A Thermodynamic Model of Sulfur Distribution Ratio between CaO–SiO<Subscript>2</Subscript>–MgO–FeO–MnO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript> Slags and Molten Steel during LF Refining Process Based on the Ion and Molecule Coexistence Theory

A thermodynamic model for calculating the sulfur distribution ratio between ladle furnace (LF) refining slags and molten steel has been developed by coupling with a developed thermodynamic model for calculating the mass action concentrations of structural units in LF refining slags, i.e., CaO–SiO₂–MgO–FeO–MnO–Al₂O₃ hexabasic slags, based on the ion and molecule coexistence theory (IMCT). The calculated mass action concentrations of structural units in CaO–SiO₂–MgO–FeO–Al₂O₃–MnO slags equilibrated or reacted with molten steel show that the calculated equilibrium mole numbers or mass action concentrations of structural units or ion couples, rather than mass percentage of components, in the slags can represent their reaction abilities. The calculated total sulfur distribution ratio shows a reliable agreement with the measured or the calculated sulfur distribution ratio between the slags and molten steel by other models under the condition of choosing oxygen activity based on (FeO)–[O] equilibrium. Meanwhile, the developed thermodynamic model for calculating sulfur distribution ratio can quantitatively determine the respective contribution of free CaO, MgO, FeO, and MnO in the LF refining slags. A significant difference of desulfurization ability among free component as CaO, MgO, FeO, and MnO has been found with approximately 87–93 pct, 11.43–5.85 pct, 0.81–0.60 pct and 0.30–0.27 pct at both middle and final stages during LF refining process, respectively. A large difference of oxygen activity is found in molten steel at the slag–metal interface and in bulk molten steel. The oxygen activity in molten steel at the slag–metal interface is controlled by (FeO)–[O] equilibrium, whereas the oxygen activity in bulk molten steel is controlled by [Al]–[O] equilibrium. Decreasing the high-oxygen-activity boundary layer beneath the slag–metal interface can promote the desulfurization reaction rate effectively or shorten the refining period during the LF refining process.     

A Thermodynamic Model of Phosphorus Distribution Ratio between CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags and Molten Steel during a Top–Bottom Combined Blown Converter Steelmaking Process Based on the Ion and Molecule Coexistence Theory

A thermodynamic model for calculating the phosphorus distribution ratio between top–bottom combined blown converter steelmaking slags and molten steel has been developed by coupling with a developed thermodynamic model for calculating mass action concentrations of structural units in the slags, i.e., CaO-SiO₂-MgO-FeO-Fe₂O₃-MnO-Al₂O₃-P₂O₅ slags, based on the ion and molecule coexistence theory (IMCT). Not only the total phosphorus distribution ratio but also the respective phosphorus distribution ratio among four basic oxides as components, i.e., CaO, MgO, FeO, and MnO, in the slags and molten steel can be predicted theoretically by the developed IMCT phosphorus distribution ratio prediction model after knowing the oxygen activity of molten steel at the slag–metal interface or the Fe _t O activity in the slags and the related mass action concentrations of structural units or ion couples in the slags. The calculated mass action concentrations of structural units or ion couples in the slags equilibrated or reacted with molten steel show that the calculated equilibrium mole numbers or mass action concentrations of structural units or ion couples, rather than the mass percentage of components, can present the reaction ability of the components in the slags. The predicted total phosphorus distribution ratio by the developed IMCT model shows a reliable agreement with the measured phosphorus distribution ratio by using the calculated mass action concentrations of iron oxides as presentation of slag oxidation ability. Meanwhile, the developed thermodynamic model for calculating the phosphorus distribution ratio can determine quantitatively the respective dephosphorization contribution ratio of Fe _t O, CaO + Fe _t O, MgO + Fe _t O, and MnO + Fe _t O in the slags. A significant difference of dephosphorization ability among Fe _t O, CaO + Fe _t O, MgO + Fe _t O, and MnO + Fe _t O has been found as approximately 0.0 pct, 99.996 pct, 0.0 pct, and 0.0 pct during a combined blown converter steelmaking process, respectively. There is a great gradient of oxygen activity of molten steel at the slag–metal interface and in a metal bath when carbon content in a metal bath is larger than 0.036 pct. The phosphorus in molten steel beneath the slag–metal interface can be extracted effectively by the comprehensive effect of CaO and Fe _t O in slags to form 3CaO·P₂O₅ and 4CaO·P₂O₅ until the carbon content is less than 0.036 pct during a top–bottom combined blown steelmaking process.     

A Thermodynamic Model of Phosphate Capacity for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags Equilibrated with Molten Steel during a Top–Bottom Combined Blown Converter Steelmaking Process Based on the Ion and Molecule Coexistence Theory

A thermodynamic model for predicting the phosphate capacity of CaO-SiO₂-MgO-FeO-Fe₂O₃-MnO-Al₂O₃-P₂O₅ slags at the steelmaking endpoint during an 80-ton top–bottom combined blown converter steelmaking process has been developed based on the ion and molecule coexistence theory (IMCT). The phosphate capacity has a close relationship with the phosphate capacity index, whereas the logarithm of phosphate capacity is 12.724 greater than that of phosphate capacity index at 1873 K (1600 °C). The developed phosphate capacity prediction model can be also used to predict the phosphate capacity index with reliable accuracy compared with the measured and the predicted phosphate capacity index of the slags by other models in literatures. The results from the IMCT phosphate capacity prediction model show that the comprehensive effects of iron oxides and basic components control the dephosphorization reaction with an optimal ratio of (pct FeO)/(pct Fe₂O₃) as 0.62. The determined contribution ratio of Fe _t O, CaO + Fe _t O, MgO + Fe _t O, and MnO + Fe _t O to the phosphate capacity or phosphate capacity index of the slags is approximately 0.0 pct, 99.996 pct, 0.0 pct, and 0.0 pct, respectively. The generated 2CaO·P₂O₅, 3CaO·P₂O₅, and 4CaO·P₂O₅ as products of dephosphorization reactions accounts for 0.016 pct, 96.01 pct, and 3.97 pct of the phosphate capacity or phosphate capacity index of the slags, respectively.     

Sulfide capacity of CaO-CaF2-SiO2 slags

The sulfide capacityC _S ^2- = (pct S^2-) · (P _{O 2}/P _{S 2})^1/2) of CaO-CaF₂-SiO₂ slags saturated with CaO, 3CaO · SiO₂ or 2CaOSiO₂ was determined at 1200 °C, 1250 °C, 1300 °C, and 1350 °C by equilibrating molten slag, molten silver, and CO-CO₂ gas mixtures. Higher sulfide capacities were obtained for CaO-saturated slags. A drastic decrease was observed in those values when the ratio pct CaO/pct SiO₂ is less than 2. The sulfur partition between carbon-saturated iron melts and presently investigated slags was calculated by using the sulfide capacities obtained and the activity coefficient of sulfur in carbon-saturated iron, which was also experimentally determined. For slags saturated with CaO, partitions of sulfur as high as 10,000 were obtained at 1300 °C and 1350 °C. Correlations between the sulfide capacity and other basicity indexes such as carbonate capacity and theoretical optical basicity were also discussed. Formerly with the Department of Metallurgy, The University of Tokyo.     

The effect of CaF2 on the viscosities and structures of CaO-SiO2(-MgO)-CaF2 slags

The viscosities of CaO-SiO₂(-MgO)-CaF₂ slags were measured to clarify the effect of CaF₂ on the viscous flow of molten slags at high temperatures and the solidification behavior of slags. Furthermore, the infrared (IR) spectra of the quenched slags were analyzed to understand the structural role of CaF₂ in the modification of slag structure. The CaF₂ affects the critical temperature (T _CR) of the slags; that is, the higher the content of CaF₂, the lower the T _CR of the slags. It is suggested that some extent of undercooling as a driving force is needed for the precipitation of solid particles in the melt. In the composition of B (≡(mass pct CaO)/(mass pct SiO₂)) = 1.0, the T _CR was decreased about 150 to 200 K by addition of 10 mass pct MgO, while the T _CR was increased about 100 K by MgO addition at B = 1.3. The effect of CaF₂ on the viscous flow of molten slags can be understood based on a decrease in the degree of polymerization by F⁻ as well as by O²⁻ ions and this was confirmed by the IR spectra of the quenched slags. The relative intensity of the IR bands for [SiO₄]-tetrahedra with low NBO/Si decreased, while that of the IR bands for [SiO₄]-tetrahedra with high NBO/Si increased with increasing CaF₂ content. The decrease in viscosity of the CaO-SiO₂-MgO-CaF₂ (B = 1.0) system by CaF₂ addition was negligible, while the effect of CaF₂ on the viscosity was significant in the more basic system (B = 1.3).     

Solubility of nitrogen and carbon in CaO-Al2O3 melts in the presence of graphite

CaO-Al₂O₃ slags were melted in graphite crucibles under N₂–CO–Ar gas mixtures at 1600°C. The contents of total nitrogen, cyanide and total carbon of the slags were determined by chemical analyses of quenched samples taken by suction from the melt. The nitrogen is present in the melt as nitride N⁻³ ion and cyanide CN⁻¹ ion, and carbon as cyanide and carbide C ₂ ²⁻ ion. The equilibrium constants for the respective reactions were evaluated. It is found that the nitride capacity of the melt decreases whereas the cyanide and carbide capacities increase with increasing CaO/Al₂O₃ ratio.     

Activity of chromic oxide in the CaF2−CaO−Cr2O3 and the CaF2−Al2O3−Cr2O3 systems

The values of the activity of Cr₂O₃ in the slags based on the CaF₂−CaO−Cr₂O₃ and the CaF₂−Al₂O₃−Cr₂O₃ systems which may be used in the electroslag remelting (E.S.R.) process have been determined at 1450, 1500 and 1550°C by equilibrating the slags with Pt−Cr alloys of known chromium activity under known oxygen partial pressure and studying the equilibrium 2[Cr] alloy+3/2 O₂(g)=(Cr₂O₃)_slag. It was found that activity of Cr₂O₃ decreases with the addition of CaO and Al₂O₃ in the respective systems. In slags containing less than about 20 wt pct CaO and in the Al₂O₃ bearing slags, solutions of Cr₂O₃ showed a positive deviation from ideality and in slags containing more than 20 wt pct CaO, they showed a negative deviation. Both the authors were formerly with the Department of Metallurgy, University of Sheffield, England     

Thermodynamics of Arsenic in FeOx-CaO-SiO<Subscript>2</Subscript> Slags

The distribution of arsenic between calcium ferrite slag and liquid silver (wt pct As in slag/ wt pct As in liquid silver) with 22 wt pct CaO and between iron silicate slag with 24 wt pct SiO₂ and calcium iron silicate slags was measured at 1573 K (1300 °C) under a controlled CO-CO₂-Ar atmosphere. For the calcium ferrite slags, a broad range of oxygen partial pressure (10^–11 to 0.21 atm) was covered, whereas for the silicate slags, the oxygen partial pressure was varied from 10^–9 to 3.1 × 10^–7 atm. The measured relations between the distribution ratio of As and the oxygen partial pressure indicates that the oxidation state of arsenic in these slags is predominantly As³⁺ or AsO_1.5. The measured distribution ratio of arsenic between the calcium ferrite slag and the liquid silver was about an order of magnitude higher than that of the iron silicate slag. In addition, an increasing concentration of SiO₂ in the calcium-ferrite-based melts resulted in decreases in the distribution of arsenic into the slag. Through the use of measured equilibrium data on the arsenic content of the metal and slag in conjunction with the composition dependent on the activity of arsenic in the metal, the activity of AsO_1.5 in the slags was deduced. These activity data on AsO_1.5 show a negative deviation from the ideal behavior in these slags.     

On the Dissolution Behavior of Sulfur in Ternary Silicate Slags

Sulfur dissolution behavior, in terms of sulfide capacity (C _S), in ternary silicate slags (molten oxide slags composed of MO – NO – SiO₂, where M and N are Ca, Mn, Fe, and Mg), is discussed based on available experimental data. Composition dependence of the sulfur dissolution, at least in the dilute region of sulfur, may be explained by taking into account the cation–anion first-nearest-neighbor (FNN) interaction (stability of sulfide) and the cation–cation second-nearest-neighbor (SNN) interaction over O anion (oxygen proportions in silicate slags). When the Gibbs energy of a reciprocal reaction MO + NS = MS + NO is positive, the sulfide capacity of slags with virtually no SiO₂ or low SiO₂ concentration decreases as the concentration of MO increases. However, in some slags, as SiO₂ concentration increases, replacing NO by MO at a constant SiO₂ concentration may increase sulfide capacity when the basicity of NO is less than that of MO. This phenomenon is observed as rotation of iso-C _S lines in ternary silicate slags, and it is explained by simultaneous consideration of the stability of sulfide and oxygen proportions in the silicate slags. It is suggested that a solution model for the prediction of sulfide capacity should be based on the actual dissolution mechanism of sulfur rather than on the simple empirical correlation.     

Sulfide capacities of fayalite-base slags

The sulfide capacities of fayalite-base slags were measured by a gas-slag equilibration technique under controlled oxygen and sulfur potentials similar to those encountered in the pyrometallurgical processing of nonferrous metals. The oxygen pressure range was from 10^−9.5 to 10⁻¹¹ MPa and the sulfur pressure range from 10⁻³ to 10^−4.5 MPa, over a temperature range of 1473 to 1623 K. The slags studied were FeO-SiO₂ at silica saturation and those with addition of CaO, MgO, and Al₂O₃ to determine their effect on sulfide capacities. For these slags, the sulfide capacities were found to vary from 10^−3.3 to 10⁻⁵. The sulfide capacities increased with increasing temperature from 1473 to 1623 K. A comparison of the reported plant data on sulfur content of industrial slags shows good agreement with the present experimental results. The present data will be useful in estimating metal losses in slag due to metal sulfide entrainment in nonferrous smelters.     

Solubility of carbon in CaO-B2O3 and BaO-B2O3 slags

The solubility of carbon in molten CaO-B₂O₃ and BaO-B₂O₃ slags at high temperatures was measured to understand the dissolution mechanism of carbon into the slags. The B₂O₃-bearing slags, which have a wide range of liquids, at the temperature of interest have been applied to investigate the effect of basicity on the solubility of carbon from the saturation of acidic or basic components. The solubility of carbon, as a function of the composition of slags, shows a minimum value, and it is suggested that carbon dissolves by different mechanisms in the acidic and basic slags, respectively. From the infrared spectra measurements, the wave number indicating the B-C bond was found to be about 1150 cm⁻¹ in the acidic region of slags; hence, the incorporation of carbon into the borate network was confirmed qualitatively. The carbide capacity was compared to the nitride capacity, showing that the dissolutions of carbon and nitrogen into the slags are similar.     

The rate of reaction of solid iron with oxidized “FeO”-CaO-SiO2-Al2O3 slags at 1360 °C—the chemical diffusivity of iron oxide

Measurements have been made of the rate of reduction of oxidized iron oxide-containing 41CaO-38SiO₂-21Al₂O₃ (wt pct) slags at 1360 °C by a rotating disc of solid iron. For initial total iron concentrations of between 1.8 and 13.4 wt pct and rotation speeds up to 1000 rpm, the rate is shown to be determined by mass transfer in the liquid phase. The chemical diffusivity of iron oxide (in cm² s⁻¹) is found to be given by the empirical expression log D = −6.11 + 0.08 (wt pct Fe). It is concluded that the values of the diffusivity are for melts at close to iron saturation. It is shown that the available measurements of the diffusivity of iron oxide in liquid slags are consistent with increasing diffusivity with increasing state of oxidation, with about a tenfold increase between melts in equilibrium with iron and those in equilibrium with oxygen at 1 atm.     

Calculation and Analysis of Sulfide Capacities for CaO-Al2O3-SiO2-MgO-TiO2 Slags

The empirical models of sulfide capacity calculated by traditional optical basicity do not consider the charge compensation of alkaline metal ions to Al³⁺ in the molten slags, so that the deviations between the calculated values and measured ones of sulfide capacity are inevitable. The relation between sulfide capacity and the corrected optical basicity put forward by Mills considering the charge compensation was investigated. Combined with the relation between sulfide capacity and temperatures, a novel and accurate calculation model of sulfide capacity was proposed, which was applied to calculate the sulfide capacities of CaO-Al₂O₁-SiO₂-MgO and CaO-Al₂O₁-SiO₂-MgO-TiO₂ systems, where the sum of the CaO and MgO concentrations in the slags must be not lower than the Al₂O₃ concentration. It was also found that the calculated values were in a good agreement with the measured values, and the mean deviations were 2. 57% and 2. 65%, respectively.     

Effects of CaO, Al2O3, and MgO additions on the copper solubility, ferric/ferrous ratio, and minor-element behavior of iron-silicate slags

The effects of CaO, Al₂O₃, and MgO additions, singly or in combination, on the copper solubility, the Fe³⁺/Fe²⁺ ratio in slag, and on the minor-element behavior of silica-saturated iron silicate slags were examined at 1250 °C and a p _O2 of 10⁻¹² to 10⁻⁶ atm. The results indicated that copper solubility in slag was lowered with the addition of CaO, MgO, and Al₂O₃, in decreasing order. The Fe³⁺/Fe²⁺ ratio in the slag decreased with the additions, but this effect was smaller at lower oxygen potentials. The presence of small amounts (about 4 pct) of CaO, Al₂O₃, and MgO in the slag resulted in increased absorption of Bi and Sb into molten copper, but had a smaller effect at large additions (about 8 to 11 pct). The distribution behavior of Pb was a function of oxygen partial pressure, which indicates the oxidic dissolution of Pb in the slag as PbO, while the behavior of Bi, Sb, and As was found to be independent of oxygen potential, supporting the atomic (neutral) dissolution hypothesis of these elements in the slag. The distribution behavior of Pb and As was not significantly affected by the additions. The activity coefficients of Bi and Sb in the slags were determined to be as follows: (1) for no addition, γ _Bi=40 and γ _Sb=0.4; (2) for small additions (about 4.4 pct), γ _Bi=70 to 85 and γ _Sb=0.8; and (3) for large additions (about 8 to 11 pct), γ _Bi=60 to 75 and γ _Sb=0.5 to 0.7.     

Rate of interfacial reaction between molten CaO-SiO2-Al2O3-Fe x O and CO-CO2

Measurements of the rates of reduction of iron oxide from molten CaO-SiO₂-Al₂O₃-Fe _x O slags by Ar-CO mixtures have been made using a thermogravimetric method. The apparent first-order rate constant, with respect to the partial pressure of CO, of the gas/slag interfacial reaction was deduced from the measured rates, where the effects of the mass transfer in the gas and slag phases were minimized. It was found that the apparent first-order rate constant decreased with the concentration of ‘FeO’ from 100 to 20 wt pct, whereas it remained essentially constant in the range from 5 to 20 wt pct ‘FeO’. At a given iron oxide concentration, the reduction-rate constant increased significantly with an increase in the CaO/SiO₂ ratio. For fixed slag compositions, the reduction rate increased slightly with the oxidation state of the slags. When the rate constant is expressed in the form of k=k′(Fe³⁺/²⁺)^α, the values of α range from 0.15 to 0.25. The effect of temperature in the range from 1673 to 1873 K on the reduction rate of iron oxide in a 40.4CaO-40.4SiO₂-14.2Al₂O₃-5‘FeO’ (wt pct) slag was studied. The calculated activation energy, based on these results, is 165 kJ/mol.     

Activity of Chromium Oxide in CaO‐SiO2 based Slags at 1873 K

Thermodynamic properties of chromium oxides in molten slags are very important for optimization of stainless steel refining processes as well as reduction processes of chromium ores. The solubility of chromite into molten slags has been found to vary drastically with oxygen partial pressure and slag composition in the former studies by the authors. In the present study, activity data and redox equilibria of chromium oxides measured under moderately reducing conditions, P_O2= 6.95×10^?11 atm, at 1873 K are summarized. For the CaO‐SiO₂‐CrO_x system, the activity coefficient of chromium oxide increased with increasing basicity and the optimized slag composition for stainless steel refining is assessed as that saturated with CaCr₂O₄ and Cr₂O₃ using the phase relations determined. On the other hand, the presence of MgO and Al₂O₃ brings about different behaviour of chromium oxide activity and redox equilibria and the 44 mass per cent CaO ‐ 39 mass per cent SiO₂ ‐11 mass per cent Al₂O₃ ‐ 6 mass per cent MgO slag is recommended to reduce the chromium oxidation loss in the practical stainless steel refining process at 1873 K.     

The interdiffusivity matrix of Fe2O3-CaO-SiO2 melt at 1693 to 1773 K

The diffusion couple method was used at 1693 to 1773 °K on liquid slags with their average compositon of 20 wt pct Fe₂O −₃−35 wt pct CaO-45 wt pet SiO₂. After diffusion runs for 40 min, the samples have been quenched to glassy state. The samples were sectioned, polished, and analyzed by a X-ray micro analyzer. The diffusivities matrix obtained from the penetration curves can be expressed by the following equations,D ³⁰ ₁₀₋₁₀ = 3.27 exp (−50000―RT)(cm²/s)D ³⁰ ₁₀₋₂₀ = -11.1 exp (−50000―RT)(cm²/s)D ³⁰ ₂₀₋₁₀ = 8.30 exp (−56300―RT)(cm²/s)D ³⁰ ₂₀₋₂₀ = 11.5 exp (−56200―RT)(cm²/s) where 10, 20, and 30 mean Fe₂O₃, CaO and SiO₃, respectively and the activation energies are in Cal per mol. The elements obtained satisfy the restriction derived from the second law of thermodynamics. The diffusion-composition paths obtained are consistent with the Cooper's parallelogram.     

Calcium deoxidation and nitrogen distribution in liquid nickel equilibrated with CaO-Al2O3 slags

The Wagner’s first-ordere _o ^Ca and second-order (r _o ^Ca ) interaction parameters between Ca and O in liquid nickel were determined as −1220 and 1.35 x 105, respectively, at 1873 K in the equilibrium experiments between liquid nickel and CaO-Al₂O₃ slags in an A1₂O₃ or CaO crucible. The values fore _Ca ^O , (−3060), r _Ca ^o (8.47 × 105), r _Ca ^O,Ca (6.76 x 10⁵), and r _Ca ^O,Ca (6.76 x 105) were also estimated. Nitride capacities, C(_N), defined by (mass pct N)·P ₂ ^3/4 PskN₂1/2 were obtained by using the present results for nitrogen distribution ratio, L_N =(mass pct N)/[mass pct N], and the reported values for the activity of Al₂O₃.     

Vacuum distillation of copper matte to remove lead,arsenic, bismuth,and antimony

Vacuum-refining experiments were carried out on copper matte melts, containing 35 to 73 pct Cu, to measure the removal rates of lead, bismuth, arsenic, and antimony over the temperature range of 1373 to 1523 K under pressures in the range of 50 to 130 Pa. High rates of refining, controlled by mass transport in the liquid phase, were achieved for all impurities in melts containing up to 65 pct Cu and for chamber pressures less than 100 Pa. After 40 to 60 minutes of treatment, lead elimination was between 70 and 96 pct, bismuth elimination was between 88 and 98 pct, arsenic, elimination was between 60 and 93 pct, and antimony elimination was between 40 and 92 pct. The overall mass transfer coefficients for vacuum refining for the impurities considered fell in the range of 5×10⁻⁵ to 2×10⁻⁴ m s⁻¹. The values were insensitive to small changes in melt temperature but decreased with increasing pressure above 250 Pa. Also, the rates of refining were seen to be influenced by the sulfur and oxygen activity in the melt. The evaporation and subsequent elimination of the impurities were mathematically modeled by extending previously published models beyond consideration only of evaporation of monomers to consideration of the evaporation of monomers and dimer compounds. The model showed that due to the contributions to the refining by evaporation of each of the metallic, oxide, or sulfide vapor species, arsenic and antimony exhibited a maximum in refining rates atP _{o 2} andP _{s 2} potentials corresponding to matte grades of about 55 pct copper, whereas lead showed a minimum at about the same matte grade, and bismuth showed a continuously decreasing rate of refining with increasing matte grade. The model was also used to simulate the refining behavior of copper matte melts. An example of a commercial-scale operation is given.