Extraordinary Indentation Strain Stiffening Produces Superhard Tungsten Nitrides

Transition-metal light-element compounds are a class of designer materials tailored to be a new generation of superhard solids, but indentation strain softening has hitherto limited their intrinsic load-invariant hardness to well below the 40 GPa threshold commonly set for superhard materials. Here we report findings from first-principles calculations that two tungsten nitrides, hP4-WN and $\mathrm{hP}6\text{−}{\mathrm{WN}}_2$, exhibit extraordinary strain stiffening that produces remarkably enhanced indentation strengths exceeding 40 GPa, raising exciting prospects of realizing the long-sought nontraditional superhard solids. Calculations show that hP4-WN is metallic both at equilibrium and under indentation, marking it as the first known intrinsic superhard metal. An x-ray diffraction pattern analysis indicates the presence of hP4-WN in a recently synthesized specimen. We elucidate the intricate bonding and stress response mechanisms for the identified structural strengthening, and the insights may help advance rational design and discovery of additional novel superhard materials.

Figure 1

(a) The crystal structure of hP4-WN at equilibrium (top) and projected onto the ($1\overline{1}0$) plane (bottom); (b) calculated stress responses under tensile strains along various high-symmetry directions; [(c) and (d)] calculated stress responses under pure shear and indentation shear strains in the ($1\overline{1}0$) plane along the [001] or [110] shear direction, and the W-W bond length ($l$) in the (001) plane up to the peak indentation strain. The bottom panels show the structural snapshots at two key points before and after the large drop of stress on each stress-strain curve under pure and indentation strains shown in (c) and (d).

Figure 2

(a) The crystal structure of $\mathrm{hP}6\text{−}{\mathrm{WN}}_2$ at equilibrium (top) and projected onto the ($1\overline{1}0$) plane (bottom); (b) calculated stress responses under tensile strains along various high-symmetry directions; [(c) and (d)] calculated stress responses under pure shear and indentation shear strains in the ($1\overline{1}0$) plane along the [001] or [110] shear direction, and the W-W bond length ($l$) in the (001) plane up to the peak indentation strain. The bottom panels show the structural snapshots at two key points before and after the large drop of stress on each stress-strain curve under pure and indentation strains shown in (c) and (d).

Figure 3

(a) Fitting experimental XRD on a synthesized tungsten nitride specimen [34] by the cP6-WN phase. (b) Fitting experimental XRD on another tungsten nitride specimen by separating the measured spectra into two sets, one from the reactant cP6-WN phase and the other from the resultant hP4-WN phase. The x-ray wavelength is ${\lambda }_{\mathrm{Cu}}=1.5406\AA$.