De Novo Inverse Design Superhard C–N Compounds via Global Machine Learning Interatomic Potentials and Multiobjective Optimization Algorithm

A major challenge in the field of superhard materials is the identification of compounds with a hardness exceeding that of diamond. In this study, we developed a variable-composition inverse material design (VC-IMD) approach for designing C-N superhard materials. In this approach, an improved multiobjective optimization algorithm is introduced, utilizing structure similarity constraint to prevent convergence toward local minima. Combined with active learning, it trains global machine learning interatomic potentials (<i>g</i>-MLIPs) while exploring target materials. By comparing several <i>g</i>-MLIPs and selecting the best, the resulting <i>g</i>-MLIPs achieved reasonable precision within three iterations. Through multiple searches, 38 novel and stable C-N superhard materials not present in major computational materials databases were identified. Notably, the material C₃(<i>P</i>6₄22) with a hardness of 97.4 GPa was discovered, potentially exceeding that of diamond (94.0 GPa). This approach provided a new pathway for materials design with target properties.