Discovering novel VC1− compounds through hybrid first-principles and evolutionary algorithms

Acta Crystallogr Sect B

2019

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.

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Acta Crystallogr Sect B

2019

“…This figure demonstrates that the TaC, α‐Ta 2 C, and Ta 6 C 5 structures are thermodynamically stable as initially reported by Yu et al In addition, our search identifies that a Ta 3 C 2 phase with the same metal atom ordering as the ζ‐Ta 4 C 3 phase (which lies just of the convex hull in the work of Yu et al), lies on the convex hull. The failure of all previous work to find the zeta phase using evolutionary algorithms may be a result of the large number of atoms in the primitive unit cell of the Ta 3 C 2 structure to be described below. This new finding here indicates that the stability is not marginal, but rather it lies firmly on the convex hull along with the other tantalum carbides found by Yu et al It also matches the experimental evidence of the zeta phase being at compositions of approximately TaC 0.67.…”

Section: Resultsmentioning

confidence: 99%

A computational search for the zeta phase in the tantalum carbides

2018

J Am Ceram Soc

A systematic electronic structure density functional theory search for the zeta phase in the tantalum carbon system has been conducted, demonstrating that the zeta phase does indeed lie on the convex hull, establishing low‐temperature thermodynamic stability, and is structurally stable. Even though the zeta phase is most oft reported as a R3¯m ζ‐Ta4C3‐x structure, these new computational results reveal that the perfectly ordered zeta phase occurs at the Ta3C2 composition and belongs to the C2/m space group. Furthermore, these results suggest that the R3¯m space group may be a result of an order‐disorder transition and potential deviations from ideal stoichiometry at higher temperatures. The structure of this Ta3C2 compound can be described as ordered strings of carbon vacancies on a single carbon plane, which is also the preferred plane where additional carbon vacancies or interstitials form. These defects have modest formation energies, which provides further explanation for the small homogeneity range in zeta phase.

“…We now transition to the group VB carbides, starting this discussion with the V‐C system . Yu et al found 2 carbides to lie on the convex hull from DFT, the α‐V 2 C (Pbcn) structure and V 6 C 5 , with the latter structure having 3 essentially degenerate forms with space groups of C2/m, P3 1 12, and C2/c, all within 1 meV/atom.…”

Section: Phase Stability Predictionsmentioning

confidence: 89%

“…Yu et al found 2 carbides to lie on the convex hull from DFT, the α‐V 2 C (Pbcn) structure and V 6 C 5 , with the latter structure having 3 essentially degenerate forms with space groups of C2/m, P3 1 12, and C2/c, all within 1 meV/atom. The work by Xie et al demonstrated that a Pnnm V 2 C structure was slightly lower energy than α‐V 2 C (Pbcn) and also confirmed that P3 1 12 V 6 C 5 was on the convex hull. Xie et al claimed that the Pnnm V 2 C phase was a completely new structure; however, this structure is simply the C35 structure (CaCl 2 prototype), and its relationship to close‐packing in the HCP crystal as well as the rutile structure is well described in reference .…”

Section: Phase Stability Predictionsmentioning

confidence: 95%

Review of phase stability in the group IVB and VB transition‐metal carbides

2018

J Am Ceram Soc

This review summarizes the phase stability in the group IVB (Ti‐C; Zr‐C; Hf‐C) and group VB (V‐C; Nb‐C; Ta‐C) transition‐metal carbides. The order parameter functional (OPF) method and density functional theory (DFT) method have been used to predict phase equilibria in these systems. Extensive experimental investigations have attempted to determine both phase stability as a function of composition as well the crystal structures present using X‐ray diffraction, neutron diffraction, electron backscatter detection, and selected area electron diffraction. These investigations have demonstrated that the structures that form are based on the close‐packing of the metal atoms and the arrangement of the carbon atoms in the octahedral interstices. In general, the rocksalt B1 phase is stable for all of the transition‐metal carbides, with their substoichiometry tolerance increasing with temperature; vanadium carbide is the exception due to its negative vacancy formation energy. Vacancy‐ordered M6C5 phases have been predicted and experimentally confirmed in both groups of carbides; however, kinetic limitations often inhibit the formation of vacancy‐ordered phases, which has contributed to controversy in phase identification. The vacancy‐ordered M4C3 phase has been predicted for select carbides and has only been observed in zirconium carbide. In contrast, the stacking fault phase ζ‐M4C3−x has been readily reported in the group VB carbides (but not in the group IVB carbides). The vacancy‐ordered M3C2 has been predicted by DFT for the group IVB carbides but not in the group VB carbides, whereas OPF predicts its stability in both carbides. Vacancy‐ordered M3C2 phases have been experimentally observed in the Ti‐C and Hf‐C systems. Finally, the M2C phase has been predicted in both group carbides, except for hafnium carbide, with an order‐disorder transition with temperature. These factors result in phase diagrams that are similar among all the carbides, but each phase diagram is unique due to subtle differences in bonding that result in slight differences in thermodynamically stable phases.