Hardness analysis of cubic metal mononitrides from first principles

Abstract

Density functional theory calculations are performed to evaluate the hardness of various cubic metal nitrides: rocksalt TiN, VN, ZrN, NbN, AlN, and SiN; zincblende AlN and BN; and diamond C for comparison. The isotropic elastic stiffness constants ${c}_{ij}$, bulk modulus $K$, shear modulus $G$, Young's modulus $E$, and isotropic Poisson's ratio $\overline{\ensuremath{\nu}}$ are calculated. From simulated uniaxial stress-strain curves, ideal strength values ${\ensuremath{\sigma}}_{\mathrm{max}}$ in the [100], [110], and [111] directions are also evaluated for all systems. In particular, rocksalt AlN is found to possess both high elastic moduli and ideal strength. These quantities are then compared for correlations with existing experimental Vicker's hardness data. The bulk modulus is found to be a poor indicator of hardness, while $E$, $G$, $1/\overline{\ensuremath{\nu}}$, and ${\ensuremath{\sigma}}_{\mathrm{max}}$ all exhibit stronger correlations. With a view to circumvent the need to run computationally expensive relaxation steps, different methodologies for approximating uniaxial stress-strain curves are introduced. Utilizing the anisotropic Poisson's ratio to approximate the relaxed transverse lattice parameters at a given axial strain is a good approximation to stress-strain curves, and the ideal strengths obtained in this way exhibit strong correlations to experimental Vicker's hardness values.