The binary Al-Mn system has been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the modified quasichemical model to account for short-range ordering. The results have been combined with those of our previous optimizations of the Al-Mg and Mg-Mn systems to evaluate and optimize the Mg-Al-Mn system. All available data for the ternary system are reproduced with only one small ternary model parameter for the liquid phase.

A thermodynamic model has been developed in the framework of the modified quasichemical model in the quadruplet approximation to permit the calculation of solubilities of various gaseous species (sulfide, sulfate, nitride, carbide, water, etc.) in molten slags. The model calculates the solubilities solely from knowledge of the thermodynamic activities of the component oxides and the Gibbs energies of the pure liquid components (oxides, sulfides, sulfates, etc.). In the current article, it is shown that solubilities of sulfur as sulfide in Al₂O₃-CaO-FeO-Fe₂O₃-MgO-MnO-SiO₂-TiO₂-Ti₂O₃ multicomponent slags, which are predicted from the current model with no adjustable model parameters, are in good agreement with all available experimental data. The article also provides a thorough review of experimental sulfide capacity data for this system. The model applies at all compositions from pure oxides to pure sulfides and from basic to acidic slags. By coupling this database with other evaluated databases, such as those for molten metal and gaseous phases, and with general software for Gibbs energy minimization, practically important slag/metal/gas/solid equilibria can be computed such as S-distribution ratios.

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.