Computational Study of the Phase Diagram of Tungsten-Nitride

There has been considerable interest in the Tungsten Nitride (WN) system, as various calculations predict that structures of WN$_2$, WN$_3$, and WN$_4$ may be ultra-compressible and perhaps as hard as diamond. The predicted stability of these structures is based on vibrational stability and a negative formation enthalpy ($\Delta$H) relative to $\alpha$N$_2$ and bcc W. A negative value of $\Delta$H does not guarantee a compound exists, as it may be above the tie-line constructed from other compounds with lower enthalpies. The determination of the tie-line is complicated by the fact that the ground state of WN is not well determined by experiment or theory. We have used AFLOW, extended to include a large variety of Nitrogen containing structures, to compute the formation energy of the WN system over a large range of compositions. In this talk we discuss the ground state of the WN system, the relationship of our predicted structure to experiment, and the relative stability of the possible ``superhard'' WN$_x$ compounds. We find that this behavior depends on whether a GGA or LDA functional is used, probably because of the inability of these functionals to handle van der Waals forces in N$_2$ crystals.