Abstract
The reaction abilities of structural units in Fe–C binary melts over a temperature range above the liquidus lines have been evaluated by a thermodynamic model for calculating the mass action concentrations N i of structural units in Fe–C binary melts based on the atom–molecule coexistence theory (AMCT), i.e., the AMCT-N i model, through comparing with the predicted activities aR,i of both C and Fe by 14 collected models from the literature at four temperatures of 1833, 1873, 1923, and 1973 K. Furthermore, the Raoultian activity coefficient \( \gamma_{\text{C}}^{0} \) of C in infinitely dilute Fe–C binary melts and the standard molar Gibbs free energy change \( \Delta_{\text{sol}} G_{{{\text{m, C}}_{{{\text{dis}} .}} ( {\text{l)}} \to [ {\text{C]}}_{{_{{{{w}}_{{[ {\text{C]}}}}}} {= 1.0}}}}}^{{\Theta,{{\%}}}} \) of dissolved liquid C for forming w[C] as 1.0 in Fe–C binary melts referred to 1 mass% of C as reference state have also been determined to be valid. The determined activity coefficient ln γC of C and activity coefficient ln γFe of Fe including temperature effect for Fe–C binary melts can be described by a quadratic polynomial function and a cubic polynomial function, respectively.
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Abbreviations
- a i :
-
Activity of element i or compound i;
- a R,i :
-
Activity of element i or compound i relative to pure liquid i or saturated liquid or solid i or pure solid i or diatomic gas i2 as standard state with mole fraction x i as concentration unit and following Raoult’s law under condition of taking ideal solution as reference state, i.e., aR,i = γ i x i ;
- \( a_{\text{R,C}}^{\text{AMCT}} \) :
-
Converted activity aR,C of C in Fe–C binary melts by developed AMCT-N i model;
- a %,i :
-
Activity of element i referred to 1 mass% of element i as standard state with mass percentage w[i] as concentration unit and obeying Henry’s law under condition of taking infinitely dilute ideal solution as reference state, i.e., \( a_{{{{\%,}}i}} = f_{{{{\%,}}i}} w_{[i]} \);
- \( a_{{{{\%,{\rm C}}}}}^{\text{AMCT}} \) :
-
Calculated a%,C of C in Fe–C binary melts by developed AMCT-N i model;
- a H,i :
-
Activity of element i relative to hypothetical pure liquid i as standard state with mole fraction x i as concentration unit and following Henry’s law under condition of taking infinitely dilute ideal solution as reference state, i.e., aH,i = fH,i x i ;
- \( a_{\text{H,C}}^{\text{AMCT}} \) :
-
Calculated aH,C of C in Fe–C binary melts by developed AMCT-N i model;
- b i :
-
Mole number of element i in 100 g metallic melts before reaction equilibrium for forming associated molecules or compounds, having the same meaning with \( n_{i}^{0} \) (mol);
- f %,i :
-
Activity coefficient of element i in metallic melts related with activity a%,i;
- f H,i :
-
Activity coefficient of element i in metallic melts related with activity aH,i;
- \( \Delta_{\text{r}} G_{{{\text{m,}}i}}^{{\Theta,{\text{R}}}} \) :
-
Standard molar Gibbs free energy change of reaction for forming compound i based on activity aR,i for reactants and products (J/mol);
- \( \Delta_{\text{sol}} G_{{{\text{m,}}i_{{{\text{dis}} .}} ( {\text{l)}} \to [i ]_{{{\text{w}}_{{[ {}i ]}} {= 1} . 0}}}}^{{\Theta,{{\%}}}} \) :
-
Standard molar Gibbs free energy change of dissolved liquid element i into metallic melts based on activity a%,i (J/mol);
- \( K_{i}^{{\Theta,{\text{R}}}} \) :
-
Standard equilibrium constant of chemical reaction for forming compound i based on activity aR,i for reactants and products;
- M i :
-
Relative atomic mass of element i;
- \( n_{i}^{0} \) :
-
Mole number of element i in 100 g metallic melts before reaction equilibrium for forming associated molecule or compound, having the same meaning of b i (mol);
- n i :
-
Equilibrium mole number of structural unit i in 100 g metallic melts based on AMCT (mol);
- \( \Sigma n_{i} \) :
-
Total equilibrium mole number of all structural units in 100 g metallic melts based on AMCT (mol);
- N i :
-
Mass action concentrations of structural unit i in metallic melts based on AMCT;
- \( N_{i}^{\prime} \) :
-
Converted mass action concentrations of structural unit i in metallic melts based on AMCT;
- R :
-
Gas constant, 8.314 J/(mol K);
- T :
-
Absolute temperature (K);
- x i :
-
Mole fraction of element i or compound i in metallic melts;
- w [i] :
-
Mass percentage of element i or compound i in metallic melts (%);
- i dis.(l):
-
Dissolved element i or compound i in liquid state;
- γ i :
-
Activity coefficient of element i related with activity aR,i;
- \( \gamma_{i}^{0} \) :
-
Raoultian activity coefficient of element i in infinitely dilute metallic melts relative to pure liquid i or saturated liquid i or pure solid i or diatomic gas i2 (g) as standard state and taking infinitely dilute ideal solution as reference state, i.e., equal to value of \( \gamma_{{i,x_{i} \to 0.0}} \);
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Acknowledgements
This work is supported by the Beijing Natural Science Foundation (Grant No. 2182069) and the National Natural Science Foundation of China (Grant No. 51174186).
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Yang, Xm., Li, Jy., Duan, Dp. et al. Thermodynamic evaluation of reaction abilities of structural units in Fe–C binary melts based on atom–molecule coexistence theory. J. Iron Steel Res. Int. 25, 37–56 (2018). https://doi.org/10.1007/s42243-017-0008-9
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DOI: https://doi.org/10.1007/s42243-017-0008-9