An experimental and computational study of high speed two-particle impacts of Ag nanoparticles Free

Thick films are produced via several related aerosol-based manufacturing processes by impacting particles onto a substrate at high velocity (300–1000 m/s). A distinguishing characteristic between these manufacturing processes is the significant differences between the particle sizes of the impacting particles. The cold spray process utilizes 5–25 μm particles to produce thick films over large areas,^1–3 whereas the aerosol deposition method (ADM) has been developed to deposit finer 100–400 nm particles into patterned thick films.^4,5 We have developed the laser ablation of microparticle aerosol (LAMA) process, where even finer 2–40 nm nanoparticles (NPs) are impacted to produce patterned microscale thick films.^6–8 

It has been previously established that dislocation plasticity plays a large role in the impact deformation and resulting film microstructures for deposition of micrometer-sized particles such as those used in cold spraying.^2,3,9,10 However, there is less understanding of the deformation and film formation mechanisms for finer particles at similar impact velocities. Empirical evidence and a theoretical basis suggest that the deformation behavior of finer particles is considerably different from that of larger particles.^3,11 One reason for this is that a critical particle size exists below which glissile dislocations are not stable, and thus dislocations in very fine NPs may spontaneously move to the NP surface, where they are annihilated, leaving dislocation-free or nearly dislocation-free NPs.¹² Plasticity in dislocation-starved NPs is dependent on dislocation nucleation, which requires higher stresses than dislocation propagation from pre-existing dislocations.¹³ 

Further indirect support for size-dependent impact behavior is evident in the experimental work of Akedo et al.,¹⁴ who observed that particles with an initial size of 120 nm produced relative film densities for Ag of 85%–90%, which is considerably lower than that observed for films produced from micrometer-sized metallic particles impacted as similar velocities via cold spraying.¹ The relative densities of films are an indirect measure of the amount of deformation that occurred upon impact, because densification requires deformation to fill the interstices between the particles. Our own experimental work with 2–40 nm Ag NPs impacted at velocities of 1000 m/s also showed significant differences compared to deposition of larger particles at similar velocities. With 2–40 nm particles, porous polycrystalline films were produced with a relative density of only about 70%.^15,16 Unlike films produced from micrometer-sized particles, films produced from these very fine NPs are composed of grains having relatively low aspect ratios (near unity).⁸ Taken together, these experimental findings suggest that the magnitude of deformation that occurs upon impact decreases with decreasing particle size.

In this study, we investigate the morphologies of several high-speed particle-on-particle impact events of 2–40 nm particles using transmission electron microscopy (TEM) for the first time. These studies reveal that a range of impact morphologies result even for particles with nominally similar sizes and impacted at similar impact velocities. This suggests that there are additional impact parameters beyond those that have been previously identified (particle size and impact velocity)¹⁷ that play a role in determining whether impact leads to epitaxial or polycrystalline deposition. It should be noted that important information about the particles prior to impact, such as particle crystallographic orientations and particle–particle crystallographic misorientations, cannot be controlled experimentally or ascertained from postmortem observations. For this reason, molecular dynamics (MD) simulations have also been employed in this study. These simulations allow the impact parameters to be controlled and independently varied so that the influence of specific impact parameters on deformation behavior and the final microstructures obtained during particle-to-particle impact events can be studied. These simulations show that, in addition to particle size and velocity, other impact parameters including particle orientation and particle–particle misorientation also significantly influence the final state following impact. The similarities in the particle morphologies between those obtained from experiments and those obtained from the final states of the simulations provide evidence that the dynamic events observed in the simulations capture the essential mechanisms responsible for the observed behaviors.

A schematic drawing of the laser ablation apparatus used to produce the nanoparticle aerosol is shown in Fig. 1(a). A pulsed, KrF excimer laser (Lumonics PM-848, Light Machinery, Inc., Ottawa, Canada) with a nominal wavelength of λ = 248 nm, a maximum power output of 80 W, and a pulse length of 12 ns was used at its maximum repetition rate of 200 Hz. Two cylindrical lenses of focal lengths f₁ = 110 cm and f₂ = 14 cm were used to focus the beam both horizontally and vertically. The laser beam energy was set at 250 mJ and the beam area at the ablation zone was measured to be 0.08 cm² (height: 4 mm, width: 2 mm), resulting in a fluence on the MPs of 3.1 J/cm², which was well above the breakdown threshold for ablation for Ag microparticles (MPs) (0.8 J/cm²).¹⁸ 

The MP aerosol was fed into the ablation zone through a coaxial nozzle at a gas velocity of approximately 80 cm/s so that the laser beam struck the MPs only once as they traveled through the ablation zone. Both the central gas and the coaxial sheath gas were He at a pressure of 1 atm. The center flow (Q₁) was adjusted to achieve the desired 80 cm/s velocity, depending on the cross-sectional area of the feed nozzle. The sheath flow (Q₃) was first laminarized and then fed around the center flow to constrain the center flow and maintain laminar flow past the ablation zone and into the skimmer. The center flow as well as part of the sheath gas was captured by the skimmer, and the remaining gas flow exited to a fume hood. To remove any unablated MPs or agglomerated NPs from the ablated aerosol, a virtual impactor was used with a cutoff size set at 500 nm (e.g., only particles smaller than 500 nm were passed to the deposition chamber).

The NP aerosol was accelerated through a flat-plate nozzle by the pressure differential between the ablation chamber held at atmospheric pressure (760 Torr) and the deposition chamber which was pumped using a mechanical vacuum pump to a pressure of approximately 200 mTorr, as shown in Fig. 1(b). The nozzle aspect ratio was fixed at 1:1 so that the nozzle diameter and plate thickness were both equal to 0.25 mm. This result in choked flow was maintained through the nozzle.

Huang et al. developed a model to predict the velocity reached by Ag NPs, taking into account the gas dynamics through the nozzle and the drag force of the gas on NPs.⁸ The partial differential equation that describes the NP speed developed by Huang et al. was solved numerically and the maximum speed and deposition energies reached by the NPs were calculated and are presented in Fig. 2. Note that the deceleration that occurs prior to impact is negligible for the range of experimental conditions that are typically used in LAMA.⁸ Using He as a carrier gas, the maximum predicted velocity reached by a typical 5 nm particle for a 0.25 mm nozzle is predicted to be approximately 1000 m/s upon impact (corresponding to a kinetic energy of 0.6 eV/atom). The deposition velocity for more massive 20 nm particles is less than 800 m/s (corresponding to a kinetic energy of approximately 0.35 eV/atom).

Previous TEM observations reveal that the as-produced Ag particles from LAMA are spherical, range in diameter from 2 to 40 nm, and are free of a measurable surface oxide. Some of the particles contain defects such as stacking faults and twins, depending on processing conditions.^8,19 To further investigate the final morphology of particle following impact by the LAMA process, TEM grids with a Formvar® support film (Model 200M-TH, Ted Pella Inc., Redding, CA) were clamped onto a flat substrate and NPs were deposited onto the TEM grids. A large nozzle-to-substrate distance equal to about 10 times the nozzle diameter was used for these experiments in order to minimize damage to the delicate support TEM films. The stage was translated beneath the deposition nozzle fast enough (approximately 5 mm/s) so that some of the particles deposited onto the grid or into the Formvar film were individual NPs or small clusters of nanoparticles.

A TEM (2010F, JEOL, Tokyo, Japan) was used to image the NPs at sufficiently high magnification such that lattice planes were visible. In some cases, regions of the images were cropped, and Fourier transforms were performed to obtain diffraction patterns from selected regions. The diffraction patterns were used to identify whether specific regions were monocrystalline or polycrystalline and to analyze the nature of defects such as stacking faults.

Molecular dynamics (MD) simulations of the impact of an NP onto a stationary NP were conducted using LAMMPS²⁰ implemented on the Lonestar Linux cluster at the Texas Advanced Computing Center (TACC)²¹ at the University of Texas at Austin. The embedded-atom-method (EAM) potential for Ag from the NIST Interatomic Potentials Repository Project was used.²² The simulation volume was 100 × 100 × 150 lattice constants (lattice constant = 0.409 nm for Ag), with the larger dimension in the z direction, which corresponded to the NP impact direction.

Representative spherical particles with diameters 13.6 nm for the impacting particle and 32 nm for the stationary impacted particle (∼80 000 atoms and ∼1 000 000 atoms, respectively) were studied using the simulations. Details on why this particular configuration was studied using MD simulations are presented in Sec. III. We considered only particles that were free of stacking imperfections to limit the parameter space to a reasonable number of variables and, consistent with experimental observations, we assumed that the particles were free of surface oxides. Since the influence of NP size on the final microstructures has been previously studied in detail,¹⁷ nanoparticle size was not varied in the current study.

The two NPs in the simulations were placed so that they were not touching the simulation boundary at the start of the simulation, which is equivalent to a vacuum interface at the edges of the NPs. The edges of the simulation volume were treated by LAMMPS as periodic in all three dimensions. During the simulation, the particles never contacted the edges of the simulation volume and therefore they did not interact across the periodic boundaries. The Ag atoms in the larger stationary NP and the smaller impacting NP were allowed to thermalize at 300 K for 50 ps before the smaller NP was set in motion in the z direction. A temperature of 300 K was chosen because the stagnation conditions for impact experiments are approximately 300 K and one atmosphere, and the residence times are extremely short in the region where the gas temperatures are significantly depressed at the exit of the nozzle,⁸ which results in particle temperatures that are near 300 K at impact. The angular momentum of the impacting NP was set to zero at every timestep during thermalization to control particle orientation during thermalization, and the linear momentum in the bottom 50% of the stationary NP was set to zero every timestep during the impact to prevent the particle from moving out of the simulation volume.

Following the thermalization, a constant velocity was imparted to all atoms in the impacting NP. The time integration for the equilibration of the system to 300 K and for the subsequent impact was performed with a time step of 0.002 ps (2 fs) using Nose–Hoover style, non-Hamiltonian equations of motion on the isothermal-isobaric (npt) ensemble,²⁵ which generated positions and velocities of the atoms at every time step. The positions of all atoms were recorded at intervals of 0.5 ps for the first 80 ps after impact and at intervals of 80 ps for the remaining 240 ps. Although there were minor fluctuations in atom and grain boundary positions in some cases, a simulation time of 320 ps was selected to represent the final state because the deformation and microstructure were no longer noticeably evolving at this time.

Applying a Langevin condition to a few layers of atoms below the region of impact is one of the methods that has been used previously to effectively damp the compressional waves that are launched upon impact and to prevent their undesirable reflection back to the impact interface.^23,24 For our simulations, we observed that the range of impact velocities is not high enough to produce shock waves, and the back-reflected acoustic waves are negligible. To confirm this, simulations were performed both with and without the Langevin condition, and it was observed that the Langevin condition did not affect the microstructural evolution following impact. Thus, subsequent simulations did not include the Langevin condition.

Visualizations of the atomic positions were conducted offline using the OVITO visualization software.²⁶ Polyhedral template matching (PTM) was used to identify the local atomic environments for all atoms in the simulations, which allowed the local stacking sequence for the atoms to be determined.²⁷ The visualizations were color-coded with this information with green representing the local regions of FCC stacking and red representing regions with a local HCP stacking. When the atomic stacking sequence could not be identified (e.g., at grain boundaries or where the atoms were disordered), atoms were colored white.

The impact of many clusters of NPs was studied in the TEM to ascertain their final microstructures after NP impact. Most impacts resulted in either single particle or multiparticle depositions. To allow for unambiguous analysis, only the rarer cases of two-particle impacts were analyzed and are presented here. Observations using the high resolution TEM revealed examples of two general types of final particle morphologies for two-particle impact events: (1) nonepitaxial deposition and (2) epitaxial deposition. The term nonepitaxial is used when the final microstructure for the impacted NP and the particle onto which it impacted contain one or more grain boundaries, and the term epitaxial deposition is used when the final microstructure consists of a single crystallographic orientation. Multiple examples of each type of final microstructure were observed experimentally and representative examples are shown below. Although detailed statistical analysis of the fraction of particles that deposited epitaxially could not be performed given the small fraction of two-particle impacts, evidence of both epitaxial and nonepitaxial depositions was readily observed in many of the multiparticle impacts.

Two examples of nonepitaxial deposition are shown in Fig. 3. In Fig. 3(a), a spherical NP is still clearly visible after impacting onto a previously deposited NP. The lattice fringes in the TEM image show that there is no continuity of the crystallographic planes across the original boundary between the two NPs, indicating that this was a nonepitaxial deposition. A closer look at the crystallographic arrangements within the spherical NP shows periodic changes in contrast that are consistent with planar defects. A 12 nm Ag particle impacted onto a larger Ag particle is shown in Fig. 3(b). Again, the lattice fringes in the TEM image show that there is a sharp discontinuity in the crystallographic planes across the original boundary between the two NPs defined by connecting the two regions of concave curvature. In this case, the smaller NP is itself clearly polycrystalline, consisting of a number of grains smaller than 5 nm.

The TEM image of a particular two-particle impact event where a 13.6 nm NP impacted epitaxially onto a 32 nm NP is shown in Fig. 4(a). Lattice fringes are apparent in the upper portion of the smaller 13.6 nm particle with a spacing of 0.24 nm, which is consistent with the known {111} interplanar spacing for Ag. Dark bands, perpendicular to the direction of impact and parallel to the interface between the impacting and the impacted particle, are visible in the micrograph. The dark bands are likely stacking faults or twins²⁸ that appear as bands because the TEM micrograph was slightly misoriented with respect to a zone axis.

The orientations of the lattice planes can be followed starting in the impacting particle and progressing down into the impacted particle. It is apparent that these planes are continuous across the interface between the impacting and the impacted particle, suggesting that this impact resulted in epitaxial deposition. Fourier transforms of the impacting and impacted particles were generated by masking off regions of the image so that only the particles of interest were visible before performing the transform. The upper inset shows that the Fourier transform for the impacting particle contains two spots, consistent with the single set of planes that is visible in the image. The streaking of these spots is due to slight changes in orientations of the lattice planes that occur as the planes intersect the stacking faults. The Fourier transform for the impacted particle contains the same two spots, in the same orientations as the Fourier transform for the impacting particle. This confirms that the particles have approximately the same orientation. Note that the left side of the impacted particles contains two additional pairs of lattice fringes that are much weaker than the primary lattice planes. The corresponding Fourier transform contains two additional but weaker pairs of spots associates with these fringes. Since the right side of the impacted particle does not exhibit these additional lattice fringes, we believe that the fringes on the left side of the particle result from a slight tilt of this portion of the crystal resulting from stacking faults/partial dislocations that terminate within the impacted particle. This tilt makes additional planes visible that are not visible in the impacting particle or the right side of the impacted particle. Analysis of the angles between these spots and the relative distances between colinear spots suggests that these additional lattice fringes are from {111} and {200} planes. A similar example of an epitaxial deposition is shown in Fig. 4(b).

The TEM images reveal that a range of particle morphologies and defect states result from particle impact under nominally identical conditions. The mechanism for nonepitaxial deposition shown in Fig. 4 in which a grain boundary is formed at the interface between the impacting and the impacted particle is intuitively obvious. Instead, we focus on the conditions and mechanism that produce epitaxial deposition in a two-particle impact. To do this, we study in detail a particular impact event shown in Fig. 4(a) that leads to epitaxial deposition. The NP diameters can be inferred from the TEM images and the NP impact velocities can be estimated from Ref. 8. However, information about the particles prior to impact such as particle crystallographic orientation and particle–particle crystallographic misorientation is not known. Thus, molecular dynamics (MD) simulations were used to study the influence of uncontrollable or unknown experimental impact parameters on the final microstructures obtained during this particle-to-particle impact event.

A schematic of the two-particle event studied using MD simulations is shown in Fig. 5 and is based on the TEM image shown in Fig. 4(a). The particle size for the impacting particle was determined to 13.6 nm for the impacting NP and 32 nm for the impacted NP, based on the areas of the particles and assuming the particles were spherical prior to impact. The impact velocity of the 13.6 nm particle was calculated using Fig. 2, and was determined to be 860 m/s. This velocity was used in the simulation of the two-particle impact which was subsequently followed from the instant the two particles made contact until the final microstructure was formed by both particles reaching a steady state. Snapshots of a cross section containing 5 atomic layers from the region near the central cross sections of the particle are shown for each MD simulation. A {110} type cross section in the impacting NP is chosen consistently for viewing in all the simulations.

Statistical fluctuations in atomic positions from thermal vibrations result in variations in experiments that can also be simulated. To determine if these fluctuations were the cause of the observed variability in the observed final states for experiments, several simulations were conducted under nominally identical conditions: an initially defect-free 13.6 nm NP was impacted at 300 K onto a stationary 32 nm NP at 860 m/s, with the particles initially having a 45° crystallographic misorientation about the axis of impact. The results of these simulations after the particles had reached a steady state are shown in Figs. 6(a)–6(c). Although there are very minor atomistic differences between the final states from these three simulations conducted under the same impact conditions, all aspects of the deformation microstructures are similar. In each case, the final morphology consists of a nonepitaxial deposition, with multiple grain boundaries present in the original impacting NP. In addition, stacking faults are present, primarily in the impacting NP. Since stacking faults in FCC metals can result from either deformation or rapid crystallization, it cannot be ascertained which mechanism gave rise to the faults from observations of these final states. Nevertheless, it is clear from these simulations that thermal fluctuations result in only minor atomistic differences in the final states and, thus, these fluctuations cannot be responsible for the large range in final morphologies from polycrystalline to epitaxial that were observed experimentally under nominally identical deposition conditions.

The impact velocity of 860 m/s that was assumed in the previous set of simulations was based on average properties of the particle and gas. However, it is likely that actual particle impact velocities are distributed about a range of impact velocities. Meinander et al.²⁹ have suggested that epitaxial deposition may be favored at higher velocities when a particle impacts a flat substrate. To determine if this trend also holds when a particle strikes another particle, a series of simulations were conducted in which the particle velocity was varied from 860 m/s to 1300 m/s.

Figure 7 shows the final states for simulations that were conducted with all variables fixed except for the particle impact velocity. Comparing Fig. 7(a) (v = 860 m/s) to Fig. 7(b) (v = 1000 m/s), it is apparent that the impacting particle is more heavily deformed at the higher velocity. However, many of the other key microstructural features such as the presence of multiple grain boundaries in the original NP and the presence of stacking imperfections is similar between the two simulations. Increasing the impact velocity further to 1300 m/s [Fig. 7(c)] results in a qualitatively different impact morphology compared to the lower impact velocities. In this case, both the impacting particle and the top part of the impacted NP are severely deformed to a degree that is significantly greater than what was observed experimentally. This suggests that the impact velocity in the experiment did not reach such extreme velocities. Comparing all the three figures, we observe that the degree of polycrystallinity decreases with impact velocity which is evident in the size of the small grains near the surface. At 860 m/s, two large surface grains are observed. When the velocity is increased to 1000 m/s, the grain that is visible on the left side of the impacting particle shrinks considerably and it disappears completely for impacts at 1300 m/s. The size of the grain on the right decreases when the velocity is increased. This trend suggests that at extremely high velocities, the grain on the right might be eliminated, leading to an epitaxial crystalline state. However, for the range of possible experimental impact velocities, epitaxial deposition was not observed in these simulations. These simulations show that impact velocity plays a significant role in the amount of deformation that occurs upon impaction and also influences the final crystalline state in the impacted particles. However, none of the simulations predicted epitaxial deposition.

Since partial dislocations and twins propagate in the $⟨110⟩$ directions on corresponding {111} planes in FCC crystals,^30–32 the influence of particle impact orientation or particle misorientation with respect to the impacted particle could affect deformation and the final state of the impacted particles. The effects of particle orientation and particle misorientation are particularly challenging to study experimentally because the orientations of the particles cannot be controlled and the orientations of the particles prior to impact cannot be ascertained by observation of the final states of the particles. Thus, simulations are essential for studying orientation and misorientation effects.

Simulations were first performed where the influence of the impact direction was studied. For these simulations, the impact directions were [001], [111], and [110]. For these simulations, the impacting and impacted particle had the same orientation (i.e., there was no misorientation between the impacting and the impacted particles). The results of these simulations are shown in Figs. 8(a)–8(c). It is observed that the overall degree of deformation varies with impact orientation. The greatest deformation is observed when the impact direction is along the particle [001] direction [Fig. 8(a)] and the least deformation occurs when the impact direction is along the particle [110] direction [Fig. 8(c)]. In the case of [001] and [111] impact orientations, the final states were polycrystalline. However, for the [110] impact orientation, where the least deformation was observed, the resulting final state was epitaxial. For all three impact orientations, many stacking imperfections are apparent that have a range of orientations relative to the impact direction.

Figures 9(a)–9(c) show the influence of NP–NP misorientation. For these simulations, NPs were impacted at 860 m/s, the impacting particle direction was fixed along the [110] direction, and the misorientation angle was varied by changing the orientation of the impacted NP. Note that Figs. 8(c) and 9(a) show the results from the same simulation for impaction along the [110] direction, with no misorientation between the impacting and the impacted particles. For Figs. 9(b) and 9(c), where there is a misorientation between the impacting and the impacted particles, the final states show that a grain boundary results near the interface between the particles. Comparing the results shown in Fig. 8 where the impact axes were varied to those shown in Fig. 9 where the degree of misorientation was varied, the differences in the overall degree of deformation and in the number and orientation of the stacking imperfections are much less dramatic in the latter case. In summary, these simulations show that the degree of deformation and the final morphology are primarily governed by impact velocity and particle orientation.

Figures 8(c) and 9(a) show the only instance predicted of epitaxial deposition among all of the conducted MD simulations. To determine the sensitivity for epitaxial deposition to small misorientations of the impacting NP with respect to the stationary impacted NP, another set of simulations was conducted in which small tilt misorientations of 5°, 10°, 15°, and 20° were introduced to the impacting NP and the particles were again impacted a velocity = 860 m/s. The small tilt misorientations were applied about the nonimpacting orthogonal $x[1¯10]$ and the y [001] axes with respect to the fixed crystallographic orientation of the impacted NP which has the following miller indices: $x[1¯10]$⁠, y [001], z [110]. Figures 10(a) and 10(b) show the preimpact tilt misorientation between the NPs for a misorientation angle of 10° about the x and y axes, respectively.

Figures 11(a)–11(d) show the final states for particles impacting with a tilt misorientation of 5° (a), 10° (b), 15° (c), and 20° (d) about the nonimpacting $x[1¯10]$ axis. This figure shows that the NPs deposit epitaxially for tilt misorientations of 5°, 10, and 15° about the nonimpacting $x[1¯10]$ axis. However, for a larger tilt misorientation angle of 20°, a low-angle grain boundary is visible, confirming that the impacting NP did not deposit epitaxially onto the stationary impacted NP. Figures 12(a)–12(c) show the final states for particles impacting with a tilt misorientation of 5° (a), 10° (b), 15° (c), and 20° (d) about the nonimpacting y [001] axis. These tilt misorientations also produced epitaxial deposition for misorientations of 5°, 10°, and 15°, but grain boundaries were again visible [see Fig. 12(e)] when the tilt misorientation was increased to 20°.

From these simulations, we can conclude that epitaxial deposition is possible at impaction velocity of 860 m/s when two NPs are tilted up to within approximately 15° of the $⟨110⟩$⁠. There is a transition predicted from epitaxial to nonepitaxial behavior when the tilt misorientation angle is increased to larger misorientations. However, we note that only 5 atomic layer thick cross sections have been shown in Figs. 11 and 12, where all final states appear to be epitaxial for tilt misorientations of 5°–15°. While studying the final microstructures for all the cases of tilt misorientations, we observed that the NPs are misoriented by 0.5°–3°. This misorientation between the NPs is accommodated at their interface by a number of stacking faults whose density increases with increasing preimpact NP–NP tilt misorientation. Since this leads to the creation of a very low-angle grain boundary between the NPs, the impaction event can still be described as epitaxial.

A final set of simulations were conducted in which small twist misorientations of 5°, 10°, and 15° about the impacting z [110] axis were introduced to the impacting NP impacting at 860 m/s to study if small twist misorientations also lead to epitaxial deposition. It was observed that the NPs in the final microstructure untwisted only by 1°–2° with respect to the initial twist misorientation between the NPs. Hence, compared to the impact events involving tilt misorientations, twist misorientations are more difficult to eliminate, leading to a high-angle grain boundary between the NPs in the final microstructure. Tilt misorientations of 5° and 10° lead to the creation of a relatively lower angle boundary which could be accommodated by stacking faults. However, for a higher tilt misorientation of 15°, the density of stacking faults accommodating the misorientation between the NPs increases rapidly leading to a disordering of the atoms at the grain boundary. These simulations show that epitaxial deposition is favorable for small tilt, but not twist misorientations of NPs impacting along a $⟨110⟩$ direction.

To better understand the mechanisms that lead to epitaxial deposition, a short-time simulation was conducted where a tilt misorientation was applied about the nonimpacting $x[1¯10]$ axis and where the stationary impacted NP was fixed with $x[1¯10]$⁠, y [001], z [110] axes. The evolutions of the microstructure and morphology were then studied. A representative case for a 10° NP–NP tilt misorientation is presented in Fig. 13, but we have confirmed that the observed mechanisms are similar for all the studied tilt and twist angles of misorientation.

Figure 13(a) shows a central cross section (5 atomic layers thick) viewed along the direction of misorientation $x[1¯10]$⁠. Solid lines are used in the figure to show the orientations of [110] for the NPs before and following impact. Figure 13(b) shows the NPs 8 ps after impaction; it is apparent that there has been significant deformation and that the impacting NP has started tilting toward the impacted NP orientation. The atoms that were part of the impacting particle and that were near the contact region have disordered (atoms colored white) upon impact. Previously, we have shown that such regions of disorder initiate in regions of high Von Mises stress.¹⁷ A large number of partial dislocations emerge from this highly stressed, disordered region and propagate along {111} planes toward the NP surface. The partial dislocations are visible as red atoms because the passage of a leading Frank partial dislocation produces a stacking fault by changing the normal ABCABC stacking sequence for fcc crystals to an ABABC stacking, e.g., a region of hcp crystal. The nucleation and propagation of partial dislocations for this orientation are similar to that observed previously when the impacting NP had its impact axis oriented along [001].¹⁷ Because of the differences in the angles between the impact orientations and {111} planes on which partial dislocations propagate, the partial dislocations that nucleate from the disordered region in the current case are localized to the region near the contact and their propagation directions occur nearly parallel to the interface between the particles. Note also that the 10° misorientation away from the $x[1¯10]$ direction induces nonsymmetric deformation on the {111} planes, and, therefore, the deformations are not symmetric about the impact direction.

A snapshot 16 ps after impact is shown in Fig. 13(c), where it is observed that the impacting NP has deformed and tilted further so that it is now nearly aligned with the impacted NP orientation. There is also an increase in the density of partial dislocations and in the size of the disordered region that exists in the vicinity of the interface between the impacting and the impacted particles. Examination of the impacting particle reveals that mass flow occurs radially outward between the two NPs in the disordered region (red rectangular regions). This mass flow is not symmetric and thus results in near-alignment of the impacting and impacted particles. The radial and asymmetric nature of this mass flow explains tilt and twist misorientations lead to very different final states. Whereas as nonsymmetric mass flow mitigates the influence of tilt misorientations, there is no corresponding mechanism that can effectively untwist misaligned particles. Since twist misorientations are more difficult to eliminate, even a small twist generally leads to nonepitaxial deposition.

Figure 13(d) shows the particles 24 ps after impact, where it is observed that the size of the disordered region between the now oriented NPs begins to decrease by recrystallization. The recrystallization growth front moves approximately vertically inward from both the top and the bottom of the amorphous region. The remaining disordered atoms completely recrystallize approximately 40 ps after impact [Fig. 13(e)], which results in the monocrystalline NP–NP system with a large number of stacking imperfections shown in Fig. 13(f). Note that the cross section shown in Fig. 13(e) appears to show an epitaxial deposition event; however, a careful analysis shows that there is a remnant 0.88° misorientation between the two NPs. This very small angle can be accommodated by a stacking fault between the two NPs.

In this study, the microstructures produced during high velocity particle-on-particle impacts of 2–40 nm NPs were investigated using TEM for the first time. These observations for specimens prepared with similar particle sizes and impact velocities revealed morphologies that ranged from polycrystalline to epitaxial. This suggested that there are additional impact parameters beyond the previously identified parameters of particle size and impact velocity¹⁷ that play a role in determining whether impact leads to epitaxial or polycrystalline deposition. MD simulations were used to study parameters that cannot be controlled experimentally or ascertained from postmortem observations, including particle crystallographic orientations and particle–particle crystallographic misorientations.

Previously, it has been shown that high velocity impact onto a substrate can result in the complete disordering of the impacting particle for some combinations of particle size and impact velocity.¹⁷ Upon cooling, the impacting particle was found to recrystallize with the orientation of the substrate, which resulted in epitaxial deposition. This mechanism of epitaxial deposition is favored for small particle sizes and high particle velocities. Increases in particle size necessitate even higher velocities to achieve complete epitaxy. In this paper, an alternative mechanism for epitaxial deposition during two-particle impacts was demonstrated that does not require complete disordering and is operative at lower particle velocities. We show that epitaxial deposition is favored when the impacting and the impacted particle axis are both near a $⟨110⟩$ orientation relative to the impact direction. When small tilt misorientations away from the $⟨110⟩$ axis were present, it was shown that asymmetric deformation and localized disordering occur, and the associated asymmetric mass flow tilts and reorients the impacting particle so that it realigns with the impacted particle. Upon cooling, the recrystallization front moves inward from both the impacting and the impacted particles, consuming the disordered regions and resulting in epitaxy. It was found that this mechanism can produce epitaxial depositions for particles with tilt misorientations of at least 15° from the $⟨110⟩$ impaction axis for an impacting particle size of 13.6 nm and a velocity of 860 m/s. Twist misorientations, however, were shown to be much more difficult to remove and thus tend to favor the polycrystalline final states.

Experiments conducted as a part of this study showed a range of final states from polycrystalline to epitaxial for particles deposited with similar particle sizes and impact velocities. MD simulations showed that variations in the orientation and tilt and twist misorientations of the particles could be responsible for the experimentally observed variations in final states. Further work is needed to determine the influence of simultaneous tilt and twist misorientations between the NPs and the influence of off-center particle impacts. An understanding of the influence of these factors could lead to combinations of particle size and velocity that extend epitaxial deposition to larger ranges of tilt and twist misorientations.

This material is based upon work supported by the National Science Foundation (NSF) under Grant No. CMMI 1435949 and the Army Research Laboratory under Grant No. GF70017-2 (NCE) through a subcontract with the University of North Texas.