Carbon nitride and other speculative superhard materials

Abstract

In 1984, the author predicted in an unpublished patent disclosure letter at the Diamond Technology Center of Norton Company that C 3N 4 may be harder than diamond, the hardest material known. According to this disclosure, C 3N 4 may exist with two phases ( α and β) that are isostructural to corresponding phases of Si 3N 4. In order to estimate the hardness of these hypothetical materials, the author contracted Professor M. Cohen to calculate the theoretical values of their bulk moduli. Cohen has since published such results and confirmed that C 3N 4 may be superhard. Bulk modulus is the best indicator of hardness for materials with diamond-like structure. An accurate regression equation for bulk modulus ( B in kb) has been derived from 24 diamond-like semiconductors made of elements in Groups III, IV, and V as follows: In B = 975 P −0.0448 D −0.423 C 0.0462, where P is the average period number of the constituent elements and D their average interatomic distance; C = 4 −Δ p/2, where Δ p is the difference of the number of p-orbital electrons between bonding atoms. Bulk moduli so calculated for the 24 semiconductors deviate by E only 1.8% on average from their literature values. Using the above equation, the bulk modulus of a hypothetical diamond-like structure made of CN was calculated to be 4.9 Mb. C 3N 4 has 24/28 of the number of bonds per formula as compared with a diamond-like structure so its bulk modulus may be reduced in proportion to 4.2 Mb. This value is on a par with diamond (4.4 Mb) but significantly higher than the 3.7 Mb for cubic boron nitride, the second hardest material known. Based on the analogy of the hardness differences between corresponding phases ( α and β) of Si 3N 4 and SiC, it is predicted, that α-C 3N 4 is harder than diamond (CC), whereas β-C 3N 4 is softer. Both phases of C 3N 4 could be more thermally stable than diamond. Hence, it may have advantages over diamond in processing and applications at high temperatures.