Data-Driven Discovery and Understanding of Ultrahigh-Modulus Crystals

High-modulus materials that yield small elastic deformation under mechanical loads hold great promise for use in a wide range of engineering applications. However, the discovery and understanding of high-modulus materials remain a long-term challenge, as the traditional experimental trial-and-error approach is time-consuming. In this work, we discovered two new ultrahigh-modulus crystals (CN2 and OsN2), exhibiting a maximum Young's modulus (1555.3 and 1382.7 GPa, respectively) greater than that of diamond (1152.0 GPa in our calculations), by data mining of 13 122 crystals and first-principles verifications. More surprisingly, the density of CN2 is lower than that of diamond, which endows it with high modulus and light weight. Furthermore, we explored the mechanical behaviors of the discovered ultrahigh-modulus crystals by performing tensile tests and found that CN2 and OsN2 also boast high strength while maintaining decent ductility. The underlying mechanism for the ultrahigh modulus of these two crystals was explained by analyses of the electron density and bond order. To further broaden our understanding, a data-driven analysis was conducted to quantify the structure-modulus correlations of 10 903 crystals, and six crucial structural and compositional features that are highly correlated to the maximum Young's moduli of crystals were identified. Based on these six features, a nonlinear classifier was developed, which successfully predicted crystals possessing a maximum Young's modulus greater than 1000 GPa and separated them from the others, making this approach useful for falsifiable prediction and discovery of high-modulus crystals. Based on this understanding, suggestions were made to guide the design and synthesis of high-modulus crystals. Additionally, the formation and stabilities of CN2 and OsN2 were explored for practical applications.