The low coordination number of nitrogen in hard tungsten nitrides: a first-principles study.

Tungsten-nitrogen (W-N) compounds are studied via a combination of first-principles calculations and variable-composition evolutionary structure searches. New candidate ground states and high-pressure phases at 3 : 2, 1 : 1, and 5 : 6 compositions are uncovered and established for possible synthesis. We found that the structures in 4/5-fold N coordination (i.e., NbO-WN and W5N6) are more favoured for the W-N system at low-pressures compared with the conventional 6-fold phases (rs-WN and δ-WN). We attribute the low N coordination feature of W-N ground states to the enhanced W 5d-N 2p orbital hybridization and strong covalent W-N bonding, which involves the full-filling of W-N bonding and antibonding states and can remarkably improve the mechanical strength and hardness. These findings not only clarify the phase diagram of the W-N system, but also shed light on the correlations of hardness with microscopic crystal and electronic structures.