Hardness and fracture toughness are some of the most important mechanical properties. Here, we propose a simple model that uses only the elastic properties to calculate the hardness and fracture toughness. Its accuracy is checked by comparison with other available models and experimental data for metals, covalent and ionic crystals, and bulk metallic glasses. We found the model to perform well on all datasets for both hardness and fracture toughness, while for auxetic materials (i.e., those having a negative Poisson’s ratio), it turned out to be the only model that gives reasonable hardness. Predictions are made for several materials for which no experimental data exist.

Superhard materials are of great interest in various practical applications, and an increasing number of research efforts are focused on their development. In this article, we demonstrate that machine learning can be successfully applied to searching for such materials. We construct a machine learning model using neural networks on graphs together with a recently developed physical model of hardness and fracture toughness. The model is trained using available elastic data from the Materials Project database and has good accuracy for predictions. We use this model to screen all crystal structures in the database and systematize all the promising hard or superhard materials, and find that diamond (and its polytypes) are the hardest materials in the database. Our results can be further used for the investigation of interesting materials using more accurate ab initio calculations and/or experiments.

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We introduce a new class of machine learning interatomic potentials-fast General Two-and Three-body Potential (GTTP) which are as fast as conventional empirical potentials and require computational time that remains constant with increasing fitting flexibility. GTTP does not contain any assumptions about functional form of two-and three-body interactions. These interactions can be modeled arbitrarily accurately potentially by thousands of parameters not affecting resulting computational cost. Time complexity is O(1) per every considered pair or triple of atoms. The fitting procedure is reduced to simple linear regression on ab initio calculated energies and forces and leads to effective two-and three-body potential which reproduces quantum many-body interactions as accurately as possible. Our potential can be made continuously differentiable any number of times at the expense of increased computational time. We made a number of performance tests on one-, two-and three-component systems. Flexibility of the introduced approach makes the potential transferable in terms of size and type of atomic systems. We show, that trained on randomly generated structures with just 8 atoms in the unit cell, it significantly outperforms common empirical interatomic potentials in the study of large systems, such as grain boundaries in polycrystalline materials.