Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the MnO-TiO2, MgO-TiO2, FeO-TiO2, Ti2O3-TiO2, Na2O-TiO2, and K2O-TiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the MnO-TiO₂, MgO-TiO₂, FeO-TiO₂, Ti₂O₃-TiO₂, Na₂O-TiO₂, and K₂O-TiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable thermodynamic and phase diagram data have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag as a function of composition and temperature and equations for the Gibbs energies of all compounds as functions of temperature. The modified quasichemical model was used for the molten slag phases.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CaO-Al2O3, Al2O3-SiO2, and CaO-Al2O3-SiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the CaO-Al₂O₃, Al₂O₃-SiO₂, and CaO-Al₂O₃-SiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable data for the binary systems have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. With these binary parameters and those from the optimization of the CaO-SiO₂ system reported previously, the quasichemical model was used to predict the thermodynamic properties of the ternary slag. Two additional small ternary parameters were required to reproduce the ternary phase diagram and ternary activity data to within experimental error limits. The calculated optimized phase diagram and thermodynamic properties are self-consistent and are the most reliable currently available estimates of the true values.     

Critical thermodynamic evaluation and optimization of the FeO-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>-MgO-SiO<Subscript>2</Subscript> system

A complete literature review, critical evaluation, and thermodynamic modeling of the phase diagrams and thermodynamic properties of all oxide phases in the FeO-Fe₂O₃-MgO-SiO₂ system at 1 bar total pressure are presented. Optimized model equations for the thermodynamic properties of all phases are obtained, which reproduce all available thermodynamic and phase-equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions and oxygen partial pressures. The complex phase relationships in the system have been elucidated, and discrepancies among the data have been resolved. The database of the model parameters can be used along with software for Gibbs-energy minimization in order to calculate all thermodynamic properties and any type of phase-diagram section. The modified quasichemical model was used for the liquid-slag phase. Sublattice models, based upon the compound-energy formalism, were used for the olivine, spinel, pyroxene, and monoxide solid solutions. The use of physically reasonable models means that the models can be used to predict thermodynamic properties and phase equilibria in composition and temperature regions where data are not available.     

A thermodynamic database for copper smelting and converting

The thermodynamic properties of the slag, matte, and liquid copper phases in the Cu-Ca-Fe-Si-O-S system have been critically assessed and optimized over the ranges of compositions of importance to copper smelting/converting based on thermodynamic and phase equilibria information available in the literature and using the modified quasichemical model. A thermodynamic database has been developed, which can be used for the calculation of matte-slag-copper-gas phase equilibria of interest for the production of copper. The model reproduces within experimental error limits all available experimental data on phase diagrams, matte-alloy miscibility gap and tie-lines, enthalpies of mixing, and activities of Cu and S in the matte and liquid alloy. The calculated solubilities of Cu in both S-free slag and slag equilibrated with matte are also in good agreement with experiment under all studied conditions, such as at SiO₂ saturation, in equilibrium with Fe, Cu, or Cu-Au alloys, at fixed oxygen or SO₂ partial pressures and at different contents of CaO in the slag. Sulfide contents (sulfide capacities) of the slags are predicted within experimental error limits from the modified Reddy-Blander model, with no adjustable parameters. As an example of the application of the database, the stability field of matte/slag equilibrium is calculated, and the matte and slag compositions are plotted vs iron to silica ratio in the slag at various SO₂ pressures over this field. The matte-slag two-phase field is limited by the calculated lines corresponding to precipitation of copper, silica, and magnetite.     

Thermodynamic optimization of the systems PbO-SiO2, PbO-ZnO, ZnO-SiO2 and PbO-ZnO-SiO2

Liquidus-phase equilibrium data of the present authors for the PbO-ZnO-SiO₂ system, combined with phase equilibrium and thermodynamic data from the literature, were optimized to obtain a self-consistent set of parameters of thermodynamic models for all phases. The modified quasichemical model was used for the liquid slag phase. From these model parameters, the optimized ternary-phase diagram was back-calculated.     

Experimental Study and Thermodynamic Optimization of the FeO-V203 System

Optimization of the phase diagram of FeO-V20a system is a part of an on-going research project to develop a self-consistent multi-component thermodynamic database for vanadium slag from hot metal. Due to the lack o{ ex- perimental data for optimization, a novel experimental investigation has been carried out by thermal analysis （DSC） with a series of slags on different V2 03 contents （i. e. 3mass%- 12mass%）. All available thermodynamic and phase diagram data for the binary systems have been simultaneously optimized with CALPHAD （Calculation of Phase Dia- grams） methods to give one set of model equations for the Gibbs free energy of the liquid slag as functions of compo- sition and temperature. The modified quasi-chemical model was used to describe the binary slag system. It was dem- onstrated that the calculated phase diagram with the optimized parameters was in good agreement with the experi- mental data.     

Thermodynamic modeling of lead distribution among matte, slag, and liquid copper

Recently, a thermodynamic database was developed for the calculation of equilibria involved in the production of copper. The present study is concerned with the further development of the thermodynamic models and the database of model parameters for the matte, slag, and blister copper phases with a view to including Pb in the database and permitting calculations in the seven-component system Pb-Cu-Ca-Fe-Si-O-S. Thermodynamic and phase equilibrium data available in the literature are reviewed, critically assessed, and optimized with the modified quasi-chemical model. When used with the Gibbs energy minimization software and other databases of the FACT thermodynamic computing system, the database developed in the present study can be used for the calculation of matte-slag-copper-gas phase equilibria during copper smelting and converting. The distribution of lead among these phases can be computed. For example, the distribution of lead among matte, silica-saturated slag, and copper has been calculated at metal saturation, or under fixed partial pressure of SO₂, and has been compared with the available experimental data. The Pb distributions among the equilibrium phases have been calculated under various conditions, which are difficult to study experimentally, such as at magnetite saturation or under various oxygen partial pressures and iron to silica ratios in the slag.     

Lead solubility in FeO x -CaO-SiO2 slags at iron saturation

Experiments have been carried out to determine the equilibria between FeO _x -CaO-SiO₂ slag and lead metal in iron crucibles at temperatures ranging from 1473 to 1573 K. It has been found that the highest lead solubilities are observed in the silica-saturated iron silicate slags, while the lowest solubilities are observed in the CaO-saturated calcium ferrite slags. The activity coefficient of PbO varies from 0.15 to 3, depending on the slag composition. Changes in temperature do not have a significant impact on the activity coefficient. The activity of FeO and pct Fe³⁺/pct Fe²⁺ ratios have been determined as a function of slag composition. These new experimental data have been incorporated into an optimized thermodynamic slag model using the computer package FACT.     

The Effect of MgO on the Viscosity of the CaO‐SiO2‐20 wt%Al2O3‐MgO Slag System

The viscosities of CaO‐SiO₂‐20 wt%Al₂O₃‐MgO slags (CaO/SiO₂ = 1.0–1.2, wt%MgO = 5–13) were measured to estimate the effect of MgO on the viscous behaviour at elevated temperatures. The slag viscosity at 1773 K decreased with increasing MgO contents, which was typical of a basic oxide component at relatively low basicity (CaO/SiO₂) of 1.0. The FT‐IR spectroscopic analysis of the slag structure seems to verify this behaviour. However, an unexpected contradiction with the temperature dependence was observed above 10 wt%MgO and above CaO/SiO₂ of 1.2. Although the apparent activation energy was expected to decrease with additions of the basic oxide component MgO, the apparent activation energy increased. This unexpected behaviour seems to be related to the change in the primary phase field correlating to the phase diagram corresponding to the slag composition. Therefore, in order to understand the viscosity at both high Al₂O₃ and MgO, not only should the typical depolymerization of the slag structure with high MgO content be considered but also the primary phases of which the molten slag originates.     

Effect of the Heat Treatment on the Chromium Partition in CaO-MgO-SiO2-Cr2O3 Synthetic Slags

Mg-spinel phase is known to be important for control of Cr leaching from Cr-containing slags. The objective of the present study is to get an understanding of the phase relationships in the CaO-MgO-SiO₂-Cr₂O₃ system with a view to control the precipitation of Cr-spinel in the slag phase. The equilibrium phases in CaO-MgO-SiO₂-Cr₂O₃ slag system in the range of 1673 K to 1873 K (1400 °C to 1600 °C) have been investigated experimentally and compared with the results from thermodynamic calculations. The slag compositions close to the industrial slag systems were chosen. The Cr₂O₃ and MgO contents in the slag were fixed to be 6 and 8 wt pct, respectively. The basicity (CaO/SiO₂) of the slag was varied in the range of 1.0 to 2.0. The slags were synthesized at a pre-determined oxygen partial pressure (10^?4) or air (2.13 × 10⁴ Pa) at a temperature above the liquidus temperature. The samples were then soaked at targeted temperatures for 24 hours in controlled atmosphere in order to achieve the equilibrium state before quenching in water. Four different heat-treatment regimes (defined as Ia, Ib, II.a and II.b) in Section II–D) were used in the present experiments. The lower oxygen partial pressure was maintained by a suitable mixture of CO and CO₂ gases. Phases present and their compositions in the quenched slags were studied using scanning electron microscopy coupled with energy-dispersive spectroscopy and X-ray diffraction techniques. The chromium content in the phases present was analyzed using wavelength-dispersive spectrometer. The experimental results obtained are compared with the calculation results from Factsage software. The size of spinel crystals increased drastically after slow-cooling from 1873 K (1600 °C) followed by annealing at 1673 K (1400 °C) for 24 hours (heating regimes II) compared to samples being quenched directly after soaking at 1873 K (1600 °C) (heating regime I.a). It was found that the amount of foreign elements in the spinel phase, and other phases decreased after soaking at oxygen partial pressure of 10^?4 Pa resulting in phases with less defects and foreign oxide contents compared to those treated in air. The size of spinel crystals was found to be larger in samples with lower basicity.     

Experimental studies of the viscosities in the CaO-Fe n O-SiO2 slags

In the present work, the viscosities in the CaO-Fe _n O-SiO₂ ternary system have been measured by the rotating cylinder method involving a spindle and crucible made of iron. Nine slag compositions in the ternary system have been chosen with CaO varying between 5.5 and 45.5 pct mass, FeO between 10.0 and 70.0 pct mass, and one measurement each in the binary Fe _n O-SiO₂ and CaO-SiO₂ melts. The measurements have been carried out in the temperature range of 1423 to 1753 K. The viscosity in this system is described as a function of temperature and composition using the model approach developed earlier at the present laboratory. The isoviscosity lines have been predicated at 1573, 1673, and 1723 K. Good agreement between the calculated results and the experimental data has been obtained.     

Thermodynamic evaluation and optimization of the LiF-NaF-KF-MgF2-CaF2 system using the modified quasi-chemical model

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the LiF-NaF-KF-MgF₂-CaF₂ system and optimized model parameters have been found. The model parameters obtained for binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The modified quasi-chemical model for short-range ordering (SRO) was used for the molten salt phase. For solutions with NaF or KF together with MgCl₂ or CaCl₂, the calculations indicate a large degree of ordering on the cationic sublattice, with Mg-alkali and Ca-alkali second-nearest-neighbor (SNN) pairs being favored.     

Investigation of Liquidus Temperatures and Phase Equilibria of Copper Smelting Slags in the FeO-Fe2O3-SiO2-CaO-MgO-Al2O3 System at PO2 10?8?atm

Copper concentrates and fluxes can contain variable levels of SiO₂, CaO, and MgO in addition to main components Cu, Fe, and S. Metal recovery, slag tapping, and furnace wall integrity all are dependent on phase equilibria and other properties of the phases and are functions of slag composition and operational temperature. Optimal control of the slag chemistry in the copper smelting, therefore, is essential for high recovery and productivity; this, in turn, requires detailed knowledge of the slag phase equilibria. The present work provides new phase equilibrium experimental data in the FeO-Fe₂O₃-SiO₂-CaO-MgO-Al₂O₃ system at oxygen partial pressure of 10⁻⁸ atm within the range of temperatures and compositions directly relevant to copper smelting. For the range of conditions relevant to the Kennecott Utah Copper (South Magna, UT) smelting furnace, it was confirmed experimentally that increasing concentrations of MgO or CaO resulted in significant decreases of the tridymite liquidus temperature and in changes in the position of the tridymite liquidus in the direction of higher silica concentration; in contrast, the spinel liquidus temperatures increase significantly with the increase of MgO or CaO. Olivine and clinopyroxene precipitates appeared at high MgO concentrations in the liquid slag. The liquidus temperature in the spinel primary phase field was expressed as a linear function of 1/(wt pctFe/wt pctSiO₂), wt pctCaO, wt pctMgO, and wt pctAl₂O₃. The positions of each of the liquidus points (wt pctFe)/(wt pctSiO₂) at a fixed temperatures in the tridymite primary phase field were expressed as linear functions of wt pctCaO, wt pctMgO, and wt pctAl₂O₃.     

Thermodynamic evaluation and optimization of the LiCl-NaCl-KCl-RbCl-CsCl-MgCl2-CaCl2 system using the modified quasi-chemical model

A complete critical evaluation of all available phase-diagram and thermodynamic data has been performed for all condensed phases of the LiCl-NaCl-KCl-RbCl-CsCl-MgCl₂-CaCl₂ system, and optimized model parameters have been found. The model parameters obtained for binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The modified quasi-chemical model for short-range ordering was used for the molten salt phase. Particularly in solutions with MgCl₂ and KCl, RbCl, or CsCl, the calculations indicate a large dregree of ordering on the cationic sublattice, with Mg-Alkali second-nearest-neighbor pairs being favored.     

Modeling of viscosities of the partly crystallized slags in the Al2O3-CaO-“FeO”-SiO2 system

A viscosity model of the partly crystallized slag in the Al₂O₃-CaO-‘FeO’-SiO₂ system has been developed in conjunction with the thermodynamic computer package F*A*C*T. Proportions of solids crystallized out of the liquid phase and compositions of the remaining liquid phase predicted by F*A*C*T are used in the viscosity model. Various heterogeneous viscosity models have been tested using large experimental dataset in the Al₂O₃-CaO-‘FeO’-SiO₂ system in reducing conditions close to the equilibrium with metallic iron. The Roscoe equation with new empirical parameters was found to provide reasonable agreement with experimental data. Examples of model application to industrial nonferrous smelting slag systems are presented. This model can also be applied to coal ash slags.     

Review of experimental data and modeling of the viscosities of fully liquid slags in the Al2O3-CaO-‘FeO’-SiO2 system

A general model based on the Urbain formalism has been developed, which enables the viscosities of liquid slags to be predicted for all compositions in the Al₂O₃-CaO-‘FeO’-SiO₂ system in equilibrium with metallic iron. Available experimental viscosity data have been analyzed and critically reviewed. The Urbain formalism has been modified to include compositional dependent model parameters. Experimental data in unaries, binaries, ternaries, and the quaternary system have been described by the model over the whole compositional and temperature ranges using one set of model parameters. This viscosity model can now be applied to various industrial slag systems.     

Computer simulation of equilibrium relations in managanese ferroalloy production

The complex heterogeneous equilibria associated with the production of manganese ferroalloys have been simulated using recently developed thermochemical databases. Over 600 measured equilibrium data have been used to verify and calibrate the model calculations. Good agreement is obtained for many important technical relations such as carbon solubility, equilibrium diagrams and phase relations, and element distribution as a function of temperature and composition. Experimental slag/metal and slag/metal/gas equilibria in MnO-SiO₂ binary, MnO-SiO₂-CaO and MnO-SiO₂-Al₂O₃ ternary, MnO-SiO₂-CaO-Al₂O₃ quaternary, and MnO-SiO₂-CaO-Al₂O₃-MgO quinary systems can be reproduced within experimental uncertainties. The influence of temperature, CO partial pressure, and slag chemistry on the Mn- and Si-distribution equilibria has been quantitatively evaluated. This leads to a sound basis for optimizing the manganese ferroalloy production processes.     

Kinetics of Reduction of CaO-FeO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>-MgO-PbO-SiO<Subscript>2</Subscript> Slags by CO-CO<Subscript>2</Subscript> Gas Mixtures

Kinetics of the reaction of lead slags (PbO-CaO-SiO₂-FeO _x -MgO) with CO-CO₂ gas mixtures was studied by monitoring the changes in the slag composition when a stream of CO-CO₂ gas mixture was blown on the surface of thin layers of slags (3 to 10 mm) at temperatures in the range of 1453 K to 1593 K (1180 °C to 1320 °C). These measurements were carried out under conditions where mass transfer in the gas phase was not the rate-limiting step and the reduction rates were insensitive to factors affecting mass transfer in the slag phase. The results show simultaneous reduction of PbO and Fe₂O₃ in the slag. The measured specific rate of oxygen removal from the melts varied from about 1 × 10^?6 to 4 × 10^?5 mol O cm^?2 s^?1 and was strongly dependent on the slag chemistry and its oxidation state, partial pressure of CO in the reaction gas mixture, and temperature. The deduced apparent first-order rate constant increased with increasing iron oxide content, oxidation state of the slag, and temperature. The results indicate that under the employed experimental conditions, the rate of formation of CO₂ at the gas-slag interface is likely to be the rate-limiting step.     

A thermodynamic model of nickel smelting and direct high-grade nickel matte smelting processes: Part II. distribution behaviors of Ni, Cu, Co, Fe, As, Sb, and Bi

A thermodynamic model has been developed to predict the distribution behavior of Ni, Cu, Co, Fe, S, As, Sb, and Bi in nickel smelting and direct high-grade nickel matte smelting processes. The model has been validated by numerous experimental data and industrial data with a wide range of operating conditions. The effect of operating conditions on the distributions of Ni, Cu, Co, As, Sb, and Bi among the gas, matte, and slag phases has been investigated. It was found that the distribution behavior of Ni, Co, Cu, As, Sb, and Bi in the nickel smelting furnace depends on process parameters such as the smelting temperature, matte grade, oxygen enrichment, Fe/SiO₂ ratio in the slag, Cu/Ni ratio in charge, and oil/air ratio. The parameters also have an influence on the behavior of Fe₃O₄ in the slag.     

Kinetics of chromium oxide reduction from a basic steelmaking slag by silicon dissolved in liquid iron

The reduction of chromium oxide from a basic steelmaking slag (45 wt pct CaO, 35 wt pct SiO₂, 10 wt pct MgO, 10 wt pct A1₂O₃) by silicon dissolved in liquid iron at steelmaking temperatures was studied to determine the rate-limiting steps. The reduction is described by the reactions: (Cr₂O₃) + Si = (SiO₂) + (CrO) + Cr [1] and 2 (CrO) +Si = (SiO₂) + 2 Cr [2] The experiments were carried out under an argon atmosphere in a vertical resistance-heated tube furnace. The slag and metal phases were held in zirconia crucibles. The course of the reactions was followed by periodically sampling the slag phase and analyzing for total chromium, divalent chromium, and iron. Results obtained by varying stirring rate, temperature, and composition defined the rate-limiting mechanism for each reaction. The rate of reduction of trivalent chromium (reaction [1] above) increases with moderate increases in stirring of the slag, and increases markedly with increases in temperature. The effects of changes in composition identified the rate-limiting step for Cr⁺³ reduction as diffusion of Cr⁺³ from the bulk slag to the slag-metal interface. The rate of reduction of divalent chromium does not vary with changes in stirring of the slag, but increases in temperature markedly increase the reaction rate. Thus, this reaction is limited by the rate of an interfacial chemical reaction. The reduction of divalent chromium is linearly dependent on concentration of divalent chromium, but is independent of silicon content of the metal phase.