*3.2. Material Dislocation Plasticity*

As is evident in Figure 8, plasticity of material dislocation at 10 ps on the circular side of its flattened base for which heterogeneous nucleation of Shockley with Burgers vector 1/6 -112 leading partial dislocation segments was observed. In the particle/substrate interfacial zone, the evolution of the microstructure corresponds to various ductile materials, where the perfect dislocation, the stair dislocations, and partial dislocations in Shockley is colored in blue, purple, and green, respectively. The yellow and sky-blue dislocation segmen<sup>t</sup> corresponds to the Hirth and Frank type, respectively. In the first step, Shockley partial dislocations emerge successively from the particle/substrate contact surface and disperse within the substrate and the particle. Then, with the growth of plastic deformation, the Shockley partial dislocations at 10 ps cover the particle/substrate interfacial zone. These imperfect dislocations normally act as carriers of energy for the face-centered cubic (fcc) system's intrinsic stacking faults [71]. With cold gas dynamic spray proceeding, the Burgers vector of 1/6 -112 with Shockley partial dislocations intersect and change to be Burgers vector of 1/6 -110 with the Stair-rod dislocations. Within the particle/substrate contact zone, the Burgers vector of 1/2 -110 appears, which is the perfect dislocation. The atoms on the circular edge of the particle flattened base steadily grow with the unstructured form of the atomic crystal. Moreover, dislocations are likely to move to the middle of the Al particle, to the edge and bottom of the Ni and Cu particle, as well as to the bottom of the Ag particle, as seen in Figure 8a–d.

**Figure 8.** The evolution of dislocation segmen<sup>t</sup> in the particle/substrate interfacial zone during the cold gas dynamic spray processes at 10 ps for particles of (**a**) Al (**b**) Ni (**c**) Cu and (**d**) Ag impacting Cu substrate.

In all particles, during the particle impact at 1000 m/s, several dislocation segments emerge, which are due to severe plastic deformations as demonstrated in Figure 9. Additionally, on the substrate surface, the lower atoms at the base of the particles form a metal-to-metal coating region. Owing to the inadequate slip on the middle part of the Al particle, there is a significant surface protrusion in the final Al particle designated at the x–z plane, which forms a "peak-shaped" coating configuration and the ultimate particle shape is rectangular in the x–z region. For the Ni particle, the absolute form of the particle on the x–z plane is comparatively flat because of the adequate slip along the direction of material flow, and the final structure in x–z plane is like a mushroom. For the Cu and Ag particle, the final structure in the x–z plane is pyramidal and hemispheric.

**Figure 9.** Cross-section view (**a1**–**d1**) and plan view (**a2**–**d2**) for the evolution of dislocation segmen<sup>t</sup> in the impacting particles of (**a1**,**a2**) Al/Cu, (**b1**,**b2**) Ni/Cu, (**c1**,**c2**) Cu/Cu, and (**d1**,**d2**) Ag/Cu after cold gas dynamic at 15 ps and 1000 m/s.

Figure 10 demonstrates the time-dependence of the dislocation density for different particles at 1000 m/s impact velocity. The Ni particle plastic deformation rate is the maximum following the dislocation segmen<sup>t</sup> evolution as shown in Figure 10a, followed by the Cu particle, then the Ag particle, and the Al particle is the lowest. In Figure 10c, the evolution of the particle dislocation density during cold gas dynamic spraying is shown between 0 ps and 20 ps. In all the different material combinations, the displacement density of all particles is near zero at the early stage of cold gas dynamic spray between 0 ps and 2 ps because no major plastic deformation exists. Then the dislocation density within various material particles from 2–20 ps increases steadily at different rates until it reaches the equilibrium after impact. The dislocation growth rate in Ni particles is about 55.4%, 33.8%, and 10.7% higher than in Al, Ag and Cu particles, respectively. In Al particle atoms, the kinetic energy is used mainly to transfer atoms along with the position of longitudinal intrinsic stacking faults. However, in Ag particles, a portion of the particle atoms' kinetic energy is utilized in the particle/substrate atomic motion, while the particle/substrate interaction, creating several dislocations by consuming the kinetic energy that remains. The particle atoms' kinetic energy of the Ni and Cu particle is primarily absorbed by the intense interaction between the intrinsic stacking faults in the lower part of the particle, which increases the dislocation density rapidly. Figure 10b shows the dislocation segments distribution in the Al, Ni, Cu and Ag particles at 20 ps. The dislocation density increases to the value of 2.9 × 10<sup>16</sup> m<sup>−</sup>2, 4.3 × 10<sup>16</sup> m<sup>−</sup>2, 5.8 × 10<sup>16</sup> m<sup>−</sup>2, and 6.5 × 10<sup>16</sup> m<sup>−</sup><sup>2</sup> for Al, Ag, Cu, and Ni particles, respectively, then decreases slightly. The extreme plastic deformation at the interface of the substrate and material particle contributes to the creation of a jet region around the interface region of particle/substrate.

**Figure 10.** (**a**) Total dislocation segmen<sup>t</sup> of the particle at 20 ps (**b**) Dislocations segmen<sup>t</sup> distribution in the Al, Ag, Cu, Ni particles at 20 ps. (**c**) Particle dislocation density at 1000 m/s, 273 K and 20 ps after impact for the Al, Ni, Cu, and Ag particles.

### *3.3. Particle Impact Velocity E*ff*ect on Microstructure Evolution*

The microstructural snapshot of the full Ni splat region coated at different times on the Cu substrate for an impact speed of 1000 m/s is shown in Figure 11a–c. The local atomic structure is colored based on common neighbor analysis (CNA) approach [63,64]: FCC (green), HCP (red), BCC (blue) and grey (atoms without crystalline structure). The circles designated the jet formation at the periphery as the atoms flow upward from the substrate. The snapshots presenting the particle and substrate separately of the illustrative atoms. The material jet initiation at the periphery is often correlated with the outward flow of atoms as shown by the circles from the substrate.

**Figure 11.** The microstructure snapshots of the Ni particle (**a1**–**a4**) and Cu substrate (**b1**–**b4**) at times of (**a1**,**b1**) 5 ps, (**a2**,**b2**) 10 ps, (**a3**,**b3**) 15 ps, and (**a4**,**b4**) 20 ps. (after impact) at 1000 m/s. The local atomic structure: FCC (green), HCP (red), blue (BCC), and grey (atoms without crystalline structure). The circles designated the jet formation at the periphery as the atoms flow upward from the substrate.

During MD simulations of single material impact for a particle impact velocity of 500 m/s, 700 m/s, 1000 m/s, and 1500 m/s, the microstructure evolution and recrystallization behavior are also investigated. The recrystallization potential varies at impact speeds as establish in the cold dynamic gas sprayed splats created during 20 ps, which shows the local atomic structure at 273 K in Figure 12. With a particle velocity of the impact of 500 m/s, recrystallized structures are very few, as indicated in Figure 12a, in contrast with the 1500 m/s particle impact velocity with large structural transformation as displayed in Figure 12d. The increased number of new atomic structures can be associated with the reliance of recrystallization phenomenon associated with strain energy to indicate the unique recrystallization mechanisms [69,72] involved in the molecular dynamics predicted microstructures given the extreme deformation of the atomic structure at the interface. In addition to the recrystallization in the creation of new structures, atomic structure boundary migration [73] could also play a critical position. For convenience, in this manuscript, the development of a new atomic structure is called recrystallization. Metal plastic deformation is more severe with a higher impact velocity of 1500 m/s, and therefore greater temperatures are produced during the impact time at the particle/substrate interfacial region as shown in Figure 13. Some experimental cold gas dynamic sprays have achieved a similar consensus on the recrystallization phenomenon [74–76]. In the past, the embedded atomic potential (EAM/alloy) [60] used in this study has shown a recrystallization of aluminum uniaxial loading, demonstrating its ability to capture the phenomenon accurately [77]. Figure 14 shows that, at the interface, some of this recrystallized atomic structure is split between particle and substrate. These findings show that recrystallization at some region at the interfacial zones will help form the metallurgical bond between the substrate and the particle.

**Figure 12.** Microstructural snapshots presenting a structural transformation of a cold gas dynamic spray splat at 20 ps for: (**a**) 500 m/s, (**b**) 700 m/s, (**c**) 1000 m/s, and (**d**) 1500 m/s.

**Figure 13.** The temperature evolution at the periphery of the Cu/Cu interfacial region at different impacting velocity of 500 m/s, 700 m/s, 1000 m/s, and 1600 m/s of single particle impact.

**Figure 14.** Microstructural snapshots presenting a structural transformation (**a**) at 0 ps (**b**) at 20 ps of a cold gas dynamic spray splat at 1500 m/s (**c**) splat microstructure at 20 ps (**d**) substrate microstructure at 20 ps. Structural transformation at the interfacial zone between the substrate and particle after impact is evident here.
