Thermodynamic Analysis on the Minimum of Oxygen Content in the Deoxidation Equilibrium Curve in Liquid Iron

The minimum of oxygen content in the deoxidation equilibrium in liquid iron was thermodynamically analyzed in the present paper. Two criteria were developed to determine the existence of the minimum. The first criterion was $$0 \le x\gamma _{\rm{M}}^{\rm{M}} + y\gamma _{\rm{O}}^{\rm{M}} \le \min ({x \mathord{\left/{\vphantom {x {4.606[\% {\rm{M}}]_{{\rm{ex}}}^2}}} \right.\kern-\nulldelimiterspace} {4.606[\% {\rm{M}}]_{{\rm{ex}}}^2}},{{{{(xe_{\rm{M}}^{\rm{M}} + ye_{\rm{O}}^{\rm{M}})}^2}} \mathord{\left/{\vphantom {{{{(xe_{\rm{M}}^{\rm{M}} + ye_{\rm{O}}^{\rm{M}})}^2}} {3.474x}}} \right.\kern-\nulldelimiterspace} {3.474x}})$$ with $$xe_{\rm{M}}^{\rm{M}} + ye_{\rm{O}}^{\rm{M}} \lt 0$$, or $$x\gamma _{\rm{M}}^{\rm{M}} + y\gamma _{\rm{O}}^{\rm{M}}{\rm{\lt 0}}$$. And the second criterion was $$(xe_{\rm{M}}^{\rm{O}} + ye_{\rm{O}}^{\rm{O}}) + {y \mathord{\left/{\vphantom {y {2.303{{[\% {\rm{O}}]}_{{\rm{ex}}}}}}} \right.\kern-\nulldelimiterspace} {2.303{{[\% {\rm{O}}]}_{{\rm{ex}}}}}} \gt 0$$. The criteria in terms of first-order activity interaction parameters were the special case of present thermodynamic analysis with neglecting the second-order activity interaction parameters. They were not fit for the case of $$xe_{\rm{M}}^{\rm{M}} + ye_{\rm{O}}^{\rm{M}} \gt 0$$, in which case the criteria in terms of second-order activity interaction parameters should be taken into account to determine the existence of the minimum. The value 0.11 of $$e_{{\rm{Si}}}^{{\rm{Si}}}$$ was smaller based on the existence of the minimum for the Fe-O-Si system. It was guaranteed that the minimum value of oxygen content on the deoxidation equilibrium curve existed at silicon content 20 mass%, when the value 0.32 of $$e_{{\rm{Si}}}^{{\rm{Si}}}$$ was chosen, and the second-order activity interaction coefficients $$\gamma _{{\rm{Si}}}^{{\rm{Si}}}$$ and $$\gamma _{\rm{O}}^{{\rm{Si}}}$$ satisfied the condition $$\gamma _{{\rm{Si}}}^{{\rm{Si}}} + 2\gamma _{\rm{O}}^{{\rm{Si}}} = - 1.54 \times {10^{- 3}}$$.