Machine learning and evolutionary prediction of superhard B-C-N compounds

We build random forests models to predict elastic properties and mechanical hardness of a compound, using only its chemical formula as input. The model training uses over 10,000 target compounds and 60 features based on stoichiometric attributes, elemental properties, orbital occupations, and ionic bonding levels. Using the models, we construct triangular graphs for B-C-N compounds to map out their bulk and shear moduli, as well as hardness values. The graphs indicate that a 1:1 B-N ratio can lead to various superhard compositions. We also validate the machine learning results by evolutionary structure prediction and density functional theory. Our study shows that BC₁₀N, B₄C₅N₃, and B₂C₃N exhibit dynamically stable phases with hardness values >40 GPa, which are superhard materials that potentially could be synthesized by low-temperature plasma methods.