# Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride
## 3 Results
### Deformation Behavior
Necking occurs as a result of the branching of secondary dislocation planes from a primary dislocation plane [42], as can be observed in Figure 3.  
The finding that UN slips primarily along the \(\{111\}\) planes is interesting because it contradicts the principal slip system reported by [PERSON] and [PERSON] for UN, which is \(\{110\}\)[9]. \(\{110\}\) planes are the preferred slip system for purely ionic crystals [32; 46]. For crystals with a mixed ionic-covalent bonding environment (as in the case of UN), slip might principally occur along other planes, e.g., \(\{111\}\) and \(\{100\}\)[20; 46]. More interestingly, the primary slip planes in uranium monocarbide (UC) and titanium carbide, two compounds closely related to UN, have been reported to be \(\{111\}\)[9; 47], which raises questions about the physical reason for this discrepancy. [PERSON] and [PERSON] attempted to explain the different slip systems of UN and UC in another study [46] by formulating a hard-sphere model for MX compounds with the NaCl crystal structure, in which the radius ratio, i.e., \(R_{\rm X}/R_{\rm M}\), affected the saddle point configuration of the \(\frac{1}{2}\langle 110\rangle\) dislocation during its motion. Based on this model, three cases arose: (\(a\)) crystals with \(R_{\rm X}/R_{\rm M}\approx 0.414\) slip on \(\{110\}\); (\(b\)) for \(0.414<R_{\rm X}/R_{\rm M}<0.633\), slip is on \(\{111\}\); and (\(c\)) for \(R_{\rm X}/R_{\rm M}>0.633\), slip occurs on \(\{100\}\). They further assumed that \(R_{\rm M}\) was equal to the metallic radius, and \(R_{\rm X}=a_{\rm MX}/2-R_{\rm M}\), where \(a_{\rm MX}\) is the lattice parameter of the compound MX. Based on this definition, the authors found that for UN, \(R_{\rm X}/R_{\rm M}=0.41\), which predicts slip on \(\{110\}\), whereas for UC, \(R_{\rm X}/R_{\rm M}=0.43\), which predicts slip on \(\{111\}\). However, the choice of the metallic radius, \(R_{\rm M}\), was rather arbitrary. To confirm that we are observing dislocations along slip planes, the DXA was applied to the supercell immediately after fracture, and it was found that perfect dislocations (of both edge and screw characters) with \(\mathbf{b}=\frac{1}{2}\langle 110\rangle\) (which is the usual [PERSON] vector in ionic crystals [32]) reside along the planes with a high CSP. We also observed several  
Figure 3: (Color online) \(\{111\}\) slip planes generated in the \(150\times 30\times 30\) supercell when strained at 300 K and a strain rate of \(10^{9}\) s\({}^{-1}\) under PBCs, as modeled by the Tseplyaev potential. Atoms have been colored in OVITO according to their CSP, where dark purple atoms have zero CSP and yellow atoms have high CSP. For better visibility, the maximum CSP has been set to 20 Å\({}^{2}\). Similar slip planes have been observed at a strain rate of \(5\times 10^{8}\) s\({}^{-1}\). Shockley partials with a Burgers vector \(\frac{1}{6}\langle 112\rangle\) along the slip planes. Historically, the existence of Shockley partials in ionic crystals has been the source of much debate in the literature [33; 48]. Based on geometrical and energetic arguments, it was shown that for an ionic MX compound that has the NaCl crystal structure and slips on the \(\{111\}\) planes, only perfect dislocations can exist, because the presence of the smaller X atoms prevents the occurrence of Shockley partials [46]. Thus, the observed Shockley partials may be either an artifact of the dislocation analysis algorithm or an intermediate metastable state predicted by the Tseplyaev potential. Another possibility is that the Tseplyaev potential overestimates the covalency of UN. In Figure 3, we can also see signs of cross-slip along planes of the \(\{111\}\) family. This is expected, as cross-slip of screw dislocations with \(\mathbf{b}=\frac{1}{2}\langle 110\rangle\) can occur only by glide on planes other than \(\{110\}\), as only one \(\langle 110\rangle\) direction lies in a given \(\{110\}\) plane [32].