Thermodynamic second-order interaction coefficients of nitrogen with nickel and chromium in liquid steel

The authors propose a simple theory of thermodynamic properties of liquid nitrogen solutions in alloys of the Fe – Ni and Fe – Cr systems. The theory is analogous to the theory of these systems proposed previously by the authors in 2019 and 2021. It is based on lattice model of the Fe – Ni and Fe – Cr solutions. The model assumes a FCC lattice. At the sites of this lattice are the atoms of iron, nickel and chromium. Nitrogen atoms are located in octahedral interstices. Nitrogen atom interacts only with the metal atoms located in the lattice sites neighboring to it. This interaction is pairwise. It is assumed that the energy of this interaction depends neither on composition nor on temperature and the liquid solutions of Fe – Ni and Fe – Cr systems are perfect. For an infinitely nitrogen-diluted solution of this element in the Fe – j alloy ( j = Ni, Cr), a rational nitrogen activity coeffi­cient \(\gamma _{\rm{N}}^0\) is determined. Next, we considered the expansion of the function ln\(\gamma _{\rm{N}}^0\) at a constant temperature in a series in powers of the argument c j , where c j is the concentration of the j component, expressed in mole fractions. The coefficient J n in the term of the n th degree of this expansion is called the thermodynamic n th order interaction coefficient of nitrogen with j element in liquid steel. In this case J 1 = \(\varepsilon _{\rm{N}}^j\) is called Wagner interaction coeffi­cient, J 2 = \(\rho _{\rm{N}}^j\) – the second order interaction coefficient. Within the framework of the presented theory the simplest relationship between the interaction coefficients \(\varepsilon _{\rm{N}}^j\) and \(\rho _{\rm{N}}^j\) was found. The formula looks like: \(\rho _{\rm{N}}^j = \frac{1}{{12}}{\left( {\varepsilon _{\rm{N}}^j} \right)^2}\). To verify this formula, experimental data on the solubility of nitrogen in liquid alloys of the Fe – Ni and Fe – Cr systems at a temperature of 1873 K, obtained by Satir-Kolorz and Feichtinger (1991) were used. From these data follows: \(\varepsilon _{\rm{N}}^{{\rm{Ni}}}\) = 2.6; \(\varepsilon _{\rm{N}}^{{\rm{Cr}}}\) = –10.2; \(\rho _{\rm{N}}^{{\rm{Ni}}}\) = 0.8; \(\rho _{\rm{N}}^{{\rm{Cr}}}\) = 6.3. The theoretical values calculated using the above formula are as follows: \(\rho _{\rm{N}}^{{\rm{Ni}}}\) = 0.56; \(\rho _{\rm{N}}^{{\rm{Cr}}}\) = 8.67. Bearing in mind the significant uncertainty in the experimental determination of the second order interaction coefficient of nitrogen with alloying elements in iron-based binary alloys, the correspondence between the theoretical and experimental results should be considered satisfactory.