Origin of the low compressibility in hard nitride spinels

Abstract

A microscopic investigation of first-principles electron densities of $\ensuremath{\gamma}\ensuremath{-}{\mathrm{A}}_{3}{\mathrm{N}}_{4}$ (A:C,Si,Ge) spinels reveals a clear relationship between the compressibility and the chemical bonding of these materials. Three striking findings emanate from this analysis: (i) the chemical graph is governed by a network of highly directional strong bonds with covalent character in $\ensuremath{\gamma}\ensuremath{-}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ and different degrees of ionic polarization in $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ and $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Ge}}_{3}{\mathrm{N}}_{4},$ (ii) nitrogen is the lowest compressible atom controlling the trend in the bulk modulus of the solids, and (iii) the group-IV counterions show strong site dependent compressibilities enhancing the difficulty in the synthesis of the spinel phases of these nitrides.