Explorative prediction of novel superhard carbon allotropes with lager cell: Density functional theory-assisted deep learning

Searching for superhard materials with excellent properties has been a key challenge in materials science over the past decades. In this study, based on high throughput and density functional theory (DFT), we identified 24 new stable carbon allotropes from 50 initially identified candidates through structural optimization by removing repetitive structures and mechanically, molecularly dynamic, and thermally unstable structures. In addition, we built a crystal convolution residual neural network (CCRNN) to predict the elastic properties and mechanical hardness of the carbon allotropes and used chemical formulas as inputs to the model. The model used nearly 9979 target compounds, monomers, and 143 element-based features such as covalent radius, electronegativity, volume, and magnetic moment. To accurately predict carbon allotropes, we added lattice constants (a,b,c) and lattice angles (alpha,beta,gamma) as inputs after the feature descriptors. Random forest (RF) and gradientboosted decision tree (GBDT) regression algorithms were constructed, and the r of the CCRNN model was 0.978 and 0.955 for the bulk and shear moduli, respectively, and the best model (CCRNN) was chosen to predict the bulk and shear moduli of the stabilized carbon allotropes obtained from high-throughput calculations. Density functional theory validated the machine learning results. This study not only revealed 7 new superhard carbon allotropes, but also proposed a new deep learning model, and these newly discovered superhard carbon allotropes had wide-ranging potential applications in the fields of industry, electronics, aerospace, geology, and biomedicine. Our research has provided an important theoretical and experimental basis for the development of new superhard materials and applications and was significant in advancing the field of materials science and engineering.