Predicting superhard materials via a machine learning informed evolutionary structure search

The computational prediction of superhard materials would enable the in silico design of compounds that could be used in a wide variety of technological applications. Herein, good agreement was found between experimental Vickers hardnesses, Hv, of a wide range of materials and those calculated by three macroscopic hardness models that employ the shear and/or bulk moduli obtained from: (i) first principles via AFLOW-AEL (AFLOW Automatic Elastic Library), and (ii) a machine learning (ML) model trained on materials within the AFLOW repository. Because \(H_{\mathrm{v}} {{\mathrm{ML}}}\) values can be quickly estimated, they can be used in conjunction with an evolutionary search to predict stable, superhard materials. This methodology is implemented in the XtalOpt evolutionary algorithm. Each crystal is minimized to the nearest local minimum, and its Vickers hardness is computed via a linear relationship with the shear modulus discovered by Teter.