Effect of carbon and sulphur on the surface tension of molten iron

Surface tensions of Fe‐4%C‐S alloys were measured at 1623 and 1823 K using the sessile drop technique. Thermodynamic models based on Butler's equation for surface tension of liquid alloys have been compared with experimental results. Calculated values are found to be in good agreement with those of the experimental data of the system. At the same sulphur activity, the effect of carbon on the surface tension of Fe‐C‐S alloys was found to extrude only when the sulphur content was less than 0.005 %.     

Thermodynamics of surfaces and adsorption in the Fe-O and Fe-O-N systems at 1823 K

The present investigation calculates the surface tension and adsorption functions of the Fe-O and Fe-O-N melts at 1823 K using the modified form of Butler’s equations and the derived values of the surface interaction parameters of the systems. The calculated values are found to be in good agreement with those of the experimental data of the systems. The present analysis indicates a characteristic saturation behavior of oxygen in the Fe-O system at 1823 K, whereas a linear adsorption behavior is observed in the Fe-N system. An inverse relationship in the adsorption behavior, which exists between oxygen and nitrogen in the Fe-O-N system, is similar to that observed in our earlier study of the Fe-S-N system.     

Thermodynamics of surfaces and adsorption in the Fe-S, Fe-N, and Fe-S-N systems at 1823 K

The present investigation calculates the surface tension and adsorption functions of the Fe-S, Fe-N, and Fe-S-N melts at 1823 K using the modified form of Butler’s equations and the derived values of the surface interaction parameters of the systems. The calculated values are found to be in good agreement with those of the experimental data of the systems. The present analysis indicates similar adsorption behavior of sulfur for the Fe-S and Fe-S-N systems at 1823 K. Although a linear adsorption behavior is observed in the Fe-N system, an inverse relationship in the adsorption behavior exists between sulfur and nitrogen in the Fe-S-N system.     

Applicability of butler’s equation in interpreting the thermodynamic behavior of surfaces and adsorption in Fe-S-O melts

Expressions for various second-order derivatives of surface tension with respect to composition at infinite dilution in terms of the interaction parameters of the surface and those of the bulk phases of dilute ternary melts have been presented. A method of deducing the parameters, which consists of repeated differentiation of Butler’s equations with subsequent application of the appropriate boundary conditions, has been developed. The present investigation calculates the surface tension and adsorption functions of the Fe-S-O melts at 1873 and 1923 K using the modified form of Butler’s equations and the derived values for the surface interaction parameters of the system. The calculated values are found to be in good agreement with those of the experimental data of the system. The present analysis indicates that the energetics of the surface phase are considerably different from those of the bulk phase. The present research investigates a critical compositional range beyond which the surface tension increases with temperature. The observed increase in adsorption of sulfur with consequent desorption of oxygen as a function of temperature above the critical compositional range has been ascribed to the increase of activity ratios of oxygen to sulfur in the surface relative to those in the bulk phase of the system.     

Surface Tension of Liquid Fe-O Alloys: Revisiting Belton’s Two-Step Adsorption Model

The effect of oxygen adsorption on the surface tension of liquid iron was investigated using the constrained drop method. Experiments were carried out at 1823 K and 1873 K (1550 °C and 1600 °C) under a CO₂-H₂ gas mixture. The experimental results were interpreted using the Langmuir ideal adsorption model and Belton’s two-step adsorption model; the latter model showed better agreement with the experimental results. According to the two-step model, the surface tension of liquid Fe-O alloys at 1823 K and 1873 K (1550 °C and 1600 °C) can be respectively expressed as follows: $$ \sigma = 1882 - 260[0.25\ln (1 + 2407a_{\text{O}} ) + 0.75\ln (1 + 72a_{\text{O}} )]\quad \left[ {T = 1823\,{\text{K}}\left( {1550\,^\circ {\text{C}}} \right)} \right], $$ $$ \sigma = 1834 - 267[0.25\ln (1 + 1445a_{\text{O}} ) + 0.75\ln (1 + 46a_{\text{O}} )]\quad \left[ {T = 1873\,{\text{K}}\left( {1600\,^\circ {\text{C}}} \right)} \right]. $$      

A Chemical Approach of the Molecular Entity Vacancy Model to the CaO‐Al2O3‐SiO2 Ternary Silicate Melt

A chemical approach of the molecular entity vacancy model (MEVM) to the CaO‐Al₂O₃‐SiO₂ ternary silicate melts has been suggested. The activities of all components in the melts were simultaneously predicted by using only the binary parameters of its sub‐binary melts which were determined by fitting the activities of their two components. The results indicated that the predicted values of activity of SiO₂ were in good agreement with the experimental data at both temperatures 1823 K and 1873 K, and those of CaO and Al₂O₃ were in reasonable agreement with the experimental data at 1823 K and were smaller than the graphical integration data of the Gibbs‐Duhem equation at 1873 K. The approach may be extended to some solution systems with the chemical interaction.     

Viscosities of the Quaternary Al2O3‐CaO‐MgO‐SiO2 Slags

Viscosities of some quaternary slags in the Al₂O₃‐CaO‐MgO‐SiO₂ system were measured using the rotating cylinder method. Eight different slag compositions were selected. These slag compositions ranging in the high basicity region were directly related to the secondary steel making operations. The measurements were carried out in the temperature range of 1720 to 1910 K. Viscosities in this system and its sub‐systems were expressed as a function of temperature and composition based on the viscosity model developed earlier at KTH. The iso‐viscosity contours in the Al₂O₃‐CaO‐MgO‐SiO₂ system relevant to ladle slags were calculated at 1823 K and 1873 K for 5 mass% MgO and 10 mass% MgO sections. The predicted results showed good agreement with experimental values and the literature data.     

Thermodynamic calculations for Nb-containing high-speed steels and white-cast-iron alloys

Thermodynamical equilibria have been calculated for a wide variety of high-speed steel compositions belonging to the multicomponent system Fe-C-W-Mo-V-Cr-Nb as well as for two series of white-cast-iron alloys containing niobium. Some temperature-concentration diagrams for both classes of alloys are presented and calculated quantities (melting and transformation temperatures, amounts and compositions of phases) are compared with experimental data. Good agreement between calculated and experimental information has been obtained, with the exception of the MC phase compositions and transformation temperatures for white-cast-iron alloys with high carbon and chromium contents. These differences can, however, be satisfactorily explained by plausible kinetic effects.     

A Pseudo-Multicomponent Approach to Important Ternary Silicate Melts

For the CaO-Al₂O₃-SiO₂, CaO-FeO-SiO₂, and MnO-FeO-SiO₂ ternary silicate melts, there are few models that can accurately predict their component activities. One model that can make a good correlation between the ternary activities and their sub-binary ones is a pseudo-multicomponent approach based on the molecular interaction volume model (MIVM). It does not need any linear or power series composition functions of binary parameters and also does not require any ternary adjustable parameters in addition to its composition equation. The results show that in the CaO-Al₂O₃-SiO₂ system, the predicted values of SiO₂ activity are in good agreement with the experimental data at 1873?K (1600?°C), and those of CaO and Al₂O₃ are in reasonable agreement with the graphical integration of data using the Gibbs?CDuhem equation at 1873?K (1600?°C) and experimental data at 1823?K (1550?°C). In the CaO-FeO-SiO₂ and MnO-FeO-SiO₂ systems, the predicted values of FeO and MnO activity are in good agreement with the experimental data, and those of CaO and SiO₂ are in reasonable agreement with the experimental data at 1823?K, 1873?K, and 1803?K (1550?°C, 1600?°C, and 1533?°C).     

Aluminum deoxidation equilibrium in liquid Ni-Fe alloys equilibrated with CaO-Al2O3 slags

The deoxidation equilibrium for Al in Ni-Fe alloys was studied in the equilibrium experiments between CaO-Al₂O₃ slags and Fe-30, 50 and 70 % Ni alloys at 1873 K. By using the values for the first and second order interaction parameters between oxygen and nickel in liquid iron and those between oxygen and iron in liquid nickel, the effect of Ni on the activity coefficient of Al in liquid iron and that of Fe on the activity coefficient of Al in liquid nickel were determined in the whole composition range of Ni-Fe alloys. The oxygen contents in Ni-Fe alloys calculated by the iterative method based on pure iron were in good agreement with those based on pure nickel in the range of [% Al] < 0.03. From this fact, it was found that the Wagner's approximation relating to the multi-component solution was applicable to the deoxidation equilibrium in the whole composition range of Ni-Fe alloys in the restricted concentration of a deoxidizer.     

Surface tension of liquid Fe-Cr-O alloys at 1823 K

The surface tension of liquid Fe-Cr-O alloys has been determined by using the sessile drop method at 1823 K. It was found that the surface tension of liquid Fe-Cr-O alloy markedly decreases with oxygen content at constant chromium content, and the surface tension at a given oxygen content remains almost constant, regardless of the chromium content. When the surface tension of liquid Fe-Cr-O alloys is plotted as a function of oxygen activity, with an increase in the chromium content, the surface tension shows a much steeper decrease with respect to oxygen activity. The surface tension of liquid Fe-Cr-O alloys at 1823 K is given as follows: σ=1842-279 ln (1+K _O a _O). Here, assuming a Langmuir-type adsorption isotherm, the adsorption coefficient of oxygen, K _O(Fe-Cr), as a function of chromium content, was shown to be K _O=140+4.2 × [wt pct Cr]+1.14 × [wt pct Cr]².     

Density and Surface Tension of Liquid Fe-Mn Alloys

The density and surface tension of liquid Fe-Mn alloys were determined by using the sessile drop method at 1823  K (1550 °C). The density of liquid Fe-Mn alloys decreased with increasing Mn content. When the molar volume was plotted with respect to the mole fraction of Mn, a linear relationship was obtained. Consequently, it was found that there is no excess volume in liquid Fe-Mn alloy. The surface tension of liquid Fe-Mn alloys was found to decrease with increasing Mn content. The current experimental data were higher than the reported results but close to the calculated results using Butler’s equation.     

Si Al、Si Ba和Al Ba二元合金熔体组元活度的计算

 根据Miedema二元合金生成热模型，结合相关热力学数据，对硅钙钡系中的各二元合金在1 873 K下的活度进行计算。结果表明，采用该模型对Si Al合金活度的计算结果与实测结果吻合较好；并对Si Ba和Al Ba合金熔体1 873 K下各组元的活度进行了计算，为含钡合金的成分设计和生产提供理论依据。     

Problem of the thermodynamic properties of liquid aluminum alloys with scandium

The standard enthalpies of formation of intermetallic compounds in the Al-Sc system are calculated using a well-known semiempirical model. The determined values agree satisfactorily with the most reliable experimental data. The thermodynamic simulation made it possible to calculate the equilibrium characteristics for Al-Sc liquid alloys in the temperature range from 1873 to 2073 K.     

Application of a thermodynamic database to the calculation of surface tension for iron-base liquid alloys

Thermodynamic models based on Butler's equation for surface tension of liquid alloys has been discussed. In alloys, in which activities of components deviate largely from Raoult's law, the calculated surface tensions are found to be affected by the selection of the ratio of the coordination number in the surface phase to that in the bulk phase. Then, the surface tension of liquid Fe-Al, Fe-Co, Fe-Cr, Fe-Mn, Fe-Mo, Fe-Ni, Fe-Si, Fe-Ti and Fe-W binary alloys and liquid Fe-Cr-Ni ternary alloys have been calculated from thermodynamic data in a database constructed by Kaufman. The calculated results reproduce the concentration dependence of the surface tension in those alloys reported so far, but their absolute values are dependent upon the selection of surface tension values for pure elements.     

Thermodynamic Activities of “FeO” in some Binary “FeO”‐Containing Slags

In the present investigation, experimental measurements of the thermodynamic activities of iron oxide in the Al₂O₃‐“FeO”, CaO‐“FeO” and “FeO”‐SiO₂ systems were performed in the temperature range 1823‐1873 K by using gas equilibration technique. The molten slag, kept in a Pt‐crucible was brought to equilibrium with a gas mixture of known oxygen partial pressure. A part of the Fe from the “FeO” was reduced during the equilibration and got dissolved in the Pt phase. The samples were quenched after the required equilibration time and the slag phase as well as the platinum crucible was subjected to chemical analysis. The activities of “FeO” in the slag were calculated from the experimental data using thermodynamic information on the Fe‐Pt binary metallic system generated and assessed earlier. The experimental results are compared with earlier thermodynamic studies of the slag systems. Reassessment with the KTH slag model is performed and the results are compared with other thermodynamic models, viz. F*A*C*T? and Thermo‐Calc? respectively. The experimental activities predicted by the KTH slag model are in good agreement with the experimental data available in the literature. A general agreement between the various models is also observed.     

Prediction of activities of three components in the ternary molten slag CaO-FeO-SiO2 by the molecular interaction volume model

In this article, a novel thermodynamic model—the molecular interaction volume model (MIVM)—was employed to predict the activities of three components in the ternary molten slag CaO-FeO-SiO₂ at different temperatures. The results show that the predicted values of activity of CaO and SiO₂ are in reasonable agreement with the experimental data in a range of lower concentrations, which are about x _CaO<0.2 for CaO and about x _{SiO 2}=0.15 to 0.50 for SiO₂ at 1823 K, respectively, and that the predicted values of activity of FeO are in good agreement with the experimental data in a range of entire concentrations at 1623, 1823, and 1873 K. This shows that MIVM is an alternative for the estimation of activity coefficients of all components in a ternary molten slag, where its activity data are absent or their accuracies are questionable only when its sub-binary activities are known and reasonably reliable.     

Mullite as an electrochemical probe for the determination of low oxygen activity in liquid iron

Oxygen activities in liquid iron deoxidized with aluminium were measured at 1873 K, using a mullite electrolyte having a Cr-Cr₂O₃ reference mixture. These results were compared with those obtained using commercial tube-type ZrO₂-8 mol% MgO and plug-type ZrO₂-9 mol% MgO probes, along with oxygen activities calculated from analysis. Oxygen activities from EMF measurements using mullite and plug-type probes were found to be in agreement with those calculated from the Al /AI₂O₃ equilibrium and those estimated from analyzed oxygen contents. Polarization effect due to electrochemical oxygen transport was observed in a commercial tube-type ZrO₂-based probe. Supersaturation in liquid iron deoxidized with aluminium was also measured at 1873 K.     

Partitioning of Calcium Between Liquid Silver and Liquid Iron

The partitioning of calcium between liquid silver and liquid iron at 1823 K and 1873 K (1550 °C and 1600 °C) was studied experimentally using a closed molybdenum container. The calcium potential in the container was controlled by the composition of the alloys in equilibrium. The results agreed well with previous experimental measurements and indicated that the effect of temperature was not very pronounced in the temperature range studied.     

Theoretical Calculations of the Surface Tension of Liquid Transition Metals

The surface tension of pure liquid mercury in the temperature range 273 K to 523 K (0 °C to 250 C°) was calculated using our previously reported equation. The results were compared with the experimental data and showed a good agreement. The surface tension of mercury decreases linearly with temperature, confirming a negative slope, and therefore shows the usual linear temperature dependence. The calculated surface excess entropy (0.21) is in excellent consistence with the experimental value (0.22). The surface tension also was calculated for many d-block metals (Ti, Zr, Fe, Co, Ni, Cu, Zn, Cd, Ag, Au, Pd, and Pt) at their melting points. The calculated values were compared with the existing experimental data.