Based on ab initio calculations within the density functional theory and crystal structure prediction algorithms, the structure and stability of iron-nitrogen compounds in the pressure range of 100-400 GPa and temperatures up to 4000 K were determined. Three new iron nitrides Fe4N3-Imm2, Fe2N-Pnma, and Fe3N-C2/m were predicted. Fe4N3 was shown to be stable at pressures up to 266 GPa and then decompose into Fe2N + 2FeN. Predicted Fe2N-Pnma becomes stable with respect to the decomposition reaction 9Fe2N = Fe4N3 + 2Fe7N3 at pressures above 221 GPa. Fe3N-C2/m stabilizes with respect to decomposition into 2Fe + Fe7N3 at pressures above 265 GPa. Also, it was shown that β-Fe7N3 synthesized in diamond anvil cell experiments has an orthorhombic Pbca structure, and at pressures above ∼320 GPa decomposes into 2Fe2N + Fe3N. All predicted Fe-rich iron nitrides, except Fe4N3-Imm2, have structural analogs among iron carbides. Considering the temperature effect, we observed that FeN-P213, Fe2N-Pnma, and Fe3N-C2/m can be stable at the Earth's inner core pressures and temperatures up to 4000 K, whereas Fe4N3-Imm2 and β-Fe7N3 are thermodynamically unstable in the entire studied temperature range. Although Fe7N3-Pbca is thermodynamically unstable at inner core pressures, it shows the closest coincidence of the S- and P-wave velocities with seismic observations among the studied Fe-nitrides. Overall, Fe-nitrides cannot be the major compounds in the inner core of the Earth and can only substitute other elements such as carbon in Fe-carbides in minor amounts.
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