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.     

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.     

Thermodynamic assessment of the CaO-MgO-SiO2 system

The phase equilibrium and thermodynamic information of the CaO-MgO-SiO₂ system at 1 atm was reviewed and assessed by using thermodynamic models for the Gibbs energy of all the phases. The assessment was based on recent assessments of the CaO-MgO, CaO-SiO₂, and MgO-SiO₂ systems. Two thermodynamic models were used: the two-sublattice model for ionic liquids for the liquid phase, and the compound energy model for the solid solution phases. The model parameters were evaluated by fitting to the selected experimental data by means of a computer program, which can accommodate a variety of experimental data. A consistent set of parameters was obtained that sat-isfactorily described most of the experimental information. The models were found to be well-suited for the present system, and only a small number of adjustable parameters were needed. Extensive comparisons were made between the calculations and experimental data. Formerly Research Associate, Royal Institute of Technology     

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.     

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.     

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.     

Thermodynamic evaluation and optimization of the Li, Na, K, Mg, Ca//F, Cl reciprocal system using the modified quasi-chemical model

A complete critical evaluation of all available ternary reciprocal phase diagram data has been performed for all condensed phases of the LiF-LiCl-NaF-NaCl-KF-KCl-MgF₂-MgCl₂-CaF₂-CaCl₂ system and optimized model parameters have been found. The model parameters obtained for ternary reciprocal subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent reciprocal system. The modified quasi-chemical model in the quadruplet approximation was used for the molten salt phase. This model takes into account, simultaneously, both first-nearest-neighbor (FNN) and second-nearest-neighbor (SNN) short-range-ordering (SRO) and the coupling between them. The predictions are significantly better than those obtained with previous models.     

Thermodynamic evaluation and optimization of the MnO-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and MnO-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript> systems and applications to inclusion engineering

All available thermodynamic and phase-diagram data have been critically evaluated and optimized for the liquid-slag phase and for all solid phases at 1 bar pressure from 298 K to above the liquidus temperatures for the systems MnO-Al₂O₃ and MnO-Al₂O₃-SiO₂, and a database of model parameters has been prepared. The modified quasichemical model was employed for the molten-slag phase. Calculations using the database were performed with applications to inclusion engineering for Mn/Si killed steel.     

Thermodynamic optimization and calculation of phase diagrams of YbCl3-MCl (M=Na, K, Rb, Cs)

YbCl3-MCl (M = Na, K, Rb, Cs) systems were optimized and calculated using the CALPHAD (CALculation of PHAse Diagram) technique. The modified quasi-chemical model in the pair-approximation for short-range ordering was used to describe the Gibbs energies of liquid phase in the systems. On the basis of the measured phase diagram data and experimental thermodynamic properties, a series of thermodynamic functions were optimized and calculated through an interactive computer-assisted analysis. Furthermore, some reasonable discussions on the thermodynamic parameters for these strong interaction binary systems were carried out. The results showed that the optimized parameters and experimental data are thermodynamically self-consistent.     

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 Assessment of DyCl3-MCl （M= Na, K, Rb, Cs） Systems

Using the CALPHAD （Calculation of Phase Diagram） technique, the DyCl3-MCl （M = Na, K, Rb, Cs） systems were optimized and calculated. The modified quasi-chemical model in the pair approximation for short-range ordering was used to describe the Gibbs energies of the liquid phase in these systems. From the measured phase diagram data and experimental thermodynamic properties, a series of thermodynamic functions were optimized base on an interactive computer-assisted analysis. The optimized parameters and the experimental data were thermodynamically self-consistent. The optimized results were discussed.     

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.     

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.     

Thermodynamic assessment of the Nb-N system

The phase equilibrium and thermodynamic information of the Nb-N system was reviewed and assessed by using thermodynamic models for the Gibbs energy of individual phases. Although there was a large amount of experimental information of the system, heat capacity data of the Nb₂N and NbN were not available either in low or high temperatures. In the present study, low-temperature heat capacity and the^o S ₂₉₈ values were estimated using estimated entropy Debye temperatures. Only the Nb₂N (hcp) and NbN (fcc) nitrides were considered to be the true binary phases and were included in the present evaluation in addition to the N₂ gas, liquid, andα-solid solution (bcc). Three thermodynamic models were used: a two-sublattice model for the solid solution phases, a substitutional model for the liquid phase, and an ideal-gas model for the N₂ gas. The model parameters were evaluated by fitting to the selected data by means of a computer program. A consistent set of parameters was obtained which satisfactorily described most of the experimental and estimated data.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3-SiO2-CaO system

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃-SiO₂-CaO system from 298 K to above the liquidus temperatures at all compositions under reducing conditions and at low CaO concentrations under oxidizing conditions. All reliable data have been simultaneously optimized to obtain 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. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

An investigation of the thermodynamics of solvent extraction of metals I. Calculation of the activity coefficients of non-electrolytes in the UO2Cl2-TBP system

The possibility of calculating the thermodynamic equilibrium data in the metal extraction system UO₂Cl₂—TBP by using the existing theories of solution is discussed. A systematic thermodynamic approach for calculating component activity coefficients in the ternary organic phase is described. Seven models have been investigated and compared for calculation of the activity coefficients of non-electrolytes in organic phases. Among them, the Scatchard-Hildebrand model and Guggenheim quasi-lattice model are the most simple and convenient for practical use.     

The Ca(SO<Subscript>4</Subscript>)-Na<Subscript>2</Subscript>(SO<Subscript>4</Subscript>)-Ca<Subscript>3</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>2</Subscript>-Na<Subscript>3</Subscript>(AsO<Subscript>4</Subscript>) phase diagram

The phase diagram of the CaSO₄-Na₂SO₄-Ca₃(AsO₄)₂-Na₃(AsO₄) system was measured by differential thermal analysis and by an equilibration and quenching technique. Thermodynamic models were developed giving the Gibbs energies of all phases as functions of temperature and composition. Optimized model parameters were obtained by assessment of all available thermodynamic and phase equilibrium data. The models, which reproduce all the data within experimental error limits, were used to calculate the liquidus surface of the system. The modified quasi-chemical model in the quadruplet approximation was used for the liquid solution. For the various solid solution phases, the modified quasi-chemical model, which accounts simultaneously for short-range-ordering among first-nearest-neighbor (FNN) and second-nearest-neighbor (SNN) pairs, was used for the first time within the framework of the compound energy formalism. The distinction between true model parameters and formalism parameters is made. Implications of the work for the potential use of sulfate fluxes for copper refining are discussed.     

Experimental Study and Thermodynamic Optimization of the FeO-V_2O_3 System

Optimization of the phase diagram of FeO-V2O3 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 of experimental data for optimization,a novel experimental investigation has been carried out by thermal analysis(DSC)with a series of slags on different V2O3 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 Diagrams)methods to give one set of model equations for the Gibbs free energy of the liquid slag as functions of composition and temperature.The modified quasi-chemical model was used to describe the binary slag system.It was demonstrated that the calculated phase diagram with the optimized parameters was in good agreement with the experimental data.