Zhang Ruifeng; Zhang Shihao; Guo Yuanyuan; Fu Zhongheng; Legut Dominit; Germann Timothy Clark; Vepřek Stanislav. First-principles design of strong solids: Approaches and applications. Physics Reports-Review Section of Physics Letters. 2019, vol. 826, s. 1-49. ISSN 0370-1573, eISSN 1873-6270, DOI: https://doi.org/10.1016/j.physrep.2019.09.004.
The Review published in Phys. Reports 2019 is devoted to the design rules of superhard solids. It is based on over a decade of our works to find intrinsic and extrinsic parameters to design superhard solids, i.e. a solid that not only would be at least as hard as 50% of diamond but many times cheaper leading to economical and widespread industrial applications. In our pioneering works of Tm-diborides [PRB 2010] (cited 50x) and [PRL 2012] (cited 122x), we have shown that it is not enough for the components of the material to have high bulk modulus, high valence electrons, and high melting temperature to become superhard. Using quantum mechanical calculations, we found that a combination of the covalent bonding (brought by elemental, boron, nitrogen, oxygen, or carbon) with transition metals have its limits far below industrially requested superhardness. The addition of the sp-elements (B, C, N, O) to bring more covalency has also its limits in tensile and shear strengths, the latter to be related with the onset of plasticity that corresponds to the load invariant Vickers hardness measured by nanoindentations (probing a defect-free crystal). The hardness is related with the start of the dislocation motion that could be characterized by the semi-discrete Peierls-Nabarro model, i.e. determination of the sliding atomic planes including dislocation (i.e. determination of the gamma-surface energies via first-principle methods for the misfit energy) as well as the quantum mechanical calculations for the elastic part across the gliding plane. The connection of these two leads to the development of the Peierls-Nabarro dislocation model and its analysis by the PNADIS code (CPC 2019). Determination of the Peierls stress along the slip system is the state-of-the-art property related to hardness. Next, in the review, we design the possible routes with intrinsic and extrinsic rules to overcome these limitations. The intrinsically superhard materials need to possess high Peierls resistance to dislocation motion, 3D network of covalent bonding, high shear moduli, and dynamical stability, e.g. borides, carbides, oxides with some transitional metals. The extrinsic parameters needed to achieve superhardness are nanosized crystallites or grains and/or atomically thin interface with strong covalent bonding to avoid Friedel oscillations and failure of material at small deformations.