The crystal structure and phase stability of the zeta phase in the group VB transition metal carbides: a computational investigation

Abstract

The crystal structure and composition of the zeta phase in the group VB transition metal carbides are not completely understood despite decades of experimental studies. As such, the phase rarely appears on phase diagrams of the group VB transition metal carbides. There is currently renewed interest in this phase, as tantalum carbide composites exhibit high fracture toughness in the presence of this phase. This work extends the initial computational study using density functional theory of the phase stability of the zeta phase in the tantalum carbide system, where the tantalum carbide zeta‐phase crystal structure and stability were determined, to the niobium and vanadium carbides. It is shown that the zeta phases in the three systems share the same crystal structure and it is an equilibrium phase at low temperatures. The carbon atom ordering in the three different phases is explored and it is demonstrated that the zeta phase in the tantalum carbides prefers to order carbon atoms differently than in the niobium and vanadium carbide zeta phases. Finally, the properties of this crystal are computed, including elastic constants, electronic densities of states and phonon dispersion curves, to illustrate that this crystal structure is similar to other transition metal carbides.

A computational examination of the zeta and eta phases in the hafnium nitrides

“…The ‐HfN phase, at higher temperatures, presumably has higher configurational entropy which leads to a narrowing of the phase field region of the ‐Hf 4 N 3− x phase field. Similar effects are observed in the ordering the carbides, notably the ordered phase field regions of Nb 6 C 5 and V 6 C 5 phases 30,48 …”

“…The convex hull construction at the HfN 0.667 composition gives the lowest energy structure as the ‐Hf 3 N 2 structure, but it is essentially energetically degenerate with a ‐Hf 3 N 2 structure with the stacking sequence of the zeta phase. This ‐Hf 3 N 2 structure is found to be isomorphous with our recently discovered ‐Me 3 C 2 phases in the group IVB carbides, 29,30 which unquestionably lie on their respective convex hulls and thus will be referred to as the newly discovered ζ‐Hf 3 N 2 structure. The lattice constants are a = 5.575 Å, b = 9.656 Å, c = 10.54 Å and β = 79.79° with the crystal structure described in Ref.…”

“…Images of and details of the crystal structure can be found in Ref. [29,30]. The ‐Hf 12 N 7 structure is similarly related to the ‐Hf 3 N 2 phase and is shown in Figure 2A,B.…”

“…Similar effects are observed in the ordering the carbides, notably the ordered phase field regions of Nb 6 C 5 and V 6 C 5 phases. 30,48…”

“…The disagreement with experiments can be partially understood by our latest work on the zeta phase in the group VB transition metal carbides. Notably, we found that stoichiometric ‐Me 4 C 3 are not thermodynamically stable in these systems, 28 but we did find a new structure, ‐Me 3 C 2 , that has the correct metal atom stacking sequence and lies on the convex hull 29,30 . Thus, we wish to understand if this new structure is stable in the hafnium nitrides as well and if, using a similar search approach, other eta phase structures can be found in the hafnium nitrides.…”