Abstract
The hypothetical spinel carbon nitride (γ-C3N4) has received a large amount of attention due to its predicted hardness being comparable to that of diamond. The group 14 spinel binary nitrides that have been synthesized are limited so far to: γ-Si3N4, γ-Ge3N4 and γ-Sn3N4. However, there still remains significant interest in γ-C3N4 in the hope that it will eventually be synthesized, but there are no successful reports, thus making the study of γ-C3N4 strictly theoretical. Through an empirical relationship that correlates hardness, crystal structure and the electronic band gap, we examine a series of group 14 spinel nitrides: γ-C3N4 γ-Si3N4, γ-Ge3N4 and γ-Sn3N4, as well as their ternary compounds. The hardness and electronic band gap of these materials are calculated using ab initio density functional theory. These results show that in the case of the solid solutions, γ-(Si,Ge)3N4 and γ-(Ge,Sn)3N4, the tetrahedral site is filled first by the larger cation, Ge and Sn, respectively. Furthermore, the deviation of carbon containing group 14 spinel nitrides from the expected hardness and bandgap trend suggests that γ-Si3N4 may remain the hardest known group 14 spinel nitride. Additionally, an improved method to calculate the hardness using the nitrogen bonding tetrahedron provides more unambiguous results and the trend of the hardness agrees with experimental measurements.
