Solubility Products and Equilibrium Equations of Carbonitrides in Steels: Thermodynamic Calculations

Thermodynamic models are established to deduce solubility products of titanium, niobium and vanadium carbonitrides in austenite and ferrite containing solid solution elements, respectively. Equilibrium equations are introduced to approximate the fraction and specific chemical formula of carbonitride in steels under given compositions. The thermodynamic interaction parameters in the solubility product expressions of these carbonitrides are sifted through the best agreements on calculation results and measured data from references. It is shown that (i) the deduced solubility products in this study are in accordance with previous studies; (ii) the fraction and specific chemical formula of carbonitride depends on both the temperature and the composition of the steel; and (iii) the formation of niobium carbonitride in steels can promote the precipitation of niobium when the mole ratio of carbon in carbonitride is small. This study can guide titanium, niobium and vanadium microalloying in low carbon steels and provide references for solubility product deducing and the fraction and chemical formula calculations of other ternary compounds in steels. The deduced solubility products of carbonitrides are (solubility products of carbides and nitrides are referenced from our previous work)

\(\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{{\mathrm{TiC}}_{ x}{\mathrm{N}}_{1-x}}\cong x\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{\mathrm{TiC}}+\left(1-x\right)\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{\mathrm{TiN}}+x\left(1-x\right)\frac{121}{T}+x\mathrm{log}x+\left(1-x\right)\mathrm{log}\left(1-x\right)\)

\(\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{{\mathrm{NbC}}_{ x}{\mathrm{N}}_{1-x}}\cong x\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{\mathrm{NbC}}+\left(1-x\right)\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{\mathrm{NbN}}+x\left(1-x\right)\frac{98}{T}+x\mathrm{log}x+\left(1-x\right)\mathrm{log}\left(1-x\right)\)

\(\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{{\mathrm{VC}}_{ x}{\mathrm{N}}_{1-x}}\cong x\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{\mathrm{VC}}+\left(1-x\right)\mathrm{log}{{}{}^{\gamma /\mathrm{\alpha }}K}_{\mathrm{VN}}+x\left(1-x\right)\frac{13}{T}+x\mathrm{log}x+\left(1-x\right)\mathrm{log}\left(1-x\right)\)