Origin of the low compressibility in hard nitride spinels

A microscopic investigation of first-principles electron densities of $\gamma -{\mathrm{A}}_3{\mathrm{N}}_4$ (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 $\gamma -{\mathrm{C}}_3{\mathrm{N}}_4$ and different degrees of ionic polarization in $\gamma -{\mathrm{Si}}_3{\mathrm{N}}_4$ and $\gamma -{\mathrm{Ge}}_3{\mathrm{N}}_4,$ (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.