# Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride
## 3 Results  
### Deformation Behavior  
The results of the stress-strain computations for single-crystal UN are presented in Figure 2. Additionally, the Young's moduli of UN along the [100] direction, as calculated by Equation (1) using experimental and potential-predicted elastic constants as reported in [12,40], respectively, are presented in Table 1. In MD stress-strain simulations, a numerical artifact arises, where the stress continues to oscillate around zero after fracture due to the interference between the tensile wave and its reflection off the fractured free surface, which results in regions with significant compressive stresses [41]. The stress-strain curves in Figure 2 were truncated before displaying these oscillations. Comparing Figure 2a,c to Table 1, it can be seen that the small-strain \(E_{[100]}\) predicted by the Tseplyaev potential (522.7 GPa) is overestimated compared to the large-strain value extracted from the stress-strain curve (410-430 GPa), which is closer to the experimental value (387 GPa), with the supercell having free surfaces showing the closest agreement. On the contrary, the small-strain \(E_{[100]}\) predicted by the Kocevski potential (354.1 GPa, Table 1) is closer to the experimental value than the large-strain value (300 GPa) as shown in Figure 2b,d. However, both supercells with PBCs and free surfaces have essentially the same [PERSON]'s modulus. The [PERSON]'s moduli of nanocrystalline UN are relevant for bulk UN because [PERSON]'s modulus is only slightly affected by structural miniaturization [42]. The yield stresses predicted by the [PERSON] potential for nanocrystalline UN strain under PBCs (Figure 2a) are larger than those predicted by the Kocevski potential (Figure 2b) by more than a factor of 2. The ultrahigh yield stresses in the range of about 30 GPa \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Tseplyaev** & **Kocevski** & **Experimental** \\ \hline \(E_{[100]}\) [GPa] & 522.7 & 354.1 & 387.0 [40] \\ \(H\) [GPa] & 25.38 & 9.28 & 7.8 \(\pm\) 0.2 [44], 9.7 \(\pm\) 0.4 [43] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Small-strain Young’s modulus along the [100] direction, \(E_{[100]}\) (Equation (1)), as well as the nanoindentation hardness, \(H\), of UN as predicted by both potentials and compared to experimental values at room temperature. The nanoindentation hardness value of [PERSON] et al. [43] represents an average of measurements with loads \(<\) 0.01 N, where the indentation size effect is not apparent. Figure 2: (Color online) Stress–strain curves of UN computed at 300 K by (**a**) the Tseplyaev potential and (**b**) the Kocevski potential under different strain rates, with PBCs applied in all directions. Stress–strain curves of UN computed at 300 K by (**c**) the Tseplyaev potential and (**d**) the Kocevski potential under different strain rates, with PBCs applied only along the loading direction. To suppress the effect of pressure oscillations on the stress–strain curves for supercells with free surfaces, the curves calculated by the Tseplyaev and Kocevski potentials have been smoothed by a moving average with windows of 2 and 4 ps, respectively. Note that the \(y\)-axis range is the same for each potential, whereas the \(x\)-axis is unique for each figure. predicted by the Tseplyaev potential are characteristic of purely covalent nanomaterials like Si and SiC [6], which is not the case for UN, whose bonding environment has both ionic and covalent character [45]. At all strain rates, the Kocevski potential predicts brittle fracture for nanocrystalline UN (Figure 2b). Interestingly, however, for strain rates of \(5\times 10^{8}\) and \(10^{9}\) s\({}^{-1}\), the Tseplyaev potential predicts sustainable plastic deformation by dislocation motion along the \(\{111\}\) planes (Figure 3). The stress-strain curves show signs of stress relaxation after yielding and multiple slip planes develop along the entire length of the specimen. The drop in the stress-strain curve after yielding is attributed to the development of dislocation planes [42].