Theory of Superhard Materials

Thanks to recent progress, it has become possible to reasonably accurately compute the hardness of materials theoretically, from crystal structures. The existing models have, however, some weaknesses in dealing with complex low-symmetry structures and layered, chain, or molecular structures. The reason is that while the strengths of individual chemical bonds are taken into account in these models, the topological arrangement of these bonds in space is disregarded. Taking into account structural topology by means of multicolor graph theory, and using bond valence model for more accurate representations of bond strengths, we substantially improved the accuracy and predictive power of the well-known model of Li et al. and similar improvements are expected for other models as well. Combining such models with global optimization techniques, such as the evolutionary algorithm USPEX, one obtains a powerful new tool for the systematic search for new hard materials. Using such an approach, we show that in none of its modifications can TiO2 be an ultrahard material and hardest known oxide, contrary to some claims. We show, furthermore, that in all of its modifications TiO2 should not have a hardness greater than approximately 17 GPa, which is significantly softer than that of common corundum (Al2O3). We discuss recent discoveries and predictions of new superhard allotropes of carbon and boron. In particular, we show that none of the known or hypothetical allotropes of carbon can be harder than diamond.