Elucidating Stress-Strain Relations of ZrB₁₂ from First-Principles Studies

Transition-metal boron-rich compounds exhibit favorable synthesis conditions and mechanical properties that hold great promise for wide-ranging applications. However, the complex bonding networks of these compounds produce diverse structural and mechanical behaviors that require in-depth studies. A notable case is ZrB₁₂, which has been reported to possess high Vickers hardness comparable to those of ReB₂ and WB₄. Surprisingly, first-principles calculations of stress-strain relations reveal unexpected low indentation strengths of ZrB₁₂ well below those of ReB₂ and WB₄. Such contrasting results are reconciled by noting that the additional presence of a boron-rich phase of ZrB₅₀ in the experimental synthesis process likely plays a key role in the extrinsic strengthening. These findings uncover mechanisms for the higher measured strength of ZrB₁₂ and offer insights for elucidating extrinsic hardening phenomena that may exist in other transition-metal compounds.