Superhard metallic compound ${\mathrm{TaB}}_2$ via crystal orientation resolved strain stiffening

We predict then produce superhard metallic compound ${\mathrm{TaB}}_2$ via exploring crystal orientation resolved stress-strain relations. First-principles calculations identify prominent strain stiffening that generates superhigh indentation strengths of 46–49 GPa in the (001) oriented ${\mathrm{TaB}}_2$ crystal; in sharp contrast, dynamic instability diminishes strain stiffening even causes softening, leading to notably lower strengths around 30 GPa in the (110) and (100) orientations. Ensuing experimental synthesis creates well crystallized and textured (001) oriented ${\mathrm{TaB}}_2$ that exhibits indentation hardness of 45.9 GPa and electrical resistivity of $1.71\times {10}^{-6}\mathrm{\Omega }\mathrm{m}$, validating key superhard and metallic benchmarks. The present findings showcase an enabling protocol of crystal configuration engineering for selective property optimization, opening a path for rational design and discovery of long-sought but hitherto scarcely produced superhard metallic materials among vast transition-metal compounds.

Figure 1

(a) Crystal structure of ${\mathrm{TaB}}_2$ in 3D views and in the (001) plane. (b) Calculated stress responses to the indicated PS and BIS strains. Enlarged symbols mark the highest stress and strain values right before the onset of dynamic instability without reaching the elastic limits in the PS cases and at the elastic limits in the BIS case. [(c),(d)] Bond-length changes under the (001)[100] and (001)[210] PS and BIS strains. [(e),(f)] Calculated phonon dispersions at the (001)[100] PS (prior and post dynamic instability) and BIS (elastic limit) strains, and similar results at the (001)[210] PS and BIS strains are given in Fig. 2; (g) Atomic displacements of soft phonon modes under the (001)[100] PS strains in (e) and strengthened stable bonding patterns under the (001)[100] BIS strains in (f). Main load-bearing bonds are highlighted by thicker lines.

Figure 2

Calculated phonon dispersion curves for the strained ${\mathrm{TaB}}_2$ under (a) the (001)[210] PS strains, (b) the (001)[210] BIS strains, (c) the (110)[001] PS strains, (d) the (110)[001] BIS strains, (e) the (100)[001] PS strains, and (f) the (100)[001] BIS strains. The results show the appearance of imaginary phonon modes under PS strains [as shown in (a), (c), and (e)] indicating the onset of dynamic instability of the deformed structure along the indicated deformation paths and the success [as shown in (b) at the elastic limit strain] or failure [as shown in (d) and (f)] of suppressing the dynamic instability under the corresponding BIS strains.

Figure 3

[(a),(e)] Calculated stress responses to the indicated PS and BIS strains in the (110) and (100) planes. Enlarged symbols mark the data points with the highest stress and strain values right before the onset of dynamic instability. Calculated phonon dispersions right before and after the development of imaginary phonon modes under the [(b),(c)] (110)[-110] and [(f),(g)] (100)[101] PS and BIS strains, along with [(d),(h)] the associated soft-phonon atomic displacements. Phonon dispersions showing similar imaginary modes under the (110)[001] and (100)[001] PS and BIS strains are given in Fig. 2.

Figure 4

Structural and mechanical characterization of ${\mathrm{TaB}}_2$. (a) The XRD pattern. (b) The HRTEM image, showing the 0.169 nm spacing between the (002) planes. (c) The contour plots of pole figures in the (001) and (101) planes with the stereographic projections across zenithal ($\psi =0-{81}^{\circ }$) and azimuthal ($\varphi =0-{360}^{\circ }$) angles. (d) A typical nanoindentation curve as a function of indentation displacement depth. Results from a depth range of 50–120 nm (red symbols) are used to determine the intrinsic hardness. Also shown is a calibration curve on the standard fused quartz, well reproducing its known hardness of 10 GPa [64].

Figure 5

Calculated electronic density of states (DOS) of ${\mathrm{TaB}}_2$ under selected pure shear (PS) and Berkovich indentation shear (BIS) strains along the indicated shear slip directions. The results show that the DOS at the largest strain determined by the dynamic or elastic stability, whichever occurs first, in each case remains little changed in the strained crystal structures compared to the result for the crystal at equilibrium at $\epsilon =0$, indicating robust metallicity of ${\mathrm{TaB}}_2$ under diverse loading conditions examined in this work.