Table 1 Chemical reaction formulas for possibly formed complex compounds, their standard Gibbs free energy changes, mole number, mass action concentration and equilibrium constants in 100 g CaO-MgO-Al2O3-TiO2-CaF2 slags.

From: Investigation of the Oxidation Behaviour of Ti and Al in Inconel 718 Superalloy During Electroslag Remelting

Reactions \({{\boldsymbol{\Delta }}}_{{\bf{r}}}{{\boldsymbol{G}}}_{{\bf{m}},{\boldsymbol{c}}{\boldsymbol{i}}}^{{\boldsymbol{\theta }}}\) (J/mol) Mole Number of Structural Units (mol) Mass Action Concentration of Structural Units (−) \({{\boldsymbol{K}}}_{{\bf{c}}{\boldsymbol{i}}}^{{\boldsymbol{\theta }}}\) (−)
3(Ca2+ + O2−) + (Al2O3) = (3CaO·Al2O3) −21,757–29.288 T \({n}_{{\rm{c}}1}={n}_{3{\rm{CaO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({N}_{{\rm{c}}1}=\frac{{n}_{{\rm{c}}1}}{{\sum }^{}{n}_{i}}={N}_{3{\rm{CaO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({K}_{{\rm{c}}1}^{{\rm{\theta }}}=\frac{{N}_{c1}}{{N}_{{\rm{CaO}}}^{3}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}}\)
12(Ca2+ + O2−) + 7(Al2O3) = (12CaO·7Al2O3) 617,977–612.119 T \({n}_{{\rm{c}}2}={n}_{12{\rm{CaO}}\cdot 7{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({N}_{{\rm{c}}2}=\frac{{n}_{{\rm{c}}2}}{{\sum }^{}{n}_{i}}={N}_{12{\rm{CaO}}\cdot 7{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({K}_{{\rm{c}}2}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}2}}{{N}_{{\rm{CaO}}}^{12}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}^{7}}\)
(Ca2+ + O2−) + (Al2O3) = (CaO·Al2O3) 59,413–59.413 T \({n}_{{\rm{c}}3}={n}_{{\rm{CaO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({N}_{{\rm{c}}3}=\frac{{n}_{{\rm{c}}3}}{{\sum }^{}{n}_{i}}={N}_{{\rm{CaO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({K}_{{\rm{c}}3}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}3}}{{N}_{{\rm{CaO}}}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}}\)
(Ca2+ + O2−) + 2(Al2O3) = (CaO·2Al2O3) −16,736–25.522 T \({n}_{{\rm{c}}4}={n}_{{\rm{CaO}}\cdot 2{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({N}_{{\rm{c}}4}=\frac{{n}_{{\rm{c}}4}}{{\sum }^{}{n}_{i}}={N}_{{\rm{CaO}}\cdot 2{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({K}_{{\rm{c}}4}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}4}}{{N}_{{\rm{CaO}}}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}^{2}}\)
(Ca2+ + O2−) + 6(Al2O3) = (CaO·6Al2O3) −22,594–31.798 T \({n}_{{\rm{c}}5}={n}_{{\rm{CaO}}\cdot 6{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({N}_{{\rm{c}}5}=\frac{{n}_{{\rm{c}}5}}{{\sum }^{}{n}_{i}}={N}_{{\rm{CaO}}\cdot 6{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({K}_{{\rm{c}}5}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}5}}{{N}_{{\rm{CaO}}}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}^{4}}\)
(Ca2+ + O2−) + (TiO2) = (CaO·TiO2) −79,967.9–3.35 T \({n}_{{\rm{c}}6}={n}_{{\rm{CaO}}\cdot {{\rm{TiO}}}_{2}}\) \({N}_{{\rm{c}}6}=\frac{{n}_{{\rm{c}}6}}{{\sum }^{}{n}_{i}}={N}_{{\rm{CaO}}\cdot {{\rm{TiO}}}_{2}}\) \({K}_{{\rm{c}}6}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}6}}{{N}_{{\rm{CaO}}}{N}_{{{\rm{TiO}}}_{2}}}\)
3(Ca2+ + O2−) + 2(TiO2) = (3CaO·2TiO2) −207,247–11.51 T \({n}_{{\rm{c}}7}={n}_{3{\rm{CaO}}\cdot 2{{\rm{TiO}}}_{2}}\) \({N}_{{\rm{c}}7}=\frac{{n}_{{\rm{c}}7}}{{\sum }^{}{n}_{i}}={N}_{3{\rm{CaO}}\cdot 2{{\rm{TiO}}}_{2}}\) \({K}_{{\rm{c}}7}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}7}}{{N}_{{\rm{CaO}}}^{3}{N}_{{{\rm{TiO}}}_{2}}^{2}}\)
4(Ca2+ + O2−) + 3(TiO2) = (4CaO·3TiO2) −293,076–17.58 T \({n}_{{\rm{c}}8}={n}_{4{\rm{CaO}}\cdot 3{{\rm{TiO}}}_{2}}\) \({N}_{{\rm{c}}8}=\frac{{n}_{{\rm{c}}8}}{{\sum }^{}{n}_{i}}={N}_{4{\rm{CaO}}\cdot 3{{\rm{TiO}}}_{2}}\) \({K}_{{\rm{c}}8}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}8}}{{N}_{{\rm{CaO}}}^{4}{N}_{{{\rm{TiO}}}_{2}}^{3}}\)
(Mg2+ + O2−) + (Al2O3) = (MgO·Al2O3) −18,828–6.276 T \({n}_{{\rm{c}}9}={n}_{{\rm{MgO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({N}_{{\rm{c}}9}=\frac{{n}_{{\rm{c}}9}}{{\sum }^{}{n}_{i}}={N}_{{\rm{MgO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}}\) \({K}_{{\rm{c}}9}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}9}}{{N}_{{\rm{MgO}}}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}}\)
(Mg2+ + O2−) + (TiO2) = (MgO·TiO2) −26,376.8 + 3.14 T \({n}_{{\rm{c}}10}={n}_{{\rm{MgO}}\cdot {{\rm{TiO}}}_{2}}\) \({N}_{{\rm{c}}10}=\frac{{n}_{{\rm{c}}10}}{{\sum }^{}{n}_{i}}={N}_{{\rm{MgO}}\cdot {{\rm{TiO}}}_{2}}\) \({K}_{{\rm{c}}10}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}10}}{{N}_{{\rm{MgO}}}{N}_{{{\rm{TiO}}}_{2}}}\)
(Mg2+ + O2−) + 2(TiO2) = (MgO·2TiO2) −27,632.9 + 0.63 T \({n}_{{\rm{c}}11}={n}_{{\rm{MgO}}\cdot 2{{\rm{TiO}}}_{2}}\) \({N}_{{\rm{c}}11}=\frac{{n}_{{\rm{c}}11}}{{\sum }^{}{n}_{i}}={N}_{{\rm{MgO}}\cdot 2{{\rm{TiO}}}_{2}}\) \({K}_{{\rm{c}}11}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}11}}{{N}_{{\rm{MgO}}}{N}_{{{\rm{TiO}}}_{2}}^{2}}\)
2(Mg2+ + O2−) + (TiO2) = (2MgO·TiO2) −25,539.5 + 1.26 T \({n}_{{\rm{c}}12}={n}_{2{\rm{MgO}}\cdot {{\rm{TiO}}}_{2}}\) \({N}_{{\rm{c}}12}=\frac{{n}_{{\rm{c}}12}}{{\sum }^{}{n}_{i}}={N}_{2{\rm{MgO}}\cdot {{\rm{TiO}}}_{2}}\) \({K}_{{\rm{c}}12}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}12}}{{N}_{{\rm{MgO}}}^{2}{N}_{{{\rm{TiO}}}_{2}}}\)
(Al2O3) + (TiO2) = (Al2O3·TiO2) −25,270 + 3.924 T \({n}_{{\rm{c}}13}={n}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}\cdot {{\rm{TiO}}}_{2}}\) \({N}_{{\rm{c}}13}=\frac{{n}_{{\rm{c}}13}}{{\sum }^{}{n}_{i}}={N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}\cdot {{\rm{TiO}}}_{2}}\) \({K}_{{\rm{c}}13}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}13}}{{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}{N}_{{{\rm{TiO}}}_{2}}}\)
3(Ca2+ + O2−) + 3(Al2O3) + (Ca2+ + 2F2−) = (3CaO·2Al2O3·CaF2) −44,492–73.15 T \({n}_{{\rm{c}}14}={n}_{3{\rm{CaO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}\cdot {{\rm{CaF}}}_{2}}\) \({N}_{{\rm{c}}14}=\frac{{n}_{{\rm{c}}14}}{{\sum }^{}{n}_{i}}={N}_{3{\rm{CaO}}\cdot {{\rm{Al}}}_{2}{{\rm{O}}}_{3}\cdot {{\rm{CaF}}}_{2}}\) \({K}_{{\rm{c}}14}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}14}}{{N}_{{\rm{CaO}}}^{3}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}{N}_{{{\rm{CaF}}}_{2}}}\)
11(Ca2+ + O2−) + 7(Al2O3) + (Ca2+ + 2F2−) = (11CaO·7Al2O3·CaF2) −228,760–155.8 T \({n}_{{\rm{c}}15}={n}_{11{\rm{CaO}}\cdot 7{{\rm{Al}}}_{2}{{\rm{O}}}_{3}\cdot {{\rm{CaF}}}_{2}}\) \({N}_{{\rm{c}}15}=\frac{{n}_{{\rm{c}}15}}{{\sum }^{}{n}_{i}}={N}_{11{\rm{CaO}}\cdot 7{{\rm{Al}}}_{2}{{\rm{O}}}_{3}\cdot {{\rm{CaF}}}_{2}}\) \({K}_{{\rm{c}}15}^{{\rm{\theta }}}=\frac{{N}_{{\rm{c}}15}}{{N}_{{\rm{CaO}}}^{11}{N}_{{{\rm{Al}}}_{2}{{\rm{O}}}_{3}}^{2}{N}_{{{\rm{CaF}}}_{2}}}\)