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Recent theoretical calculations predict an ideal shear strength over 50 GPa for CrB4, placing it well above ultrahard ReB2 in terms of strength and thus suggesting possible superhardness of CrB4. This result, however, is contradicted by the latest experimental measurements that produced a relatively low Vickers hardness around 23 GPa, which is about the same as the hardness value of ReB2. To solve this intriguing problem, we have performed a systematic first-principles study that unveils two fundamental constraints that limit the strength of CrB4: (i) a quantum-mechanical effect involving a transition between two-center and three-center bonding among the boron atoms that reduces the rigidity and directionality of the boron bonding and (ii) a mechanistic effect caused by the pressure beneath the indenter that drives a lateral bond and volume expansion that further stretches and weakens the boron bonds in addition to the shear deformation in the CrB4 structure under Vickers indentation hardness tests. These effects lead to considerably reduced strength of CrB4, producing an ideal (i.e., an upper bound) indentation strength of 27 GPa that is consistent with the experimental results. These constraints also explain previous results on the pure shear and indentation strength for ReB2, WB3, and MoB3, limiting their ideal (Vickers) indentation strength below 30 GPa irrespective of the composition and structural details. The present results suggest that transition-metal boron compounds are unlikely to become superhard as previously predicted.

physical review. b, condensed matter and materials physics

Fundamental constraints on the strength of transition-metal borides: The case of CrB<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>4</mml:mn></mml:msub></mml:math>

Fundamental constraints on the strength of transition-metal borides: The case of CrB4