An empirical model and ab initio calculations of the bulk moduli for covalent solids suggest possible new hard materials. The model indicates that hypothetical covalent solids between carbon and nitrogen are good candidates for extreme hardness. A prototype system, β-C₃N₄, was studied using first-principles pseudopotential calculations. The results show that materials like β-C₃N₄ can have bulk moduli comparable to or greater than diamond. The bulk modulus of covalent solids is determined by the strength and compressibility of the bonds. Diamond, with the largest bulk modulus (4.43 Mbar), is the hardest known solid. The empirical model, based on scaling arguments, predicts the bulk modulus of covalent solids as B = (19.71 - 2.20λ)/d³·⁵, where λ is the ionicity and d is the bond length. For β-C₃N₄, the calculated bulk modulus is 4.27 Mbar, which is slightly higher than the predicted value from the model due to structural differences. The structure of β-C₃N₄ consists of buckled layers stacked in an AAA... sequence, with C and N atoms in tetrahedral and triply coordinated sites, respectively. The valence charge density and elastic properties of β-C₃N₄ were calculated, showing anisotropic elastic properties. The cohesive energy of β-C₃N₄ is 5.8 eV per atom, suggesting it is a metastable structure. The study suggests that β-C₃N₄ could be synthesized with compressibility comparable to diamond. The results support the theoretical approach and provide insights for further applications. The work was supported by grants from the National Science Foundation and the U.S. Department of Energy.An empirical model and ab initio calculations of the bulk moduli for covalent solids suggest possible new hard materials. The model indicates that hypothetical covalent solids between carbon and nitrogen are good candidates for extreme hardness. A prototype system, β-C₃N₄, was studied using first-principles pseudopotential calculations. The results show that materials like β-C₃N₄ can have bulk moduli comparable to or greater than diamond. The bulk modulus of covalent solids is determined by the strength and compressibility of the bonds. Diamond, with the largest bulk modulus (4.43 Mbar), is the hardest known solid. The empirical model, based on scaling arguments, predicts the bulk modulus of covalent solids as B = (19.71 - 2.20λ)/d³·⁵, where λ is the ionicity and d is the bond length. For β-C₃N₄, the calculated bulk modulus is 4.27 Mbar, which is slightly higher than the predicted value from the model due to structural differences. The structure of β-C₃N₄ consists of buckled layers stacked in an AAA... sequence, with C and N atoms in tetrahedral and triply coordinated sites, respectively. The valence charge density and elastic properties of β-C₃N₄ were calculated, showing anisotropic elastic properties. The cohesive energy of β-C₃N₄ is 5.8 eV per atom, suggesting it is a metastable structure. The study suggests that β-C₃N₄ could be synthesized with compressibility comparable to diamond. The results support the theoretical approach and provide insights for further applications. The work was supported by grants from the National Science Foundation and the U.S. Department of Energy.