Data-driven discovery of ultraincompressible crystals from a universal correlation between bulk modulus and volumetric cohesive energy

Bulk modulus and cohesive energy are two important quantities of condensed matter. From the interatomic energy landscape, we here derived a correlation between the bulk modulus (B) and the volumetric cohesive energy (rho e), i.e. B = 2(ln2)2 rho e/9 epsilon s 2 = k rho e, where epsilon s and k are the strain-to-failure of interatomic bonds and the factor of proportionality, respectively. By analyzing numerous crystals from first principles calculations, it was shown that this correlation is universally applicable to various crystals including simple substances and compounds. Most interestingly, it was found that epsilon s of crystals with a similar structure are almost a constant, resulting in a linear relationship between B and rho e. Furthermore, we found that the value of k for any compound can be determined based on the rule of mixtures, i.e. k= n-ary sumation x i k i, where x i and k i are the atomic fraction and the factor of proportionality for each element in this compound, respectively. Finally, this correlation was used to predict the bulk moduli for a vast number of crystals with known rho e in databases. After first principles verification of the top 50 crystals with the highest predicted bulk modulus, 25 ultraincompressible crystals with a bulk modulus greater than 400 GPa that can rival diamond (436 GPa) were discovered.