# Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride
## 3 Results
### Dislocation Motion  
#### 3.2.1 Edge Dislocations  
A schematic of the supercell constructed to study edge dislocations as well as the OVITO visualization of the \(\frac{1}{2}\langle 110\rangle\{111\}\) edge dislocation and its Burgers vector after equilibration at 1 K are shown in Figure 1. It is noted that the Kocevski potential could not stabilize edge dislocations, and only the Tseplyaev potential is used for their simulation. The gray \"defect mesh\" in Figure 1b extends over about two-thirds of \(l_{x}\), as the dislocation's presence is not sensed far from the dislocation line. The defect mesh is an OVITO term for crystal regions where the atomic arrangement deviates from that of a perfect crystal. Thisimplies that the chosen supercell dimensions are indeed large enough to have a strain-free state, where PBCs are applied along the slip direction. A supercell similar to Figure 1 was constructed for the screw dislocation, and the same observation about the defect mesh applies to it. We note that after 0 K minimization, the \(\frac{1}{2}\langle 110\rangle\{111\}\) edge dislocation splits into two Shockley partials with \(\mathbf{b}=\frac{1}{6}\langle 112\rangle\). However, when the supercell is equilibrated at 1 K, the Shockley partials transform back to a perfect edge dislocation. Thus, the Tseplyaev potential predicts Shockley partials to exist only as a metastable state in UN. The displacement and stress of the \(\frac{1}{2}\langle 110\rangle\) edge dislocation as a function of time is shown in Figure 4. We can observe that the Peierls stress of the \(\frac{1}{2}\langle 110\rangle\) edge dislocation along the \(\{111\}\) plane is 2.98 GPa, whereas those for the \(\{110\}\) and \(\{112\}\) planes are 7.65 GPa and 8.82 GPa, respectively. This confirms that \(\{111\}\) is the principal slip plane in UN, as predicted by the Tseplyaev potential, because it requires the lowest stress for slip. It is also found that \(\{110\}\) is predicted to be the second preferable slip plane. A Peierls stress of 2.98 GPa is on the order of \(10^{-2}\)\(G\), \(G\)\(\sim\)100 GPa being the shear modulus of UN as predicted by the Tseplyaev potential [12]. This is the same order of magnitude of the Peierls stresses for purely covalent materials [32], which confirms our conclusion that the Tspelyaev potential very likely overestimates the covalency of the UN system. For purely ionic crystals like LiF and NaCl, the experimental values of the Peierls stress are \(1.6\times 10^{-4}\)\(G\) and \(5.0\times 10^{-4}\)\(G\), respectively [15]. Based on the OVITO visualization, it was observed that the edge dislocation moves via a kink-pair mechanism [32]. Assisted by thermal vibrations, the dislocation hops from one energy minimum to the next along the slip plane by forming unstable kink pairs, which then annihilate one another. This continuous kink-pair nucleation and annihilation process reduces the threshold stress required to move the dislocation much  
Figure 4: (Color online) Movement of the \(\frac{1}{2}\langle 110\rangle\) edge dislocation along (**a**) \(\{110\}\), (**b**) \(\{111\}\), and (**c**) \(\{112\}\) slip planes under applied strain rate of \(10^{-4}\) s\({}^{-1}\). To calculate the Peierls stress, the developed shear stress on each dislocation is also averaged and is shown in the figures. Although the kink-pair nucleation mechanism at very low stresses is often observed for screw dislocations and rarely for edge dislocations due to stress fluctuations [35; 37], it has been observed in atomistic simulations by [PERSON] et al. [52] for edge dislocations in \(\alpha\)-Fe. Due to the probabilistic nature of dislocation hopping, at relatively low stresses (\(\tau\leq 1150\) MPa) the motion is dominated by fluctuations and no steady-state velocity can be observed. When the stress is increased, fewer fluctuations are observed and a nearly steady-state velocity emerges. To be consistent, however, we calculate the velocity at all stresses as the total distance traveled divided by the total simulation time, i.e., 1 ns.