Ab initiocalculation of the ideal tensile and shear strength of cubic silicon nitride

Abstract

In this study, the ideal tensile and shear strength of the recently discovered cubic spinel silicon nitride polymorph was calculated using an ab initio density functional technique. The stress-strain curve of the cubic silicon nitride structure was calculated from simulations of applied ${\ensuremath{\varepsilon}}_{11}$ and ${\ensuremath{\varepsilon}}_{23}$ components of strain, and the ideal strengths were estimated at \ensuremath{\sim}45 and \ensuremath{\sim}49 GPa, respectively. In addition, the elastic constants of the cubic structure were determined and a value of \ensuremath{\sim}311 and \ensuremath{\sim}349 GPa was estimated for the bulk and shear modulus, respectively. The estimates of the elastic constants were found to be in reasonable agreement with existing data. Using a previously reported empirical relation, the hardness of the cubic phase was also estimated: \ensuremath{\sim}47 GPa.