# Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride
## 3 Results
### Dislocation Motion
#### 3.2.2 Screw Dislocations  
For the screw dislocations simulated using the Kocevski potential, we aimed to calculate the Peierls stress at 1 K for the \(\{110\}\), \(\{111\}\), and \(\{112\}\) planes. The \(\frac{1}{2}\langle 110\rangle\) screw dislocation moved smoothly along the \(\{110\}\) plane, as illustrated in Figure 7. When the dislocation was set to move along the \(\{111\}\) and \(\{112\}\) planes using the Kocevski potential, it was observed to cross-slip onto planes that form angles of 35.3\({}^{\circ}\) and 54.7\({}^{\circ}\) with the \(\{111\}\) and \(\{112\}\) planes, respectively. These angles precisely correspond to the angles between these planes and the \(\{110\}\) plane. Thus, the Kocevski potential predicts that the \(\{110\}\) plane is the primary slip plane of UN, despite its inability to predict any dynamic behavior, as discussed in Section 3.1, or to stabilize edge dislocations. \begin{table}
\begin{tabular}{l c c} \hline
**Parameter** & **Edge Dislocation** & **Screw Dislocation** \\ \hline Kink-pair formation energy, \(H_{0}\) [eV] & \(0.11\) & \(1.0\) \\ Exponent \(p\) & \(0.37\) & \(0.0037\) \\ Exponent \(q\) & \(0.62\) & \(0.30\) \\ Transition stress between regimes I and II, \(\tau_{t}\) [MPa] & \(1150\) & \(700\) \\ Transition velocity between regimes I and II, \(v_{t}\) [m/s] & \(10.1\) & \(20.1\) \\ Phonon drag coefficient, \(B\) [Pa\(\cdot\)s] & \(1.22\times 10^{-3}\) & \(2.20\times 10^{-4}\) \\ Mobility, \(M\) [Pa\({}^{-1}\cdot\)s\({}^{-1}\)] & \(817\) & \(4546\) \\ Additive constant, \(C\) [m/s] & \(-296\) & \(-1134\) \\ Transition stress between regimes II and III, \(\tau_{t}^{\prime}\) [MPa] & \(1725\) & \(1125\) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the mobility functions (Equations (3) and (4)) fitted to the motion of the \(\frac{1}{2}\langle 110\rangle\{111\}\) edge and \(\frac{1}{2}\langle 110\rangle\{110\}\) screw dislocations at 300 K.  
Figure 6: (a) Position versus time profile for the movement of the \(\frac{1}{2}\langle 110\rangle\{111\}\) edge dislocation under a stress of 1525 MPa. (b) Position versus time profile for the movement of the \(\frac{1}{2}\langle 110\rangle\{110\}\) screw dislocation under a stress of 1000 MPa. As opposed to the GPa stresses at which the edge dislocations move at 1 K under the Tseplyaev potential, the screw dislocation starts moving when the stress reaches 760 MPa (Figure 7). The maximum value of the stress is 790 MPa, which we designate as the Peierls stress for the screw dislocation. Despite the large stress fluctuations, this value is surprisingly relevant to the mobility calculation and corresponds to the transition stress from regime I to regime II. Only the movement along the \(\{110\}\) planes is used to fit a mobility function for the screw dislocation. The motion of the screw dislocation was tracked under constant stress in the range of 25-1200 MPa at 300 K, and an example of such a calculation is shown in Figure 6b. The results of the mobility calculation for the screw dislocation are shown in Figure 8. At stresses smaller than 100 MPa, the screw dislocation oscillates around its initial position without any observable motion. At stresses between 100 and 200 MPa, the screw dislocation performs only a few jumps on the time scale of 1 ns, which results in average velocities in the order of \(10^{-1}\) m/s. Between 200 and 700 MPa, motion by the kink-pair mechanism is observed. We fitted Equation (4) to the data points in the 200-700 MPa region and found that \(H_{0}=1.0\) eV, \(p=0.00037\), and \(q=0.30\). These values have an \(R^{2}=98.3\%\). \(p\) falls within the expected range of 0-1, although its significantly small value indicates a minor stress dependence. As for the edge dislocation, \(q\) is underestimated compared to its expected range of 1-2. \(H_{0}\) for the screw dislocation is larger than that of the edge dislocation (0.11 eV).