# Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride
## 3 Results
### Dislocation Motion
#### 3.2.1 Edge Dislocations
The variation in dislocation velocity with the applied shear stress at 300 K is shown in Figure 5a on a linear scale and Figure 5b on a semi-log scale, which is introduced to clarify the velocity trend in regime I. The parameters resulting from fitting the velocity-stress curve to Equations (3) and (4) are summarized in Table 2. For the stress range of 25-1150 MPa (i.e., regime I), the velocity-stress curve is fitted to Equation (3), with \(H_{0}=0.11\) eV, \(p=0.37\), and \(q=0.62\). The transition velocity is identified as \(v_{t}=\) 10.1 m/s, which is the velocity corresponding to the transition stress \(\tau_{t}=\) 1150 MPa. These values produce a coefficient of determination \(R^{2}=99.9\%\). A value of \(H_{0}=0.11\) eV for UN is reasonable considering that the experimental values of the same parameter for LiF, NaCl, and potassium chloride (KCl) are 0.09, 0.11, and 0.16 eV, respectively [48]. Kink-pair formation energies are sensitive to supercell dimensions, especially the dimension along the dislocation line [38]. Thus, the calculated value of \(H_{0}\) should be treated as a first estimate, and more research is required to test its convergence. A value of \(p=0.37\) falls within the expected range (i.e., \(0\leq p\leq 1\)). The value of \(q=0.62\), however, is slightly underestimated relative to the expected range (i.e., \(1\leq q\leq 2\)). At a stress of \(\tau_{t}=\) 1150 MPa, a transition to regime II occurs where the velocity varies linearly with stress. Fitting the velocity-stress curve in regime II to Equation (4), we find that the phonon drag coefficient \(B=1.22\times 10^{-3}\) Pa\(\cdot\)s. This value produces \(R^{2}=95.8\%\). The linear fit is valid until a stress \(\tau_{t}^{\prime}=\) 1725 MPa, where a deviation from linearity is apparent, i.e., a transition to regime III occurs where the uncertainty in the velocity is much higher than in regimes I and II, with a maximum standard deviation of 50 m/s. The linear dislocation mobility is calculated to be \(M=1/B=817\) Pa\({}^{-1}\cdot\)s\({}^{-1}\). To give context to this value, the mobility of edge dislocations in two iron-chromium-nickel steel systems (i.e., Fe\({}_{40}\)Cr\({}_{25}\)Ni\({}_{35}\) and Fe\({}_{50}\)Cr\({}_{20}\)Ni\({}_{30}\)) was calculated by [PERSON] et al. [19] to be \(5.01\times 10^{4}\) and \(7.04\times 10^{4}\) Pa\({}^{-1}\cdot\)s\({}^{-1}\), respectively. This implies that UN is less ductile than steel systems, which is expected considering that UN is ceramic. Figure 5: The variation in the average edge dislocation velocity in UN with shear stress (**a**) on a linear scale, and (**b**) on a semi-log scale. The error bars represent one standard deviation, and the orange lines represent piecewise curve fits. An interesting observation is that in the linear range at intermediate stresses, the steady-state movement of the dislocation is occasionally interrupted by abrupt jumps that occur within a small time interval of 20 ps, as shown in Figure 6a for \(\tau\) = 1525 MPa. These jumps have a velocity of 2977 \(\pm\) 32 m/s independent of the applied stress. This velocity compares very well with the UN average sound velocity of 2990 m/s [53]. While it is observed experimentally that dislocations move with the sound velocity at very high stresses [54], our finding suggests that at intermediate stresses, even when the edge dislocation displays a subsonic behavior, its steady-state motion can be interrupted by jumps that have a maximum velocity equal to the average sound velocity. This agrees with the picture that dislocation motion is stochastic.