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Fig. 7 Melting curves for 75 mm (3.0 in.) diam steel rods immersed in iron- carbon baths. A, high (4.6% C) iron-carbon bath; B, low (2.1% C) iron- carbon bath. Plotted is the fractional thickness (the fraction of the rod diameter remaining undissolved) versus immersion time. Source: Ref 10. The conditions existing in the bath are illustrated in Fig. 8. Figure 8(a) shows the carbon concentration profiles in the liquid bath in the vicinity of a dissolving steel bar. The meaning of the carbon concentration notation is indicated in Fig. 8(b). As indicated in Fig. 8(a), carbon diffuses across the liquid boundary layer, while equilibrium conditions are maintained at the solid/liquid interface. Thus, the carbon concentrations in the solid and the liquid at the interface are the isothermal solidus C* s S and the liquidus C* L concentrations, respectively. Dissolution takes place by isothermal conversion of the steel into a liquid, that is, by a chemical melting process. It is clear from Fig. 8(b) that as temperature increases, C* L decreases significantly. Thus, the driving force for diffusion increases with temperature. Fig. 8 Carbon concentration profiles (a) for a steel rod dissolving in an iron-carbon melt. (b) Iron- carbon phase diagram defining the carbon concentrations noted in (a). Source: Ref 10. Based on Eq 3 and Fig. 4, the flux of carbon entering the steel is: J = k m ( B L C - C* L ) (Eq 6) The carbon flux can also be defined in terms of a carbon balance: * * B B SL S L C dr JC Pdt ρ =−− l l (Eq 7) where B S ρ and ρ* L are the respective densities of solid steel and liquid iron at the liquidus composition, B S C is the bulk carbon concentration of solid steel, and dr/dt is the rate of change of the radius or thickness of the steel with time. By combining Eq 6 and 7 and integrating between the limits r = r 0 at t = 0 and r = 0 at t = t m , the isothermal melting time t m is given as: ** * (/) () BB SLLS mo B mLL CC tr kCC ρρ− = − ll l (Eq 8) In laboratory studies, Eq 8 accurately predicted steel dissolution rates in a stagnant bath (Ref 10). Research has suggested that melting times are reduced by about a factor of two in induction-stirred melts (Ref 9). Other work has indicated that t m can be reduced by an order of magnitude with strong convection (Ref 11). On the basis of Eq 8 and the mass transfer correlation for rapidly dissolving rods (Ref 12), correlations were developed relating t m to bath temperature and to carbon concentration (Ref 10). This is given in Fig. 9 for a steel thickness of 2.5 mm (0.098 in.). Because t m is directly proportional to the thickness of the steel, Fig. 9 can be used to estimate t m for a wide range of steel thickness by making the appropriate thickness correction. Checks of the predictions from Fig. 9 in production operations have indicated that predicted t m values are realistic (Ref 10). Fig. 9 Predicted melting ti mes for vertical steel plates and cylinders, 2.5 mm (0.098 in.) scrap thickness and 0.1% C composition, [(%S) i = 0.03] immersed in stagnant iron- carbon baths at different bath temperatures. Source: Ref 10. References cited in this section 1. R.I.L. Guthrie, Addition Kinetics in Steelmaking, in Proceedings of the 35th Electric Furnace Conference, Iron and Steel Society of AIME, 1978, p 30-41 2. F.A. Mucciardi and R.I.L. Guthrie, Aluminum Wire Feeding in Steelmaking, Trans. ISS, Vol 3, 1983, p 53- 59 3. J.W. Robison, Jr., "Ladle Treatment With Steel- Clad Metallic Calcium Wire," Paper 35, presented at Scaninject III, Part II, MEFOS, Lulea, Sweden, 1983 4. L. Kalvelage, J. Markert and J. Pötschke, Measurement of the Dissolution of Graphite in Liquid Iron by Following the Buoyancy, Arch. Eisenhüttenwes., Vol 50, 1979, p 107-110 5. R.G. Olsson, V. Koump, and T.F. Perzak, Rate of Dissolution of Carbon in Molten Fe-C Alloys, Trans. Met. Soc. AIME, Vol 236, 1966, p 426-429 6. O. Angeles, G.H. Geiger, and C.R. Loper, Jr., Factors Influencing Carbon Pickup in Cast Iron, Trans. AFS, Vol 74, 1968, p 3-11 7. M. Eisenberg, C.W. Tobias, and C.R. Wilke, Mass Transfer at Rotation Cylinders, Chem. Eng. Prog. Symp. Series, Vol 51, 1955, p 1-16 8. R.G. Olsson, V. Koump, and T.F. Perzak, Rate of Dissolution of Carbon Steel in Molten Iron- Carbon Alloys, Trans. Met. Soc. AIME, Vol 233, 1965, p 1654-1657 9. R.D. Pehlke, P.D. Goodell, and R.W. Dunlap, Kinetics of Steel Dissolution in Molten Pig Iron, Trans. Met. Soc. AIME, Vol 233, 1965, p 1420-1427 10. R.I.L. Guthrie and P. Stubbs, Kinetics of Scrap Melting in Baths of Molten Pig Iron, Can. Metall. Q., Vol 12, 1973, p 465-473 11. K. Mori and T. Sakuraya, Rate of Dissolution of Solid Iron in Carbon- Saturated Liquid Iron Alloys With Evolution of CO, J. Iron Steel Inst. Japan, Vol 22, 1982, p 964-990 12. P.T.L. Brian and H.B. Hales, Effects of Transpiration and Changing Diameter on Heat and Mass Transfer to Spheres, AIChE J., Vol 15, 1969, p 419-425 Purification of Metals The structure and properties of cast metals are sensitive to numerous impurities. Because purification of melts generally adds considerable cost to castings, the lowest cost and surest defense against contamination is careful selection of scrap. Purification is generally reserved for elements that are so pervasive that avoidance is impossible. This is exemplified by sulfur and oxygen removal from cast iron and steel, respectively, and removal of alkali and alkaline earth elements from aluminum. Because of their immediate importance, aspects of the physical chemistry of these processes are reviewed. Ferrous Melts One of the most important processes involved in cast iron and steel production is desulfurization. For steels, desulfurization is necessary to reduce the level of inclusions, leading to stronger and more fatigue-resistant steels. For cast iron, desulfurization is practiced in the manufacture of ductile iron castings in order to develop spherical graphite morphology. Ductile iron is used in applications where high fracture toughness is needed. Sulfur is removed from iron and steel when the metals are liquid. Although a variety of reagents are employed to remove sulfur, namely, calcium, magnesium, sodium, and rare earths, the most important is calcium. Common forms of calcium include the metal; alloys such as calcium silicon (CaSi); the oxide, calcium oxide (CaO); and the carbide, calcium carbide (CaC 2 ). Despite the use of various forms of calcium, the governing chemical reaction in all cases appears to be the same (Ref 13, 14): CaO + S = CaS + O (Eq 9) The equilibrium constant for the reaction (Eq 9) is: 9 CaSo CaOS ah k ah = (Eq 10) For both cast iron and steel, target sulfur concentrations after desulfurization are in the range of 0.006 to 0.010% S. In electric-melted cast iron and steel, the sulfur levels before desulfurization are 0.02 to 0.03% S, while input sulfur levels to the cupola are generally much higher 0.1 to 0.2% S. Requirements for Desulfurization. For reasons related to reaction kinetics and thermodynamics, the final sulfur (%S) f concentration achieved in desulfurization processes depends on three factors: • Initial sulfur concentrations (%S) i • Amount of desulfurizer used, usually expressed as the weight fraction of desulfurizer to metal, W • Extraction efficiency of the desulfurizer, which is measured by the desulfurization ratio (DR), that is, the ratio of sulfur concentrations: desulfurizer to metal The three variables can be related as follows through a mass balance on sulfur: (%) (%) 1() i f S S WDR = + (Eq 11) For liquid-desulfurizing slags that are not saturated with respect to calcium sulfide (CaS), the maximum value of DR, that is, the equilibrium value, can be predicted from thermodynamic considerations: 14 max 15 max (%) () (%) slag ss fo S cfk DR Skh == (Eq 12) where C S is the slag sulfide capacity, defined as (Ref 15): 2 2 1/2 (%) O sslag S p CS p = (Eq 13) and K 14 and K 15 are the respective equilibrium constant for the reaction: 1 2 O 2 = O (Eq 14) 1 2 S 2 = S (Eq 15) and f S is the activity coefficient for 1 wt% S in the standard state. Equation 12 can be derived from Eq 10. Using known input and desired output sulfur values, Eq 11 gives the required desulfurization ratios as a function of weight fraction desulfurizer. These data are plotted in Fig. 10 for two cases. In the electric-melting case, initial and final sulfur concentrations were assumed to be 0.03 and 0.008% S, respectively, In cupola-melting case, the equivalent concentrations were 0.10% S and 0.008% S. The cupola line applies for both cupola iron and ladle-desulfurized cupola iron. Fig. 10 Weight fraction desulfurizer required to achieve given desulfurization ratios. Plots for electric- melted iron and steel (curve A) assume initial sulfur concentrations [%(S) i = 0.03] different from those of cupola- melted iron [(%S) i = 0.10] (curve B). The relationships illustrated in Fig. 10 are useful in defining systems that will provide the necessary desulfurization conditions. Four systems are compared in Table 3. These cover cupola- and electric-melted cast iron and electric-melted steel. Also examined are two liquid slag systems: a basic cupola slag (dicalcium silicate saturated) and a CaO-saturated CaO-Al 2 O 3 slag. Table 3 Theoretical weight ratios: desulfurizer to iron to achieve 0.008% S in various systems Type of melt Slag composition T, K C S (× 10 4 ) (a) f S h O (× 10 4 ) (b) (DR) max (c) W A. cast iron cupola 44 CaO-15MgO-5Al 2 O 3 - 36SiO 2 1773 2.7 5 1.3 90 0.13 B. cast iron cupola (ladle desulfurized) CaO sat -Al 2 O 3 1773 59 5 5.0 417 0.027 C. cast iron electric CaO sat -Al 2 O 3 1773 59 5 5.0 417 0.0065 D. steel electric CaO sat -Al 2 O 3 1873 316 1 0.45 5280 0.00052 (a) C S is obtained from optical basicity correlations (Ref 15). f S is based on iron composition (Ref 16). (b) Case A: h O is governed by Si/SiO 2 equilibrium based on respective concentration in iron and slag (Ref 17). Cases B and C: h O is governed by Si/SiO 2 equilibrium with aSiO 2 = 1 due to ladle exposure to air (Ref 18). Case D: h O is governed by Al/Al 2 O 3 equilibrium with % Al = 0.05 (Ref 19), assumed no contact with air. (c) K 14 and K 15 data from Ref 20 Table 3 shows that: • The best desulfurizing cupola slags have lower sulfide capacity and desulfurization ratio than slags used in ladle desulfurization; the consequence is the need for much larger quantities of slag * • Compared to steel, cast iron desulfurization benefits from higher f S because of the presence of relatively high concentrations of carbon and silicon in cast iron • Ladle desulfurization systems that are exposed to air suffer higher h O and, as a result, poorer desulfurization than might otherwise be anticipated For the cupola slag case in Table 3, the thermodynamically predicted value of (DR) max = 90 is in good agreement with measured data (Fig. 11). This indicates that the cupola desulfurization process operates close to equilibrium levels. Further evidence for this is given Fig. 12, which plots desulfurization data for a cupola operated with varying amounts of municipal ferrous refuse in the charge. The upper portion of Fig. 12 plots C S and oxygen activity. The latter is expressed as the partial pressure of oxygen. The lower portion of Fig. 12 is a comparison of (DR), measured and calculated. The good agreement found is evidence that near-equilibrium conditions existed. Fig. 11 Desulfurization ratio- basicity comparisons for cupola (closed circles) and laboratory data (open circles). Equilibrium values are indicated by the angled line. The vertical line indicates the slag basicity above which slags are saturated at 1500 °C (2730 °F), w ith respect to dicalcium silicate. This is the point at which the observed DR should equal (DR) max . Source: Ref 14. Fig. 12 Slag sulfide capacities, oxygen activities, and desulfurization ratios, measured and calculated, for a cupola operated with municipal ferrous refuse as a charge material. Source: Ref 21. For the cases discussed above, the oxygen activity in cupola iron has been found to be governed by the reaction (Ref 17, 21): Mn+ O= MnO (Eq 16) Therefore, the overall cupola desulfurization reaction is: CaO + S+ Mn= CaS + MnO (Eq 17) Considerably lower sulfur could be achieved (Ref 14) if h O were governed by: C+ O= CO (Eq 18) However, equilibrium for this reaction has not been observed. This discussion has concerned CaS-unsaturated slags. However, a desulfurizing slag, saturated with CaS, can in many cases continue to desulfurize as long CaO is present. In this case, the ultimate sulfur levels are not as low as those for [...]... Desulfurization in an Iron-Producing Cupola, Trans AFS, Vol 92, 1984, p 16 1-1 72 22 C.F Landefeld and S Katz, Kinetics of Iron Desulfurization by CaO-CaF2, in Proceedings of the Fifth International Iron and Steel Congress, Vol 6, Iron and Steel Society of AIME, 1986, p 42 9-4 39 23 S Katz and C.F Landefeld, Plant Studies of Continuous Desulfurization with CaO-CaF2-C, Trans AFS, Vol 93, 1985, p 21 5- 22 8 24 S Katz and... Desulfurization in an Iron-Producing Cupola, Trans AFS, Vol 92, 1984, p 16 1-1 72 C.F Landefeld and S Katz, Kinetics of Iron Desulfurization by CaO-CaF2, in Proceedings of the Fifth International Iron and Steel Congress, Vol 6, Iron and Steel Society of AIME, 1986, p 42 9-4 39 S Katz and C.F Landefeld, Plant Studies of Continuous Desulfurization with CaO-CaF2-C, Trans AFS, Vol 93, 1985, p 21 5- 22 8 S Katz and B.L... the impurity Figure 21 and 22 plot p x2 versus hM, respectively, for reactions with chlorine and fluorine The oxide data were not included, because oxygen is much less effective than the halides (Ref 35) The data in Fig 21 and 22 assume aMmX2mx = 1 Fig 21 Calculated equilibria for the ternary Al-M-Cl system at 1000 K Source: Ref 35 Fig 22 Calculated equilibria for the ternary Al-M-F system at 1000 K... Press, 1988, p 26 1 -2 92 28 S.-H Kim and R.J Fruehan, Physical Modelling of Liquid/Liquid Mass Transfer in Gas Stirred Ladles, Metall Trans B, Vol 18B, 1987, p 38 1-3 90 29 J Ishida, K Yamaguchi, S Sugiura, N Demukai, and A Notoh, Denki Seiko, Vol 52, 1981, p 2- 8 30 E.T Turkdogan, Ladle Deoxidation, Desulfurization and Inclusions in Steel Part I: Fundamentals, Arch Eisenhüttenwes., Vol 54, 1983, p 1-1 0 31 E.T... equilibrium constant is: K 26 = ( a M m X 2 mx )l / m hM ( px 2 ) x (Eq 26 ) and the equilibrium X2 pressure is: ( a M X )1/ m m 2 mx px 2 = K 26 hM 1/ y (Eq 27 ) If px2 for an impurity element is less than px2 for the corresponding reaction with aluminum, then impurity removal is theoretically possible Conversely, if p x2 for the impurity element is greater than p x2 for aluminum, the aluminum... Press, 1988, p 26 1 -2 92 28 S.-H Kim and R.J Fruehan, Physical Modelling of Liquid/Liquid Mass Transfer in Gas Stirred Ladles, Metall Trans B, Vol 18B, 1987, p 38 1-3 90 29 J Ishida, K Yamaguchi, S Sugiura, N Demukai, and A Notoh, Denki Seiko, Vol 52, 1981, p 2- 8 30 E.T Turkdogan, Ladle Deoxidation, Desulfurization and Inclusions in Steel Part I: Fundamentals, Arch Eisenhüttenwes., Vol 54, 1983, p 1-1 0 31 E.T... coating on the CaO surface (Ref 23 , 24 ) A similar explanation, involving liquid-phase formation, was used to account for the higher CaO desulfurization rates of steel when aluminum was concurrently added (Ref 25 , 26 ) Fig 15 Desulfurization rates of carbon-saturated iron, containing 0.4% Si, with CaO and varying amounts of CaF2 at 1450 °C (26 40 °F) Source: Ref 22 Another rate-controlling variable in ladle... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 R.I.L Guthrie, Addition Kinetics in Steelmaking, in Proceedings of the 35th Electric Furnace Conference, Iron and Steel Society of AIME, 1978, p 3 0-4 1 F.A Mucciardi and R.I.L Guthrie, Aluminum Wire Feeding in Steelmaking, Trans ISS, Vol 3, 1983, p 5 3-5 9 J.W Robison, Jr., "Ladle Treatment With Steel-Clad Metallic Calcium Wire," Paper... exact values for [%O] or hO, equations for K 22 can be found in Ref 13 and 20 Fig 17 Deoxidation equilibria in liquid iron alloys at 1600 °C (29 10 °F) Source: Ref 30 As indicated by Eq 22 , the oxygen concentration can be reduced if a complex deoxidation product is formed so that aMxOy < 1 Common deoxidation systems of this type are Si-Mn, Al-Si-Mn, or Al-CaO An advantage, in addition to lower oxygen,... Molten Pig Iron, Trans Met Soc AIME, Vol 23 3, 1965, p 1 42 0-1 427 R.I.L Guthrie and P Stubbs, Kinetics of Scrap Melting in Baths of Molten Pig Iron, Can Metall Q., Vol 12, 1973, p 46 5-4 73 K Mori and T Sakuraya, Rate of Dissolution of Solid Iron in Carbon-Saturated Liquid Iron Alloys With Evolution of CO, J Iron Steel Inst Japan, Vol 22 , 19 82, p 96 4-9 90 P.T.L Brian and H.B Hales, Effects of Transpiration . CaO-15MgO-5Al 2 O 3 - 36SiO 2 1773 2. 7 5 1.3 90 0.13 B. cast iron cupola (ladle desulfurized) CaO sat -Al 2 O 3 1773 59 5 5.0 417 0. 027 C. cast iron electric CaO sat -Al 2 O 3 . oxygen X 2 gas: 22 1 mmx MxXMX m += (Eq 25 ) the equilibrium constant is: / 2 26 2 () () alm mmx x Mx MX K hp = (Eq 26 ) and the equilibrium X 2 pressure is: () 1/ 1/ 2 2 26 y m a mmx x M MX p Kh = . 10 -7 Cadmium 7.0 × 10 -6 Zinc 3.3 × 10 -4 Magnesium 1.3 × 10 -2 Lithium 3.4 × 10 -2 Lead 0.11 Bismuth 0.41 Calcium 39 Indium 110 Antimony 310 Source: Ref 35 Fig. 20