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.     

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.     

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.     

Calculation of sulfide capacities of multicomponent slags

The Reddy-Blander model for the sulfide capacities of slags has been modified for the case of acid slags and to include A1₂O₃ and TiO₂ as components. The model has been extended to calculatea priori sulfide capacities of multicomponent slags, from a knowledge of the thermodynamic activities of the component oxides, with no adjustable parameters. Agreement with measurements is obtained within experimental uncertainty for binary, ternary, and quinary slags involving the components SiO₂-Al₂O₃-TiO₂-CaO-MgO-FeO-MnO over wide ranges of composition. The oxide activities used in the computations are calculated from a database of model parameters obtained by optimizing thermodynamic and phase equilibrium data for oxide systems. Sulfur has now been included in this database. A computing system with automatic access to this and other databases has been developed to permit the calculation of the sulfur content of slags in multicomponent slag/metal/gas/solid equilibria. Formerly Graduate Student with the Centre for Research in Computational Thermochemistry, Ecole Polytechnique.     

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.     

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.     

Activities of boron in the binary Fe-B,Co-B,and Cu-B melts

Activities of boron in the binary Fe-B, Co-B, and Cu-B melts have been directly determined by the electromotive force (emf) measurement. Boron-saturated liquid Cu-B alloy was used as the reference electrode and a ternary 28 wt pct Al₂O₃-29 wt pct B₂O₃-43 wt pct CaO oxide melt was used as the electrolyte. Deviations of the boron activities from Raoult's law have been found largely negative for the Fe-B and Co-B systems but largely positive for the Cu-B system. Boron activities calculated from the literature data have not been in good agreement with the measured data. Activities of iron, cobalt, and copper have been calculated from the obtained boron activities by means of the Gibbs-Duhem equation. Some modifications to the liquidus curves on the Fe-B and Co-B phase diagrams have been presented. M. YUKINOBU, formerly Graduate Student, Department of Metallurgy, The University of Tokyo S. GOTO, Professor, formerly with the Department of Metallurgy, The University of Tokyo     

Review and modeling of viscosity of silicate melts: Part I. Viscosity of binary and ternary silicates containing CaO, MgO, and MnO

A structurally related model for the calculation of the viscosity of silicate melts is proposed based on the general behavior of the viscosity of binary silicate melts. It relates viscosity to the degree of polymerization, as represented by the three types of oxygen in the melts. The model parameters for binary systems were optimized to give best fit to the experimental values. For ternary systems, it was assumed as a first approximation that the model parameters were linear functions of the parameters of the two binary silicate systems. The model has been applied to the CaO-SiO₂, MgO-SiO₂, and MnO-SiO₂ binary systems and the CaO-MgO-SiO₂ and CaO-MnO-SiO₂ ternary systems. Good agreement was obtained between calculated values and experimental data over the composition and temperature ranges in which experimental data exist. Comparison was made between the present model and the Urbain model. The present model has the capability of representing changes in viscosity due to substitution of cation species in silicate melts.     

The activity coefficient of oxygen in binary liquid metal alloys

The Wagner model with one energy parameter,h, for describing the effect of alloying elements on the activity coefficients of nonmetallic solutes in liquid metals is extended to have two energy parameters,h ₁andh ₂. The validity of both the Wagner one-parameter equation and the newly derived two-parameter equation is tested using data available in the literature for twelve ternary metal-oxygen systems. In order to have consistent thermodynamic data, all the relevant binary, as well as the twelve ternary metal-oxygen systems are evaluated using the same thermodynamic values for the reference materials which were used in carrying out the experimental measurements. It is found that the twoparameter equation is capable of quantitatively accounting for the compositional dependences of the activity coefficients of oxygen in all twelve ternary systems while the Wagner one-parameter equation is not. A correlation between the Wagner parameter,h, and the thermodynamic properties of the respective binary metal-oxygen and binary metals systems is found, from which the value of this parameter may be predicted without referring to any ternary data. Accordingly, the two-parameter equation is more useful in evaluating ternary experimental data while the Wagner one-parameter equation in connection with the correlation betweenh and binary data is capable of predicting ternary data without any experimental investigation in the ternary region. Based on the one-parameter and the two-parameter equations, theoretical equations for the first-order and second-order free energy interaction parameters,(∈ ₀ ^j )_sand(ρ ₀ ^j )_s, are derived in terms of the model parameters. The values of(∈ ₀ ^j )_s and(ρ ₀ ^j )_s for all the systems are derived and are found to vary linearly with the reciprocal of temperature. Furthermore, linear relationships between these two interaction parameters and their slopes with 1/T are found, from which the temperature dependence of the interaction parameters may be estimated in the absence of experimental data.     

The relative stabilities of Cr23C6/ Cr7C3/ and Cr3C2 and the phase relationships in ternary Cr-Mo-C system

The thermodynamic properties of CrC_6/23, CrC_3/7, CrC_2/3, and MoC_1/2 reported in the literature have been correlated with the relative stabilities of these carbide phases derived from ternary phase diagrams. On the basis of the free energy of formation for one of the carbides and the free energy changes for the various equilibria occurring in ternary Mo-Cr-C system at 1300°C, free energies of formation for the stable and unstable carbide phases have been obtained. Using this free energy data, a calculated ternary Mo-Cr-C phase diagram is presented which agrees well with the experimentally determined one.     

Investigation of the phase equilibria in the Sn-Bi-In alloy system

This article presents an investigation of the phase equilibria in the Sn-Bi-In ternary alloy system, performed both by theoretical and experimental methods. Following the regular solution model and a standard thermochemical calculation, a theoretical evaluation of the phase equilibrium in the entire ternary system is conducted. The thermodynamic parameters required for the calculation are initially obtained by fitting the model to existing data available from prior studies. The theoretical results are then validated and further improved by experimental work in which alloys with several critical compositions were chosen and examined. In the experimental work, differential scanning calorimetry (DSC), X-ray diffraction (XRD), and energy-dispersive X-ray (EDX) spectroscopy were jointly used to identify the transition temperatures and the phases in the microstructure. The resulting phase diagram agrees well both with the existing data and with the data from the current experiments. However, different from previous findings, this study finds a nonbinary nature of the Sn-BiIn and Sn-BiIn₂ quasi-binaries and nine invariant reactions, one eutectic, six peritectic and two peritectoid. The phase-reaction scheme (Scheil diagram), the liquidus projection, and the phase diagram, covering entire compositional ranges, are established.     

Thermodynamic assessment of the Cu-Ti-Zr system. I. Cu-Ti system

The CALPHAD method is used for the thermodynamic assessment of the Cu-Ti system that bounds the ternary Cu-Ti-Zr system, which is capable of forming amorphous alloys. The self-consistent parameters of thermodynamic models of the phases are obtained from data on the phase equilibria and thermodynamic properties of liquid alloys and intermetallic compounds. The Gibbs energy of the liquid phase is described using the associated ideal solution model. To describe the thermodynamic properties of the Cu₄Ti and CuTi intermetallic compounds with homogeneity range, sublattice models are used. The calculated phase diagram of the system and the thermodynamic properties of the phases are in good agreement with experimental data.     

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.     

An investigation of the thermodynamics of solvent extraction of metals II. Calculation of the activity coefficient of non-electrolytes in the UO2(NO3)2(C7H15)2SO system

The thermodynamic method used in Part I for evaluating activity coefficients of mixed non-electrolytes in the ternary organic phase of a metal extraction system has been extended successfully to a quaternary organic phase. Experimental and calculated results indicate that both the Scatchard-Hildebrand model and the Guggenheim quasi-lattice model are applicable for calculation of the activity coefficients in the organic phase of the (C₂H₁₅)₂SOC₆H₄(CH₃)₂UO₂(NO₃)₂ · 2 (C₇H₁₅)₂SOH₂O system.     

A study on the microstructural evolution of Al-25 at. pct V-12.5 at. pct M (M = Cu,Ni, Mn) powders by planetary ball milling

The alloying behavior of Al-25 at. pct V-12.5 at. pct M (M = Cu, Ni, Mn) by planetary ball milling of elemental powders hours as been investigated in this study. In Al₃V binary system, an amorphous phase was produced after 6 hours and the amorphous phase was mechanically crystallized after 20 hours. The large difference in the diffusivities between Al and V atoms in Al matrix results in the formation of the amorphous phase when the homogeneous distribution of all the elements in a powder was achieved at 6 hours. According to thermal analyses, the amorphous phase in the binary Al₃V was crystallized at 350 °C. The addition of ternary elements (Cu, Ni, Mn) increased the activation energy for the crystallization to D0₂₂ phase by interfering with the diffusion process. Therefore, ternary element addition improved the thermal stability of the amorphous structures. The amorphous phase in the 12.5 at. pct Ni added Al₃V was crystallized to D0₂₂ phase at 540 °C. The mechanical crystallization of the amorphous phase in the ternary element-added Al-V system either occurred later or was not observed during ball milling up to 100 hours. It is thought that the amorphous intermetallic compacts could be produced more easily in ternary element-added alloys by using an advanced consolidation method.     

Thermodynamic evaluation of the Cr-Ni-C system

Evaluation of thermodynamic parameters of the Cr-C and Cr-Ni-C systems has been made by using sublattice models. The Gibbs energies of formation of Cr₂₃C₆, Cr₇C₃, and Cr₃C₂ were reassessed from the experimental data. The interaction between chromium and carbon in the nickel-rich face-centered cubic (fcc) phase of the ternary Cr-Ni-C system and the Gibbs energies of formation of metastable Ni₂₃C₆ and Ni₇C₃ in the binary Ni-C system have been estimated from the experimental data of the ternary Cr-Ni-C alloys. The assessments were carried out simultaneously by using a computerized optimization technique. The thermodynamic parameters optimized in the present work are able to reproduce appropriately the experimental results in the Cr-C and Cr-Ni-C systems.