Influence of carbon vacancy formation on the elastic constants and hardening mechanisms in transition metal carbides

For group VB transition metal carbides, as compared to group IVB carbides, an anomalous rise in hardness occurs for substoichiometric carbon concentrations as compared to the stoichiometric monocarbides. Here we report the computationally derived elastic constants, electronic density of states, and activation energies for carbon vacancy migration as a function of carbon content to elucidate their effect on the hardening responses. The changes in elastic properties with respect to carbon vacancy concentration show similar behaviors of elastic softening and decreasing hardness for all of the cubic carbides. The consistent trends of vacancy diffusion energy barriers between all of the group IVB and VB transition metal carbides also suggests that carbon diffusion may not be a significant contributor to the reported hardness differences. Consequently, we propose that the anomalous hardening for substoichiometric behavior is a competition between elastic constant softening and a microstructural-based effect, i.e. domain hardening, that is present in group VB carbides but not in group IVB carbides.