# Fabrication of Magnesium-Aluminum Composites under High-Pressure Torsion: Atomistic Simulation
## 2 Computational Methods  
To study the process of atomic mixing under deformation treatment near the interface of different metals, MD modeling of Mg-Al sample, containing an interfacial boundary was used. The cubic sample contained 54,170  
atoms and was a simulation box with a dimension of 10.0 \(\times\) 10.0 \(\times\) 10.0 nm\({}^{3}\). The contact surfaces of Mg and Al were (0001) and (001) planes, respectively. The Al and Mg layers were 5.0 nm thick. The schematic of the initial structure is shown in Figure 1, where the face-centered cubic (FCC) Al is bordered by the hexagonal (HPC) Mg. The atomic radius of Al was 143 pm and for Mg was 160 pm; atomic masses were 26.98 for Al and 24.307 for Mg. The interlayer distance between two crystals was calculated as \((a_{Mg}+a_{Al})/2\) = 3.6 A. Periodic boundary conditions were applied along \(x\), \(y\), and \(z\). Melting temperatures of Al and Mg were close and equal to 660 \({}^{\circ}\)C and 650 \({}^{\circ}\)C, respectively. The sample with the minimized interfacial boundary energy was used for modeling. To obtain the initial structure in an equilibrium state, the minimal energy of the system was achieved by the multiple corrections of the atomic positions with the help of the steepest descent method, terminated if the variation in the energy or force was less than a given value. The initial structure was relaxed until the local or global minimum of the potential energy was reached. The simulation run was terminated when one of the stopping criteria (energy or force) was satisfied. The main goal of the relaxation process, in this case, was to obtain equilibrium stresses on the interface. After several numerical experiments with different parameters of minimization, stopping tolerance energy \(10^{-24}\) and stopping tolerance force \(10^{-26}\) eV/A were chosen. In the present case, the setting of tolerance force \(10^{-26}\) means no \(x\), \(y\), and \(z\) component of the force on any atom will be larger than \(10^{-26}\) eV/A after minimization. Figure 1: Schematic of the initial sample. After the minimization process at 300 K, the simulation box was initially stress-free. The equilibrium state implies that normal stresses \(\sigma_{zz}\) in the two crystals are zero; the summation of stress \(\sigma_{xx}\) in the two crystals and the summation of stress \(\sigma_{yy}\) in the two crystals are zero. Moreover, the two dimensions of the sample (\(x\) and \(y\)) were not arbitrarily chosen because of the incommensurate nature of the FCC and HCP crystals but were determined such that the strains imposed on Al and Mg semi-infinite perfect crystals were minimized, ensuring periodic boundary conditions and equilibrium of the initial structure. The simulations were carried out by MD using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package. For temperature control, the Nose-Hoover thermostat was applied. Verlet algorithm to integrate the Newtonian equation of motion with an integration time-step of 2 fs was used. The well-approved Mg-Al embedded atom method (EAM) potential [32] was used in the molecular dynamics model. The EAM potentials for Al and Mg have been constructed on the basis of the experimental data and successfully used for a previous simulation in [33]. To obtain the composite structure and mixing of the atoms near the Al-Mg interface, uniaxial compression normal to the Al-Mg interface (\(\varepsilon_{zz}\) < 0), combined with shear in the interface plane (\(\varepsilon_{xy}\) in this case), was applied. It should be noted that in accordance with the deformation mechanism inserted in the LAMMPS simulation package, shear deformation is simply the change of the \(xy\), \(xz\), and \(yz\) tilt factors of the simulation box with the given strain rate [34]. To apply compression deformation, change of the specified dimension of the box via constant displacement (in this case, it was applied along \(z\)-dimension), which is effectively a constant engineering strain rate, occurred.