A thermodynamic model for representation reaction abilities of structural units in full composition range of Fe-Si binary melts based on the atom-molecule coexistence theory

Abstract A thermodynamic model for calculating the mass action concentrations of structural units in Fe-S binary melts based on the atom-molecule coexistence theory, i.e., AMCT-N i model, has been developed and verified through a comparison with the reported activities of both S and Fe in Fe-S binary melts with changing mole fraction \( x_{\text{S}} \) of S from 0.0 to 0.095 at temperatures of 1773 K, 1823 K, and 1873 K (1500 °C, 1550 °C, and 1600 °C) from the literature. The calculated mass action concentration \( N_{\text{S}} \) of S is much smaller than the reported activity \( a_{\text{R, S}} \) of S in Fe-S binary melts with changing mole fraction \( x_{\text{S}} \) of S from 0.0 to 0.095. The calculated mass action concentration \( N_{\text{S}} \) of S can correlate the reliable 1:1 corresponding relationship with the reported activity \( a_{\text{R, S}} \) or \( a_{\%,\text {S}} \) of S through the introduced transformation coefficients with absolutely mathematical meaning or through the defined comprehensive mass action concentration of total S with explicitly physicochemical meaning. The calculated mass action concentrations \( N_{i} \) of structural units from the developed AMCT-N i thermodynamic model can be applied to describe or predict the reaction abilities of structural units in Fe-S binary melts. The reaction abilities of Fe and S show a competitive relationship each other in Fe-S binary melts in a temperature range from 1773 K to 1873 K (1500 °C to 1600 °C). The calculated mass action concentration \( N_{{{\text{FeS}}_{ 2} }} \) of FeS2 is very small and can be ignored because FeS2 can be incongruently decomposed above 1016 K (743 °C). The very small values for the calculated mass action concentrations \( N_{{{\text{FeS}}_{ 2} }} \) of FeS2 in a range of mole fraction \( x_{\text{S}} \) of S from 0.0 to 1.0 as well as a maximum value for the calculated mass action concentration \( N_{\text{FeS}} \) of FeS with mole fraction \( x_{\text{S}} \) of S as 0.5 are coincident with diagram phase of Fe-S binary melts. A spindle-type relationship between the calculated mass action concentration \( N_{i} \) and the calculated equilibrium mole number \( n_{i} \) can be found for FeS and FeS2 in Fe-S binary melts. The Raoultian activity coefficient \( \gamma_{S}^{0} \) of S relative to pure liquid S(l) as standard state and the infinitely dilute solution as reference state in Fe-S binary melts can be determined as 1.0045 in a temperature range from 1773 K to 1873 K (1500 °C to 1600 °C). The standard molar Gibbs free energy change \( \Updelta_{\text{sol}} G_{{{\text{m, S }}({\text{l}}) \to [{\text{S}}]_{{ \, [{\text{pct \, S}}] = 1.0}} }}^{{\Uptheta,\%}} \) of dissolving liquid S for forming [pct S] as 1.0 in Fe-S binary melts relative to 1 mass percentage of S as standard state can be formulated as \( \Updelta_{\text{sol}} G_{{{\text{m, S }}({\text{l}}) \to [{\text{S}}]_{{ \, [{\text{pct \, S] }} = \, 1.0}} }}^{{\Uptheta,\, \%}} \,\, = -0.219\,-\,33.70T\,\,\left( {\text{J/mol}} \right).\)