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The search for new superhard materials is of great interest for extreme industrial applications. However, the theoretical prediction of hardness is still a challenge for the scientific community, given the difficulty of modeling plastic behavior of solids. Different hardness models have been proposed over the years. Still, they are either too complicated to use, inaccurate when extrapolating to a wide variety of solids or require coding knowledge. In this investigation, we built a successful machine learning model that implements Gradient Boosting Regressor (GBR) to predict hardness and uses the mechanical properties of a solid (bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio) as input variables. The model was trained with an experimental Vickers hardness database of 143 materials, assuring various kinds of compounds. The input properties were calculated from the theoretical elastic tensor. The Materials Project’s database was explored to search for new superhard materials, and our results are in good agreement with the experimental data available. Other alternative models to compute hardness from mechanical properties are also discussed in this work. Our results are available in a free-access easy to use online application to be further used in future studies of new materials atwww.hardnesscalculator.com.

The density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard correction to treat strongly correlated electronic states. Unfortunately, the values of the HubbardUandJparameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore theUandJparameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchange-correlation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largestUcorrection. PBE has the smallest standard deviation and itsUandJparameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction.