Development of the PhDi software package for the calculation of phase diagrams of binary systems using parameters of state equations and thermodynamic models for solutions

The PhDi software package developed earlier for calculations of phase equilibria by the convex hull method was modified by incorporating two additional modules: “State equations” and “Local composition thermodynamic models.” The possibility of the application of the convex hull method with cubic state equations to construct phase diagrams of binary systems was shown. A new database containing parameters of the corresponding thermodynamic models has been added to the initial version of the PhDi package. The efficiency of the performance of the package in solving the problem of choosing an appropriate state equation to predict conditions of phase equilibria in binary systems was demonstrated.     

Analysis of thermodynamic properties and phase equilibria in the Si-P system

A self-consistent analysis of the available data on thermodynamic properties and phase equilibria in the Si-P system is performed. Thermodynamic properties of solid and liquid solutions of phosphorus in silicon are approximated on the basis of the concepts of dilute and ideal associated solutions. The thermodynamic properties and phase boundaries in the range of compositions 0 ≤ x(P) ≤ 0.5 are adequately described.     

Phase Transitions and Critical Behaviour of Binary Liquid Mixtures

Summary.  Compared to the simple one-component case, the phase behaviour of binary liquid mixtures shows an incredibly rich variety of phenomena. In this contribution we restrict ourselves to so-called binary symmetric mixtures, i.e. where like-particle interactions are equal (Φ₁₁(r) = Φ₂₂(r)), whereas the interactions between unlike fluid particles differ from those of likes ones (Φ₁₁(r) ≠ Φ₁₂(r)). Using both the simple mean spherical approximation and the more sophisticated self-consistent Ornstein-Zernike approximation, we have calculated the structural and thermodynamic properties of such a system and determine phase diagrams, paying particular attention to the critical behaviour (critical and tricritical points, critical end points). We then study the thermodynamic properties of the same binary mixture when it is in thermal equilibrium with a disordered porous matrix which we have realized by a frozen configuration of equally sized particles. We observe – in qualitative agreement with experiment – that already a minute matrix density is able to lead to drastic changes in the phase behaviour of the fluid. We systematically investigate the influence of the external system parameters (due to the matrix properties and the fluid–matrix interactions) and of the internal system parameters (due to the fluid properties) on the phase diagram. Received June 27, 2001. Accepted July 2, 2001     

Phase Transitions and Critical Behaviour of Binary Liquid Mixtures

 Compared to the simple one-component case, the phase behaviour of binary liquid mixtures shows an incredibly rich variety of phenomena. In this contribution we restrict ourselves to so-called binary symmetric mixtures, i.e. where like-particle interactions are equal (Φ₁₁(r) = Φ₂₂(r)), whereas the interactions between unlike fluid particles differ from those of likes ones (Φ₁₁(r) ≠ Φ₁₂(r)). Using both the simple mean spherical approximation and the more sophisticated self-consistent Ornstein-Zernike approximation, we have calculated the structural and thermodynamic properties of such a system and determine phase diagrams, paying particular attention to the critical behaviour (critical and tricritical points, critical end points). We then study the thermodynamic properties of the same binary mixture when it is in thermal equilibrium with a disordered porous matrix which we have realized by a frozen configuration of equally sized particles. We observe – in qualitative agreement with experiment – that already a minute matrix density is able to lead to drastic changes in the phase behaviour of the fluid. We systematically investigate the influence of the external system parameters (due to the matrix properties and the fluid–matrix interactions) and of the internal system parameters (due to the fluid properties) on the phase diagram.     

Optimization and Calculation of the EuCl<Subscript>3</Subscript>–MCl (M = Na,K, Rb,Cs) Phase Diagrams

By using the CALPHAD technique, an optimization of the binary EuCl₃–MCl (M = Na, K, Rb, Cs) systems has been carried out. To describe the Gibbs energies of liquid phases in these systems the new modified quasi-chemical model was used in the pair-approximation for short-range ordering. From the measured phase equilibrium data and the experimental thermo-chemical properties, the EuCl₃–MCl phase diagrams were optimized and calculated. A set of thermodynamic functions has been optimized based on an interactive computer-assisted analysis. The calculated phase diagrams and thermodynamic data are self-consistent.     

Phase Behavior of Aqueous Na–K–Mg–Ca–Cl–NO<Subscript>3</Subscript> Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na⁺, K⁺, Mg²⁺, Ca²⁺, Cl⁻ and NO₃⁻ ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 °C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 °C. The measurements have been performed using Oak Ridge National Laboratory’s (ORNL) previously designed gravimetric isopiestic apparatus, which can also detect solid phase precipitation. In addition to various Na–K–Mg–Ca–Cl–NO₃ systems, results are reported for LiCl solutions. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid–liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor–liquid and solid–liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems.     

Calculation of phase behavior and chemical transformations in H<Subscript>2</Subscript>O-NH<Subscript>3</Subscript>-CO<Subscript>2</Subscript> system using a modified hole quasichemical model

A technique for calculation of phase equilibria over a wide range of temperatures and pressures for fluid systems, where chemical interactions lead to the formation of ionic species, was developed. A hole quasichemical model was modified to account for chemical reactions and electrostatic interactions in the liquid phase. The densities and dielectric permittivity as function of a solution composition was taken into account in describing the electrostatic contribution to the Gibbs energy (Pitzer approximation) and Born contribution, that is required for thermodynamic consistency of simulation results. A method of assessing the appropriate relationships for mixtures of ammonia-water and ternary solutions was suggested. Calculations of the phase behavior of the H₂O-NH₃ system in the entire range of concentrations in the temperature interval 373–588 K at pressures up to 200 bar, and also of H₂O-NH₃-CO₂ system containing NH₃ to 30 mol% and CO₂ up to 14 mol% in the temperature range 373–473 K at pressures to 88 bar gave satisfactory agreement with experimental data. Concentrations of the molecular and ionic individuals in the liquid phase, depending on the overall composition of the mixture were evaluated.     

Thermodynamic properties of Al-Y system melts

The thermochemical properties of Al-Y melts were determined by isoperibolic calorimetry. It was established that the minimal value of integral mixing enthalpies is equal to −40.8 + 0.4 kJ/mol at 1770 K and x _Y = 0.41. The thermodynamic properties of liquid alloys were modeled by the developed procedure using the coordinates of a liquidus line in the phase diagram of the Al-Y system, and by the theory of ideal associated solutions. The component activities exhibit high negative deviations from the Raoult law. The Gibbs energies of mixing of Al-Y melts have a minimum of −30.6 kJ/mol at x _Y = 0.48.     

Calculation of phase diagrams of ternary M-Ga-Sb (M = In,Al) systems by convex hull approach

The ternary semiconductor phase diagrams of M-Ga-Sb (M = In, Al) are calculated by means of the convex hull approach. The software package TernAPI is tested as an effective tool for these purposes. The new facilities and advantages of this package are proven. It enables one to construct ternary phase diagrams based on thermodynamic properties of all phases existing in systems. The changes in phase region shapes and phase transformations with temperature can be studied by means of the TernAPI package. Selection of reliable thermodynamic models of solutions is of crucial importance for correct calculations of phase equilibria. It is shown that an adequate phase diagram can be constructed when a polynomial model of liquid solutions in the Al-Ga-Sb system is used.     

Revised Phase Diagram of the System NaF–NaBF4

Summary. The phase diagram of the binary system NaF–NaBF₄ was determined using the thermal analysis method. Subsequent coupled analysis of the thermodynamic and phase diagram data was carried out to calculate the thermodynamically consistent phase diagram. The system NaF–NaBF₄ forms a simple eutectic phase diagram with the calculated coordinates of the eutectic point: 8.1 mol% NaF, 91.9 mol% NaBF₄, and 385.7°C. The probable inaccuracy in the calculated binary phase diagram is 9°C.     

Experimental study and thermodynamic modeling of the MgO–NiO–SiO2 system

The MgO–NiO–SiO₂ system has been studied by a combination of thermodynamic modeling and experimental measurements of phase equilibria. A complete literature review, critical evaluation and thermodynamic modeling of phase diagrams and thermodynamic properties of all oxide phases in the MgO–NiO–SiO₂ system at 1 atm total pressure are presented. To resolve the contradictions in the literature data, a new experimental investigation has been carried out over the temperature range from (1400 to 1650) °C using an equilibration and quenching technique followed by electron probe X-ray microanalysis (EPMA). Tie-lines between olivine and monoxide, olivine and proto-pyroxene, liquid and olivine and liquid and cristobalite have been measured. The whole set of experimental data, including the new experimental results and previously published data, has been taken into consideration in thermodynamic modeling of oxide phases in the MgO–NiO–SiO₂ system. The Modified Quasichemical Model has been used for the liquid phase. A simple random mixing model with a polynomial expansion of the excess Gibbs energy has been used for the monoxide solid solution. The models for olivine and proto-pyroxene were developed within the framework of the Compound Energy Formalism. The optimized model parameters reproduce all available thermodynamic and phase diagram data within experimental error limits.     

The thermodynamic properties of solutions and phase equilibria in the water-2-butanol-sodium chloride system

Fragments of the phase diagram of the H₂O-2-C₄H₉OH-NaCl system were studied experimentally at 298 and 313 K. The thermodynamic properties of sodium chloride in three-component solutions with ionic strengths up to 1.9 mol/kg and alcohol content in the solvent 4.97 and 10 wt % were measured at 298 and 323 K by the electromotive force method with ion-selective electrodes. The eNRTL (electrolyte Non-Random Two-Liquids) model parameters correctly describing the results of electrochemical measurements of the partial properties of NaCl and phase equilibria in the water-2-butanol-sodium chloride ternary system and binary subsystems constituting it were determined. The isothermal sections of the phase diagram of the H₂O-2-C₄H₉OH-NaCl system were calculated using the method of convex hulls implemented in the TernAPI package.     

Thermodynamic calculations of phase equilibria in the neodymium-barium-copper-oxygen system: A model of the Nd1 + x Ba2 ? x Cu3O6 + z phase

A thermodynamic model of the Nd_{1 + x} Ba_{2 − x} Cu₃O_{6 + z} phase is suggested. The model allows the properties and boundaries of the regions of various phase polymorphs to be described within the framework of a unified solid solution. Analytic equations for the Gibbs energy and chemical potentials of the components and the other thermodynamic functions of Nd_{1 + x} Ba_{2 − x} Cu₃O_{6 + z} were obtained. Original Russian Text ? V.A. Lysenko, 2007, published in Zhurnal Fizicheskoi Khimii, 2007, Vol. 81, No. 8, pp. 1358–1363.     

Experimental study and modeling of the thermodynamic properties of magnesium silicates

The thermodynamic properties of all MgO-SiO₂ system phases were studied by Knudsen mass spectrometry over a wide temperature range (1571–1873 K) and the whole range of compositions. An approach based on the generation of volatile interaction products formed in the reduction of oxide components was used. The reducing agents were Nb, Ta, and Mo. The observed ion current intensity ratios I(Mg⁺)/I(SiO⁺) were used to calculate the activities and partial thermodynamic functions of the components in liquid and crystalline MgO-SiO₂ mixtures and the integral thermodynamic functions of formation of magnesium ortho-and metasilicates. For the first time, direct and reliable information about the thermodynamic properties of all system phases at high temperatures was obtained. These results in combination with all the available data on the thermodynamic properties and phase equilibria in the MgO-SiO₂ system were used to develop a statistical-thermodynamic model of liquid magnesium silicates based on treating them as associated liquids. Simultaneously, the problem of obtaining self-consistent data on the thermodynamic functions of all phases and conditions of equilibria between them was solved. In addition to polymeric silicon-oxygen structures of arbitrary sizes and spatial configurations, heteromolecular complexes such as MS, M₂S, and M₃S (S=SiO₂ and M=MgO) were found to exist in liquid MgO-SiO₂ mixtures. The correctness of the results obtained was substantiated by the virtually complete coincidence of the calculated thermodynamic properties and phase equilibrium conditions with experimental data and their conformity to the general patterns characteristic of binary silicate systems.     

Thermodynamics of vaporization of gallium trichloride

The unsaturated and saturated pressures of gallium trichloride vapor were measured by the static method with membrane-gauge manometers in wide pressure (0.2–760 Torr) and temperature (313–1071 K) intervals. Scanning calorimetry was used to determine the thermodynamic characteristics of GaCl₃ fusion. The thermodynamic characteristics were obtained for sublimation, fusion, vaporization, and association in the vapor of GaCl₃ molecules. The enthalpies of formation and the absolute entropies of GaCl₃ in the liquid and gaseous phases and Ga₂Cl₆ in the gaseous phase were calculated using literature data. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1266–1269, July, 2007.     

Thermodynamic Properties of silicate glasses and melts: VIII. System MgO-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript>

Vaporization of the system MgO-Al₂O₃-SiO₂ in the temperature range 1770–1890 K was studied and activities of MgO and SiO₂ were determined. Activities of the components, isothermal sections of the phase diagram, and the position of the liquidus line in the studied system were calculated using the Gay-Kapoor-Frohberg model. The correlation of the found values of thermodynamic properties and phase equilibriua in isothermal sections of the phase diagram of the studied system was illustrated.     

Thermodynamic evaluation and optimization of the (NaCl + KCl + AlCl3) system

All available phase equilibrium and thermodynamic data for the (NaCl + KCl + AlCl₃) system were collected and critically evaluated. An optimization was performed to obtain the parameters of one set of model equations for each phase (solids, liquid, gas) in order to best reproduce all the data simultaneously. In this way the data are rendered self-consistent, discrepancies among the data are identified, and extrapolations and interpolations can be performed. For the molten phase the Modified Quasichemical Model for short-range ordering was used, with monomeric Al³⁺ ions (corresponding to AlCl₄⁻ complexes in earlier models) predominating in alkali-rich melts, and dimeric aluminum species (corresponding to Al₂Cl₇⁻ complexes in previous models) predominating in AlCl₃-rich melts. No ternary model parameters were required for the liquid phase; the binary parameters suffice. The models can be used with Gibbs free energy minimization software to calculate phase diagram sections, vapor pressures, and all thermodynamic properties at all compositions and over extended ranges of temperature and pressure.