Solubility Product and Equilibrium Equations of Nonstoichiometric Niobium Carbonitride in Steels: Thermodynamic Calculations

Abstract

Thermodynamic models were established based on our previous studies to describe the equilibrium between the nonstoichiometric compound Nb(C,N) and the Fe-base solid solution (austenite and ferrite). With the assumption of equilibrium between fcc Nb and the Fe-based solid solution, the solubility of fcc Nb in the Fe-based solid solution was developed. Thus, the solubility product and equilibrium equations of NbC_xN_y in the Fe-base solid solution were further deduced. Two other thermodynamic interaction parameters for NbC_xN_y were considered in this study. The deduced solubility product of NbC_xN_y was in accordance with previous studies. The calculation results on compound NbC_xN_y in this study were in good agreement with both the measured data from the references and the calculation results from ThermoCalc. The deduced solubility expressions of fcc Nb provided references for developing solubility products of nonstoichiometric fcc Nb compounds in Fe-based solid solutions. This study offers guidance on the equilibrium of nonstoichiometric compounds in solid solutions. The solubility product of NbC_xN_y is (the solubility products of NbC and NbN are referenced from our previous work)

$$\log {}_{ }^{{\alpha /{\upgamma }}} K_{{{\text{NbC}}_{ x} {\text{N}}_{y} }}^{ } \cong x\log {}_{ }^{{\alpha /{\upgamma }}} K_{{{\text{NbC}}}}^{ } + y\log {}_{ }^{{\alpha /{\upgamma }}} K_{{{\text{NbN}}}}^{ } + \left( {1 - x - y} \right)\log {}_{ }^{{\alpha /{\upgamma }}} K_{{{\text{Nb}}}}^{ } + xy\frac{98}{T} - x\left( {1 - x - y} \right)\frac{4439}{T} - y\left( {1 - x - y} \right)\frac{3413}{T} + x{\text{log}}x + y{\text{log}}y + \left( {1 - x - y} \right){\text{log}}\left( {1 - x - y} \right)$$

$$\begin{gathered} \log {}_{ }^{\alpha } K_{{{\text{Nb}}}}^{ } = 1.92 + \frac{1227}{T} + \left( {0.051 - \frac{46.8}{T}} \right)\left[ {\text{wt pct Mn}} \right] + \left( {0.013 - \frac{6.0}{T}} \right)\left[ {\text{wt pct Ni}} \right] \hfill \\ \end{gathered}$$

$$\begin{gathered}\log {}_{ }^{\gamma } K_{{{\text{Nb}}}}^{ } = 1.65 + \frac{1365}{T} + \left( {0.008 - \frac{20.9}{T}} \right)\left[ {\text{wt pct Mn}} \right] + \left( {0.012 + \frac{23.3}{T}} \right)\left[ {\text{wt pct Ni}} \right] + \left( {0.003 - \frac{9.7}{T}} \right)\left[ {\text{wt pct Cr}} \right] - 0.004\left[ {\text{wt pct Mo}} \right] \hfill \\ \end{gathered}$$

Appendix

See Table AI

Table A1 Nomenclature