Pressure-stabilized hafnium nitrides and their properties

We report hafnium nitrides under pressure using first-principles evolutionary calculations. Metallic $P{6}_3/mmc$-HfN (calculated Vickers hardness 23.8 GPa) is found to be more energetically favorable than NaCl-type HfN at zero and high pressure. Moreover, NaCl-type HfN actually undergoes a phase transition to $P{6}_3/mmc$-HfN below 670 K at ambient pressure. ${\mathrm{HfN}}_{10}$, which simultaneously has infinite armchairlike polymeric N chains and ${\mathrm{N}}_2$ molecules in its crystal structure, is discovered to be stable at moderate pressure above 23 GPa and can be preserved as a metastable phase at ambient pressure. At ambient conditions (298 K, 0 GPa), the gravimetric energy densities and the volumetric energy densities of ${\mathrm{HfN}}_{10}$ are 2.8 kJ/g and 14.1 kJ/${\mathrm{cm}}^3$, respectively.

Figure 1

Pressure-composition phase diagram of the Hf-N system.

Figure 2

Enthalpy-pressure diagrams of ${\mathrm{Hf}}_2\mathrm{N}$ and ${\mathrm{Hf}}_3{\mathrm{N}}_4$. $Cmcm-{\mathrm{Hf}}_2\mathrm{N}$ and $I\overline{4}3d-{\mathrm{Hf}}_3{\mathrm{N}}_4$ are taken as a reference for ${\mathrm{Hf}}_2\mathrm{N}$ and ${\mathrm{Hf}}_3{\mathrm{N}}_4$, respectively. $Fd\overline{3}m-{\mathrm{Hf}}_3{\mathrm{N}}_4$ belongs to the spinel type.

Figure 3

Enthalpy-pressure diagrams of HfN and ZrN in (a), (b) GGA and (c), (d) LDA, respectively (relative to the NaCl-type HfN and NaCl-type ZrN), and (e), (f) free enthalpy as a function of temperature of $P{6}_3/mmc$ and NaCl-type structures for HfN and ZrN obtained by the quasiharmonic approximation (QHA) method and the GGA.

Figure 4

ELF isosurface ($\text{ELF}=0.85$) of (a) $P{6}_3/mmc$-HfN and (c) $Immm-{\mathrm{HfN}}_{10}$ at 0 GPa, (b) density of states and COHP for $P{6}_3/mmc$-HfN, and (d) the composition illustration of $Immm-{\mathrm{HfN}}_{10}$ (the bond length is in Å). Hf-centered polyhedra are dark yellow; part of the infinite N chain and $\mathrm{N}\equiv \mathrm{N}$ bonds are also displayed in (d). Large gray spheres, Hf atoms; small blue spheres, N atoms.