Finding the stable structures of N1−xWx with an ab initio high-throughput approach

Using density functional theory calculations, many researchers have predicted that various tungsten nitride compounds N1−xWx (x < 12 ) will be “ultraincompressible” or “superhard,” i.e., as hard as or harder than diamond. Necessary conditions for such compounds are that they have large bulk and shear moduli, greater than approximately 200 GPa, and are elastically and vibrationally stable. Compounds with such desirable properties also must be energetically stable against decomposition into other compounds. This test for stability can only be found after the determination of the convex hull for N1−xWx , which connects the lowest enthalpy structures as a function of composition. Unfortunately, the experimental phase diagram of the N-W structure is uncertain, as it is difficult to break the N2 bond to form compounds with tungsten. Experiment also indicates that there are a large number of partially filled sites in most N-W structures. This introduces computational difficulties since we cannot easily model randomly placed vacancies. In addition, van der Waals forces play a significant role in determining the structure of solid N2 and the nitrogen-rich compounds. This makes it difficult to determine the relative energies of these compounds, as there is no universally accepted density functional incorporating van der Waals interactions. The exact shape and even composition of the convex hull is dependent upon the choice of density functional, even if we only chose between the local density approximation and a generalized gradient functional. Despite these difficulties, computations can determine much about the ground-state form of the convex hull. Here, we use high-throughput calculations to map out the hull and other low-energy structures for the N-W system. The lowest-energy structures all have vacancies, on the tungsten sites in hexagonal-based compounds, and on both the nitrogen and tungsten sites in cubic compounds. We find that most of the N-W structures proposed in the literature, both theoretical and experimental, are above the convex hull, in some cases by over 0.2 eV/atom. One of the ground-state phases, N-W in the NbO structure, has relatively large bulk (>300 GPa) and (>200 GPa) shear moduli, and so is a candidate superhard material. This will require further investigation.