Abstract

A simple theory of thermodynamic properties of liquid nitrogen solution in Fe–Mn alloys is proposed. This theory is completely analogous to the theory for liquid nitrogen solution in alloys of the Fe–Cr system proposed previously by the authors in 2019. The theory is based on the lattice model of the considered Fe–Mn solutions. The model assumes a FCC lattice. The atoms of Fe and Mn are in these lattice sites. 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 and it is assumed that the energy of this interaction depends neither on the composition nor on the temperature. Furthermore, the solution in the Fe–Mn system is assumed to be perfect. Within the framework of the proposed theory, a relation was obtained that expresses the value of the Sieverts law constant for N solubility in liquid Mn through the similar constant for the N solubility in liquid Fe and the Wagner N–Mn interaction coefficient in liquid Fe. The values of the Sieverts law constants in this relation are taken directly from the experimental measurements of the solubility of N in liquid Fe and in liquid Mn. In this case, the obtained relation is considered as an equation with respect to the Wagner interaction coefficient \(\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}\). The equation’s solution gives the value of Wagner interaction coefficient \(\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}\) = –5.25 in liquid steel at a temperature of 1873 K. Wagner interaction coefficient \(\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}\) is related with Langenberg interaction coefficient \(e_{{\text{N}}}^{{{\text{Mn}}}}\) by the relation deduced by Lupis and Elliott in 1965. The relation includes the atomic masses of Fe and Mn. By substituting the value \(\varepsilon _{{\text{N}}}^{{{\text{Mn}}}}\) = –5.25 and solving the resulting equation with respect to \(e_{{\text{N}}}^{{{\text{Mn}}}}\), we obtain the value \(e_{{\text{N}}}^{{{\text{Mn}}}}\) = –0.0230. This value corresponds to the experimental data of Beer (1961), which is likely one of the most probable of all experimental values of \(e_{{\text{N}}}^{{{\text{Mn}}}}\) for liquid steel at 1873 K. Another such value is \(e_{{\text{N}}}^{{{\text{Mn}}}}\) = 0.0209 obtained by Shin with coworkers in 2011.

中文翻译：

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液态钢中氮与锰之间的热力学一阶相互作用系数

摘要

提出了一种简单的Fe-Mn合金液氮溶液热力学性质的理论。该理论与作者先前于2019年提出的Fe-Cr系合金液氮溶液理论完全相似。该理论基于所考虑的Fe-Mn溶液的晶格模型。该模型假设FCC晶格。Fe和Mn的原子在这些晶格位点中。氮原子位于八面体间隙中。氮原子仅与位于与其相邻的晶格位中的金属原子相互作用。该相互作用是成对的，并且假定该相互作用的能量既不依赖于组成也不依赖于温度。此外，假定Fe–Mn体系中的溶液是完美的。在提出的理论的框架内，得到了一个关系，该关系通过类似于液态Fe中N溶解度的常数和液态Fe中Wagner N-Mn相互作用系数来表达Sieverts法则常数，用于描述Mn在液态Mn中的溶解度。在这种关系中，Sieverts定律常数的值直接从N在液态Fe和液态Mn中的溶解度的实验测量中得出。在这种情况下，将获得的关系视为关于瓦格纳相互作用系数的方程式 在这种关系中，Sieverts定律常数的值直接从N在液态Fe和液态Mn中的溶解度的实验测量中得出。在这种情况下，将获得的关系视为关于瓦格纳相互作用系数的方程式 在这种关系中，Sieverts定律常数的值直接从N在液态Fe和液态Mn中的溶解度的实验测量中得出。在这种情况下，将获得的关系视为关于瓦格纳相互作用系数的方程式\（\ varepsilon _ {{\ text {N}}} ^ {{{\ text {Mn}}}} \）。该方程的解给出了在温度为1873 K的钢中瓦格纳相互作用系数\（\ varepsilon _ {{\ text {N}}} ^ {{{\ text {Mn}}}} \） = –5.25的值。Wagner相互作用系数\（\ varepsilon _ {{{text {N}}}} \ {{{\ text {Mn}}}} \}与Langenberg相互作用系数\（e _ {{\ text {N}}} ^ {{{{text {Mn}}}}} \）由Lupis和Elliott于1965年推导。该​​关系包括Fe和Mn的原子质量。通过替换值\（\ varepsilon _ {{\ text {N}}} ^ {{{\ text {Mn}}}} \} = –5.25并针对\（e _ {{\ text {N}}} ^ {{{{\ text {Mn}}}} \\）中，我们获得了该值\（e _ {{\ text {N}}} ^ {{{\ text {Mn}}}} \） = –0.0230。此值对应于Beer（1961）的实验数据，它可能是\（e _ {{\ text {N}}} ^ {{{\ text {Mn}}}}的所有实验值中最有可能的之一\）用于1873 K的液态钢。另一个这样的值是Shin和同事在2011年获得的\（e _ {{\ text {N}}} ^ {{{\ text {Mn}}}} \） = 0.0209。