Mechanical and dynamical stability of nitrides at high pressure.

The structure of the Na-N, K-N, P-N, and Fe-N solids was predicted using evolutionary algorithms and density functional theory (DFT). The pressure dependence of elastic moduli of the predicted nitrides is analyzed. Calculations of phonon dispersion important for understanding dynamical stability are accompanied by estimates of mechanical stability based on elastic constants, Born conditions, and direct calculations of eigenvalues of the stiffness matrix. All the studied structures are found to be mechanically stable indicating that elastic mechanical stability condition is the least critical compared with thermodynamical stability based on the construction of a convex hull for the enthalpy of formation and dynamical stability, based on phonon dispersion. For example, PN3 crystal with Immm symmetry group previously predicted to be stable above 200 GPa is metastable at 30 and 50 GPa according to convex hull construction, but PN3 crystal is found to be mechanically and dynamically stable at these pressures.