Accelerated Designing of Superhard B-C-O Compounds using Machine Learning and DFT

In recent decades, a wide range of applications in defense, mining, manufacturing, and space industries have driven significant interest in designing materials with superior hardness. Compounds containing lighter elements such as boron, carbon, oxygen, and nitrogen are one of the most promising classes of superhard materials due to their ability to form short and covalent bonds. Given the complex procedure, which involves extensive resources and time requirements in both computational and experimental measurements, exploring a large chemical space of such superhard materials has always remained a challenge. Herein, we attempt to accelerate the search for superhard B-C-O compounds by developing machine learning (ML) models for rapid prediction of elastic moduli as proxy properties, followed by subsequent estimation of hardness using Tian’s empirical formula [1]. The ML models have been trained on a set of 10448 compounds with density functional theory (DFT)-computed elastic constants (bulk (K) and shear (G) modulus) using the simple chemical formula derived input space. The developed models exhibit excellent accuracy with R² of 0.98 and 0.94 for bulk and shear modulus predictions, respectively. The models have further been employed on a set of ternary B-C-O, generated by enumerating a series of B_xC_yO_z compositions with x, y, z ∈ {1, 2, 3, . . . 9}. ML models recommend 335 B-C-O compositions with hardness values of more than 35 GPa among a total of 1320 B-C-O compositions. The predictions include compositions such as B₂C₃O and B₂C₅O with hardness values of 36.15 and 55.51 GPa, respectively, consistent with previous findings [2]. Next, the ML predictions have been validated using evolutionary structure predictor and DFT, which identify four unique superhard B-C-O compounds exhibiting hardness ranging from 40 Gpa to 58 Gpa. These structures show mechanical and dynamical stability with relatively lower formation energy, implying a strong possibility of experimental synthesis.

[1] Machine learning and evolutionary prediction of superhard B-C-N compounds (npj Computational Materials, 7:114 (2021))

[2] Influences of carbon concentration on crystal structures and ideal strengths of B2CxO compounds in the B-C-O system (Scientific Reports, 5,15481 (2015))