# Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride
## 2 Computational Methods
### Dislocation Motion  
Ionic crystals have a Burgers vector \(\textbf{b}=\frac{1}{2}\langle 110\rangle\) and four possible slip planes, \(\langle 110\rangle\), \(\langle 111\rangle\), \(\langle 100\rangle\), and \(\langle 112\rangle\), with the principal one being determined mainly by the bonding nature [20; 32]. Three straight edge dislocations are studied in this paper: \(\frac{1}{2}[110](1\bar{1}0)\), \(\frac{1}{2}[\bar{1}10](111)\), and \(\frac{1}{2}[\bar{1}10](\bar{1}\bar{1}2)\), where their Burgers vectors are along the \(x\)-axis and line vectors along the \(z\)-axis. To construct an edge dislocation, two half-crystals are stacked on top of one another--the top half-crystal containing one extra atomic plane compared to the bottom half-crystal. Then, strains of \(-0.5\)\(b/l_{x}\) and \(+0.5\)\(b/l_{x}\) are applied to the top and bottom crystals, respectively, with \(l_{x}\) being the length of the respective half-crystal along the \(x\)-axis [14]. That is, the top half-crystal is compressed by \(b/2\) and the bottom half-crystal is stretched by \(b/2\). Up to this point, only a misfit dislocation with a zero Burgers vector is formed [14]. To convert it into a perfect edge dislocation, the supercell energy is minimized at 0 K using a nonlinear conjugate gradient method with a minimum relative energy tolerance of \(10^{-13}\). This construction method allows periodicity along the slip direction of the edge dislocation to be maintained and naturally resolves the anisotropic features of the dislocation core. A \(\frac{1}{2}[110](\bar{1}10)\) screw dislocation is constructed by Atomsk using the Volterra construction method of the isotropic elasticity theory [32]. Periodicity is recovered along the slip direction by tilting the supercell vector parallel to the glide direction by \(b/2\). This is achieved in Atomsk by adding a \(z\)-component equal to \(b/2\) to the \(x\)-vector of the supercell. Then, the supercell energy is minimized at 0 K to resolve the anisotropic features of the dislocation core. It should be emphasized that all atoms are assumed to be neutral and charge neutrality is maintained for all supercells containing dislocations. Charge effects are often associated with dislocations in ionic crystals [33]; however, because it behaves as a metal, defects (including dislocations) in UN have no associated charge and are principally neutral [34]. For both edge and screw dislocations, the simulation environment for the 0 K minimization is set up as follows (see Figure 1 for a schematic representation for the edge dislocation): PBCs are implemented in the \(x\)- and \(z\)-directions, which are the dislocation line direction and slip direction, respectively, while a fixed boundary condition is applied in the \(y\)-direction. Atoms in the top layer, whose thickness was arbitrarily chosen as 0.05 \(l_{y}\), are restricted to move in the \(xz\) plane, whereas atoms in the bottom layer, whose thickness is also 0.05 \(l_{y}\), are fixed in all directions. Then, a multi-step conjugate-gradient minimization, with a minimum relative energy tolerance of \(10^{-13}\), is employed. For the calculation of the Peierls stress at 1 K, the supercells have approximately the same dimensions: \(l_{x}\approx 550\) A, \(l_{y}\approx 200\) A, and \(l_{z}\approx 40\) A. Similar simulation setups and supercell dimensions have been used elsewhere [14; 16; 17; 18; 19], where the supercell dimensions along the \(x\)- and \(y\)-directions have been chosen to nearly eliminate the effects of the free surfaces and periodic images on the dislocation motion. The line direction, \(l_{z}\), must be long enough to contain a kink pair, yet not too long so as to contain multiple kinks, which would lead to self-pinning [35]. The Kocevski potential was unable to resolve the initial edge dislocation structure of the misfit dislocation into a perfect edge dislocation with a finite Burgers vector. This occurred despite using energy tolerances as low as \(10^{-20}\).