Finding the Next Superhard Material through Ensemble Learning.

An ensemble machine-learning method is demonstrated to be capable of finding superhard materials by directly predicting the load-dependent Vickers hardness based only on the chemical composition. A total of 1062 experimentally measured load-dependent Vickers hardness data are extracted from the literature and used to train a supervised machine-learning algorithm utilizing boosting, achieving excellent accuracy (R  = 0.97). This new model is then tested by synthesizing and measuring the load-dependent hardness of several unreported disilicides and analyzing the predicted hardness of several classic superhard materials. The trained ensemble method is then employed to screen for superhard materials by examining more than 66 000 compounds in crystal structure databases, which show that 68 known materials have a Vickers hardness ≥40 GPa at 0.5 N (applied force) and only 10 exceed this mark at 5 N. The hardness model is then combined with the data-driven phase diagram generation tool to expand the limited number of reported high hardness compounds. Eleven ternary borocarbide phase spaces are studied, and more than ten thermodynamically favorable compositions with a hardness above 40 GPa (at 0.5 N) are identified, proving this ensemble model's ability to find previously unknown materials with outstanding mechanical properties.