Origin of hardness in nitride spinel materials

The nitride spinels are of considerable interest. The structural parameters of the nitride spinels have been calculated by first-principles. A semiempirical model for the hardness is employed to predict the hardness of nitride spinels and related compounds. The studies show that the influence of the electronic density, the bond strength, and the ionicity on the hardness of $\gamma \text{−}{\mathrm{A}}_3{\mathrm{N}}_4$ ($\mathrm{A}=\mathrm{C}$, Si, Ge) all decrease monotonously in the order of $\gamma \text{−}{\mathrm{C}}_3{\mathrm{N}}_4$, $\gamma \text{−}{\mathrm{Si}}_3{\mathrm{N}}_4$, and $\gamma \text{−}{\mathrm{Ge}}_3{\mathrm{N}}_4$. The origin of superhardness in the group-IV nitride spinels results mainly from ${\mathrm{A}}^t{\mathrm{N}}_4$ tetrahedral units rather than on ${\mathrm{A}}^o{\mathrm{N}}_6$ octahedral units. The detailed studies of the nitride poly-morphs experimentally detected and theoretically proposed indicate that the increasing of coordination cannot always result in the increasing of hardness. It has to be emphasized that the relation between the coordination numbers and hardness has to be applied with care.

Figure 1

Influence of the bond strength $E_h$, the electronic density $N_e$, and the ionic bonding effects $e^{-1.191fi}$ on the hardness of ${\mathrm{A}}^t\mathrm{N}$ and ${\mathrm{A}}^o{\mathrm{N}}_{3∕2}$ in $\gamma \text{−}{\mathrm{A}}_3{\mathrm{N}}_4$ ($\mathrm{A}=\mathrm{C}$, Si, Ge).

Figure 2

Relationship between the average coordination number $N_c^{\mu }$ and hardness $H_v$ in the $\mathrm{A}{\mathrm{N}}_x$ ($\mathrm{A}=\mathrm{C}$, Si, Ge, Zr) polyhedra.