Anchoring effect of distorted octahedra on the stability and strength of platinum metal pernitrides

The successful preparation of platinum metal pernitrides ($\mathrm{Pm}{\mathrm{N}}_2$) in high-temperature and high-pressure experiments has aroused great scientific interest, since it has long been thought that these systems could not be prepared, and also because of their intriguing mechanical properties. Although it is now widely recognized that $\mathrm{Pm}{\mathrm{N}}_2$ phases can be stabilized under high pressure, the physical origin explaining their stability remains unknown. By means of high-throughput first-principles schemes, we reveal that the choice of specific space group of these pernitrides at high pressure can be quantified by the anchoring effect of distorted $\mathrm{Pm}{\mathrm{N}}_6$ octahedra. The competition between baddeleyite and marcasite is attributed uniquely to Pm dimerization, resulting in a profound enhancement of Pm-Pm bonding and N-N $\pi$ antibonding, while Pm-N bonding plays a secondary role. The observed mechanical strength and atomic deformation mechanism of $\mathrm{Pm}{\mathrm{N}}_2$ suggest that they are ultraincompressible yet soft. This is attributed to the breaking of elongated Pm-N bonds in the $\mathrm{Pm}{\mathrm{N}}_6$ octahedra, which is accompanied by a continuous semiconductor-semimetal-metal transition for the semiconducting $\mathrm{Pm}{\mathrm{N}}_2$ during straining. These findings shed light on the physical origin of high-pressure stabilization and highlight the importance of exploring deformation mechanisms in designing novel strong solids.

Figure 1

The high-throughput screening of the most stable structures of (a) $\mathrm{Os}{\mathrm{N}}_2$, (b) $\mathrm{Ir}{\mathrm{N}}_2$, and (c) $\mathrm{Pt}{\mathrm{N}}_2$ according to the 265 crystallographic structure prototypes collected in the ICSD library. (d)–(f) The enthalpy-pressure relationships of (d) $\mathrm{Os}{\mathrm{N}}_2$, (e) $\mathrm{Ir}{\mathrm{N}}_2$, and (f) $\mathrm{Pt}{\mathrm{N}}_2$ in six selected structures, i.e., simple hexagonal $(P6/mmm)$, baddeleyite $(P{2}_1/c)$, marcasite (Pnnm), pyrite ($Pa$-3), cubic ($Fm\text{−}3m$), and simple tetragonal $(P4/mbm)$.

Figure 2

(a) Calculated formation enthalpies $\mathrm{\Delta }H$ (unit: eV/atom), PV term $PV$ (unit: eV/atom), and bond lengths $d_{\mathrm{N}\text{−}\mathrm{N}}$ (unit: $\AA$) of N-N pairs as a function of the transition metal in pernitrides assuming the baddeleyite, marcasite, and pyrite structures at 50 GPa. The inset shows an enlarged view for $\mathrm{W}{\mathrm{N}}_2\text{−}\mathrm{Pt}{\mathrm{N}}_2$. (b), (c) Calculated COHP curves of (b) baddeleyite and (c) marcasite structures of $\mathrm{Os}{\mathrm{N}}_2$, $\mathrm{Ir}{\mathrm{N}}_2$, and $\mathrm{Pt}{\mathrm{N}}_2$.

Figure 3

(a) Qualitative molecular-orbital diagram of ${\mathrm{N}}_2$ with different degrees of electron filling. (b) A comparison of a structural distortion diagram and partial density of states (PDOS) of baddeleyite- and marcasite-type structure. (c) An illustration of structural evolution of $\mathrm{Ir}{\mathrm{N}}_2$ under shear strain along the weakest path.

Figure 4

The calculated stress σ and bond length $d_{\text{Ir-N}}$ vs strain $\varepsilon$ curves of $\mathrm{Ir}{\mathrm{N}}_2$ along the weakest shearing path. We selected four snapshots of the deformed orbital-resolved band structures and the valence charge-density differences (VCDD) under different shear strains to reveal the electronic origin. The orange, blue, and green colors represent three $p$ orbitals of N, respectively. The isosurface of the VCDD corresponds to $\pm 0.022e^{-}/\mathrm{boh}{\mathrm{r}}^3$.