Critical assessment of three kinds of activity coefficients of carbon and related mixing thermodynamic functions of Fe–C binary melts based on atom–molecule coexistence theory

Raoultian activity coefficients \({\gamma}_{\text{C}}^{0}\) of C in infinitely dilute Fe–C binary melts at temperatures of 1833, 1873, 1923, and 1973 K have been determined from the converted mass action concentrations \(N_{\text{C}}^{\prime}\) of C in Fe–C binary melts by the developed AMCT-N _i model based on the atom–molecule coexistence theory (AMCT). The obtained expression of \(\gamma_{\text{C}}^{0}\) by the developed AMCT-N _i model has been evaluated to be accurate based on the reported ones from the literature. Meanwhile, three activity coefficients \(\gamma_{\text{C}}\), \(f_{{\%,{\text{ C}}}}\), and \(f_{\text{H, C}}\) of C coupled with activity \(a_{\text{R, C}}\) or \(a_{{\%,{\text{ C}}}}\) or \(a_{\text{H, C}}\) have been obtained by the developed AMCT-N _i model and assessed through comparing with the predicted ones by other models from the literature. The first-order activity interaction coefficients \(\varepsilon_{\text{C}}^{\text{C}}\), \(e_{\text{C}}^{\text{C}}\), and \(h_{\text{C}}^{\text{C}}\) related to \(\gamma_{\text{C}}\), \(f_{{\%,{\text{ C}}}}\), and \(f_{\text{H, C}}\) are also determined and assessed in comparison with the reported ones from the literature. Furthermore, the integral molar mixing thermodynamic functions such as \(\Delta_{\text{mix}} H_{{{\text{m, Fe}} - {\text{C}}}}\), \(\Delta_{\text{mix}} S_{{{\text{m, Fe}} - {\text{C}}}}\), and \(\Delta_{\text{mix}} G_{{{\text{m, Fe}} - {\text{C}}}}\) of Fe–C binary melts over a temperature range from 1833 to 1973 K have been determined and evaluated to be valid based on the determined ones from the literature.