  Through machine learning force field accelerated structure search combined
with first-principles calculations, we have studied the structures of new C-N
compounds with different stoichiometric ratios, and found twelve new superhard
C-N compounds, the energies of these structures are similar to c-C3N4 , which
is possibly synthesized by high pressure experiment, the XRD of Pa-3(C4N)
P3(C4N) and C2/m(C2N) are consistent with previous experimental data and can be
used as the structural candidate. According to the macro hardness model, they
are all superhard structures, with Vickers hardness over 40GPa, even, the
hardness of Pa-3 (C4N) as high as 82.2GPa, and Pa-3 (C4N) combines high tensile
and shear resistance. Compared with the hardness calculated by macro hardness
model and bond resistance model, we obtained the relationship between the
hardness and chemical concentration of C-N compounds under the two models,
besides that, we also calculated the fracture toughness of these structures.
According to Niu's model, P2_1/c(C4N) has the best fracture toughness, which is
higher than WC in calculation, This also indicated the superior mechanical
properties of the novel C-N compounds. Moreover, for nitrogen-rich structures,
they have the potential to be used as high energy density, the energy density
of Pa-3(CN3), P-3c1 (CN4), and I-42d (CN4) are 7.076kJ/g, 7.742kJ/g and
8.045kJ/g, which is close or higher than CL-20, therefore, the C-N compounds
synthesized under high pressure have great potential as ideally superhard
materials and high energy density materials(HEDMs).
