## 2 Materials and Methods  
### Statement of MD Task  
A study of the long-term behavior of the representative system containing dislocation and \(\theta^{\prime}\) phase is performed with the molecular dynamics (MD) calculations. The statement of the problem is similar to that used in [34], while a much longer evolution of MD system is traced in the present work. The \(x\)-, \(y\)- and \(z\)-axes of coordinates are oriented along \([\overline{1}10]\), \([111]\) and \([1\overline{12}]\) crystallographic directions, respectively. Such an orientation of MD system is consistent with the directions of the edge dislocation in fcc crystal. The system is periodic along the \(x\)- and \(z\)-axes. The dimensions of the system were chosen equal to 51 \(\times\) 60 \(\times\) 9.87-22 nm\({}^{3}\), in the first case the system contains of about 2,000,000 atoms, and in the last one--about 5,000,000. In the first step, \(\theta^{\prime}\) phase is placed into an ideal aluminum lattice. Precipitates of \(\theta^{\prime}\) have a tetragonal lattice [64] with constants equal to 0.404 and 0.508 nm. In the aluminum matrix, \(\theta^{\prime}\) occurs as plate-like inclusions. The flat surface of \(\theta^{\prime}\) is coherent with the aluminum lattice and the inclusion rim is semicoherent [23; 28]. The mutual arrangement of copper and aluminum atoms is shown in Figure 1, where panel (a) is the cross section of matrix-surrounded precipitate and (b) is the view of the flat surface of the cylindrical inclusion without the aluminum matrix. The inclusion is created in the form of a cylinder of 2.2 nm thickness; and two diameters of inclusions are considered, 5 and 18 nm. The flat surface of the cylinder is parallel to the \((100)\) plane of aluminum. In the second step, edge dislocation is introduced into the aluminum matrix by addition of one atomic half-plane to the upper half of the crystal and superimposing the displacements of atoms of the system according to the dislocation stress field; the ATOMSK software package is used [65]. The dynamics of the created system containing \(\theta^{\prime}\) phase and dislocation (Figure 2) is simulated using the LAMMPS package [66]. Interactions between atoms are described with ADP potential [67], developed for the Al-Cu system based on the EAM formalism supplemented by accounting the quadrupole moments. This potential reproduces well the elastic constants of both metals, the energies of various defects in them, as well as the structure of intermetallic phases. Using this potential previously allowed the description of the dynamic properties of dislocations in pure aluminum [68; 69], as well as the processes of interaction of dislocation with strengthening phases in Al-Cu alloys [34; 57; 58; 60; 68]. Currently, machine learning potentials are being actively developed; despite the emergence of these new potentials, ADP potential by [PERSON] for an Al-Cu system is considered as one of the best classical physically based potentials [70]. Investigation of the dislocation dynamics is preceded by the relaxation, which lasts for 20 ps. The pressure and temperature of the MD system is controlled to be constant during calculations. The barostat controls only the diagonal components of the stress tensor. Other stress components arising during relaxation do not exceed 10-20 MPa, which is insignificant in comparison with those acting during the dislocation-precipitate interaction. Two Shock-ley partial dislocations are formed from the initially perfect dislocation (see Figure 2); such behavior is typical for aluminum. Change in the structure of inclusion during relaxation is not observed. The temperatures of 100, 300, 500 and 700 K are considered. Figure 1: Structure and form of \(\theta^{\prime}\) precipitate. Panel (**a**) is cross section of matrix-surrounded precipitate and (**b**) is view of inclusion flat surface without aluminum matrix Aluminum atoms are colored in gray, copper atoms are red.