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

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 M 6 C 5 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 M 4 C 3 phase has been predicted for select carbides and has only been observed in zirconium carbide. In contrast, the stacking fault phase ζ‐M 4 C 3− x has been readily reported in the group VB carbides (but not in the group IVB carbides). The vacancy‐ordered M 3 C 2 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 M 3 C 2 phases have been experimentally observed in the Ti‐C and Hf‐C systems. Finally, the M 2 C 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.