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We present a symmetry-based systematic approach to explore the structural and compositional richness of two-dimensional materials. We use a ‘combinatorial engine’ that constructs candidate compounds by occupying all possible Wyckoff positions for a certain space group with combinations of chemical elements. These combinations are restricted by imposing charge neutrality and the Pauling test for electronegativities. The structures are then pre-optimized with a specially crafted universal neural-network force-field, before a final step of geometry optimization using density-functional theory is performed. In this way we unveil an unprecedented variety of two-dimensional materials, covering the whole periodic table in more than 30 different stoichiometries of form A_nB_mor A_nB_mC_k. Among the discovered structures, we find examples that can be built by decorating nearly all Platonic and Archimedean tessellations as well as their dual Laves or Catalan tilings. We also obtain a rich, and unexpected, polymorphism for some specific compounds. We further accelerate the exploration of the chemical space of two-dimensional materials by employing machine-learning-accelerated prototype search, based on the structural types discovered in the systematic search. In total, we obtain around 6500 compounds, not present in previous available databases of 2D materials, with a distance to the convex hull of thermodynamic stability smaller than 250 meV/atom.

 

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.

 

Abstract A two-dimensional material – Mg 2 B 4 C 2 , belonging to the family of the conventional superconductor MgB 2 , is theoretically predicted to exhibit superconductivity with critical temperature T c estimated in the 47–48 K range (predicted using the McMillian-Allen-Dynes formula) without any tuning of external parameters such as doping, strain, or substrate-induced effects. The origin of such a high intrinsic T c is ascribed to the presence of strong electron-phonon coupling and large density of states at the Fermi level. This system is obtained after replacing the chemically active boron-boron surface layers in a MgB 2 slab by chemically inactive boron-carbon layers. Hence, the surfaces of this material are inert. Our calculations confirm the stability of 2D Mg 2 B 4 C 2 . We also find that the key features of this material remain essentially unchanged when its thickness is increased by modestly increasing the number of inner MgB 2 layers.