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.

A model of hardness and fracture toughness of solids

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.

Computational discovery of hard and superhard materials

With a combination of first-principles calculations and thermodynamics formalism of configurational mixing entropy, we have constructed three-dimensional phase diagram in terms of thermodynamic and structural parameters including the configurational mixing entropy and enthalpy, the temperature of the melting point, and the lattice constant difference of the constitute carbides for fifteen equiatomic quaternary high-entropy metal carbide (HEMC) ceramics of group IVB and VB refractory metals (RM = Ti, Zr, Hf, V, Nb, and Ta). We further predicted nine new HEMCs and provided an explanation for the existence of six experimentally realized quaternary HEMCs. In addition, our calculations of the melting points and mechanical properties show that the HEMCs have the unique properties of high hardness, high fracture toughness, and ultrahigh melting points. The computational procedure involved in this work may be used to design new high-entropy ceramics for specific applications.

Phase stability, mechanical properties and melting points of high-entropy quaternary metal carbides from first-principles

${\mathrm{WN}}_{6}$ phase discovered at 126--165 GPa after heating of W in nitrogen XRD refinements reveal a unit cell in space group $R\overline{3}m$ which is consistent with the ${\mathrm{WN}}_{6}$ structure with armchairlike hexazine (${\mathrm{N}}_{6}$) rings, while strong ${A}_{1g}$ Raman mode confirms its $\mathrm{N}─\mathrm{N}$ single bonds Density functional theory (DFT) calculations reveal balanced contributions of attractive interactions between W and covalent ${\mathrm{N}}_{6}$ rings, and repulsions between ${\mathrm{N}}_{6}$ rings that make ${\mathrm{WN}}_{6}$ ultrastiff and tough The ${\mathrm{WN}}_{6}$ phase displays long bond lengths in the nearest N-N and pressure-enhanced electronic band gap, which pave the way for finding novel nitrides

Tungsten Hexanitride with Single-Bonded Armchairlike Hexazine Structure at High Pressure.

Molybdenum borides were studied theoretically using first-principles calculations, parameterized lattice model, and global optimization techniques to determine stable crystal structures. Our calcul...

Structure, Stability, and Mechanical Properties of Boron-Rich Mo-B Phases: A Computational Study.

Fracture toughness $K_{IC}$ plays an important role in materials design. Along with numerous experimental methods to measure fracture toughness of materials, its understanding and theoretical prediction is very important. However, theoretical prediction of fracture toughness is challenging. By investigating the correlation between fracture toughness and elastic properties of materials, we have constructed a fracture toughness model for covalent and ionic crystals. Furthermore, by introducing an enhancement factor, which is determined by the density of states at the Fermi level and atomic electronegativities, we have constructed a universal model of fracture toughness for covalent and ionic crystals, metals and intermetallics. The predicted fracture toughnesses are in good agreement with experimental values for a series of materials. All the parameters in the proposed model of fracture toughness can be obtained from first-principles calculations, which makes it suitable for practical applications.

Simple and accurate model of fracture toughness of solids

Fracture toughness K I C plays an important role in materials design. Along with numerous experimental methods to measure the fracture toughness of materials, its understanding and theoretical prediction are very important. However, theoretical prediction of fracture toughness is challenging. By investigating the correlation between fracture toughness and the elastic properties of materials, we have constructed a fracture toughness model for covalent and ionic crystals. Furthermore, by introducing an enhancement factor, which is determined by the density of states at the Fermi level and atomic electronegativities, we have constructed a universal model of fracture toughness for covalent and ionic crystals, metals, and intermetallics. The predicted fracture toughnesses are in good agreement with experimental values for a series of materials. All the ingredients of the proposed model of fracture toughness can be obtained from first-principles calculations or from experiments, which makes it suitable for practical applications.

Shiwei Niu

Papers

Simple and accurate model of fracture toughness of solids

Simple and accurate model of fracture toughness of solids