Critical assessment of mixing thermodynamic functions of Fe–Al binary melts based on atom–molecule coexistence theory

Abstract

In order to further verify the accuracy and feasibility of the calculated mass action concentrations $N_{i}$ of Al and Fe by the developed atom and molecule coexistence theory (AMCT) model, i.e., AMCT–$N_{i}$ model, for representing activities $a_{{{\text{R, }}i}}^{{}}$ of Al and Fe in Fe–Al binary melts reported in the first part of the serial studies, the molar mixing thermodynamic functions of Fe–Al binary melts over a temperature range from 1823 to 1973 K have been calculated based on $N_{i}$ of Al and Fe as well as the effect of temperature on activity coefficients $\gamma_{i}^{{}}$ of Al and Fe as ${{\partial \ln \gamma_{i} } \mathord{\left/ {\vphantom {{\partial \ln \gamma_{i} } {\partial T}}} \right. \kern-0pt} {\partial T}} = {{\partial \ln \left( {{{N_{i} } \mathord{\left/ {\vphantom {{N_{i} } {x_{i} }}} \right. \kern-0pt} {x_{i} }}} \right)} \mathord{\left/ {\vphantom {{\partial \ln \left( {{{N_{i} } \mathord{\left/ {\vphantom {{N_{i} } {x_{i} }}} \right. \kern-0pt} {x_{i} }}} \right)} {\partial T}}} \right. \kern-0pt} {\partial T}}$ by the developed AMCT–$N_{i}$ model, where T is absolute temperature and x_i is the mole fraction of element i or compound i in metallic melts. The reported molar mixing thermodynamic functions of Fe–Al binary melts as well as the reported excess molar mixing thermodynamic functions of Fe–Al binary melts relative to ideal solution as a basis from the available literatures have been critically assessed and applied as criteria to verify the developed AMCT–$N_{i}$ model. The effect of changing temperature on $\gamma_{i}^{{}}$ of Al and Fe, i.e., activity coefficient gradients ${{\partial \ln \gamma_{\text{Al}}^{{}} } \mathord{\left/ {\vphantom {{\partial \ln \gamma_{\text{Al}}^{{}} } {\partial T}}} \right. \kern-0pt} {\partial T}}$ and ${{\partial \ln \gamma_{\text{Fe}}^{{}} } \mathord{\left/ {\vphantom {{\partial \ln \gamma_{\text{Fe}}^{{}} } {\partial T}}} \right. \kern-0pt} {\partial T}}$, which are two indispensable parameters to calculate the molar mixing thermodynamic functions of Fe–Al binary melts, can be accurately obtained by the developed AMCT–$N_{i}$ model and expressed by the cubic polynomial functions. Not only the partial molar mixing thermodynamic functions of Al and Fe in Fe–Al binary melts but also the integral molar mixing thermodynamic functions of Fe–Al binary melts can be accurately calculated by the developed AMCT–$N_{i}$ model. Furthermore, the excess partial and integral molar mixing thermodynamic functions of Fe–Al binary melts relative to ideal solution as a basis can also be precisely calculated by the developed AMCT–$N_{i}$ model.