**3. Results and Discussion**

### *3.1. Atomic Structure Evolution and Material Jet Initiation*

Continuum models [34] recently proposed that jetting initiation in the course of the impact of single-particle is due to the pressure waves propagating and interacting with the particle/substrate interfacial region. The formation of a jet is due to the ejection of particulate material at the edge of the bonded interfacial region which is attributed to the creation of a tensile area resulting in a process of "spall" because of the tensile pressures produced by the particle/substrate edge. The interaction of the pressure wave at the particle/substrate periphery is suggested as a significant factor for jetting initiation instead of the shear localization process, and adiabatic shear instability has been suggested as a consequence, instead of the cause, of jetting. This phenomenon, powered by hydrodynamic pressures, is similar to that seen in fluid–particle impacts (Kelvin–Helmholtz instability); jetting is experiential when the velocity of the shock wave surpasses the velocity at the particle/substrate peripheries [66,67].

Therefore, the molecular dynamics simulations are conducted to analyze the function of the components of pressure wave generation and the creation of thermal boost-up region leading to adiabatic shear instability at the interface. The temperature evolution in the interfacial zone is contrasted with the impacts of various ductile materials such as Al/Cu, Ni/Cu, Cu/Cu, and Ag/Cu at 1000 m/s. The impact of an Ag particle creates the highest pressure wave propagating into the substrate and particle from the point of impact till around 15 ps, resulting in deformation of particles and substrate as well as heat generation followed by that of Cu, Ni, and Al impact, respectively, as shown in Figure 2. Comparative snapshots of jet-forming microstructure are shown in Figure 3 for the material combination.

**Figure 2.** The pressure wave evolution at the periphery of the particle/substrate interfacial region at 1000 m/s of single-particle impact.

In Figure 4, the evolution of pressure wave interaction at particle/substrate interfacial region at 1000 m/s and 273 K in the thin cross-section through the middle of the particle is shown at 10 ps. The delineation levels are selected to provide a good visual image of the interactions between the compressive shockwave and the particle/substrate periphery if any, and its position in jet initiation. The e ffect produces a compressive wave of approximately 2.8 GPa for the Ag particle impact at the impact speed of 1000 m/s in the impacted interface. This compressive wave moves via the particle at the

rear as well as through the interface of particle/substrate region, in conflict with particle/substrate lateral shear motion, as Figure 4 indicates. The shock wave reaches the periphery of the particle/substrate edge, in this case, leading to the external materials flow and causing the particle and substrate to form a jet. This jet initiation phenomenon resulted in the substrate and particle pressure drop and discharge at the interfacial zone as Figure 2 shows. In this context, previous research at the continuum level typically characterizes the mechanism of jetting associate with a particle only, while the MD simulations also display the position of the substrate in jet formation. In comparison, the Al/Cu, Ni/Cu, Cu/Cu, and Ag/Cu impact produces a maximum pressure wave of 1.63 GPa, 1.68 GPa, 2.28 GPa, and 2.82 GPa, respectively. The pressure wave evolution in Al/Cu impact does not seem to interfere with the interface boundary of the particle/substrate periphery and a jet initiation for Al/Cu impact is not observed, as displayed in Figure 4a.

**Figure 3.** Splat morphologies of different material combination at 20 ps: (**a**) Al/Cu (showing no jet) for the whole simulation period (**b**) Cu/Cu, (**c**) Ni/Cu, and (**d**) Ag/Cu (b-c showing jet initiation) for 273 K.

**Figure 4.** The evolution of pressure wave interaction at particle/substrate interfacial region at 1000 m/s and 273 K for (**a**) Al/Cu (**b**) Ni/Cu and (**c**) Cu/Cu, and (**d**) Ag/Cu (after impact at 10 ps).

While the position of the pressure wave interactions at jet initiation build-up is important, the full picture of this phenomenon should be given to further variable trends such as temperatures and von Mises stresses (flow stress) evolution. The progressive temperatures evolution at 1000 m/s impact velocity of single-particle e ffect for di fferent material combinations are illustrated in Figure 5 for 20 ps simulation time. The Ag/Cu impact produces the highest interface temperatures in the particle/substrate impacting region. The temperatures in these regions are about 460 K, which is lower than the melting temperature of Ag estimated by the force field (interatomic potential). The existence and position of these elevated temperatures zones make the flow of material at the periphery of the particle/substrate interface easier. Figure 5 shows that while the high-temperature values may occur, leading to substantial material softening, the temperature gradually decreasing after reaching the peak while the outward material flow continues. The temperature spike is instigated by the emergence of the plastic deformation wave at the periphery of the particle/substrate interface, and the emergence of the waves causes the material to flow outward and the temperature drops at the interfacial edge. The corresponding flow stress evolution (von Mises) is also displayed in Figure 6 with respect to time. For clarity of visualization, atoms with the non-fcc structure that are defined in the adaptive common neighbor algorithm (CAN) are shown. At the peripheries of the contact zone of particle/substrate interface, the maximum value of von Mises stress value for the particle impact is approximately 28.2 GPa, which can be related to imminent yield and propagated rapidly within the particle with progressive flattening. In the regions near the boundary, material flow stress also increases, radially reduces to the middle of the particle interface, and falls after reaching a peak, as shown in Figure 6.

The Radial Distribution Function (RDF) is also available for testing the atomic crystallinity and providing an average, global insight of the structure of atoms in the required region of importance. The measured radial distribution function for the jetting region strongly demonstrates an amorphous structure of various combinations of materials as shown in Figure 7 after 20 ps in all particles. The RDFs results in the particle jet zone are nearly identical as shown in Figure 7. The first peak was observed at 2.50 Å, which is the closest neighbor range between the impacted pair atoms. After the initial peak comes a weak peak at approximately 3.5 Å, which is nearly close to both the gaps between pairs of atoms. Then, at 4.40 Å, 5.32 Å, and 5.75 Å, are the next three separate peaks, suggesting the development of an amorphous structure, in agreemen<sup>t</sup> with earlier experimental findings [68–70].

**Figure 5.** The temporal temperature evolution at the periphery of the particle/substrate interfacial region at 1000 m/s of single-particle impact.

**Figure 6.** (**a**) Deformed particle diagram where arrows show the observation path and (**b**) von Mises stress evolution on the particle bottom after 5 ps in CGDS of the defects induced by impact.

**Figure 7.** Radial distribution function with a different material combination of Al/Cu, Ni/Cu, Cu/Cu, and Ag/Cu after the cold gas dynamic spray at 20 ps.
