First principles of calculation of the energy of mixing and magnetic moments of components of alloys $\mathrm{Fe}$–$\mathrm{Mn}$, $\mathrm{Fe}$–$\mathrm{Cr}$ and $\mathrm{Fe}$–$\mathrm{Ni}$–$\mathrm{C}$ with BCC and FCC lattices

The concentration dependence of mixing energy and magnetic moments on the atoms of components in FCC and BCC solid substitution solutions of manganese, chromium and nickel in iron. It was established that mixing energy in the $\alpha$-and $\gamma$-solutions not only have different values, but also the sign. It is shown that for $\alpha$-solid solution near $10\% \mathrm{Cr}$ and $1,5\% \mathrm{Mn}$ there is thermodynamic anomaly — changing the concentration dependence of the mixing energy.