Bonding Effects on the Slip Differences in the $B1$ Monocarbides

Differences in plasticity are usually attributed to significant changes in crystalline symmetry or the strength of the interatomic bonds. In the $B1$ monocarbides, differences in slip planes exist at low temperatures despite having the same structure and very similar bonding characteristics. Our experimental results demonstrate concretely that HfC slips on $\{110\}$ planes while TaC slips on $\{111\}$ planes. Density functional theory calculations rationalize this difference through the formation of an intrinsic stacking fault on the $\{111\}$ planes, formation of Shockley partials, and enhanced metallic bonding because of the valence filling of electrons between these transitional metal carbides.

Figure 1

(a) Representative schematic and optical micrograph of the $10\times 10$ array of Vickers indents in a carbide specimen. TEM bright field micrographs of typical dislocation structures found in HfC (b) and TaC (c).

Figure 2

DFT calculated generalized stacking fault energy curves for fractional shear along (a) [110] on both the (111) and (110) planes and (b) for the partial dissociation [112] (111) for both HfC and TaC. Note the intrinsic stacking fault in TaC which is absent in HfC. Associated PN model misfit density plots for (c) HfC and (d) TaC, with the distance normalized by the Burgers vector. The preference for splitting into partials is evident in TaC and not HfC.

Figure 3

DFT isoconcentration charge surfaces for HfC and TaC in a zero and fraction shear state for various slip conditions.The dashed arrow indicates the fault plane highlighted by the solid box region. The top row shows the unsheared conditions with the bottom row being the designated shear indicated by the fraction value. The compass arrows indicate the viewing prospective.