The FactSage computer package consists of a series of information, calculation and manipulation modules that enable one to access and manipulate compound and solution databases. With the various modules running under Microsoft Windows® one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. This paper presents a summary of the developments in the FactSage thermochemical software and databases during the last six years. Particular emphasis is placed on the new databases and developments in calculating and manipulating phase diagrams.

FactSage thermochemical software and databases, 2010–2016

Further improvements to the modified quasichemical model in the pair approximation for short-range ordering in liquid and solid solutions are presented. The energy of pair formation is expanded in terms of the pair fractions rather than the component fractions, and coordination numbers are permitted to vary with composition. A formalism is introduced whereby the quasichemical equations are shown to be equivalent to the equations of an associate model if the pairs are formally treated as fractional associates. The model is applied to the liquid phase in a new optimization of the KCl-MgCl2 system.

https://www.crct.polymtl.ca/courses/17-MQM-1.pdf

The Modified Quasichemical Model I— Binary Solutions

Further improvements to the modified quasi-chemical model in the pair approximation for shortrange ordering (SRO) in liquids are extended to multicomponent solutions. The energy of pair formation may be expanded in terms of the pair fractions or in terms of the component fractions, and coordination numbers are permitted to vary with composition. The model permits complete freedom of choice to treat any ternary subsystem with a symmetric or an asymmetric model. An improved general functional form for “ternary terms” in the excess Gibbs energy expression is proposed. These terms are related to the effect of a third component upon the binary pair interaction energies. It is shown how binary subsystems that have been optimized with the quasi-chemical model can be combined in the same multicomponent Gibbs energy equation with binary subsystems that have been optimized with a random-mixing Bragg-Williams model and a polynomial expression for the excess Gibbs energy. This is of much practical importance in the development of large databases for multicomponent solutions. The model also applies to SRO in solid solutions as a special case, when the number of lattice sites and coordination numbers are constant.

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The modified quasi-chemical model: Part II. Multicomponent solutions

Reprint of: FactSage thermochemical software and databases, 2010–2016

The modified quasi-chemical model is further extended, in the quadruplet approximation, to treat, simultaneously, first-nearest-neighbor (FNN) and second-nearest-neighbor (SNN) short-range ordering (SRO) in solutions with two sublattices. When one sublattice is occupied by only one species, or is empty, the model reduces to the modified quasi-chemical model for one sublattice in the pair approximation. The coordination numbers and the ratio of the number of sites on the two sublattices are permitted to vary with composition, thereby making the model ideally suited to the treatment of liquid solutions such as molten salts. The model also applies to solid solutions if the number of sites and coordination numbers are held constant and may be combined with the compound-energy formalism to treat SRO in a wide variety of types of solutions. A significant computational simplification is achieved by formally treating the quadruplets as the “components” of the solution.

The modified quasi-chemical model: Part IV. Two-sublattice quadruplet approximation

The Fe-Zn-O phase diagram in air was studied over the temperature range from 900 °C to 1500 °C. The compositions of the phases in quenched samples were obtained by electron probe X-ray microanalysis (EPMA). This experimental technique is not affected by zinc losses resulting from vaporization of zinc at high temperatures. The model for the spinel solid solution was developed within the framework of the compound-energy formalism (CEF). The choice of parameters of the CEF and the sequence of their optimization can have a major influence on the predictions in multicomponent phases. These choices can only be made rationally by reference to the specific model being represented in the CEF. This is discussed for the case of the two-sublattice spinel model. In the limiting case, the proposed model reduces to the model by O’Neill and Navrotsky for spinels. When the CEF is used in combination with the equation of Hillert and Jarl to describe the magnetic contribution to thermodynamic functions of a solution, it is necessary to assign certain values of magnetic properties to all pseudocomponents and to magnetic interaction parameters to obtain the most reasonable approximation of the magnetic properties of a solution. It was shown how this can be done based on very limited experimental data. The same equations can be used when the Murnaghan or the Birch-Murnaghan equation is combined with the CEF to describe the pressure dependence of thermodynamic functions. The polynomial model was used to describe the properties of wustite and zincite, and the modified quasichemical model was used for the liquid slag. All thermodynamic and phase-equilibria data on the Fe-O and Fe-Zn-O systems were critically evaluated, and parameters of the models were optimized to give a self-consistent set of thermodynamic functions of the phases in these systems. All experimental data are reproduced within experimental error limits. These include the thermodynamic properties of phases (such as specific heat, heat content, entropy, enthalpy, and Gibbs energy); the cation distribution between octahedral and tetrahedral sites in spinel; the oxygen partial pressure over single-phase, two-phase, and three-phase regions; the phase boundaries (liquidus, solidus, and subsolidus); and the tie-lines.

Experimental study of phase equilibria and thermodynamic optimization of the Fe-Zn-O system

Thermodynamic modelling of the system Al2O3SiO2CaOFeOFe2O3 to predict the flux requirements for coal ash slags

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

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr2O3, CrO-Cr2O2-Al2O3, and CrO-Cr2O2-CaO systems from 298 K to above the liquidus temperatures and for oxygen partial pressures ranging from equilibrium with metallic Cr to equilibrium with air in the case of the first two systems and toP
O
2 = 10−3 atm for the CrO-Cr2O3-CaO system. 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.

S. Degterov

Papers

The Modified Quasichemical Model I— Binary Solutions

Experimental study of phase equilibria and thermodynamic optimization of the Fe-Zn-O system

Thermodynamic modelling of the system Al2O3SiO2CaOFeOFe2O3 to predict the flux requirements for coal ash slags

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

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3, CrO-Cr2O3-Al2O3, and CrO-Cr2O3-CaO systems