An unusual variation of stability and hardness in molybdenum borides

Molybdenum borides are currently raising great expectations for superhard materials, but their crystal structures and mechanical behaviors are still under discussion. Here, we report an unexpected reduction of stability and hardness from porous hP16-MoB ₃ and hR18-MoB ₂ to dense hP20-MoB ₄ and hR21-Mo ₂B ₅, respectively. Furthermore, we demonstrate that this anomalous variation has its electronic origin. These findings not only manifest that the long-recognized hP20-MoB ₄ (hP3-MoB ₂) and hR21-Mo ₂B ₅ should be hP16-MoB ₃ and hR18-MoB ₂, respectively, but also challenge the general design principle for ultrahard materials only pursuing the dense transition-metal borides with high boron content.