# Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride
## 2 Computational Methods
### Dislocation Motion
Then, the \(x\)-coordinate of the dislocation is calculated as the average among the \(x\)-coordinates of all atoms belonging to the dislocation core. Based on visual inspection and comparison with the DXA applied to the U sublattice, we found that CSP \(\geq\) 2 A\({}^{2}\) exclusively selects the atoms belonging to the dislocation core. A limitation of this methodology is that it assumes that atoms belonging to the dislocation core only move as a single unit along a single slip plane. For all calculations in this paper, we confirmed by visual inspection that this is indeed the case. However, this methodology can be extended to study, e.g., the cross-slip of screw dislocations by tracking both the \(x\)- and \(y\)-coordinates of the dislocation core. In general, there exist three regimes for dislocation motion depending on the values of the shear stress (or, equivalently the strain rate) and temperature:  
(_a_) Regime I: Under very low stresses/temperatures, dislocations move via the kink-pair nucleation mechanism, where the dislocations are nearly straight lines, which suggests the existence of only one kink pair at any given time [35]. Under these circumstances, the dislocation motion is thermally activated, and has an Arrhenius-like dependence on temperature [35; 37]:  
\[v_{\rm I}=v_{\rm t}\sqrt{s}\exp\biggl{[}-\frac{H_{0}}{2k_{B}T}(1-s^{p})^{q} \biggr{]} \tag{3}\]  
where \(v_{\rm t}\) is the velocity corresponding to the transition from the exponential thermally activated regime (regime I) to the linear phonon drag regime (regime II); \(s=\tau/\tau_{t}\) is the shear stress normalized by the transition stress, \(\tau_{t}\), between the two regimes; and \(H_{0}(1-s^{p})^{q}\) is the stress-dependent kink-pair nucleation enthalpy, with \(H_{0}\) being the kink-pair formation energy at zero temperature and zero stress. \(H_{0}\) can be calculated from stress-relaxation measurements or molecular statics [35; 38]. In this work, however, \(H_{0}\) is treated as a fitting parameter. According to linear elasticity theory, \(p=0.5\) and \(q=1.25\) for a sinusoidal potential. For more complex potentials, \(p\) and \(q\) are treated as fitting parameters, which is our approach in this work, and they have the following ranges: \(0\leq p\leq 1\) and \(1\leq q\leq 2\). (\(b\)) Regime II: As the temperature and/or stress are increased, kink-pair nucleation and propagation have comparable rates (i.e., kink-pair nucleation is no longer the rate-limiting step) leading to rough dislocation lines [35]. Under these conditions, the stress is large enough so that there is no thermal barrier to motion, and the velocity varies linearly with stress [17,18]. This viscous drag mainly arises from dislocation interactions with lattice phonons [17]. In this regime, the velocity takes the form  
\[v_{\Pi}=\frac{b\tau}{B}+C \tag{4}\]  
where \(b\) is the magnitude of Burgers vector, \(B\) is the linear drag coefficient, and \(C\) is an additive constant that has the units of velocity. The linear dislocation mobility in this regime is calculated as \(M=1/B\). (\(c\)) Regime III: Under even higher stresses, the relation between \(v\) and \(\tau\) becomes nonlinear due to a combination of phonon and radiative damping, with the velocity asymptotically approaching the transverse sound velocity [17]. Radiative damping results from wave emission by moving dislocations and is independent of temperature [39]. In fracture mechanics, energy dissipation is primarily governed by crack formation rather than radiative damping [39]. As a result, radiative damping is more relevant to high-velocity deformation scenarios, such as shock loading, than to cracking-induced failures such as those expected in nuclear fuels under extreme conditions. Therefore, while we identify the transition stress between regimes II and III, \(\tau_{i}^{\prime}\), regime III is beyond the scope of this study, and the fitted mobility function is restricted to regimes I and II.