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

Abstract

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.