Oxygen pressure dependence of tracer diffusivities of ca and fe in liquid CaO-SiO2-FexO system

The tracer diffusivities of calcium and iron in a steel-making slag of 33 pct CaO-27 pct SiO₂-40 pct Fe₂O₃ by charge composition have been measured at 1360 to 1460°C as a function of temperature and oxygen pressure in the gas phase. The results expressed in cm₂/s (in SI unit of m₂/s, the following equation should be divided by 10,000) are given by $$D^{tr} = D_0 [P_{O_2 } ]^{1/x} \exp \left[ { - \frac{E}{{RT}}} \right] (at 1360 to 1460^\circ C)$$ where for tracer diffusion of iron,D _o is 0.2,x is 8.5, andE is 26 kcal/mol (1.09 x 10⁴ J/ mol) and for tracer diffusion of calcium,D _o is 0.1,x is 12.5, andE is 28 kcal/mol (1.17 x 10⁴ J/mol). Prior to diffusion runs, the slag was equilibrated with the gas mixture of carbon monoxide and dioxide with an oxygen pressure of 10^-1 to 10^-8 atm. The diffusivity was measured by the instantaneous plane source method, using radioactive tracers of calcium and iron. The increase of the tracer diffusivities with the oxygen pressure was interpreted in relation to a probable increase of the divalent cation vacancies in the slag.     

The self diffusion of iron in Fe2SiO4 and CaFeSiO4 melts

The self diffusion of iron in Fe₂SiO₄ and CaFeSiO₄ melts has been measured in the temperature range 1250° to 1540°C using Fe⁵⁹ as the radio tracer and the capillary-liquid reservoir method of diffusion measurement. The results obtained are represented by $$log D_{Fe} = - \frac{{3800 \pm 500}}{T} - 2.74 \pm 0.29$$ for Fe₂SiO₄, and $$log D_{Fe} = - \frac{{5450 \pm 620}}{T} - 1.93 \pm 0.37$$ for CaFeSiO₄. Excellent agreement is obtained with the self-diffusivity of iron calculated from the measured interdiffusivity of iron and oxygen in iron oxide melts.     

Interdiffusivities matrix of CaO-Al2O3-SiO2 melt at 1723 K to 1823 K

Ternary oxide mixtures of lime, alumina, and silica were premelted and quenched to produce glassy cylinders. A diffusion couple was selected from the mixtures of six different compositions in such a way that the average composition could be 40 wt pct CaO-20 wt pct A1₂O₃ = 40 wt pct SiO₂. Penetration curves of the components were measured with a X-ray microprobe analyzer. The interdiffusivities matrix defined with the Matano interface has been obtained from 52 successful diffusion runs at 1723 K to 1823 K as follows; 1 $$\begin{gathered} \tilde D_{10 - 10}^{30} = 8.9 \times 10^{ - 11} \exp ( - \frac{{253,700}}{{RT}})(m^2 /s) \hfill \\ \tilde D_{10 - 20}^{30} = - 2.5 \times 10^{ - 11} \exp ( - \frac{{194,300}}{{RT}})(m^2 /s) \hfill \\ \end{gathered} $$ 2 $$\begin{gathered} \tilde D_{20 - 10}^{30} = - 4.0 \times 10^{ - 11} \exp ( - \frac{{177,600}}{{RT}})(m^2 /s) \hfill \\ \tilde D_{20 - 20}^{30} = 6.12 \times 10^{ - 11} \exp ( - \frac{{318,400}}{{RT}})(m^2 /s) \hfill \\ \end{gathered} $$ where symbols, 10, 20, and 30 mean CaO, A1₂O₃, and SiO₂, respectively, and the activation energies are in Joules per mole. The diffusion composition paths obtained are discussed in relation to Cooper’s parallelogram. The composition dependency of the above interdiffusivities is estimated from the quasibinary interdiffusivities in all composition ranges of the present oxide system in liquid state.     

Interdiffusivities matrix of CaO-AI2O3-SiO2 melt at 1723 k to 1823 k

Ternary oxide mixtures of lime, alumina, and silica were premelted and quenched to produce glassy cylinders. A diffusion couple was selected from the mixtures of six different compositions in such a way that the average composition could be 40 wt pct CaO-20 wt pct AI₂O₃ = 40 wt pct SiO₂. Penetration curves of the components were measured with a X-ray microprobe analyzer. The interdiffusivities matrix defined with the Matano interface has been obtained from 52 successful diffusion runs at 1723 K to 1823 K as follows; $$ \begin{gathered} \tilde D_{10 - 10}^{30} = 8.9 \times 10^{ - 11} \exp \left( { - \frac{{253,700}} {{RT}}} \right)\left( {m^2 /s} \right) \hfill \\ \tilde D_{10 - 20}^{30} = - 2.5 \times 10^{ - 11} \exp \left( { - \frac{{194,300}} {{RT}}} \right)\left( {m^2 /s} \right) \hfill \\ \tilde D_{20 - 10}^{30} = - 4.0 \times 10^{ - 11} \exp \left( { - \frac{{177,600}} {{RT}}} \right)\left( {m^2 /s} \right) \hfill \\ \tilde D_{20 - 20}^{30} = 6.12 \times 10^{ - 11} \exp \left( { - \frac{{318,400}} {{RT}}} \right)\left( {m^2 /s} \right) \hfill \\ \end{gathered} $$ where symbols, 10, 20, and 30 mean CaO, A1₂O₃, and SiO₂, respectively, and the activation energies are in Joules per mole. The diffusion composition paths obtained are discussed in relation to Cooper’s parallelogram. The composition dependency of the above interdiffusivities is estimated from the quasibinary interdiffusivities in all composition ranges of the present oxide system in liquid state.     

Self-diffusion of copper in Cu−Al solid solutions

Self-diffusion coefficients of copper in Cu?Al solid solutions in the concentration interval 0 to 19 at. pct Al and in the temperature range 800° to 1040°C have been determined by the residual activity method using the isotope Cu⁶⁴. The values of the self-diffusion coefficients in the concentration interval 0 to 14.5 at. pct Al satisfy the Arrhenius relation and their temperature dependence can be expressed by the following equations $$\eqalign{ & D_{Cu}^{Cu} = \left( {0.43_{ - 0.11}^{ + 0.15} } \right) exp \left( { - {{48,500 \pm 700} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 2.80 at. pct Al}^{Cu} = \left( {0.46_{ - 0.16}^{ + 0.23} } \right) exp \left( { - {{48,000 \pm 900} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 5.50 at. pct Al}^{Cu} = \left( {0.30_{ - 0.07}^{ + 0.09} } \right) exp \left( { - {{47,000 \pm 600} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 8.83 at. pct Al}^{Cu} = \left( {0.46_{ - 0.09}^{ + 0.11} } \right) exp \left( { - {{47,100 \pm 500} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 11.7 at. pct Al}^{Cu} = \left( {0.61_{ - 0.13}^{ + 0.17} } \right) exp \left( { - {{47,200 \pm 600} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 14.5 at. pct Al}^{Cu} = \left( {4.2_{ - 1.5}^{ + 2.2} } \right) exp \left( { - {{51,110 \pm 1000} \over {RT}}} \right) cm^2 /\sec \cr} $$ An analysis of the results leads to the conclusion that, in the concentration interval 0 to 11.7 at. pct Al, the frequency factor and activation enthalpy concentration dependences can be described by the following equations whereD _0Cu ^Cu and ΔH _Cu ^Cu are diffusion characteristics for self-diffusion in pure copper,X _Al is the atomic percent of aluminum, andK andB are experimental constants.     

Effect of Slag Composition on the Concentration of Al2O3 in the Inclusions in Si-Mn-killed Steel

The thermodynamic equilibria between CaO-Al₂O₃-SiO₂-CaF₂-MgO(-MnO) slag and Fe-1.5 mass pct Mn-0.5 mass pct Si-0.5 mass pct Cr melt was investigated at 1873 K (1600 °C) in order to understand the effect of slag composition on the concentration of Al₂O₃ in the inclusions in Si-Mn-killed steels. The composition of the inclusions were mainly equal to (mol pct MnO)/(mol pct SiO₂) = 0.8(±0.06) with Al₂O₃ content that was increased from about 10 to 40 mol pct by increasing the basicity of slag (CaO/SiO₂ ratio) from about 0.7 to 2.1. The concentration ratio of the inclusion components, \( {{X_{{{\text{Al}}_{2} {\text{O}}_{3} }} \cdot X_{\text{MnO}} } \mathord{\left/ {\vphantom {{X_{{{\text{Al}}_{2} {\text{O}}_{3} }} \cdot X_{\text{MnO}} } {X_{{{\text{SiO}}_{2} }} }}} \right. \kern-0pt} {X_{{{\text{SiO}}_{2} }} }} \) , and the activity ratio of the steel components, \( {{a_{\text{Al}}^{2} \cdot a_{\text{Mn}} \cdot a_{\text{O}}^{2} } \mathord{\left/ {\vphantom {{a_{\text{Al}}^{2} \cdot a_{\text{Mn}} \cdot a_{\text{O}}^{2} } {a_{\text{Si}} }}} \right. \kern-0pt} {a_{\text{Si}} }} \) , showed a good linear relationship on a logarithmic scale, indicating that the activity coefficient ratio of the inclusion components, \( {{\gamma_{{{\text{SiO}}_{2} }}^{i} } \mathord{\left/ {\vphantom {{\gamma_{{{\text{SiO}}_{2} }}^{i} } {\left( {\gamma_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{i} \cdot \gamma_{\text{MnO}}^{i} } \right)}}} \right. \kern-0pt} {\left( {\gamma_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{i} \cdot \gamma_{\text{MnO}}^{i} } \right)}} \) , was not significantly changed. From the slag-steel-inclusion multiphase equilibria, the concentration of Al₂O₃ in the inclusions was expressed as a linear function of the activity ratio of the slag components, \( {{a_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{s} \cdot a_{\text{MnO}}^{s} } \mathord{\left/ {\vphantom {{a_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{s} \cdot a_{\text{MnO}}^{s} } {a_{{{\text{SiO}}_{2} }}^{s} }}} \right. \kern-0pt} {a_{{{\text{SiO}}_{2} }}^{s} }} \) on a logarithmic scale. Consequently, a compositional window of the slag for obtaining inclusions with a low liquidus temperature in the Si-Mn-killed steel treated in an alumina ladle is recommended.     

A mass-spectrometric study of the thermodynamics of the Fe−Cu and Fe−Cu−C(sat) systems at 1600°C

The Knudsen cell-mass spectrometer combination has been used to study the Fe?Cu and Fe?Cu?C_(sat) alloys at 1600°C. Activity coefficients in the Fe?Cu system are closely represented by the equations $$\begin{gathered} \ln \gamma _{Fe} = 1.86N_{Cu}^2 + 0.03, (0< N_{Fe}< 0.7) \hfill \\ \ln \gamma _{Cu} = 2.25N_{Fe}^2 - 0.19, (0.7< N_{Fe}< 1.0) \hfill \\ \end{gathered} $$ with an uncertainty in the quadratic terms of about 5 pct. For the iron-rich carbon-saturated alloys, the activity coefficient of copper is given by the equation $$\ln \gamma _{Cu} = 2.45(N'_{Fe} )^2 + 0.3N'_{Fe} + 0.03, (0< N'$$ to within an uncertainty of about 10 pct. N _Fe ^′ represents the fraction N_Fe/(N_Fe+N_Cu), etc. The activity coefficient of iron in this region is found to be essentially constant at 0.69±0.05.     

Distribution Ratios of Phosphorus Between CaO-FeO-SiO<Subscript>2</Subscript>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/Na<Subscript>2</Subscript>O/TiO<Subscript>2</Subscript> Slags and Carbon-Saturated Iron

In order to effectively enhance the efficiency of dephosphorization, the distribution ratios of phosphorus between CaO-FeO-SiO₂-Al₂O₃/Na₂O/TiO₂ slags and carbon-saturated iron (\( L_{\text{P}}^{\text{Fe-C}} \)) were examined through laboratory experiments in this study, along with the effects of different influencing factors such as the temperature and concentrations of the various slag components. Thermodynamic simulations showed that, with the addition of Na₂O and Al₂O₃, the liquid areas of the CaO-FeO-SiO₂ slag are enlarged significantly, with Al₂O₃ and Na₂O acting as fluxes when added to the slag in the appropriate concentrations. The experimental data suggested that \( L_{\text{P}}^{\text{Fe-C}} \) increases with an increase in the binary basicity of the slag, with the basicity having a greater effect than the temperature and FeO content; \( L_{\text{P}}^{\text{Fe-C}} \) increases with an increase in the Na₂O content and decrease in the Al₂O₃ content. In contrast to the case for the dephosphorization of molten steel, for the hot-metal dephosphorization process investigated in this study, the FeO content of the slag had a smaller effect on \( L_{\text{P}}^{\text{Fe-C}} \) than did the other factors such as the temperature and slag basicity. Based on the experimental data, by using regression analysis, \( \log L_{\text{P}}^{\text{Fe-C}} \) could be expressed as a function of the temperature and the slag component concentrations as follows:

$$ \begin{aligned} \log L_{\text{P}}^{\text{Fe-C}} & = 0.059({\text{pct}}\;{\text{CaO}}) + 1.583\log ({\text{TFe}}) - 0.052\left( {{\text{pct}}\;{\text{SiO}}_{2} } \right) - 0.014\left( {{\text{pct}}\;{\text{Al}}_{2} {\text{O}}_{3} } \right) \\ \, & \quad + 0.142\left( {{\text{pct}}\;{\text{Na}}_{2} {\text{O}}} \right) - 0.003\left( {{\text{pct}}\;{\text{TiO}}_{2} } \right) + 0.049\left( {{\text{pct}}\;{\text{P}}_{2} {\text{O}}_{5} } \right) + \frac{13{,}527}{T} - 9.87. \\ \end{aligned} $$

     

Thermal Conductivity Measurements of Some Synthetic Al2O3-CaO-SiO2 Slags by Means of a Front-Heating and Front-Detection Laser-Flash Method

The thermal conductivities of some synthetic slags containing Al₂O₃, CaO, and SiO₂ have been determined in the temperature range between 1623?K (1350?°C) and 1823?K (1550?°C) by applying a front-heating front-detection laser-flash method. In this method, the temperature response curve is measured in the short initial time period immediately after irradiating a laser pulse. The resultant values obtained by this method are unaffected by the radiative heat transfer. The temperature dependence of the thermal conductivity values were found not to be significant for all slag samples currently investigated. The thermal conductivity (??) of samples is represented with standard deviation less than 2?pct of its value as a function of compositions as follows: $$ \lambda = - 0.48\left[ {{\text{Al}}_{ 2} {\text{O}}_{ 3} } \right] - 0.57\left[ {\text{CaO}} \right] - 0.55\left[ {{\text{SiO}}_{2} } \right] + 57.1{\text{ W m}}^{ - 1} {\text{ K}}^{ - 1} $$ where [Al₂O₃], [CaO], and [SiO₂] are molar percent of Al₂O₃, CaO and SiO₂, respectively. The equation is suggested to cover the region of the following compositions: 8.0?mol pct < Al₂O₃ <21.0?mol pct, 31.5?mol pct < CaO <41.5?mol pct and 43.0?mol pct < SiO₂ <58.1?mol pct. The addition of Al₂O₃ to slags with a constant CaO/SiO₂ molar ratio resulted in an increase in thermal conductivity. In contrast, the effects of addition of SiO₂ and CaO are found to be insignificant.     

Thermodynamics of iron oxide in Fe x O-dilute CaO+Al2O3+Fe x O fluxes at 1873 K

The distribution of iron between Fe _x O-dilute CaO+Al₂O₃+Fe _x O fluxes and Pt+Fe alloys, as well as the redox equilibrium of iron ions in these fluxes, was experimentally investigated in pressure-controlled CO₂/CO gas at 1873 K. Total iron content in flux (pct Fe ^T ) and the ratio of (pct Fe²⁺) to (pct Fe ^T ) in fluxes with constant can be related to the activity of iron, α _Fe, and the partial pressure of oxygen, a _Fe, using the following equation:

Iron redox equilibria in CaO-Al2O3-SiO2 and MgO-CaO-Al2O3-SiO2 slags

Measurements have been made of the ratio of ferric to ferrous iron in CaO-Al₂O₃-SiO₂ and MgO-CaO-Al₂O₃-SiO₂ slags at oxygen activities ranging from equilibrium with pCO₂/pCO≈0.01 to as high as air at temperatures of 1573 to 1773 K. At 1773 K, values are given by $\begin{gathered} \log {\text{ }}\left( {\frac{{Fe^{3 + } }}{{Fe^{2 + } }}} \right) = 0.3( \pm {\text{ }}0.02){\text{ }}Y + {\text{ }}0.45( \pm {\text{ }}0.01){\text{ }}\log \hfill \\ \left( {\frac{{pCO_2 }}{{pCO}}} \right) - 1.24( \pm {\text{ }}0.01) \hfill \\ \end{gathered} $ where Y=(CaO+MgO)/SiO₂, for melts with the molar ratio of CaO/SiO₂=0.45 to 1.52, 10 to 15 mol pct Al₂O₃, up to 12 mol pct MgO (at CaO/SiO₂≈1.5), and with 3 to 10 wt pct total Fe. Available evidence suggests that, to a good approximation, these redox equilibria are independent of temperature when expressed with respect to pCO₂/pCO, probably from about 1573 to 1873 K. Limited studies have also been carried out on melts containing about 40 mol pct Al₂O₃, up to 12 mol pct MgO (at CaO/SiO₂≈1.5), and 3.6 to 4.7 wt pct Fe. These show a strongly nonideal behavior for the iron redox equilibrium, with $\frac{{Fe^{3 + } }}{{Fe^{2 + } }} \propto \left( {\frac{{pCO_2 }}{{pCO}}} \right)^{0.37} $ The nonideal behavior and the effects of basicity and Al₂O₃ concentration on the redox equilibria are discussed in terms of the charge balance model of alumino-silicates and the published structural information from Mössbauer and NMR (Nuclear Magnetic Resonance) spectroscopy of quenched melts.     

Influence of chromium and nickel on the dissociation of CO2 on carbon-saturated liquid iron

At 1600 °C, under conditions where the rate was not significantly affected by liquid-phase or gasphase mass transfer, the rate of dissociation of CO₂ was determined from the rate of decarburization of iron-based carbon-saturated melts containing varying amounts of chromium and nickel. The rate was determined by monitoring the change in reacted gas composition with an in-line spectrometer. The results indicate that neither chromium nor nickel had a strong effect on the kinetics of dissociation of CO₂ on the surface of the melt. Sulfur was found to significantly decrease the rate, as is the case for alloys without chromium or nickel, and the rate constant is given by $$k = \frac{{k^0 }}{{1 + K_s a_s }} + k_r $$ where k ⁰ denotes the chemical rate on pure iron, K _s is the adsorption coefficient of sulfur, a _s is the activity of sulfur corrected for Cr, and k _r represents the residual rate at a high sulfur level. The rate constants and adsorption coefficient were determined to be: $$\begin{array}{*{20}c} {k^0 = 1.8 \times 10^{ - 3} mol/cm^2 s atm} \\ {k_r = 6.1 \times 10^{ - 5} mol/cm^2 s atm} \\ {K_s = 330 \pm 20} \\ \end{array} $$ Experiments run at lower carbon contents showed that only a very small quantity of chromium was oxidized, immediately forming a protective layer. However, this oxidation occurred at a higher carbon content (2 pct) than what was expected from the thermodynamics.     

Lattice and grain boundary diffusion of cerium and neodymium in nickel

Diffusion of cerium and neodymium in nickel has been studied by the serial sectioning technique using radioactive tracers¹⁴¹Ce and¹⁴⁷Nd, in the temperature ranges 700° to 1100°C for volume and 500° to 875°C for grain boundary diffusion respectively. Volume diffusivities can be expressed as: $$\begin{gathered} D_{Ce/Ni} = (0.66 \pm 0.18)\exp \left( { - \frac{{60,800 \pm 810}}{{RT}}} \right)cm^2 /\sec \hfill \\ D_{Nd/Ni} = (0.44 \pm 0.13)\exp \left( { - \frac{{59,820 \pm 830}}{{RT}}} \right)cm^2 /\sec \hfill \\ \end{gathered} $$ and grain boundary diffusivities by: $$\begin{gathered} Dg_{Ce/Ni} = 0.11\exp \left( { - \frac{{29,550}}{{RT}}} \right)cm^2 /\sec \hfill \\ Dg_{Nd/Ni} = 0.07\exp \left( { - \frac{{28,580}}{{RT}}} \right)cm^2 /\sec \hfill \\ \end{gathered} $$ Results of volume diffusion have been compared with those calculated from the theories of diffusion based on size and charge difference between the solute and the solvent atoms. Whipple and Suzuoka methods have been used to evaluate the grain boundary diffusion coefficients. Both the methods give similar results.     

Determination of diffusion coefficient of oxygen in γ-iron from measurements of internal oxidation in Fe-Al alloys

The internal oxidation of iron alloys containing between 0.069 and 0.274 wt pct aluminum was investigated in the temperature range from 1223 to 1373 K for the purpose of determining the diffusion coefficients in γ-iron as well as in the internal oxidation layer. A parabolic rate law is obeyed in the internal oxidation of the present alloys. The rate constant for penetration of the oxidation front, the oxide formed, and the concentration of aluminum in the oxidation layer were determined. Pronounced enrichment of aluminum in the oxidation layer was observed, resulting from the counterdiffusion of aluminum. The oxygen concentration at the specimen surface was determined by combining the thermodynamic data on the dissociation of FeO and the solution of oxygen in y-iron. The diffusion coefficient of oxygen in the internal oxidation layer,D _o ¹⁰ , was evaluated on the basis of the rate equation for internal oxidation.D _o ¹⁰ increases at a given temperature as the volume fraction of oxide,f ¹⁰, in the oxidation layer increases. The diffusion coefficient of oxygen in γ-iron,D _o, was determined by extrapolation ofD _o ¹⁰ = 0.D _o may be expressed as $$D_o = \left( {1.30\begin{array}{*{20}c} { + 0.80} \\ { - 0.50} \\ \end{array} } \right) \times 10^{ - 4} \exp \left[ { - \frac{{166 \pm 5(kJ \cdot mol^{ - 1} )}}{{RT}}} \right]m^2 \cdot s^{ - 1} .$$ D _o is close to the diffusion coefficients of carbon and nitrogen in γ-iron.     

The thermodynamic properties of liquid Fe−Si alloys

The thermodynamic properties of liquid Fe?Si alloys have been determined electrochemically by use of the following galvanic cells: $$\begin{gathered} Cr - Cr_2 O_3 (s)|ZrO_2 (CaO)|Fe - Si(l), SiO_2 (s) \hfill \\ Cr - Cr_2 O_3 (s)|ThO_2 (Y_2 O_3 )|Fe - Si(l), SiO_2 (s) \hfill \\ \end{gathered} $$ The free energy of formation of SiO₂ was measured and is ?139.0 and ?134.3 kcals per mole at 1500° and 1600°C, respectively. The activity coefficients of iron and silicon for the atom fraction of siliconN _Si<0.35 at 1600° and 1500°C can be represented by the quadratic formalism. $$\begin{gathered} \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.12 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.12 N_{Fe}^2 - 0.22} \\ \end{array} } \right\}1600^ \circ C (2912^ \circ F) \hfill \\ \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.50 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.50 N_{Fe}^2 - 0.13} \\ \end{array} } \right\}1500^ \circ C (2732^ \circ F) \hfill \\ \end{gathered} $$ The results indicate that an excess stability peak occurs at about the equimolar composition. Combining the heats of solution determined in this study with previous data indicates that the heats also follow the quadratic formalism. The partial molar heats, \(\bar L_{Si} \) and \(\bar L_{Fe} \) , are represented by $$\begin{gathered} \bar L_{Si} = - 31 N_{Fe}^2 - 4 kcals per mole \hfill \\ \bar L_{Fe} = - 31 N_{Si}^2 kcals per mole \hfill \\ \end{gathered} $$ ForN _Si less than 0.35 and by $$\begin{gathered} \bar L_{Si} = - 22 N_{Fe}^2 \hfill \\ \bar L_{Fe} = - 22 N_{Fe}^2 - 7.0 \hfill \\ \end{gathered} $$ forN _Fe less than 0.35. There is an inflection point in the transition region similar to an excess stability peak for the excess free energies. At 1600°C the ThO₂(Y₂O₃) electrolyte exhibited insignificant electronic conductivity at oxygen partial pressures as low as that in equilibrium with Si?SiO₂ (2×10^?16 atm).     

Enrichment Mechanism of Phosphate in CaO-SiO2-FeO-Fe2O3-P2O5 Steelmaking Slags

The phosphate-enrichment behavior has experimentally been investigated in CaO-SiO₂-FeO-Fe₂O₃-P₂O₅ steelmaking slags. The reaction ability of structural units in the slags has been represented the mass action concentration \( N_{i} \) from the developed ion and molecule coexistence theory (IMCT)- \( N_{i} \) model based on the IMCT. The defined enrichment possibility \( N_{{{\text{c}}i{\text{ {-}c}}j}} \) and enrichment degree \( R_{{{\text{c}}i{\text{{-}c}}j}} \) of solid solutions containing P₂O₅ from the developed IMCT- \( N_{i} \) model have been verified from the experimental results. The effects of binary basicity, the mass percentage ratio \( {{ ( {\text{pct Fe}}_{t} {\text{O)}}} \mathord{\left/ {\vphantom {{ ( {\text{pct Fe}}_{t} {\text{O)}}} { ( {\text{pct CaO)}}}}} \right. \kern-0pt} { ( {\text{pct CaO)}}}} \) , and mass percentage of P₂O₅ in the initial slags on phosphate-enrichment behavior in the slags has also been discussed. The results show that the P₂O₅ component can easily be bonded by CaO to form tricalcium phosphate 3 CaO·P₂O₅, and the formed 3CaO·P₂O₅ can react with the produced dicalcium silicate 2CaO·SiO₂ to generate solid-solution 2CaO·SiO₂-3CaO·P₂O₅ under fixed cooling conditions. The maximum value of the defined enrichment degree \( R_{{{\text{C}}_{ 2} {\text{S{-}}} {\text{C}}_{ 3} {\text{P}}}} \) of solid-solution 2CaO·SiO₂-3CaO·P₂O₅ is obtained as 0.844 under conditions of binary basicity as 2.5 and the mass percentage ratio \( {{ ( {\text{pct Fe}}_{t} {\text{O)}}} \mathord{\left/ {\vphantom {{ ( {\text{pct Fe}}_{t} {\text{O)}}} { ( {\text{pct CaO)}}}}} \right. \kern-0pt} { ( {\text{pct CaO)}}}} \) as 0.955 at fixed cooling conditions.     

Thermodynamic properties of Na2O-SiO2-CaO melts at 1000 to 1100 °C

The thermodynamic properties of Na₂O-SiO₂ and Na₂O-SiO₂-CaO melts have been measured using the galvanic cell Activities of Na₂O were calculated from the reversible emf of the cell. This is possible because the activity of Na₂O in the Na₂O-WO₃ liquid is known from previous work. Data for the binary Na₂O-SiO₂ system were obtained between 1000 and 1100 °C and for compositions ranging from 25 wt pct to 40 wt pct Na₂O. At 1050 °C, Log varied from approximately 10.2 at 25 wt pct Na₂O to approximately −8.3 at 40 wt pct Na₂O, the dependence with respect to composition being nearly linear. The Gibbs-Duhem equation was used to calculate the activities of SiO₂(s), and the integral mixing properties,G ^M, H^M, andS ^M, were derived. At the di-silicate composition,G ^M = −83 kJ/mol,H ^M = −41 kJ mol andS ^M = 33 J/mol K at 1000 °C. (Standard states are pure, liquid Na₂O and pure, solid tridymite.) The activity data are interpreted in terms of the polymeric nature of silicate melts. Activities of Na₂O in the Na₂O-CaO-SiO₂ system were measured for the 25, 30 and 35 wt pct Na₂O binary compositions with up to 10 wt pct CaO added. The addition of CaO caused an increase in the activity of Na₂O at constant . The experimental data agree well with the behavior predicted by Richardson’s ternary mixing model.     

Study of Reaction Between Slag and Carbonaceous Materials

The chemical interaction of a typical slag of EAF with three different carbon sources, coke, rubber-derived carbon (RDC), coke-RDC blend, was studied in atmospheric pressure at 1823 K (1550 °C). Using an IR-gas analyzer, off-gases evolved from the sample were monitored. While the coke-RDC blend exhibited the best reducing performance in reaction with molten slag, the RDC sample showed poor interaction with the molten slag. The gasification of the coke, RDC, and coke-RDC blend was also carried out under oxidizing conditions using a gas mixture of CO₂ (4 wt pct) and Ar (96 wt pct) and it was shown that the RDC sample had the highest rate of gasification step \( C_{0} \mathop{\longrightarrow}\limits{{k_{3} }}{\text{CO}} + nC_{\text{f}} \) (11.6 site/g s (×6.023 × 10²³/2.24 × 10⁴)). This may be attributed to its disordered structure confirmed by Raman spectra and its nano-particle morphology observed by FE-SEM. The high reactivity of RDC with CO₂ provided evidence that the Boudouard reaction was fast during the interaction with molten slag. However, low reduction rate of iron oxide from slag with RDC can be attributed to the initial weak contact between RDC and molten slag implying that the contact between carbonaceous matter and slag plays significant roles in the reduction of iron oxide from slag.     

Thermodynamics of iron oxide in Fe x O-dilute CaO + Al2O3 + MgO + Fe x O slags at 1873 K

In order to determine the ferrous and ferric ion capacities: 3