Hardness and fracture toughness of brittle materials: A density functional theory study

Abstract

The focus of the paper is to study the correlation between hardness and fracture toughness of brittle materials. To this end, density functional theory (DFT) is used to calculate materials parameters such as the surface energies, the unstable stacking fault energies, the Young's modulus, the bulk modulus, the shear moduli, and the Poisson's ratio of crystalline ${\mathrm{B}}_{6}\mathrm{O}$ as well as the surface energies of $c\mathrm{B}\mathrm{N}$ and $3\mathrm{C}\mathrm{Si}\mathrm{C}$. With these calculated materials parameters as well as reported ones, the theoretical fracture toughness of diamond, $c\mathrm{B}\mathrm{N}$, ${\mathrm{B}}_{6}\mathrm{O}$, $3\mathrm{C}\mathrm{Si}\mathrm{C}$, and Si are obtained and compared with experimental hardness. We find that the theoretical fracture toughness, proportional to the product of shear modulus and surface energy, can better characterize hardness of diamond, $c\mathrm{B}\mathrm{N}$, ${\mathrm{B}}_{6}\mathrm{O}$, $3\mathrm{C}\mathrm{Si}\mathrm{C}$, Si, and possibly other brittle materials than shear modulus alone [D. M. Teter, MRS Bull. 23, 22 (1998)]. This finding could be helpful in searching for new hard materials.