Crystal structures and elastic properties of superhardIrN2andIrN3from first principles

First principles calculations were performed to investigate the structural, elastic, and electronic properties of $\mathrm{Ir}{\mathrm{N}}_{2}$ for various space groups: cubic $Fm\text{\ensuremath{-}}3m$ and $Pa\text{\ensuremath{-}}3$, hexagonal $P{3}_{2}21$, tetragonal $P{4}_{2}∕mnm$, orthorhombic $Pmmn$, $Pnnm$, and $Pnn2$, and monoclinic $P{2}_{1}∕c$. Our calculation indicates that the $P{2}_{1}∕c$ phase with arsenopyrite-type structure is energetically more stable than the other phases. It is semiconducting (the remaining phases are metallic) and contains diatomic N-N with the bond distance of $1.414\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. These characters are consistent with the experimental facts that $\mathrm{Ir}{\mathrm{N}}_{2}$ is in lower symmetry and nonmetallic. Our conclusion is also in agreement with the recent theoretical studies that the most stable phase of $\mathrm{Ir}{\mathrm{N}}_{2}$ is monoclinic $P{2}_{1}∕c$. The calculated bulk modulus of $373\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ is also the highest among the considered space groups. It matches the recent theoretical values of $357\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ within 4.3% and of $402\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ within 7.8%, but smaller than the experimental value of $428\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ by 14.7%. Chemical bonding and potential displacive phase transitions are discussed for $\mathrm{Ir}{\mathrm{N}}_{2}$. For $\mathrm{Ir}{\mathrm{N}}_{3}$, cubic skutterudite structure $(Im\text{\ensuremath{-}}3)$ was assumed. Our calculation indicated that it is also promising to be superhard due to the large bulk modulus of $358\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and shear modulus of $246\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. The diatomic N-N bond distance is even shorter $(1.272\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$.