Computational materials discovery is a booming field of science, which helps in predicting new unexpected materials with optimal combinations of various physical properties. Going beyond the targeted search for new materials within prespecified systems, the recently developed method, Mendelevian search, allows one to look for materials with the desired properties across the entire Periodic Table, indicating possibly superhard (or other) materials that could be obtained experimentally. From this viewpoint, we discuss the recently developed methods for crystal structure prediction and empirical models of Vickers hardness and fracture toughness that allow fast screening for materials with optimal mechanical properties. We also discuss the results of the computational search for hard and superhard materials obtained in the last few years using these novel approaches and present a “treasure map” of hard and superhard materials, which summarizes known and predicted materials and points to promising future directions of superhard materials discovery.
Nitrides, carbides, and borides of transition metals are an attractive class of hard materials. Our recent preliminary explorations of the binary chemical compounds indicated that chromium-based materials are among the hardest transition metal compounds. Motivated by this, here we explore in detail the binary Cr-B, Cr-C, and Cr-N systems using global optimization techniques. Calculated enthalpy of formation and hardness of predicted materials were used for Pareto optimization to define the hardest materials with the lowest energy. Our calculations recover all numerous known stable compounds (except CrC with its large unit cell) and discover a novel stable phase Pmn2-CrC. We resolve the structure of CrN and find it to be of anti-CaCl type (space group Pnnm). Many of these phases possess remarkable hardness, but only CrB is superhard (Vickers hardness 48 GPa). Among chromium compounds, borides generally possess the highest hardnesses and greatest stability. Under pressure, we predict stabilization of a layered TMDC-like phase of CrN, a WC-type phase of CrN, and a new compound CrN. Nitrogen-rich chromium nitride CrN is a high-energy-density material featuring polymeric nitrogen chains. In the presence of metal atoms (e.g., Cr), polymerization of nitrogen takes place at much lower pressures; CrN becomes stable at ∼15 GPa (cf. 110 GPa for synthesis of pure polymeric nitrogen).
In this study, we perform a systematic search to find the possible lowest energy structure of silicon nanoclusters Si ( = 8-80) by means of an evolutionary algorithm. The fitness function for this search is the total energy of density functional tight binding (DFTB). To be on firm ground, we take several low energy structures of DFTB and perform further geometrical optimization by density functional theory (DFT). Then we choose structures with the lowest DFT total energy and compare them with the reported lowest energy structures in the literature. In our search, we found several lowest energy structures that were previously unreported. We further observe a geometrical transition at = 27 from elongated to globular structures. In addition, the optical gap of the lowest energy structures is investigated by time-dependent DFTB (TD-DFTB) and time-dependent DFT (TD-DFT). The results show the same trend in TD-DFTB and TD-DFT for the optical gap. We also find a sudden drop in the optical gap at = 27, precisely where the geometrical transition occurs.
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