Thermodynamic assessment of liquid Mn-Fe-C system by unified interaction parameter model

The present study assesses the available experimental data and proposes a model based on the Unified Interaction Parameter Formalism to describe the solution properties of the Mn-Fe-C system. The experimental information developed from the recent works by Katsnelson et al., Fenstad, and Kim et al. defines the solution properties as the ratio of the activity of C to Mn in the Mn-Fe-C system. These data were used to determine the activity coefficient of carbon at infinite dilute solution of Mn in the Mn-C system at various temperatures. In y(C)degrees(Mn)=0.32-2 679/T(K) (1628-1773 K) A determination of the individual activity of C and Mn from experimental data requires additional information. As it meets the necessary condition for the task by virtue of satisfying the Gibbs-Duhem relationship, the Unified Interaction Parameter (UIP) model was correlated with the experimental data of the Mn-Fe-C system. The interaction parameters of the UIP model were determined by multiple regression analysis of the correlated equations. The activity coefficients of carbon and manganese in reference to graphite and liquid Mn as respective standard states in the Mn-Fe-C system are determined as follows: ln gamma(C)=gamma(C)degrees(Mn)+epsilon(CC)[x(C)-1/2x(C)(2)]+epsilon(CFe)[x(Fe)-x(C)x(Fe)]+epsilon(FeFe)[-1/2x(Fe)(2)]+epsilon(CCC)[x(C)(2)-2/3x(C)(3)] + epsilon(CCFe)[2x(C)x(Fe)-2x(C)(2)x(Fe)]+epsilon(CFeFe)[x(Fe)(2)-2x(C)x(Fe)(2)]+epsilon(FeFeFe)[-2/3x(Fe)(3)] ln gamma(Mn)=epsilon(CC)[-1/2x(C)(2)]+epsilon(CFe)[-x(C)x(Fe)]+epsilon(FeFe)[-1/2x(Fe)(2)]+epsilon(CCC)[-2/3x(C)(3)]+epsilon(CCFe)[-2x(C)(2)x(Fe)]+epsilon(CFeFe)[-2x(C)x(Fe)(2)]+epsilon(FeFeFe)[-2/3x(Fe)(3)] where epsilon(CC)=9.24-16060/T, epsilon(CCC)=-51.8+157800/T, epsilon(CFe)=7.52-7250/T, epsilon(CCFe)=-8.39+16190/T, epsilon(CFeFe)= -9.93+12790/T, epsilon(FeFe)=0, and epsilon(FeFeFe)=0.