Hardness of Carbon-Based Materials

Amorphous carbon (a-C) films generally present high hardness with increasing sp3 content, but their hardness can exceed 20 GPa even with low sp3 content. Using molecular dynamics modeling, we show that dangling bonds are inherently present in a-C films, which leads to various incomplete structural motifs. An interpretable machine learning framework integrating the XGBoost model and SHAP analysis is utilized to statistically investigate the structure–property relationships and identify the key structural features governing hardness. In high-density a-C films, the tetrahedral structure predominantly determines the hardness, exhibiting a specific hardness range based on its content and aggregation degree. In low-density a-C films, where tetrahedral structures diminish, the hardness correlates inversely with the average bond length, which increases with the C–C/C═C ratio and decreases with dangling bond proportion. Therefore, high hardness can be achieved by increasing the proportion of double bonds and dangling bonds even when the sp3 content is small.