We have studied the formation of dislocations in $M_2\mathrm{Al}\mathrm{C}$ ($M=\mathrm{Ti}$, V, Cr) using ab initio calculations at the gradient-corrected density-functional level. In the $\left[1\overline{2}10\right]\left(0001\right)$ slip system, dislocations can be formed. This is, in turn, consistent with the experimentally reported ductile behavior of these phases [M. W. Barsoum, Prog. Solid State Chem. 28, 201 (2000)]. This rather unusual ductile behavior of metal carbides may, in part, be understood based on the electronic structure. According to the crystal-orbital Hamilton population analysis, three bonding types are found in $M_2\mathrm{Al}\mathrm{C}$: strong directional $M–\mathrm{C}$ bonding and weaker nondirectional $M–\mathrm{Al}$ and $M–M$ bonding. We suggest that the latter two facilitate ductile behavior of these ternary carbides.

The compressibility of the nanolaminated $M_2\mathrm{Al}\mathrm{C}$ phases (space group $P{6}_3∕mmc$) with $M=\mathrm{Ti},\mathrm{Zr},\mathrm{Hf}$ [valence electron concentration (VEC) of the $M$ element of 4], V, Nb, Ta $(\mathrm{VEC}=5)$, and Cr, Mo, W $(\mathrm{VEC}=6)$ is systematically studied in the pressure range from $0\text{to}\sim 70\mathrm{GPa}$ using ab initio calculations. These phases are characterized by interleaving of MC and Al layers. For $\mathrm{VEC}=4$, we observe a larger compressibility along the $c$ axis as compared to the $a$ axis. As the VEC is increased to 5, the compressibility in the $c$ direction decreases and becomes comparable to the compressibility in the $a$ direction, whereas at $\mathrm{VEC}=6$, the compressibility in the $a$ direction is larger than that along the $c$ direction. These results are consistent with recent experimental work. Based on a systematic study of the VEC-induced changes in bond stiffness, bond angle, and bond energy, we conclude that the geometric alteration of the bonding configuration in combination with the increase in $M–\mathrm{C}$ bond stiffness is mainly responsible for the observed compressibility change.