**2. Computational Approach**

The simulations of molecular dynamics (MD) were used to analyze the deposition behaviour of ductile nanoscale material particles in compliance with material combination and impact velocities. The large-scale atomic/molecular massively parallel simulator (LAMMPS) package [54] has been used to conduct MD simulations of nano-scale particles impaction. To understand the deformation process during particle deposition, OVITO [55], an accessible visualization tool, was used to examine the cross-section of the impact region. Figure 1 displays a diagram of the preliminary 3D simulation model for the deposition of nanoscale particles onto a Cu substrate. The analysis of the deposition characteristic of nanoscale ductile material preparation was considered in deformable spherical nano-scale Al, Ni, Cu, and Ag particles of 400 Å diameter and impact velocities of 500 to 1500 m/s. The particle material consists of around 2,051,820 atoms. The substrate is aligned in the [1 0 0], [0 1 0] and [0 0 1] for x-, y- and z- crystallographic direction, respectively. The substrate material consists of a face-centered cubic (FCC), with 3.61 Å lattice constant. The Cu substrate dimensions along an x-, y-, and z-direction are 700 Å × 700 Å × 600 Å. The initial distance from the particles to the substrate surface is 20 Å. The x-, y-, and z-directions are subjected to periodic boundary conditions (p p p). The substrate consists of the fixed boundary layer (700 Å × 700 Å × 50 Å), the thermostat layer (700 Å × 700 Å × 100 Å) and dynamic layer (700 Å × 700 Å × 500 Å. The phase time is 1.0 fs.

**Figure 1.** Cold gas dynamic spray MD simulation model.

In the setup of the first simulation, the thermal region maintained at 273 K was set into contact with the system via thermostat layer. This thermally linked area (the "heat sink") was the channel for the heat produced by the impact of the system to be expelled out of the system. The movement equations of the

atoms in the thermal layer were incorporated into the Nosé–Hoover thermostat of NVT ensemble [56], while the motion equations of dynamic layer and particle were incorporated into the NVE ensemble. In the NVT ensemble, a particle-substrate system was equilibrated for 20 ps. For the second simulation setting in the NVE ensemble also for dynamic layer, an MD simulation was performed that removes the heat coupling and processes the whole system as thermally isolated. The particle spray velocity ranges from 500 m/s to 1500 m/s in the perpendicular direction to the substrate surface to preserve adhesion and prevent erosive wear behaviour [57–59]. The molecular dynamics simulation time for CGDS is 20 ps. Note, the CGDS process will not last for 20 ps, this simulation time was only allowed to ensure that the effect is completely applied is the CGDS time set. The model sizes and parameters of the simulation are presented in Table 1. The particle/substrate atomic interactions are represented by the Zhou et al. [60] embedded-atom method (EAM) potential as shown in Equation (1).

$$PE\_n = \gamma\_a \left(\sum\_{m \neq n} \rho\_\beta(R\_{mn})\right) + 0.5 \sum\_{m \neq n} \mathcal{S}\_{a\beta}(R\_{mn}) \tag{1}$$

where *PEn* of atom *m* is the potential energy, *Rmn* is a distance from atoms *n* to *m*, the pair-wise potential function is denoted by ϑαβ, ρβ is the influence of atom type β to the electron-charge density at atomic *n*, and γ is the embedding function that denotes the energy needed to position type α of atom *m* in the electron cloud. For the analysis of the atomic stress, the stress tensor's six components are calculated based on the atomic viral stress spatial and temporal averages, as shown in Equation (2).

$$
\sigma\_{ab} = -\left( m \upsilon\_{b} \upsilon\_{b} + 0.5 \sum\_{n=1}^{n\_{p}} \left( R\_{1a} F\_{1b} + R\_{2a} F\_{2b} \right) \right) \tag{2}
$$

where σ*ab* is the components of the atomic stress arranged in *a*, *b*(*<sup>x</sup>*, *y or <sup>z</sup>*), *mvavb* is the kinetic energy input and 0.5 *np <sup>n</sup>*=<sup>1</sup>(*<sup>R</sup>*1*aF*1*<sup>b</sup>* + *<sup>R</sup>*2*aF*2*<sup>b</sup>*) is the pair-wise energy input that is connected with the nearby atoms from *n* = 1 to *np*. The von Mises stress is mostly used to research plastic deformation in the CGDS process, as deduced in Equation (3).

$$
\sigma\_{\rm au}(i) = \left( 0.5 \sum \left( \sigma\_{\rm aa}(i) - \sigma\_{bb}(i) \right)^2 + 6 \sum \sigma\_{ab}^2(i) \right)^{0.5} \tag{3}
$$

where <sup>σ</sup>*va*(*i*) is the atom von Mises stress *i*, <sup>σ</sup>*ab*(*i*)) is the component of atomic stress tensor arrange in a, b (x, y, or z). The atomicity is computed from each MD timestep using the interatomic interaction, atomic velocity and atomic distance; Equation (3) is an abridged representation, the measurement method information is in [61,62]. The common neighbor analysis (CNA) [63,64] is implemented to classify atoms into various local lattice frameworks for atomization (fcc- face-centered cubic, bcc- body-centered cubic, hcp- hexagonal close-packed, etc.), and jetting zone atoms (without lattice structures). Additionally, the dislocation extraction algorithm (DXA) [65] is used to classify the dislocation arrangemen<sup>t</sup> in crystals and generate dislocation segments.

**Table 1.** Schematic molecular dynamics simulation calculation plans.

