By electron and x-ray diffraction we establish that the CrB${}_4$ compound discovered over 40 years ago crystallizes in the $oP10$ (Pnnm) structure, in disagreement with previous experiments but in agreement with a recent first-principles prediction. The 3D boron network in this structure is a distorted version of the rigid carbon $s{p}^3$ network proposed recently for the high-pressure C${}_4$ allotrope. Our systematic density functional theory analysis of the electronic, structural, and elastic properties in ten related transition metal TMB${}_4$ tetraborides (TM = Ti, V, Cr, Mn, Fe and Y, Zr, Nb, Mo, Tc) identifies CrB${}_4$ as the prime candidate to be a superhard material. In particular, the compound's calculated weakest shear and tensile stresses exceed 50 GPa, and its Vickers hardness is estimated to be 48 GPa. We compare the reported and estimated Vickers hardness for notable (super)hard materials and find that the CrB${}_4$ calculated value is exceptionally high for a material synthesizable under standard ambient-pressure conditions.

• Received 9 August 2011

DOI:https://doi.org/10.1103/PhysRevB.85.144116