Structure-strength relations of distinct MoN phases from first-principles calculations

Molybdenum mononitrides (MoN) exhibit superior strength and hardness among the large class of transition-metal light-element compounds, but the underlying atomistic mechanisms for their outstanding mechanical properties and the variations of those properties among various MoN phases adopting different crystal structures remain largely unexplored and require further investigation. Here we report first-principles calculations that examine the stress-strain relations of these materials, and systematically compare results under pure and indentation shear deformations. In particular, we examine the distinct bonding structures and the associated mechanical properties in four different crystal phases of MoN that have been experimentally synthesized and stabilized under various physical conditions. Our results reveal evolution patterns of bonding configurations and the resulting structural deformation modes in these MoN phases, which produce diverse stress responses and unexpected strength variations. These findings elucidate the structural and bonding characters that are responsible for the rich and distinct mechanical properties in various MoN structures, providing insights for understanding the experimentally observed phenomena and further exploring advanced superhard materials among the promising transition-metal nitrides, borides, and carbides.

Figure 1

The crystal structures of the four experimentally synthesized and characterized phases of MoN.

Figure 2

(a) Calculated stress-strain relations of ${\delta }_3$-MoN under pure shear and (Vickers) indentation shear along the $\left(1\overline{1}0\right)\left[110\right]$ direction. (b) Selected structural snapshots under the pure shear deformation. (c) Selected structural snapshots under the (Vickers) indentation shear deformation.

Figure 3

(a) Calculated stress-strain relations of ${\delta }_3$-MoN under pure shear and (Vickers) indentation shear along the $\left(1\overline{1}0\right)\left[001\right]$ direction. (b) Selected structural snapshots under the pure shear deformation. (c) Selected structural snapshots under the (Vickers) indentation shear deformation.

Figure 4

(a) Calculated stress-strain relations of ${\delta }_3$-MoN under pure shear and (Vickers) indentation shear along the (110)$\left[1\overline{1}0\right]$ direction. (b) Selected structural snapshots under the pure shear deformation. (c) Selected structural snapshots under the (Vickers) indentation shear deformation.

Figure 5

Calculated stress-strain relations and structural snapshots of ${\delta }_1$-MoN under pure shear and (Vickers) indentation shear along the two inequivalent directions: (a, b) in the $\left(1\overline{1}0\right)\left[001\right]$ direction, and (c, d) in the $\left(1\overline{1}0\right)\left[110\right]$ direction.

Figure 6

Calculated stress-strain relations and structural snapshots of ${\delta }_2$-MoN under pure shear and (Vickers) indentation shear along the two inequivalent directions: (a, b) in the $\left(1\overline{1}0\right)\left[001\right]$ direction, and (c, d) in the $\left(1\overline{1}0\right)\left[110\right]$ direction.

Figure 7

Simulated and measured [10] XRD patterns of MoN. The experimental XRD patterns are measured at $1300{}^{\circ }\mathrm{C}$.

Figure 8

(a) Calculated stress-strain relations and (b) structural snapshots of $\gamma$-MoN under pure shear and (Vickers) indentation shear along the (001)[110] direction.