Carbon nitride and other speculative superhard materials

In 1984, the author predicted in an unpublished patent disclosure letter at the Diamond Technology Center of Norton Company that C3N4 may be harder than diamond, the hardest material known. According to this disclosure, C3N4 may exist with two phases (alpha and beta) that are isostructural to corresponding phases of Si3N4. 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 C3N4 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 = 9.75P(-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 - Delta p/2, where Delta 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. C3N4 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 (alpha and beta) of Si3N4 and SiC, it is predicted that alpha-C3N4 is harder than diamond (CC), whereas beta-C3N4 is softer. Both phases of C3N4 could be more thermally stable than diamond. Hence, it may have advantages over diamond in processing and applications at high temperatures.