The structural phase transition and elastic properties of CoN are investigated by ab initio plane-wave pseudopotential density function theory method. The equilibrium lattice parameters a₀, elastic constants C_{ij}, bulk modulus B₀ and its derivative B'₀ are calculated. From the usual condition of equal enthalpy, the phase transition of CoN from zinc-blende to rocksalt structure occurs at 35.4 GPa with a volume collapse of about 15.6%, consistent with the calculated result 36 GPa (FP-LDA), but an uncertainty is about 4.4 GPa compared with the 31 GPa (ASA-GGA). All three independent elastic constants, C₁₁, C₁₂, and C₄₄ for CoN are calculated from direct computation of stresses generated by small strains. Both C₁₂ and C₄₄ are less sensitive to pressure as compared with C₁₁. The calculated conclusions offer theoretical data for the further research of the mechanical properties for CoN.
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