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.     

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.     

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.     

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 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     

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 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.     

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.     

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.     

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 investigation and thermodynamic calculation of the phase equilibria in the Cu-Sn and Cu-Sn-Mn systems

The phase equilibria in the Cu-rich portion of the Cu-Sn binary and Cu-Sn-Mn ternary systems have been determined using the diffusion-couple method, differential scanning calorimetry (DSC), high-temperature electron diffraction (HTED), and high-temperature X-ray diffraction (HTXRD) techniques. The present experimental results on the binary Cu-Sn system show the presence of the two-stage, second-order reaction A2 → B2 → D0₃ in the bcc-phase region, rather than a two-phase equilibrium between the disordered bcc (A2) and the ordered bcc (D0₃) phases, as reported before. Phase equilibria in the Cu-Sn-Mn ternary system in the composition range of 0 to 30 at. pct Sn and 0 to 30 at. pct Mn at 550 °C, 600 °C, 650 °C, and 700 °C have been determined, and a ternary compound (Cu₄MnSn) with a very small solubility has been detected. A thermodynamic analysis of the Cu-Sn-Mn ternary system including the Cu-Sn and Mn-Sn binary systems has also been carried out by the CALPHAD (Calculation of Phase Diagrams) method, in which the Gibbs energy of the bcc phase is described by the two-sublattice model in order to take into account the second-order A2/B2 ordering reaction. A consistent set of optimized thermodynamic parameters for the Cu-Sn-Mn system for describing the Gibbs energy of each phase results in a better fit between calculation and experiment.     

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.     

Computation of Ni-Cr phase diagramvia a combined first-principles quantum mechanical and CALPHAD approach

A first-principles quantum-mechanical computational code has been used to compute the energy of formation for selected ordered and topologically close-packed (TCP) phases in a Ni-base alloy. The thermodynamic data are incorporated into an existing database for Ni alloys and used in conjunction with the CALPHAD approach to compute the binary Ni-Cr phase diagram. In addition, a thermodynamic model is used to treat long-range ordering and the formation of the Ni₂Cr. The phase field for ordering is compared against that predicted by the Thermo-Calc to elucidate possible implications on the long-term phase stability of Ni-base alloys in a nuclear waste repository environment.     

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.     

Al2O3-V2O5体系的热力学优化

在对Al₂O₃-V₂O₅体系相图、热力学数据以及晶体结构数据进行综述与评估的基础上,采用相图计算方法对Al₂O₃-V₂O₅体系进行热力学优化.液相采用修正的似化学模型进行描述,利用对近似处理液相中存在的短程有序.将液相模型的最大短程有序设置在AlVO₄处,将VO₄3-当作液相中V₂O₅的基本组成单元.体系中AlVO₄相看作线性化合物.计算结果很好的重现了选定的实验数据,获得了一套合理、可靠、自洽的模型参数用来描述体系中各相的热力学性质,为Al₂O₃负载V₂O₅型催化剂催化性能的提高打下坚实的基础.