High-pressure stability and mechanical properties of manganese nitrides: A DFT study

Abstract

Based on the evolutionary algorithms and the density functional theory, an extensive search for the stable manganese–nitrogen compounds and their structures was conducted in the pressure range of 0–200 GPa. As a result, one new manganese nitride Mn${}_5$N${}_2$ was predicted, and the stability fields of the manganese nitrides were determined. It was demonstrated that there are six stable compounds in the Mn–N system at a pressure up to 200 GPa, namely Mn${}_3$N, Mn${}_2$N, Mn${}_5$N${}_2$, MnN, MnN${}_2$, and MnN${}_4$. Mn${}_3$N is stable in the form of the $P\bar{6}m2$ structure up to 191 GPa without any structural phase transition, and above this pressure, it decomposes into the isochemical mixture. Mn${}_2$N has one stable modification $P{6}_3/mmc$, which remains its stability in the entire considered pressure range. Previously unknown nitride Mn${}_5$N${}_2$ stabilizes above 180 GPa in the $C2/m$ structure. MnN${}_2$ stabilizes above 8 GPa and has three stable modifications $P{2}_1/m$, $P\bar{1}$, and $Cmc{2}_1$. MnN${}_2$-$Pm$, which has a narrow stability pressure range (145–147 GPa), was shown to be metastable when taking into account the zero-point energy contribution and the temperature effect. MnN${}_4$ is formed above 38 GPa and has one stable modification $P\bar{1}$. The calculations of phonon spectra and elastic constants indicate that all predicted manganese nitrides exhibit dynamic and mechanical stability in the corresponding pressure ranges. Meanwhile, for the first time, the P–T phase diagrams of Mn${}_3$N, Mn${}_5$N${}_2$, MnN${}_2$, and MnN${}_4$ were successfully determined using the quasiharmonic approximation. In addition, for the predicted phases, the mechanical properties were estimated and, as a result, four manganese nitrides (namely MnN${}_4$-$P\bar{1}$, Mn${}_3$N-$P\bar{6}m2$, Mn${}_5$N${}_2$-$C2/m$, and MnN${}_2$-$P{2}_1/m$) were observed to be hard materials.