Toughening a superstrong carbon crystal: Sequential bond-breaking mechanisms

A complex orthorhombic carbon allotrope in $Pbam$ symmetry with 32 atoms in its unit cell, thus termed $Pbam$-32 carbon, was recently predicted [C. Y. He et al., Phys. Rev. Lett. 121, 175701 (2018)]. Its crystal structure comprises alternating fivefold, sixfold, and sevenfold carbon rings and exhibits reduced bonding anisotropy compared to diamond, raising the prospects of finding a superstrong material with distinct and favorable mechanical properties. Here we report findings from first-principles calculations that reveal peculiar stress-strain relations in $Pbam$-32 carbon. The obtained stress responses under various tensile and shear strains display outstanding characteristics contrasting those of traditional superhard materials like diamond and cubic boron nitride ($c$-BN). The $Pbam$-32 carbon undergoes structural deformations that produce highly isotropic stress responses under a wide variety of large tensile and shear strains, showcasing unprecedented nearly degenerate stress-strain curves along multiple deformation paths extended over ultralarge, including full-range, strains up to the bond-breaking points. These deformation modes impede or even suppress the graphitization process commonly seen in highly strained diamond and $c$-BN crystals while still sustaining large peak stresses comparable to those in diamond. Most notably, we find conspicuous bond-weakening and -breaking mechanisms stemming from bonding symmetry reduction in $Pbam$-32 carbon. At large tensile strains, a sequential bond elongation process occurs, generating a more ductile deformation past the peak stress; at large shear strains, the crystal structure goes through a similar sequential bond elongation process and, interestingly, transforms into a distinct three-dimensional network containing mixed $s{p}^{2}$ and $s{p}^{3}$ bonding states, suppressing the usual graphitization process. These more gradual bonding-state changes in the severely strained $Pbam$-32 carbon improve ductility and toughness in this superstrong carbon crystal. These insights elucidate mechanisms for toughening superstrong covalent crystals via microstructural arrangements, which shed light on rational design and development of a distinct class of superstrong materials that exhibit more isotropic mechanical responses with improved toughness under diverse loading conditions.