a database of model parameters has been prepared. The Modified Quasichemical Model was employed for the molten oxide phase. The thermodynamic modeling predicts the existence of a liquid oxide Al 2 O 3 -Ti 2 O 3 -TiO 2 phase at secondary steelmaking conditions. The database was used to calculate the inclusion diagram for Al-Ti deoxidation at 1 600°C.KEY WORDS: thermodynamic modeling; Al 2 O 3 -Ti 2 O 3 -TiO 2 , Al-Ti deoxidation, inclusion; FactSage.and Ti 3ϩ ions are distributed as independent particles in the liquid solution, not as ion pairs.) The following short-range ordering quasichemical reactions are taken into account: , and (A-B) represents a second-nearest-neighbor A-B pair. The Gibbs energies of this reaction Dg AB are the model parameters, which can be expanded as empirical functions of composition. The Gibbs energies and all second-nearest-neighbor "coordination numbers" of the three liquid components used in the model are the same as in previous studies. 11,12) That is, the coordination number of Ti 3ϩ is identical to that of Al 3ϩ , which is 3/4 that of Ti 4ϩ . Optimized model parameters for the Ti 2 O 3 -TiO 2 binary liquid phase were recently reported, 12) while optimized parameters for the Al 2 O 3 -TiO 2 and Al 2 O 3 -Ti 2 O 3 binary liquids are reported in the present study. The properties of the ternary slag solution are estimated from the optimized binary model parameters using an asymmetric "Toop-like" 13) approximation with TiO 2 as the "asymmetric component". No additional adjustable ternary model parameters are used for the liquid phase. The optimized model parameters are listed in The corundum phase is an Al 2 O 3 -rich solid solution, with a trigonal structure based on the hcp oxygen-packing scheme which dissolves a small amount of Ti 2 O 3 . The ilmenite phase is a Ti 2 O 3 -rich solid solution, with a hexagonal structure, which dissolves a limited amount of Al 2 O 3 . In the absence of any experimental data, it is assumed that TiO 2 is stable only to a negligible extent in both phases.The molar Gibbs energies of the corundum and ilmenite phases are modeled as ideal ionic substitutional Henrian solutions by the following expressions: Kang et al. 12) in order to reproduce the experimental solubility data over a wide range of temperatures. The thermodynamic model of Kang et al. 12) is adopted in the present study with no modification.
D. Stoichiometric CompoundsThe Gibbs energy functions of several Magnéli phases (Ti n O 2nϪ1 , nՆ4) and Ti 3 O 5 are taken from the previous studies 11,12) with no modification. The Gibbs energies of Al 2 TiO 5 (tialite) and Al 4 TiO 8 are evaluated in the present study. In the absence of any experimental evidence to the contrary, all of these phases are assumed to be stoichiometric compounds. 12) reoptimized the model parameters of the liquid oxide and rutile phases in order to reproduce the phase diagram more accurately. The details of the thermodynamic modeling and model parameters can be found in the previous study.
Critical Evaluation and12) Iso...