Wagner interaction coefficients of nitrogen with chromium and molibdenum in liquid nickel-based alloys

Abstract

The authors propose a simple theory of thermodynamic properties of liquid nitrogen solutions in alloys of the Fe – Ni – Cr and Fe – Ni – Mo systems. This theory is analogous to the theory for liquid nitrogen solutions in binary alloys of the Fe – Cr and Fe – Ni systems proposed previously by the authors in 2019 and 2021. The theory is based on lattice model of ternary liquid solutions of the Fe – Ni – Cr and Fe – Ni – Mo systems. The model assumes a FCC lattice. Atoms of Fe, Ni, Cr and Mo are deposed in the sites of the lattice. Nitrogen atoms are located in octahedral interstices. The 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. It is supposed that the liquid solutions in the Fe – Ni – Cr and Fe – Ni – Mo systems are perfect. Within the framework of the proposed theory, the relation is obtained that expresses the Wagner interaction coefficient between nitrogen and chromium in liquid nickel-based alloys \(\varepsilon _{\rm{N}}^{{\rm{Cr}}}\)(Ni). The right-hand part of the appropriate formula is a function of the Wagner interaction coefficients between nitrogen and chromium \(\varepsilon _{\rm{N}}^{{\rm{Cr}}}\)(Fe) and between nitrogen and nickel \(\varepsilon _{\rm{N}}^{{\rm{Ni}}}\)(Fe) in liquid iron-based alloys. A similar relation is obtained for the Wagner interaction coefficient between nitrogen and molybdenum in liquid nickel-based alloys \(\varepsilon _{\rm{N}}^{{\rm{Mo}}}\)(Ni). According to the first of these formulas, the value \(\varepsilon _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –21,9 at a temperature of 1873 K is calculated. This corresponds to the value of the Langenberg interaction coefficient \(e _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –0,108, which coincides with experimental estimate. According to the second formula, the value \(\varepsilon _{\rm{N}}^{{\rm{Mo}}}\)(Ni) = –14,3 is calculated at a temperature 1873 K. This corresponds to the value of the Langenberg interaction coefficient \(e _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –0,036, which is in satisfactory agreement with the experimental estimate \(\varepsilon _{\rm{N}}^{{\rm{Mo}}}\)(Ni) = –15,1; \(e _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –0,038.