Interaction parameter formalisms for the determination of carbon activities in the Fe–C–Si system

The determination of carbon activities in the Fe–C–Si system is important in thermodynamic calculations and in particular for predicting equilibrium compositions in slag–metal reactions. In this research, the interaction parameters required to describe the activity of carbon were calculated from previously published carbon solubility data. These parameters were referred to as ternary interaction parameters &phis; and were fitted to equations as a function of the carbon and silicon contents and temperature. Subsequently, the various interaction parameter formalisms were utilised to calculate the activity of carbon. In dilute solutions, all formalisms were in excellent agreement with a previously published regular solution model. At low silicon and high carbon contents, the unified formalism was in excellent agreement, while the substitutional formalism was in good agreement with the regular solution model. However, in high silicon alloys with low carbon contents, the substitutional and unified formalisms showed only limited agreement with the regular solution model.