Anisotropic hardness prediction of crystalline hard materials from the electronegativity

We have presented an efficient method to predict the anisotropic hardness of crystalline materials along different crystallographic directions or on different crystallographic planes in terms of electronegativity. Bond stretching and bending strengths, respectively, are proposed to characterize the ability of a chemical bond to resist stretching and bending deformation, which are the main microscopic deformations in single crystals when measuring indentation hardness. Good agreement between the calculated and experimental values of anisotropic hardness for a large range of crystalline materials has been achieved, including sphalerite, wurtzite and rocksalt structured materials, as well as oxides (e.g. α-SiO₂ and LaGaO₃) and graphite. The anisotropic hardness values of other important materials, such as B₁₂ analogs, group IVA nitrides, tungsten carbide structured materials, and transition metal di- and tetra-borides, were quantitatively predicted. We found that materials with the same crystal structure have the same or similar hardness anisotropy. Furthermore, the more orderly bond arrangement in single crystals and the greater bond ionicity often result in greater hardness anisotropy. This work shines a light on the nature of hardness and on studies of the anisotropy of other macroscopic properties of crystalline materials.