Indentation strength of ultraincompressible rhenium boride, carbide, and nitride from first-principles calculations

Using a recently developed first-principles approach for determining indentation strength [Z. Pan, H. Sun, and C. Chen, Phys. Rev. Lett. 98, 135505 (2007); Z. Pan, H. Sun, and C. Chen, Phys. Rev. Lett. 102, 055503 (2009)], we performed calculations of the ideal strength of hexagonal Re, Re${}_{3}$N, Re${}_{2}$N, Re${}_{2}$C, Re${}_{2}$B, and ReB${}_{2}$ in various shear deformation directions beneath the Vickers indentor. Our results show that the normal compressive pressure beneath the indentor weakens the strength of these electron-rich rhenium boride, carbide, and nitride compounds that belong to a distinct class of ultraincompressible and ultrahard materials. The reduction of indentation strength in these materials stems from lateral bond and volume expansions driven by the normal compressive pressure mediated by the high-density valence electrons in these structures. We compare the calculated indentation strength to the Poisson's ratio, which measures the lateral structural expansion, for the rhenium boride, carbide, and nitride compounds as well as diamond and cubic boron nitride. Our analysis indicates that although the normal pressure beneath the indentor generally leads to more significant reduction of indentation strength in materials with larger Poisson's ratios, crystal and electronic structures also play important roles in determining the structural response under indentation. The present study reveals structural deformation modes and the underlying atomistic mechanisms in transition-metal boride, carbide, and nitride compounds under the Vickers indentation. The results are distinctive from those of the traditional covalent superhard materials. The insights obtained from this work have important implications for further exploration and design of ultrahard materials.