Hard and superhard materials have brought substantial interest because of their wide technological applications in industry and the fundamental importance in condensed-matter physics. In conventional design of superhard materials such as diamond and cubic boron nitride, the pure covalent bonding network based on B-C-N-O systems is believed to provide both the low elastic compressibility and the high resistance to plastic deformation. Nevertheless, such pure localized covalence bonds also discourage electron transport in the B-C-N-O systems, making them large-gap insulators and severely limit their diverse applications such as hard coating, anvils of large volume press, etc. In this sense, employing high electrical conductivity to superhard materials to make “metallic diamond” becomes an urgent task for the research of superhard materials.

After careful exploration, Dr Xiaohui Yu, Dr Hui Li, Ma Teng, Xu Zheng, Prof. Changqing Jin, from Institute of Physics, Chinese Academy of Sciences, have found the high-boron-content TM borides, ZrB₁₂, can possess both superhard mechanical properties and extremely high electrical conductivity.

Figure 1 shows the crystal structure of ZrB₁₂ with space group of Fm3m refined from XRD pattern. The crystal structure of ZrB₁₂ is tessellated by truncated octahedrons, where the B atoms occupy the vertices～forming the basic frameworks and the Zr atoms locate in the center of cages. Remarkably, these highly symmetrical polyhedrons formed by B-B bonds show no prominent shear path and the B-B bonds with bonding distances of 1.68 and 1.78 Å. Both of the above features predict the high resistance to the plastic deformation of ZrB₁₂.

The Vickers hardness measurements were performed on the bulk polycrystalline and single crystal samples. As shown in Figure 2, the determined Vickers hardness of polycrystalline ZrB₁₂ is ~ 45.0 (1.5) GPa under the load of 25 g and 40.2 (1.2) GPa under the load of 50 g, which exhibits the superhard property. When the load is increased from 25 g to 500 g, the measured Vickers hardness decreases and saturates at ~27.0 GPa, suggesting that ZrB₁₂ is intrinsically in the regime of hard materials. Furthermore, the measurements of the Vickers hardness on single crystal ZrB₁₂ show highly isotropic property on the {100}, {110}, {111} planes, which should be due to the high symmetric frameworks formed by B-B clusters.

In order to underline the physical origin of high hardness of ZrB₁₂, the researchers have performed the first principle calculations. The anisotropic ideal shear strength of ZrB₁₂ is accordingly derived from the calculated stress-strain relationships along different slip systems which are presented in Figure 3. It is seen that the shear strengths of ZrB₁₂ is nearly isotropic within {111} planes with the minimum value of 34.5 GPa appearing along {111} [-1-12] deformation path, which is comparable to that B6O (38 GPa). Such results are in consistency with our experiments.

As shown in Figure 4, all the electric resistivity curves in different planes of ZrB₁₂ show metallic behavior and a sharp superconducting transition at Tc= 5.5 K. In the case of ZrB₁₂, the Zr atoms are constrained in the B-B truncated octahedrons, the distance between two nearest-neighbor Zr atoms (5.2 Å) is much larger than its Van der Waals diameter (3.2 Å), indicating the valence electrons cannot freely parade between Zr atoms. Surprisingly, the ZrB₁₂ possesses such low electrical resistivity ～18 μΩ · cm (at RT), which is comparable to that of Pt～20 μΩ · cm (RT). Furthermore, the Seebeck coefficient of ZrB₁₂ is only 2.0 μV/K at RT, which is also comparable to that of Cu and Pt, and could identify its excellent electrical transport behaviors as a metallic conductor.

To figure out the origin of the high electron conductivity of ZrB₁₂, the projected electronic density of states (PDOS) is calculated and shown in Figure 5, which exhibits the bulk ZrB₁₂ is metallic (Figure 5a). Twelve intersections between conduction bands and the Fermi level have been found on band structure throughout all the symmetry pathways in the Brillouin zone, as shown in Figure 5b. Therefore, based on the first principles calculation, we have confirmed the π-bonds between 2 icosahedral B12 motifs and Zr 4d orbitals can form highly dispersive bands at the Fermi level. Such conducting channels make ZrB₁₂ a great conductor (Figure 5c-f).

This study entitled “Ultrastrong Boron Frameworks in ZrB₁₂ : A Highway for Electron Conducting” was published on Advanced Materials. The study was supported by National Science Foundation of China.