Toward Superior Stiffness in Carbon: The Interplay between Bond Strength and Anisotropic Response

Carbon's ability to form diverse structures with varying hybridizations motivates the search for novel materials surpassing diamond's exceptional mechanical rigidity. We analyze previously predicted superhard phases and find that some exhibit average bond stiffness and density higher than those of diamond, hinting at potentially superior stiffness. However, these structures show a lower bulk modulus. We delve into this contradiction and demonstrate that it stems from the structures' anisotropic response to isotropic deformation. The concept of strain anisotropy is introduced to quantify this phenomenon. Our findings reveal a key connection between bond stiffness and bulk modulus in carbon materials, highlighting the importance of considering anisotropic behavior for a comprehensive understanding of the mechanical properties.