almost independent of weight, which suggests that chemical kinetics is playing a smaller role in the controlling mechanism. For the median-porosity materials (CVRD and MNC) and the dense materials (Wabush and HFIO), the slope is somewhat proportional, but still shows a large deviation from a complete chemical kinetics–controlled reaction. The reason for the large deviation in proportionality with weight seems to indicate that, at the higher temperatures where sintering is comparably as fast as the reaction itself, the diffusion of gases is slower in the pores and, thus, has a higher impact to the reduction mechanism. The reduction of MNC at 900 °C with H2 is shown in Figure 8. Region III shows a higher deviation from linearity for a topochemical receding interface–controlled reaction, suggesting that the effect of mass transfer is playing a more dominant role in the mixed-control mechanism. This result does agree with the comparison of the mass-transfer– Table III. Comparison of the Initial Rate of Reduction with H2 for Different Sample Amounts Specimens
Fig. 7—The reduction of MNC (40 mg) with H2 (9 Lpm) at 600 °C replotted as various controlling mechanisms. 608—VOLUME 36B, OCTOBER 2005
Temperature Weight (°C) (mg)
PAH
350
MNC
400
HFIO
400
PAH
650
CVRD
650
Wabush
650
20 40 20 40 40 80 40 80 40 80 40 80
Rate (g/s) 1.5 2.2 2.1 3.2 1.4 2.7 5.3 6.5 2.0 2.8 1.6 2.4
105 105 105 105 106 106 104 104 104 104 104 104
Proportionality 1.47 1.54 1.85 1.23 1.40 1.45
METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 8—The reduction of MNC (40 mg) with H2 (9 Lpm) at 900 °C replotted as various controlling mechanisms.
Fig. 9—The rates as a function of H2 partial pressure for PAH and MNC from 400 °C to 900 °C (40 mg).
controlled rate and the reaction rate in the Appendix, where the difference between the two is small. At high temperatures, the rate is less sensitive to temperature compared to rates at lower temperatures, which is common when mass transfer is influencing the rate. A distinctive feature of the denser iron ores compared to the PAH sample is that the rate beyond the mixed control of region III decreases at an earlier stage compared to the PAH. This is due to the effect of sintering on MNC and, assuming the rate of sintering is comparable at temperatures between 700 °C and 900 °C, the effect of sintering is more pronounced at the lower temperature of 700 °C. However, sintering effects are not observed for the HFIO or Wabush samples due to their initially high density, where a change in volume is not readily observed. This indicates that mass transfer can play a more important role in iron ores of moderate density (MNC/CVRD) compared to very dense (HFIO/Wabush) or very porous (PAH) iron oxides.
and grow. These iron-rich regions occur in the peripheral of the particle and shows that the complete uniform internal reduction to Fe3O4 for denser iron ores, which was observed for the PAH, is not possible. Furthermore, the initiation of the reaction with the gaseous reductant seems to occur on preferred sites such as cracks, edges, or higher-energy sites, where the barrier to reduction can take place much more easily. Although beyond the scope of this research, this suggests from previous studies that at low temperatures, the mechanism of nucleation and growth should be discussed in greater detail when explaining the initial reduction of iron oxides. Beyond a 15 pct reduction, a shell of porous iron-rich layer encompasses the particle, which is typical of a topochemical reduction. With higher reduction degrees, the porous layer moves toward the core of the particle. The EDS analysis of the iron-rich layer even at this stage of reduction still shows oxygen to be present at the rim of the particle. This could suggest that mass transfer to the reaction sites is partially controlling the rate. Furthermore, with higher reduction degrees of 50 pct and greater, an enhanced view of the pores at the interface shows pore diameters of less than 100 nm. When the sizes of the pores become smaller than 100 nm, Knudsen diffusion can affect mass transfer and, although beyond the scope of this study, it is possible that, at later stages of the reduction, Knudsen diffusion becomes rate-controlling.
C. Pressure Dependence The concentration of H2 in volatiles for high volatile (HV) and medium volatile (MV) coals varies between 20 and 40 pct; therefore, verification of the partial-pressure dependency of MNC at higher temperatures was necessary. Figure 9 shows the reduction of PAH and MNC from 400 °C to 900 °C to be first-order with respect to a H2 partial pressure below 1 atm. D. Physical Observations The well-defined surface characteristics of the HFIO sample, which had fewer cracks or defects on the surface, was used as a reference material to observe the reduced layers of dense iron ores. Figure 10 shows the partially reduced HFIO under H2 at 450 °C. At a 15 pct reduction, the EDS analysis at the lighter area revealed a low concentration of oxygen compared to the dark region, which was not completely metallic iron but an iron-rich region. For low reduction degrees, only a few islands of reduced iron-rich sites are observed, which nucleate METALLURGICAL AND MATERIALS TRANSACTIONS B
E. Reduction with H2 and CO Volatiles also may contain as high as 5 pct CO. Figure 11 shows the reduction of MNC and PAH using a He-40 pct H2-5 pct CO mixture. The reaction is dominated by H2, and CO has negligible effects on the reduction. However, the reduction rate of MNC for H2-CO is slightly higher, which could be caused by the formation of Fe3C, which would inhibit the sintering effect to some degree. This has also been observed for studies done with H2-H2S and the formation of FeS. VOLUME 36B, OCTOBER 2005—609
Fig. 10—HFIO ore reduced with H2 at 450°C to (a) 15 pct, (b) 32 pct, and (c) 52 pct; (d ) enlargement of the iron-rich phase in (c).
Fig. 11—The reduction of (1) PAH with He-40 pct H2-5 pct CO, (2) PAH with He-40 pct H2, (3) MNC with He-40 pct H2-5 pct CO, and (4) MNC with He-40 pct H2 at 900 °C.
F. Effect of Sulfur (H2S) on the Rate Coal also contains sulfur, some of which comes off with the volatiles as H2S. Sulfur is known to be a surface-active element and retard reaction on iron surfaces. The composition 610—VOLUME 36B, OCTOBER 2005
Fig. 12—The effect of H2S on the reduction of PAH (40 mg) at 900 °C with (1) H2, (2) H2-0.36 pct H2S, and (3) H2-1 pct H2S (7 Lpm).
of volatiles retains as much as 1 pct H2S. Figure 12 shows that at 900 °C, the rates of reduction are not affected by the H2S, and comparable slopes are observed. However, near the final stages of reduction, the metallic Fe reacts with H2S METALLURGICAL AND MATERIALS TRANSACTIONS B
to form FeS. The formation of FeS maybe occurring simultaneously with the reduction of the iron ore, but calculations of the weight gain corresponding to the weight loss of the iron ores show the reduction reaction to be much faster, and the formation of FeS occurs subsequent to the final reduction to Fe. Apparently, sulfur retards rates on iron but not on FeO, which is the reacting surface for reduction. For the reduction of iron oxide, the effect of H2S can be neglected. G. Reduction with H2 and Carbon Assuming, at higher temperatures, that both the reduction by carbon and that by H2 occur simultaneously, Figure 13 shows the mixture of MNC and carbon reacted with H2. Compared to the reduction by H2, the effect of carbon reduction is negligible. Thus, with composite mixtures of iron ore and carbon reduced with simulated volatiles, the role of a fixed carbon reduction may be neglected. Similar results
Fig. 13—The reduction of (1) 40 mg of MNC with H2, (2) 50 mg of MNC/C (4/1) with H2, and (3) 50 mg of MNC/C (4/1) with He at 900 °C (7 Lpm).
were observed for the PAH sample. In addition, to ensure that the surface contact of carbon with the MNC is not a factor in the mechanism, Figure 14 shows the reduction of 150 mg of MNC and C at 900 °C. The reduction with larger amounts of sample had little or no effect on the reduction mechanism. In addition, the mixture of MNC and an inert Al2O3 in comparable conditions to the MNC and C also show no observable difference, which further supports the negligible contribution of a fixed carbon reduction for powder mixtures. This suggests that the reaction with H2 is much faster than the initiation of a fixed carbon reduction in the temperature range of interest. IV. SUMMARY AND CONCLUSIONS In reduction processes using mixtures of coal and ore, the volatiles may contribute to the reduction. The rate of reduction of simulated volatiles for several types of iron ore powders was investigated up to a 50 pct reduction from 400 °C to 1000 °C. The emphasis was on the reduction by H2, but the effects of CO, H2S, and carbon were also studied. The results are summarized as follows. 1. The reduction mechanism is a complex mechanism influenced by the initial density, the surface characteristics of the iron oxides, and the temperature of the reaction. 2. Although the temperature dependence is close to the chemical kinetics–controlled mechanism, the rate dependence on weight and the nonlinear slopes of the individual mechanisms suggest that a mixed control of mass transfer and chemical kinetics at the receding interface is controlling. 3. The higher-density ores (HFIO and Wabush) follow the expected linear slopes for chemical-kinetics control better, due to the controlled surfaces. 4. At temperatures higher than 600 °C, sintering affects the overall mechanism, and the reduction rates of MNC and CVRD slow significantly. 5. The effects of both CO (5 pct) and H2S (1 pct) to the reduction are negligible. The simultaneous reactions of fixed carbon and H2 at temperatures of 400 °C to 1000 °C show that the H2 reaction is dominant. It is likely that with a high concentration of H2 in the high- to medium-volatile-containing coals, the possible reaction by the volatiles can mainly be focused on the H2 reduction. APPENDIX Measurement of the bulk gas mass transfer One of the mechanisms that could have an effect on the reduction is the bulk gas mass transfer to the surface. The mass-transfer coefficient (m H2H2O) from bulk gas to or from the surface was estimated by measuring the rate of evaporation of Mg to acquire the mass-transfer coefficient of Mg in H2 (m H2Mg). Then, using the kinetics theory of gases, the masstransfer coefficient of H2O in H2 at 625 °C was extrapolated. In these experiments, the rate of evaporation of Mg in H2 was measured, for which
Fig. 14—The reduction of (1) 120 mg of MNC with H2, (2) 150 mg of MNC/C (4/1) with He, (3) 150 mg of MNC/C (4/1) with H2, and (4) 150 mg of MNC/Al2O3 (4/1) with H2 at 900 °C (7 Lpm). METALLURGICAL AND MATERIALS TRANSACTIONS B
JH2Mg
mH2Mg
° ), (PMg RT ° is the vapor pressure Where PMg
[A1]
VOLUME 36B, OCTOBER 2005—611
ACKNOWLEDGMENTS This work was sponsored by the Department of Energy Grant No. DE-FC36-01ID14208 and from the member companies of the Center for Iron and Steelmaking Research. REFERENCES
Fig. A1—The comparison of the diffusive flux for H2 (9 Lpm) against the reduction rates of the various oxides.
The results in Figure [A1] show the reaction rates to be an order higher at temperatures below 500 °C. At temperatures higher than 500 °C, the diffusive flux is higher than the measured reaction rates, but is comparatively not as high as in the low-temperature regimes. Thus, although the effect of bulk gas mass transfer is minimal compared to the pore diffusion at moderately higher temperatures, it also should be considered.
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1. J.G. Speight: The Chemistry and Technology of Coal, 2nd ed., Marcel Dekker Inc., New York, NY, 1994, p. 12. 2. J.B. Howard: Chemistry of Coal Utilization, 2nd suppl., John Wiley & Sons, New York, NY, 1981, pp. 670-722. 3. W.K. Lu: Metall. Mater. Trans. B, 2001, vol. 32B, pp. 757-62. 4. S. Sun and W.K. Lu: Iron Steel Inst. Jpn. Int., 1999, vol. 39 (2), pp. 123-29. 5. N.A. Warner: Trans. TMS-AIME, 1964, vol. 230, pp. 163-76. 6. M. Kawakami, T. Uchiyama, and K. Takahashi: ICSTI/Ironmaking Conf. Proc., 1998, pp. 827-33. 7. K.M. Hutchings, R.J. Hawkins, and J.D. Smith: Ironmaking and Steelmaking, vol. 3 (15), pp. 121-26. 8. S.K. El-Rahaiby and Y.K. Rao: Metall. Trans. B, 1979, vol. 10B, pp. 257-69. 9. R.H. Spitzer, F.S. Manning, and W.O. Philbrook: Trans. TMS-AIME, 1966, vol. 236, pp. 726-42. 10. A. Ünal: Trans. Inst. Min. Metall. Sect. C, 1986, vol. 95, pp. C179-86. 11. R.H. Tien and E.T. Turkdogan: Metall. Trans. B, 1977, vol. 8B, pp. 305-13. 12. H.Y. Sohn and J. Szekeley: Chem. Eng. Sci., 1972, vol. 27, pp. 763-78. 13. E.T. Turkdogan and J.V. Vinters: Metall. Trans., 1972, vol. 3, pp. 1561-74. 14. E.T. Turkdogan, R.G. Olsson, H.A. Wriedt, and L.S. Darken: Trans. Soc. Min. Eng. AIME, 1973, vol. 254, pp. 9-21. 15. E.T. Turkdogan: Physical Chemistry of High Temperature Technology, Academic Press, New York, NY, 1980, pp. 258-60. 16. Y.K. Rao: Metall. Trans. B, 1979, vol. 10B, pp. 243-55. 17. W.M. McKewan: Trans. TMS-AIME, 1962, vol. 224, pp. 2-5. 18. J.M. Quets, M.E. Wadsworth, and J.R. Lewis: Trans. TMS-AIME, 1960, vol. 218, pp. 545-50.
METALLURGICAL AND MATERIALS TRANSACTIONS B
