Based on the particle swarm optimization algorithm on crystal structural prediction, we first predict that TaN undergoes a phase transition from the experimental θ-TaN to a hexagonal P63/mmc structure at 87.5 GPa with volume drop of 1.6%. This hexagonal P63/mmc structure is isostructural with anti-NiAs and can be quenchable to ambient pressure by further phonon dispersions calculations. The Young's modulus E and shear modulus G as a function of crystal orientation for TaN have thus been systematically investigated. The calculated mechanical properties suggest that the P63/mmc-TaN is ultra-incompressible and hard due to its high bulk modulus (336 GPa), large shear modulus (214 GPa), originating from a staking of “N-Ta-N” sandwiches layers linked by strong covalent Ta-N bonding.
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